Chapter 3 Other fitness landscapes

3.1 Setup

library(ggplot2)
library(tidyverse)
library(knitr)
library(cowplot)
library(viridis)
library(RColorBrewer)
library(rstatix)
library(ggsignif)
library(Hmisc)
library(kableExtra)
source("https://gist.githubusercontent.com/benmarwick/2a1bb0133ff568cbe28d/raw/fb53bd97121f7f9ce947837ef1a4c65a73bffb3f/geom_flat_violin.R")
library(readr)
library(stringr)
library(ggpubr)
library(infotheo)
library(osfr)
library(scales)

These analyses were conducted in the following computing environment:

print(version)

##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          1.1                         
## year           2021                        
## month          08                          
## day            10                          
## svn rev        80725                       
## language       R                           
## version.string R version 4.1.1 (2021-08-10)
## nickname       Kick Things

# Labeler for stats annotations
p_label <- function(p_value) {
  threshold = 0.0001
  if (p_value < threshold) {
    return(paste0("p < ", threshold))
  } else {
    return(paste0("p = ", p_value))
  }
}

# Significance threshold
alpha <- 0.05

####### misc #######
# Configure our default graphing theme
theme_set(theme_cowplot())

osf_retrieve_file("p79hx") %>% osf_download(conflicts = "skip")  # Download data from osf

## # A tibble: 1 × 4
##   name                           id                       local_path     meta   
##   <chr>                          <chr>                    <chr>          <list> 
## 1 complex_fitness_landscapes.csv 612fe4d84e5ee5019e29292e ./complex_fit… <named…

data_loc <- "complex_fitness_landscapes.csv"

data <- read_csv(data_loc, na=c("NONE", "NA", ""))

data <- data %>% 
  filter(N==20, generation %%10 == 0) %>%
  mutate(
  selection_name = as.factor(case_when(
    SELECTION == 0 ~ "Tournament",
    SELECTION == 1 ~ "Fitness sharing",
    SELECTION == 2 ~ "Lexicase",
    SELECTION == 3 ~ "Eco-EA",
    SELECTION == 4 ~ "Random",
  )), 
  problem_name = as.factor(case_when(
    PROBLEM == 0 ~ "NK Landscape",
    PROBLEM == 1 ~ "Count Odds",
    PROBLEM == 2 ~ "Real-valued optimization",
    PROBLEM == 3 ~ "Sorting network",
    PROBLEM == 4 ~ "Logic-9"    
  ))
)

data <- filter(data, generation <= 2000)
final_data <- filter(data, generation==max(data$generation))

3.2 Performance

3.2.1 Over time

ggplot(
    data,
    aes(
      x=generation,
      y=max_performance,
      color=selection_name,
      fill=selection_name
    )
  ) +
  stat_summary(geom="line", fun=mean) +
  stat_summary(
    geom="ribbon",
    fun.data="mean_cl_boot",
    fun.args=list(conf.int=0.95),
    alpha=0.2,
    linetype=0
  ) +
  scale_y_continuous(
    name="Average trait performance"
  ) +
  scale_x_continuous(
    name="Generation"
  ) +
  scale_color_discrete("Selection") + 
  scale_fill_discrete("Selection") +
  facet_wrap(~problem_name, scales="free")

3.2.2 Final

# Compute manual labels for geom_signif
stat.test <- final_data %>%
  wilcox_test(max_performance ~ selection_name) %>%
  adjust_pvalue(method = "bonferroni") %>%
  add_significance() %>%
  add_xy_position(x="selection_name",step.increase=1)
#stat.test$manual_position <- stat.test$y.position * .5
#stat.test$manual_position <- c(110, 1100, 170, 170, 130, 110)
stat.test$label <- mapply(p_label,stat.test$p.adj)

ggplot(
    final_data,
    aes(
      x=selection_name,
      y=max_performance,
      fill=selection_name
    )
  ) +
  geom_boxplot() +
  scale_y_continuous(
    name="Average trait performance"
  ) +
  scale_x_discrete(
    name="Selection"
  ) +
  scale_fill_discrete(
    name="Selection"
  ) +
  scale_color_discrete(
    name="Selection"
  ) + 
  theme(legend.position="none") +
  facet_wrap(~problem_name, scales="free")

stat.test %>%
  kbl() %>%
  kable_styling(
    bootstrap_options = c(
      "striped",
      "hover",
      "condensed",
      "responsive"
    )
  ) %>%
  scroll_box(width="600px")

.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	y.position	groups	xmin	xmax	label
max_performance	Eco-EA	Fitness sharing	240	240	28898.5	9.49e-01	1.00e+00	ns	102283.6	Eco-EA , Fitness sharing	1	2	p = 1
max_performance	Eco-EA	Lexicase	240	240	22536.0	3.25e-05	3.25e-04	***	135739.0	Eco-EA , Lexicase	1	3	p = 0.000325
max_performance	Eco-EA	Random	240	240	38664.0	0.00e+00	0.00e+00	****	169194.5	Eco-EA, Random	1	4	p < 1e-04
max_performance	Eco-EA	Tournament	240	240	28335.5	7.59e-01	1.00e+00	ns	202649.9	Eco-EA , Tournament	1	5	p = 1
max_performance	Fitness sharing	Lexicase	240	240	21248.5	7.00e-07	6.50e-06	****	236105.4	Fitness sharing, Lexicase	2	3	p < 1e-04
max_performance	Fitness sharing	Random	240	240	40208.0	0.00e+00	0.00e+00	****	269560.8	Fitness sharing, Random	2	4	p < 1e-04
max_performance	Fitness sharing	Tournament	240	240	26515.0	1.33e-01	1.00e+00	ns	303016.3	Fitness sharing, Tournament	2	5	p = 1
max_performance	Lexicase	Random	240	240	44119.5	0.00e+00	0.00e+00	****	336471.7	Lexicase, Random	3	4	p < 1e-04
max_performance	Lexicase	Tournament	240	240	35022.0	3.93e-05	3.93e-04	***	369927.2	Lexicase , Tournament	3	5	p = 0.000393
max_performance	Random	Tournament	240	240	17928.5	0.00e+00	0.00e+00	****	403382.6	Random , Tournament	4	5	p < 1e-04

3.3 Phylogenetic diversity

3.3.1 Relationship between different types of pylogenetic diversity

First, to get a big-picture overview, we make correlation matrices of all the different phylogenetic diversity metrics:

final_data %>% 
  transmute(MinPD=min_phenotype_pairwise_distance, 
            MeanPD=mean_phenotype_pairwise_distance, 
            MaxPD=max_phenotype_pairwise_distance, 
            VarPD=variance_phenotype_pairwise_distance, 
            MinED = min_phenotype_evolutionary_distinctiveness,
            MeanED= mean_phenotype_evolutionary_distinctiveness,
            MaxED=max_phenotype_evolutionary_distinctiveness,
            VarED=variance_phenotype_evolutionary_distinctiveness,
            PD=phenotype_current_phylogenetic_diversity,  # See Faith 1992
            MRCA=phenotype_mrca_depth,  # Phylogenetic depth of most recent common ancestor
            N=phenotype_num_taxa     # Number of taxonomically-distinct phenotypes
  ) %>%
  cor_mat() %>% 
  pull_lower_triangle() %>% 
  cor_plot()

However, these correlations may well vary by selection scheme and by problem, and even over time within a selection scheme and problem. Let’s take a look at some scatter plots.

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=mean_phenotype_pairwise_distance,
        x=variance_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=mean_phenotype_pairwise_distance,
        x=max_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=variance_phenotype_pairwise_distance,
        x=max_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==500),
    aes(
        y=mean_phenotype_pairwise_distance,
        x=variance_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==500),
    aes(
        y=mean_phenotype_pairwise_distance,
        x=max_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=variance_phenotype_pairwise_distance,
        x=max_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=mean_phenotype_evolutionary_distinctiveness,
        x=variance_phenotype_evolutionary_distinctiveness,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=mean_phenotype_evolutionary_distinctiveness,
        x=max_phenotype_evolutionary_distinctiveness,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=mean_phenotype_evolutionary_distinctiveness,
        x=min_phenotype_evolutionary_distinctiveness,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==500),
    aes(
        y=mean_phenotype_evolutionary_distinctiveness,
        x=variance_phenotype_evolutionary_distinctiveness,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==500),
    aes(
        y=mean_phenotype_evolutionary_distinctiveness,
        x=max_phenotype_evolutionary_distinctiveness,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==500),
    aes(
        y=mean_phenotype_evolutionary_distinctiveness,
        x=min_phenotype_evolutionary_distinctiveness,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
  scale_x_continuous(
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

3.3.2 Over time

ggplot(
    data,
    aes(
      x=generation,
      y=mean_phenotype_pairwise_distance,
      color=selection_name,
      fill=selection_name
    )
  ) +
  stat_summary(geom="line", fun=mean) +
  stat_summary(
    geom="ribbon",
    fun.data="mean_cl_boot",
    fun.args=list(conf.int=0.95),
    alpha=0.2,
    linetype=0
  ) +
  scale_y_log10(
    name="Mean pairwise distance"
  ) +
  scale_x_continuous(
    name="Generation"
  ) +
  scale_color_discrete("Selection") +
  scale_fill_discrete("Selection") +
  facet_wrap(~problem_name, scales = "free")

3.3.3 Final

# Compute manual labels for geom_signif
stat.test <- final_data %>%
  wilcox_test(mean_phenotype_pairwise_distance ~ selection_name) %>%
  adjust_pvalue(method = "bonferroni") %>%
  add_significance() %>%
  add_xy_position(x="selection_name",step.increase=1)
#stat.test$manual_position <- stat.test$y.position * .5
#stat.test$manual_position <- c(110, 150, 170, 170, 130, 110)
stat.test$label <- mapply(p_label,stat.test$p.adj)

ggplot(
    final_data,
    aes(
      x=selection_name,
      y=mean_phenotype_pairwise_distance,
      fill=selection_name
    )
  ) +
  geom_boxplot() +
  scale_y_log10(
    name="Mean pairwise distance"
  ) +
  scale_x_discrete(
    name="Selection"
  ) +
  scale_fill_discrete(
    name="Selection"
  ) +
  scale_color_discrete(
    name="Selection"
  ) + 
  theme(legend.position = "none") +
    facet_wrap(~problem_name, scales = "free")

stat.test %>%
  kbl() %>%
  kable_styling(
    bootstrap_options = c(
      "striped",
      "hover",
      "condensed",
      "responsive"
    )
  ) %>%
  scroll_box(width="600px")

.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	y.position	groups	xmin	xmax	label
mean_phenotype_pairwise_distance	Eco-EA	Fitness sharing	240	240	2486.0	0.00e+00	0.00e+00	****	2900.227	Eco-EA , Fitness sharing	1	2	p < 1e-04
mean_phenotype_pairwise_distance	Eco-EA	Lexicase	240	240	23590.0	6.07e-04	6.07e-03	**	4498.579	Eco-EA , Lexicase	1	3	p = 0.00607
mean_phenotype_pairwise_distance	Eco-EA	Random	240	240	8274.0	0.00e+00	0.00e+00	****	6096.931	Eco-EA, Random	1	4	p < 1e-04
mean_phenotype_pairwise_distance	Eco-EA	Tournament	240	240	43940.0	0.00e+00	0.00e+00	****	7695.284	Eco-EA , Tournament	1	5	p < 1e-04
mean_phenotype_pairwise_distance	Fitness sharing	Lexicase	240	240	35067.0	3.72e-05	3.72e-04	***	9293.636	Fitness sharing, Lexicase	2	3	p = 0.000372
mean_phenotype_pairwise_distance	Fitness sharing	Random	240	240	37442.0	0.00e+00	1.00e-07	****	10891.988	Fitness sharing, Random	2	4	p < 1e-04
mean_phenotype_pairwise_distance	Fitness sharing	Tournament	240	240	57033.0	0.00e+00	0.00e+00	****	12490.340	Fitness sharing, Tournament	2	5	p < 1e-04
mean_phenotype_pairwise_distance	Lexicase	Random	240	240	26406.0	1.15e-01	1.00e+00	ns	14088.693	Lexicase, Random	3	4	p = 1
mean_phenotype_pairwise_distance	Lexicase	Tournament	240	240	36500.5	4.00e-07	4.00e-06	****	15687.045	Lexicase , Tournament	3	5	p < 1e-04
mean_phenotype_pairwise_distance	Random	Tournament	240	240	55686.0	0.00e+00	0.00e+00	****	17285.397	Random , Tournament	4	5	p < 1e-04

3.4 Phenotypic diversity

3.4.1 Relationship between different types of phenotypic diversity

First, we should assess the extent to which different metrics of phenotypic diversity are capturing different information.

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=phenotype_diversity,
        x=phenotype_num_taxa,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Phenotypic shannon diversity"
  ) +
  scale_x_continuous(
        name="Phenotypic richness",
        breaks = breaks_extended(4)
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

3.4.2 Over time

ggplot(
    data,
    aes(
      x=generation,
      y=phenotype_num_taxa,
      color=selection_name,
      fill=selection_name
    )
  ) +
  stat_summary(geom="line", fun=mean) +
  stat_summary(
    geom="ribbon",
    fun.data="mean_cl_boot",
    fun.args=list(conf.int=0.95),
    alpha=0.2,
    linetype=0
  ) +
  scale_y_continuous(
    name="Phenotypic richness"
  ) +
  scale_x_continuous(
    name="Generation"
  ) +
  scale_color_discrete("Selection") + 
  scale_fill_discrete("Selection") +
  facet_wrap(~problem_name, scales = "free")

3.4.3 Final

# Compute manual labels for geom_signif
stat.test <- final_data %>%
  wilcox_test(phenotype_num_taxa ~ selection_name) %>%
  adjust_pvalue(method = "bonferroni") %>%
  add_significance() %>%
  add_xy_position(x="selection_name",step.increase=1)
#stat.test$manual_position <- stat.test$y.position * .5
#stat.test$manual_position <- c(110, 150, 170, 170, 130, 110)
stat.test$label <- mapply(p_label,stat.test$p.adj)

ggplot(
    final_data,
    aes(
      x=selection_name,
      y=phenotype_num_taxa,
      fill=selection_name
    )
  ) +
  geom_boxplot() +
  scale_y_continuous(
    name="Phenotypic Richness"
  ) +
  scale_x_discrete(
    name="Selection"
  ) +
  scale_fill_discrete(
    name="Selection"
  ) +
  scale_color_discrete(
    name="Selection"
  ) +
  theme(legend.position = "none") +
  facet_wrap(~problem_name, scales = "free")

stat.test %>%
  kbl() %>%
  kable_styling(
    bootstrap_options = c(
      "striped",
      "hover",
      "condensed",
      "responsive"
    )
  ) %>%
  scroll_box(width="600px")

.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	y.position	groups	xmin	xmax	label
phenotype_num_taxa	Eco-EA	Fitness sharing	240	240	3513.5	0.00000	0.0000	****	1580.000	Eco-EA , Fitness sharing	1	2	p < 1e-04
phenotype_num_taxa	Eco-EA	Lexicase	240	240	17757.5	0.00000	0.0000	****	2224.444	Eco-EA , Lexicase	1	3	p < 1e-04
phenotype_num_taxa	Eco-EA	Random	240	240	38186.0	0.00000	0.0000	****	2868.889	Eco-EA, Random	1	4	p < 1e-04
phenotype_num_taxa	Eco-EA	Tournament	240	240	30723.0	0.20600	1.0000	ns	3513.333	Eco-EA , Tournament	1	5	p = 1
phenotype_num_taxa	Fitness sharing	Lexicase	240	240	39523.5	0.00000	0.0000	****	4157.778	Fitness sharing, Lexicase	2	3	p < 1e-04
phenotype_num_taxa	Fitness sharing	Random	240	240	56742.5	0.00000	0.0000	****	4802.222	Fitness sharing, Random	2	4	p < 1e-04
phenotype_num_taxa	Fitness sharing	Tournament	240	240	49804.5	0.00000	0.0000	****	5446.667	Fitness sharing, Tournament	2	5	p < 1e-04
phenotype_num_taxa	Lexicase	Random	240	240	46856.0	0.00000	0.0000	****	6091.111	Lexicase, Random	3	4	p < 1e-04
phenotype_num_taxa	Lexicase	Tournament	240	240	41709.5	0.00000	0.0000	****	6735.556	Lexicase , Tournament	3	5	p < 1e-04
phenotype_num_taxa	Random	Tournament	240	240	23410.5	0.00039	0.0039	**	7380.000	Random , Tournament	4	5	p = 0.0039

3.5 Relationship between phenotypic and phylogenetic diversity

ggplot(
    final_data,
    aes(
        y=phenotype_num_taxa,
        x=mean_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Phenotypic richness"
  ) +
  scale_x_continuous(
        name="Mean pairwise distance"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

3.6 Relationship between diversity and success

3.6.1 Earlier in run

ggplot(
    data %>% filter(generation==500),
    aes(
        y=max_performance,
        x=mean_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Average trait performance"
  ) +
  scale_x_continuous(
        name="Mean pairwise distance"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    data %>% filter(generation==500),
    aes(
        y=max_performance,
        x=phenotype_num_taxa,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Average trait performance"
  ) +
  scale_x_continuous(
        name="Phenotypic richness"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

phylogney_vs_performance <- ggplot(
    data %>% filter(generation==1000),
    aes(
        y=max_performance,
        x=mean_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Average trait performance"
  ) +
  scale_x_continuous(
        name="Mean pairwise distance"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")
  
phylogney_vs_performance

ggplot(
    data %>% filter(generation==1000),
    aes(
        y=max_performance,
        x=phenotype_num_taxa,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Average trait performance"
  ) +
  scale_x_continuous(
        name="Phenotypic richness"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

3.6.2 End of run

ggplot(
    final_data,
    aes(
        y=max_performance,
        x=mean_phenotype_pairwise_distance,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Average trait performance"
  ) +
  scale_x_continuous(
        name="Mean pairwise distance"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

ggplot(
    final_data,
    aes(
        y=max_performance,
        x=phenotype_num_taxa,
        color=selection_name,
        fill=selection_name
    )
  ) +
  geom_point() +
    scale_y_continuous(
        name="Average trait performance"
  ) +
  scale_x_continuous(
        name="Phenotypic richness"
  ) + 
  facet_wrap(
      ~selection_name*problem_name, ncol=4, scales="free"
  ) + 
  stat_smooth(
    method="lm"
  ) + 
  stat_cor(
    method="spearman", cor.coef.name = "rho", color="black"
  ) +
  theme(legend.position = "none")

3.7 Causality analysis

3.7.1 Setup

First let’s define a function we’ll use to calculate and output significance and effect size for these results:

transfer_entropy_stats <- function(res) {
  stat.test <- res %>%
    group_by(selection_name, problem_name, offset) %>%
    filter(max(value) > 0) %>% # Sorting networks have some values of 0, which won't work for Wilcox test
    wilcox_test(value ~ Type) %>%
    adjust_pvalue(method = "bonferroni") %>%
    add_significance() 
  stat.test$label <- mapply(p_label,stat.test$p.adj)
  
  # Calculate effect sizes for these differences
  effect_sizes <- res %>%
    group_by(selection_name, problem_name, offset) %>%
    filter(max(value) > 0) %>%
    wilcox_effsize(value ~ Type)
  
  stat.test$effsize <- effect_sizes$effsize
  stat.test$magnitude <- effect_sizes$magnitude
  
  stat.test %>%
    kbl() %>%
    kable_styling(
      bootstrap_options = c(
        "striped",
        "hover",
        "condensed",
        "responsive"
      )
    ) %>%
    scroll_box(width="100%")
}

3.7.2 Transfer entropy from diversity to fitness

3.7.2.1 Max pairwise distance vs. phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  fit_phylo_10 = condinformation(discretize(max_performance), discretize(lag(max_phenotype_pairwise_distance, 1)), discretize(lag(max_performance, 1))),
  fit_phylo_100 = condinformation(discretize(max_performance), discretize(lag(max_phenotype_pairwise_distance, 10)), discretize(lag(max_performance, 10))),
  fit_phylo_1000 = condinformation(discretize(max_performance), discretize(lag(max_phenotype_pairwise_distance, 100)), discretize(lag(max_performance, 100))),
    fit_pheno_10 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 1)), discretize(lag(max_performance, 1))),
      fit_pheno_100 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 10)), discretize(lag(max_performance, 10))),
      fit_pheno_1000 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 100)), discretize(lag(max_performance, 100)))
      )

res <- res %>% pivot_longer(cols=contains("o_10"))
res$offset <- str_extract(res$name, "[:digit:]*$")
res$Type <- case_when(str_detect(res$name, "phylo") ~ "Phylogenetic", TRUE ~ "Phenotypic")

ggplot(
  res %>% filter(str_detect(name, "fit_ph*")), 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_x_discrete("Lag") + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("") + 
  theme(legend.position = "bottom")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1511.0	1.30e-01	1.0000000	ns	p = 1	0.1384694	small
Eco-EA	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	701.0	0.00e+00	0.0000005	****	p < 1e-04	0.5265671	large
Eco-EA	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	979.0	1.66e-05	0.0009794	***	p = 0.0009794	0.3933818	moderate
Eco-EA	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1741.0	7.59e-01	1.0000000	ns	p = 1	0.0282693	small
Eco-EA	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1845.0	8.15e-01	1.0000000	ns	p = 1	0.0215614	small
Eco-EA	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1801.0	9.98e-01	1.0000000	ns	p = 1	0.0004811	small
Eco-EA	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1639.5	4.01e-01	1.0000000	ns	p = 1	0.0769010	small
Eco-EA	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1740.5	7.57e-01	1.0000000	ns	p = 1	0.0285085	small
Eco-EA	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1897.5	6.11e-01	1.0000000	ns	p = 1	0.0467184	small
Eco-EA	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2235.5	2.24e-02	1.0000000	ns	p = 1	0.2086678	small
Eco-EA	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1464.5	7.87e-02	1.0000000	ns	p = 1	0.1607519	small
Eco-EA	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1771.0	5.80e-01	1.0000000	ns	p = 1	0.0513765	small
Fitness sharing	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1721.0	6.80e-01	1.0000000	ns	p = 1	0.0378515	small
Fitness sharing	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1272.0	5.63e-03	0.3321700	ns	p = 0.33217	0.2529822	small
Fitness sharing	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1709.0	6.35e-01	1.0000000	ns	p = 1	0.0436011	small
Fitness sharing	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1620.0	3.46e-01	1.0000000	ns	p = 1	0.0862454	small
Fitness sharing	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1411.0	4.14e-02	1.0000000	ns	p = 1	0.1863860	small
Fitness sharing	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1595.0	2.81e-01	1.0000000	ns	p = 1	0.0986687	small
Fitness sharing	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1637.0	3.94e-01	1.0000000	ns	p = 1	0.0780987	small
Fitness sharing	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	807.0	2.00e-07	0.0000112	****	p < 1e-04	0.4757790	moderate
Fitness sharing	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	822.0	3.00e-07	0.0000171	****	p < 1e-04	0.4685921	moderate
Fitness sharing	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	796.0	1.00e-07	0.0000082	****	p < 1e-04	0.4810495	moderate
Fitness sharing	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	393.0	0.00e+00	0.0000000	****	p < 1e-04	0.6741401	large
Fitness sharing	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1807.0	9.73e-01	1.0000000	ns	p = 1	0.0033539	small
Lexicase	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1826.0	8.94e-01	1.0000000	ns	p = 1	0.0124575	small
Lexicase	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	531.0	0.00e+00	0.0000000	****	p < 1e-04	0.6080198	large
Lexicase	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1092.0	2.04e-04	0.0120360		p = 0.012036	0.3392285	moderate
Lexicase	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	2031.5	2.25e-01	1.0000000	ns	p = 1	0.1109195	small
Lexicase	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1519.0	1.41e-01	1.0000000	ns	p = 1	0.1346373	small
Lexicase	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1863.0	7.41e-01	1.0000000	ns	p = 1	0.0303585	small
Lexicase	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1816.0	9.35e-01	1.0000000	ns	p = 1	0.0077152	small
Lexicase	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1391.0	3.09e-02	1.0000000	ns	p = 1	0.1972206	small
Lexicase	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1218.0	2.13e-03	0.1256700	ns	p = 0.12567	0.2806415	small
Lexicase	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1819.5	8.98e-01	1.0000000	ns	p = 1	0.0120055	small
Lexicase	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1815.0	9.22e-01	1.0000000	ns	p = 1	0.0092350	small
Random	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1970.0	3.74e-01	1.0000000	ns	p = 1	0.0814526	small
Random	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	2096.0	1.21e-01	1.0000000	ns	p = 1	0.1418234	small
Random	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1168.0	9.18e-04	0.0541620	ns	p = 0.054162	0.3028120	moderate
Random	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1920.0	4.79e-01	1.0000000	ns	p = 1	0.0649373	small
Random	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1857.5	7.35e-01	1.0000000	ns	p = 1	0.0311145	small
Random	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1750.5	7.25e-01	1.0000000	ns	p = 1	0.0324395	small
Random	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1613.0	3.28e-01	1.0000000	ns	p = 1	0.0895979	small
Random	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1281.0	6.50e-03	0.3835000	ns	p = 0.3835	0.2486700	small
Random	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	644.0	0.00e+00	0.0000001	****	p < 1e-04	0.5538777	large
Random	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2056.0	1.80e-01	1.0000000	ns	p = 1	0.1226580	small
Random	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1271.0	5.54e-03	0.3268600	ns	p = 0.32686	0.2534613	small
Random	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1369.0	2.38e-02	1.0000000	ns	p = 1	0.2065063	small
Tournament	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1577.0	2.43e-01	1.0000000	ns	p = 1	0.1068467	small
Tournament	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1376.0	2.62e-02	1.0000000	ns	p = 1	0.2031524	small
Tournament	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1811.0	9.56e-01	1.0000000	ns	p = 1	0.0052710	small
Tournament	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	2015.0	2.60e-01	1.0000000	ns	p = 1	0.1030154	small
Tournament	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1965.0	3.88e-01	1.0000000	ns	p = 1	0.0790583	small
Tournament	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1983.0	3.33e-01	1.0000000	ns	p = 1	0.0886950	small
Tournament	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1811.0	9.26e-01	1.0000000	ns	p = 1	0.0089208	small
Tournament	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1802.0	9.89e-01	1.0000000	ns	p = 1	0.0016220	small
Tournament	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1800.0	1.00e+00	1.0000000	ns	p = 1	0.0000000	small
Tournament	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2073.0	1.53e-01	1.0000000	ns	p = 1	0.1308040	small
Tournament	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1449.0	6.58e-02	1.0000000	ns	p = 1	0.1681757	small
Tournament	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1996.5	2.60e-01	1.0000000	ns	p = 1	0.1031163	small

3.7.2.2 Mean pairwise distance vs. phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  fit_phylo_10 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_pairwise_distance, 1)), discretize(lag(max_performance, 1))),
  fit_phylo_100 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_pairwise_distance, 10)), discretize(lag(max_performance, 10))),
  fit_phylo_1000 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_pairwise_distance, 100)), discretize(lag(max_performance, 100))),
    fit_pheno_10 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 1)), discretize(lag(max_performance, 1))),
      fit_pheno_100 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 10)), discretize(lag(max_performance, 10))),
      fit_pheno_1000 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 100)), discretize(lag(max_performance, 100)))
      )

res <- res %>% pivot_longer(cols=contains("o_10"))
res$offset <- str_extract(res$name, "[:digit:]*$")
res$Type <- case_when(str_detect(res$name, "phylo") ~ "Phylogenetic", TRUE ~ "Phenotypic")

ggplot(
  res %>% filter(str_detect(name, "fit_ph*")), 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_x_discrete("Lag") + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("") + 
  theme(legend.position = "bottom")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1732.0	7.23e-01	1.0000000	ns	p = 1	0.0325810	small
Eco-EA	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	943.0	6.90e-06	0.0004095	***	p = 0.00040946	0.4106170	moderate
Eco-EA	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1289.0	7.37e-03	0.4348300	ns	p = 0.43483	0.2448608	small
Eco-EA	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1743.0	7.67e-01	1.0000000	ns	p = 1	0.0273111	small
Eco-EA	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1704.0	6.16e-01	1.0000000	ns	p = 1	0.0459976	small
Eco-EA	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1709.0	6.33e-01	1.0000000	ns	p = 1	0.0437763	small
Eco-EA	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1526.5	1.52e-01	1.0000000	ns	p = 1	0.1310431	small
Eco-EA	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1589.5	2.70e-01	1.0000000	ns	p = 1	0.1008577	small
Eco-EA	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1900.0	6.01e-01	1.0000000	ns	p = 1	0.0479180	small
Eco-EA	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2104.0	1.11e-01	1.0000000	ns	p = 1	0.1456605	small
Eco-EA	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1742.5	7.65e-01	1.0000000	ns	p = 1	0.0275502	small
Eco-EA	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1770.0	5.67e-01	1.0000000	ns	p = 1	0.0531481	small
Fitness sharing	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1699.0	5.98e-01	1.0000000	ns	p = 1	0.0483924	small
Fitness sharing	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1311.0	1.03e-02	0.6077000	ns	p = 0.6077	0.2342960	small
Fitness sharing	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1926.0	5.10e-01	1.0000000	ns	p = 1	0.0603708	small
Fitness sharing	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1559.0	2.07e-01	1.0000000	ns	p = 1	0.1154731	small
Fitness sharing	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1402.0	3.69e-02	1.0000000	ns	p = 1	0.1906982	small
Fitness sharing	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1531.0	1.57e-01	1.0000000	ns	p = 1	0.1292849	small
Fitness sharing	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1550.0	1.90e-01	1.0000000	ns	p = 1	0.1197832	small
Fitness sharing	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	823.0	3.00e-07	0.0000175	****	p < 1e-04	0.4681129	moderate
Fitness sharing	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	642.0	0.00e+00	0.0000001	****	p < 1e-04	0.5548360	large
Fitness sharing	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	949.0	8.00e-06	0.0004749	***	p = 0.00047495	0.4077422	moderate
Fitness sharing	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	373.0	0.00e+00	0.0000000	****	p < 1e-04	0.6837228	large
Fitness sharing	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1885.0	6.57e-01	1.0000000	ns	p = 1	0.0407263	small
Lexicase	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1651.0	4.36e-01	1.0000000	ns	p = 1	0.0713908	small
Lexicase	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	590.0	0.00e+00	0.0000000	****	p < 1e-04	0.5797509	large
Lexicase	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1166.0	8.84e-04	0.0521560	ns	p = 0.052156	0.3037724	moderate
Lexicase	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1879.5	6.78e-01	1.0000000	ns	p = 1	0.0380911	small
Lexicase	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1354.5	1.95e-02	1.0000000	ns	p = 1	0.2134541	small
Lexicase	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1748.0	7.86e-01	1.0000000	ns	p = 1	0.0250150	small
Lexicase	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1790.0	9.60e-01	1.0000000	ns	p = 1	0.0048220	small
Lexicase	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1409.0	3.91e-02	1.0000000	ns	p = 1	0.1885410	small
Lexicase	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1231.0	2.67e-03	0.1575300	ns	p = 0.15753	0.2743729	small
Lexicase	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1821.0	8.90e-01	1.0000000	ns	p = 1	0.0129293	small
Lexicase	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1831.0	8.37e-01	1.0000000	ns	p = 1	0.0190856	small
Random	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1781.0	9.23e-01	1.0000000	ns	p = 1	0.0091035	small
Random	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	2026.0	2.37e-01	1.0000000	ns	p = 1	0.1082841	small
Random	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1088.0	1.88e-04	0.0110920		p = 0.011092	0.3411427	moderate
Random	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1772.5	8.73e-01	1.0000000	ns	p = 1	0.0148811	small
Random	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1799.0	9.98e-01	1.0000000	ns	p = 1	0.0005411	small
Random	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1746.5	7.04e-01	1.0000000	ns	p = 1	0.0350608	small
Random	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1490.0	1.04e-01	1.0000000	ns	p = 1	0.1485312	small
Random	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1168.0	9.18e-04	0.0541620	ns	p = 0.054162	0.3028120	moderate
Random	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	518.0	0.00e+00	0.0000000	****	p < 1e-04	0.6142485	large
Random	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1918.0	5.37e-01	1.0000000	ns	p = 1	0.0565377	small
Random	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1188.0	1.33e-03	0.0784700	ns	p = 0.07847	0.2932294	small
Random	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1339.0	1.56e-02	0.9204000	ns	p = 0.9204	0.2208803	small
Tournament	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1539.0	1.72e-01	1.0000000	ns	p = 1	0.1250537	small
Tournament	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1188.0	1.33e-03	0.0784700	ns	p = 0.07847	0.2932294	small
Tournament	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1789.5	9.58e-01	1.0000000	ns	p = 1	0.0050316	small
Tournament	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1906.0	5.80e-01	1.0000000	ns	p = 1	0.0507890	small
Tournament	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1789.0	9.56e-01	1.0000000	ns	p = 1	0.0052706	small
Tournament	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1943.0	4.50e-01	1.0000000	ns	p = 1	0.0691744	small
Tournament	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1798.0	9.89e-01	1.0000000	ns	p = 1	0.0016220	small
Tournament	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1783.0	8.83e-01	1.0000000	ns	p = 1	0.0137867	small
Tournament	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1784.0	8.90e-01	1.0000000	ns	p = 1	0.0129757	small
Tournament	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1734.5	7.33e-01	1.0000000	ns	p = 1	0.0313834	small
Tournament	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1161.0	8.04e-04	0.0474360		p = 0.047436	0.3061660	moderate
Tournament	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	2123.0	6.00e-02	1.0000000	ns	p = 1	0.1719646	small

3.7.2.3 Mean pairwise distance vs. phenotypic Shannon diversity

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  fit_phylo_10 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_pairwise_distance, 1)), discretize(lag(max_performance, 1))),
  fit_phylo_100 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_pairwise_distance, 10)), discretize(lag(max_performance, 10))),
  fit_phylo_1000 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_pairwise_distance, 100)), discretize(lag(max_performance, 100))),
    fit_pheno_10 = condinformation(discretize(max_performance), discretize(lag(phenotype_diversity, 1)), discretize(lag(max_performance, 1))),
      fit_pheno_100 = condinformation(discretize(max_performance), discretize(lag(phenotype_diversity, 10)), discretize(lag(max_performance, 10))),
      fit_pheno_1000 = condinformation(discretize(max_performance), discretize(lag(phenotype_diversity, 100)), discretize(lag(max_performance, 100)))
      )

res <- res %>% pivot_longer(cols=contains("o_10"))
res$offset <- str_extract(res$name, "[:digit:]*$")
res$Type <- case_when(str_detect(res$name, "phylo") ~ "Phylogenetic", TRUE ~ "Phenotypic")

ggplot(
  res %>% filter(str_detect(name, "fit_ph*")), 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_x_discrete("Lag") + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("") + 
  theme(legend.position = "bottom")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1823.0	9.06e-01	1.0000000	ns	p = 1	0.0110201	small
Eco-EA	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1164.0	8.51e-04	0.0502090	ns	p = 0.050209	0.3047286	moderate
Eco-EA	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1192.5	1.44e-03	0.0849600	ns	p = 0.08496	0.2911021	small
Eco-EA	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1691.0	5.69e-01	1.0000000	ns	p = 1	0.0522264	small
Eco-EA	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1648.0	4.27e-01	1.0000000	ns	p = 1	0.0728295	small
Eco-EA	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1669.0	4.91e-01	1.0000000	ns	p = 1	0.0630876	small
Eco-EA	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1749.5	7.93e-01	1.0000000	ns	p = 1	0.0241963	small
Eco-EA	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1640.5	4.04e-01	1.0000000	ns	p = 1	0.0764218	small
Eco-EA	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1642.0	4.08e-01	1.0000000	ns	p = 1	0.0757076	small
Eco-EA	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1861.5	7.49e-01	1.0000000	ns	p = 1	0.0294693	small
Eco-EA	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1853.5	7.81e-01	1.0000000	ns	p = 1	0.0256339	small
Eco-EA	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1770.0	5.67e-01	1.0000000	ns	p = 1	0.0531481	small
Fitness sharing	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1568.0	2.24e-01	1.0000000	ns	p = 1	0.1111589	small
Fitness sharing	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1351.0	1.86e-02	1.0000000	ns	p = 1	0.2151307	small
Fitness sharing	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1950.0	4.33e-01	1.0000000	ns	p = 1	0.0718699	small
Fitness sharing	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1604.0	3.05e-01	1.0000000	ns	p = 1	0.0939117	small
Fitness sharing	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1437.0	5.71e-02	1.0000000	ns	p = 1	0.1739283	small
Fitness sharing	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1602.0	2.99e-01	1.0000000	ns	p = 1	0.0950882	small
Fitness sharing	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1528.0	1.54e-01	1.0000000	ns	p = 1	0.1303242	small
Fitness sharing	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	747.0	0.00e+00	0.0000020	****	p < 1e-04	0.5045270	large
Fitness sharing	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	694.0	0.00e+00	0.0000004	****	p < 1e-04	0.5299211	large
Fitness sharing	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	901.0	2.40e-06	0.0001422	***	p = 0.00014219	0.4307405	moderate
Fitness sharing	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	339.0	0.00e+00	0.0000000	****	p < 1e-04	0.7000133	large
Fitness sharing	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1773.0	8.89e-01	1.0000000	ns	p = 1	0.0129366	small
Lexicase	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1517.0	1.38e-01	1.0000000	ns	p = 1	0.1355946	small
Lexicase	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	569.0	0.00e+00	0.0000000	****	p < 1e-04	0.5898127	large
Lexicase	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1134.0	4.78e-04	0.0282020		p = 0.028202	0.3191031	moderate
Lexicase	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1754.5	8.13e-01	1.0000000	ns	p = 1	0.0218006	small
Lexicase	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1458.5	7.35e-02	1.0000000	ns	p = 1	0.1636242	small
Lexicase	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1758.0	8.27e-01	1.0000000	ns	p = 1	0.0202044	small
Lexicase	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1817.0	9.31e-01	1.0000000	ns	p = 1	0.0081974	small
Lexicase	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1435.0	5.42e-02	1.0000000	ns	p = 1	0.1760037	small
Lexicase	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1244.0	3.34e-03	0.1970600	ns	p = 0.19706	0.2681043	small
Lexicase	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1779.5	8.93e-01	1.0000000	ns	p = 1	0.0126213	small
Lexicase	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1837.0	8.06e-01	1.0000000	ns	p = 1	0.0227797	small
Random	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1754.0	8.11e-01	1.0000000	ns	p = 1	0.0220401	small
Random	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	2145.0	7.06e-02	1.0000000	ns	p = 1	0.1653009	small
Random	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	971.0	1.37e-05	0.0008083	***	p = 0.0008083	0.3972012	moderate
Random	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1896.5	5.69e-01	1.0000000	ns	p = 1	0.0522211	small
Random	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1839.0	8.19e-01	1.0000000	ns	p = 1	0.0211053	small
Random	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1830.0	8.35e-01	1.0000000	ns	p = 1	0.0193927	small
Random	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1437.0	5.71e-02	1.0000000	ns	p = 1	0.1739253	small
Random	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1185.0	1.26e-03	0.0743400	ns	p = 0.07434	0.2946668	small
Random	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	598.0	0.00e+00	0.0000000	****	p < 1e-04	0.5759178	large
Random	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1731.0	7.19e-01	1.0000000	ns	p = 1	0.0330602	small
Random	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1441.0	5.99e-02	1.0000000	ns	p = 1	0.1720087	small
Random	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1324.0	1.26e-02	0.7434000	ns	p = 0.7434	0.2280673	small
Tournament	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1574.5	2.38e-01	1.0000000	ns	p = 1	0.1080447	small
Tournament	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1441.0	5.99e-02	1.0000000	ns	p = 1	0.1720087	small
Tournament	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1925.0	5.13e-01	1.0000000	ns	p = 1	0.0599041	small
Tournament	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1823.5	9.04e-01	1.0000000	ns	p = 1	0.0112598	small
Tournament	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1827.0	8.89e-01	1.0000000	ns	p = 1	0.0129368	small
Tournament	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1898.0	6.05e-01	1.0000000	ns	p = 1	0.0474506	small
Tournament	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1794.0	9.61e-01	1.0000000	ns	p = 1	0.0048659	small
Tournament	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1802.0	9.89e-01	1.0000000	ns	p = 1	0.0016220	small
Tournament	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1800.0	1.00e+00	1.0000000	ns	p = 1	0.0000000	small
Tournament	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1784.5	9.37e-01	1.0000000	ns	p = 1	0.0074266	small
Tournament	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1680.0	5.31e-01	1.0000000	ns	p = 1	0.0574960	small
Tournament	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1885.0	6.18e-01	1.0000000	ns	p = 1	0.0457398	small

3.7.2.4 Mean evolutionary distinctiveness vs. phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  fit_phylo_10 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_evolutionary_distinctiveness, 1)), discretize(lag(max_performance, 1))),
  fit_phylo_100 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_evolutionary_distinctiveness, 10)), discretize(lag(max_performance, 10))),
  fit_phylo_1000 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_evolutionary_distinctiveness, 100)), discretize(lag(max_performance, 100))),
    fit_pheno_10 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 1)), discretize(lag(max_performance, 1))),
      fit_pheno_100 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 10)), discretize(lag(max_performance, 10))),
      fit_pheno_1000 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 100)), discretize(lag(max_performance, 100)))
      )

res <- res %>% pivot_longer(cols=contains("o_10"))
res$offset <- str_extract(res$name, "[:digit:]*$")
res$Type <- case_when(str_detect(res$name, "phylo") ~ "Phylogenetic", TRUE ~ "Phenotypic")

ggplot(
  res %>% filter(str_detect(name, "fit_ph*")), 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_x_discrete("Lag") + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("") + 
  theme(legend.position = "bottom")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1664.0	4.77e-01	1.0000000	ns	p = 1	0.0651621	small
Eco-EA	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1046.0	7.66e-05	0.0045194	**	p = 0.0045194	0.3612663	moderate
Eco-EA	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1209.5	1.96e-03	0.1156400	ns	p = 0.11564	0.2829452	small
Eco-EA	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1848.0	8.03e-01	1.0000000	ns	p = 1	0.0229988	small
Eco-EA	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1503.0	1.20e-01	1.0000000	ns	p = 1	0.1423050	small
Eco-EA	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1481.0	9.33e-02	1.0000000	ns	p = 1	0.1534575	small
Eco-EA	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1473.5	8.71e-02	1.0000000	ns	p = 1	0.1564372	small
Eco-EA	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1550.5	1.91e-01	1.0000000	ns	p = 1	0.1195439	small
Eco-EA	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1632.0	3.79e-01	1.0000000	ns	p = 1	0.0804971	small
Eco-EA	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1804.5	9.83e-01	1.0000000	ns	p = 1	0.0021563	small
Eco-EA	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1928.5	5.02e-01	1.0000000	ns	p = 1	0.0615707	small
Eco-EA	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1770.0	5.67e-01	1.0000000	ns	p = 1	0.0531481	small
Fitness sharing	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1804.0	9.85e-01	1.0000000	ns	p = 1	0.0019165	small
Fitness sharing	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1624.0	3.57e-01	1.0000000	ns	p = 1	0.0843274	small
Fitness sharing	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	2030.0	2.28e-01	1.0000000	ns	p = 1	0.1102006	small
Fitness sharing	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1685.0	5.48e-01	1.0000000	ns	p = 1	0.0551012	small
Fitness sharing	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1527.0	1.53e-01	1.0000000	ns	p = 1	0.1308056	small
Fitness sharing	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1513.0	1.31e-01	1.0000000	ns	p = 1	0.1380636	small
Fitness sharing	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1531.0	1.59e-01	1.0000000	ns	p = 1	0.1288868	small
Fitness sharing	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	908.0	2.90e-06	0.0001699	***	p = 0.00016992	0.4273866	moderate
Fitness sharing	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	747.0	0.00e+00	0.0000020	****	p < 1e-04	0.5045270	large
Fitness sharing	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	908.0	2.90e-06	0.0001699	***	p = 0.00016992	0.4273866	moderate
Fitness sharing	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1001.0	2.78e-05	0.0016402	**	p = 0.0016402	0.3828273	moderate
Fitness sharing	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	2150.0	6.66e-02	1.0000000	ns	p = 1	0.1676965	small
Lexicase	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	2178.0	4.76e-02	1.0000000	ns	p = 1	0.1811123	small
Lexicase	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	832.0	4.00e-07	0.0000225	****	p < 1e-04	0.4638007	moderate
Lexicase	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1208.0	1.91e-03	0.1126900	ns	p = 0.11269	0.2836487	small
Lexicase	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1830.5	8.75e-01	1.0000000	ns	p = 1	0.0146136	small
Lexicase	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1315.5	1.11e-02	0.6549000	ns	p = 0.6549	0.2321403	small
Lexicase	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1728.5	7.08e-01	1.0000000	ns	p = 1	0.0344334	small
Lexicase	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1771.0	8.80e-01	1.0000000	ns	p = 1	0.0139839	small
Lexicase	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1489.0	1.01e-01	1.0000000	ns	p = 1	0.1499648	small
Lexicase	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1153.0	6.38e-04	0.0376420		p = 0.037642	0.3119846	moderate
Lexicase	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1826.0	8.63e-01	1.0000000	ns	p = 1	0.0160076	small
Lexicase	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1812.0	9.38e-01	1.0000000	ns	p = 1	0.0073881	small
Random	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1742.0	7.63e-01	1.0000000	ns	p = 1	0.0277897	small
Random	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	2052.0	1.87e-01	1.0000000	ns	p = 1	0.1207415	small
Random	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1186.0	1.28e-03	0.0755200	ns	p = 0.07552	0.2941876	small
Random	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1711.0	6.00e-01	1.0000000	ns	p = 1	0.0481649	small
Random	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1821.0	9.03e-01	1.0000000	ns	p = 1	0.0113645	small
Random	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1721.0	5.73e-01	1.0000000	ns	p = 1	0.0517719	small
Random	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1539.0	1.72e-01	1.0000000	ns	p = 1	0.1250537	small
Random	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1405.0	3.84e-02	1.0000000	ns	p = 1	0.1892575	small
Random	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	457.0	0.00e+00	0.0000000	****	p < 1e-04	0.6434756	large
Random	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2155.0	6.28e-02	1.0000000	ns	p = 1	0.1700922	small
Random	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1603.0	3.02e-01	1.0000000	ns	p = 1	0.0943892	small
Random	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1947.0	4.42e-01	1.0000000	ns	p = 1	0.0704325	small
Tournament	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1484.0	9.77e-02	1.0000000	ns	p = 1	0.1514060	small
Tournament	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	940.0	6.50e-06	0.0003806	***	p = 0.00038055	0.4120544	moderate
Tournament	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1298.5	8.55e-03	0.5044500	ns	p = 0.50445	0.2402998	small
Tournament	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	2000.0	2.95e-01	1.0000000	ns	p = 1	0.0958283	small
Tournament	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1259.0	4.55e-03	0.2684500	ns	p = 0.26845	0.2592154	small
Tournament	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1581.0	2.47e-01	1.0000000	ns	p = 1	0.1059385	small
Tournament	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1791.0	9.40e-01	1.0000000	ns	p = 1	0.0072988	small
Tournament	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1778.0	8.49e-01	1.0000000	ns	p = 1	0.0178416	small
Tournament	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1776.0	8.35e-01	1.0000000	ns	p = 1	0.0194636	small
Tournament	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2019.5	2.50e-01	1.0000000	ns	p = 1	0.1051704	small
Tournament	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	969.0	1.31e-05	0.0007729	***	p = 0.0007729	0.3981630	moderate
Tournament	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1745.5	7.60e-01	1.0000000	ns	p = 1	0.0281237	small

3.7.2.5 Mean evolutionary distinctiveness vs. phenotypic Shannon diveristy

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  fit_phylo_10 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_evolutionary_distinctiveness, 1)), discretize(lag(max_performance, 1))),
  fit_phylo_100 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_evolutionary_distinctiveness, 10)), discretize(lag(max_performance, 10))),
  fit_phylo_1000 = condinformation(discretize(max_performance), discretize(lag(mean_phenotype_evolutionary_distinctiveness, 100)), discretize(lag(max_performance, 100))),
    fit_pheno_10 = condinformation(discretize(max_performance), discretize(lag(phenotype_diversity, 1)), discretize(lag(max_performance, 1))),
      fit_pheno_100 = condinformation(discretize(max_performance), discretize(lag(phenotype_diversity, 10)), discretize(lag(max_performance, 10))),
      fit_pheno_1000 = condinformation(discretize(max_performance), discretize(lag(phenotype_diversity, 100)), discretize(lag(max_performance, 100)))
      )

res <- res %>% pivot_longer(cols=contains("o_10"))
res$offset <- str_extract(res$name, "[:digit:]*$")
res$Type <- case_when(str_detect(res$name, "phylo") ~ "Phylogenetic", TRUE ~ "Phenotypic")

ggplot(
  res %>% filter(str_detect(name, "fit_ph*")), 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_x_discrete("Lag") + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("") + 
  theme(legend.position = "bottom")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1721.0	6.80e-01	1.0000000	ns	p = 1	0.0378515	small
Eco-EA	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1288.0	7.26e-03	0.4283400	ns	p = 0.42834	0.2453161	small
Eco-EA	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1076.5	1.48e-04	0.0087320	**	p = 0.008732	0.3466738	moderate
Eco-EA	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1817.0	9.31e-01	1.0000000	ns	p = 1	0.0081454	small
Eco-EA	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1462.0	7.65e-02	1.0000000	ns	p = 1	0.1619498	small
Eco-EA	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1459.0	7.24e-02	1.0000000	ns	p = 1	0.1642205	small
Eco-EA	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1687.5	5.57e-01	1.0000000	ns	p = 1	0.0539026	small
Eco-EA	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1645.5	4.19e-01	1.0000000	ns	p = 1	0.0740262	small
Eco-EA	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1327.0	1.31e-02	0.7729000	ns	p = 0.7729	0.2266338	small
Eco-EA	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1764.0	8.52e-01	1.0000000	ns	p = 1	0.0172527	small
Eco-EA	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1999.5	2.96e-01	1.0000000	ns	p = 1	0.0955910	small
Eco-EA	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1770.0	5.67e-01	1.0000000	ns	p = 1	0.0531481	small
Fitness sharing	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1709.0	6.35e-01	1.0000000	ns	p = 1	0.0436011	small
Fitness sharing	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1654.0	4.45e-01	1.0000000	ns	p = 1	0.0699534	small
Fitness sharing	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	2071.0	1.56e-01	1.0000000	ns	p = 1	0.1298450	small
Fitness sharing	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1779.0	9.14e-01	1.0000000	ns	p = 1	0.0100620	small
Fitness sharing	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1593.0	2.78e-01	1.0000000	ns	p = 1	0.0991822	small
Fitness sharing	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1595.0	2.82e-01	1.0000000	ns	p = 1	0.0985257	small
Fitness sharing	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1502.0	1.18e-01	1.0000000	ns	p = 1	0.1427816	small
Fitness sharing	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	883.0	1.50e-06	0.0000891	****	p < 1e-04	0.4393649	moderate
Fitness sharing	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	792.0	1.00e-07	0.0000073	****	p < 1e-04	0.4829660	moderate
Fitness sharing	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	862.0	9.00e-07	0.0000509	****	p < 1e-04	0.4494267	moderate
Fitness sharing	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	897.0	2.20e-06	0.0001280	***	p = 0.00012803	0.4326571	moderate
Fitness sharing	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	2041.0	2.07e-01	1.0000000	ns	p = 1	0.1154710	small
Lexicase	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	2058.0	1.77e-01	1.0000000	ns	p = 1	0.1236163	small
Lexicase	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	806.0	2.00e-07	0.0000109	****	p < 1e-04	0.4762582	moderate
Lexicase	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1160.0	7.89e-04	0.0465510		p = 0.046551	0.3066456	moderate
Lexicase	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1719.5	6.75e-01	1.0000000	ns	p = 1	0.0385703	small
Lexicase	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1426.5	5.03e-02	1.0000000	ns	p = 1	0.1789565	small
Lexicase	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1765.0	8.56e-01	1.0000000	ns	p = 1	0.0168555	small
Lexicase	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1812.0	9.52e-01	1.0000000	ns	p = 1	0.0057864	small
Lexicase	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1498.0	1.11e-01	1.0000000	ns	p = 1	0.1456250	small
Lexicase	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1157.0	6.89e-04	0.0406510		p = 0.040651	0.3100558	moderate
Lexicase	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1779.0	8.90e-01	1.0000000	ns	p = 1	0.0129291	small
Lexicase	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1820.0	8.95e-01	1.0000000	ns	p = 1	0.0123135	small
Random	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1706.0	6.24e-01	1.0000000	ns	p = 1	0.0450385	small
Random	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	2157.0	6.13e-02	1.0000000	ns	p = 1	0.1710505	small
Random	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1060.0	1.04e-04	0.0061360	**	p = 0.006136	0.3545584	moderate
Random	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1777.0	8.94e-01	1.0000000	ns	p = 1	0.0124497	small
Random	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1816.0	9.27e-01	1.0000000	ns	p = 1	0.0086623	small
Random	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1793.0	9.63e-01	1.0000000	ns	p = 1	0.0045250	small
Random	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1482.0	9.56e-02	1.0000000	ns	p = 1	0.1523643	small
Random	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1380.0	2.77e-02	1.0000000	ns	p = 1	0.2012359	small
Random	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	534.0	0.00e+00	0.0000000	****	p < 1e-04	0.6065824	large
Random	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1993.0	3.12e-01	1.0000000	ns	p = 1	0.0924727	small
Random	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1857.0	7.67e-01	1.0000000	ns	p = 1	0.0273106	small
Random	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1907.0	5.76e-01	1.0000000	ns	p = 1	0.0512672	small
Tournament	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1512.0	1.31e-01	1.0000000	ns	p = 1	0.1379903	small
Tournament	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1210.0	1.97e-03	0.1162300	ns	p = 0.11623	0.2826885	small
Tournament	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1436.0	5.64e-02	1.0000000	ns	p = 1	0.1744214	small
Tournament	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1911.5	5.60e-01	1.0000000	ns	p = 1	0.0534243	small
Tournament	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1287.0	7.15e-03	0.4218500	ns	p = 0.42185	0.2457995	small
Tournament	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1571.0	2.26e-01	1.0000000	ns	p = 1	0.1108795	small
Tournament	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1792.0	9.47e-01	1.0000000	ns	p = 1	0.0064879	small
Tournament	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1780.0	8.62e-01	1.0000000	ns	p = 1	0.0162196	small
Tournament	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1780.0	8.62e-01	1.0000000	ns	p = 1	0.0162196	small
Tournament	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2028.5	2.31e-01	1.0000000	ns	p = 1	0.1094826	small
Tournament	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1383.0	2.88e-02	1.0000000	ns	p = 1	0.1998002	small
Tournament	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1499.5	8.73e-02	1.0000000	ns	p = 1	0.1563290	small

3.7.2.6 Variance evolutionary distinctiveness vs. phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  fit_phylo_10 = condinformation(discretize(max_performance), discretize(lag(variance_phenotype_evolutionary_distinctiveness, 1)), discretize(lag(max_performance, 1))),
  fit_phylo_100 = condinformation(discretize(max_performance), discretize(lag(variance_phenotype_evolutionary_distinctiveness, 10)), discretize(lag(max_performance, 10))),
  fit_phylo_1000 = condinformation(discretize(max_performance), discretize(lag(variance_phenotype_evolutionary_distinctiveness, 100)), discretize(lag(max_performance, 100))),
    fit_pheno_10 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 1)), discretize(lag(max_performance, 1))),
      fit_pheno_100 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 10)), discretize(lag(max_performance, 10))),
      fit_pheno_1000 = condinformation(discretize(max_performance), discretize(lag(phenotype_num_taxa, 100)), discretize(lag(max_performance, 100)))
      )

res <- res %>% pivot_longer(cols=contains("o_10"))
res$offset <- str_extract(res$name, "[:digit:]*$")
res$Type <- case_when(str_detect(res$name, "phylo") ~ "Phylogenetic", TRUE ~ "Phenotypic")

ggplot(
  res %>% filter(str_detect(name, "fit_ph*")), 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_x_discrete("Lag") + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("") + 
  theme(legend.position = "bottom")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1727.0	7.04e-01	1.0000000	ns	p = 1	0.0349767	small
Eco-EA	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1192.0	1.43e-03	0.0843700	ns	p = 0.08437	0.2913129	small
Eco-EA	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1163.0	8.35e-04	0.0492650		p = 0.049265	0.3052183	moderate
Eco-EA	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1793.0	9.73e-01	1.0000000	ns	p = 1	0.0033540	small
Eco-EA	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1290.0	7.49e-03	0.4419100	ns	p = 0.44191	0.2443621	small
Eco-EA	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1332.0	1.38e-02	0.8142000	ns	p = 0.8142	0.2251351	small
Eco-EA	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1488.5	1.03e-01	1.0000000	ns	p = 1	0.1492502	small
Eco-EA	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1516.5	1.37e-01	1.0000000	ns	p = 1	0.1358344	small
Eco-EA	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1567.0	2.22e-01	1.0000000	ns	p = 1	0.1116419	small
Eco-EA	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2146.0	6.97e-02	1.0000000	ns	p = 1	0.1657941	small
Eco-EA	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	2501.5	2.34e-04	0.0138060		p = 0.013806	0.3361130	moderate
Eco-EA	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1770.0	5.67e-01	1.0000000	ns	p = 1	0.0531481	small
Fitness sharing	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	2027.0	2.35e-01	1.0000000	ns	p = 1	0.1087632	small
Fitness sharing	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1938.0	4.70e-01	1.0000000	ns	p = 1	0.0661204	small
Fitness sharing	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	2252.0	1.78e-02	1.0000000	ns	p = 1	0.2165681	small
Fitness sharing	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1650.0	4.33e-01	1.0000000	ns	p = 1	0.0718712	small
Fitness sharing	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1326.0	1.29e-02	0.7611000	ns	p = 0.7611	0.2271130	small
Fitness sharing	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1466.0	7.90e-02	1.0000000	ns	p = 1	0.1605958	small
Fitness sharing	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1352.0	1.88e-02	1.0000000	ns	p = 1	0.2146516	small
Fitness sharing	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1273.0	5.72e-03	0.3374800	ns	p = 0.33748	0.2525031	small
Fitness sharing	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1113.0	3.14e-04	0.0185260		p = 0.018526	0.3291644	moderate
Fitness sharing	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1067.0	1.21e-04	0.0071390	**	p = 0.007139	0.3512045	moderate
Fitness sharing	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	2073.0	1.53e-01	1.0000000	ns	p = 1	0.1308033	small
Fitness sharing	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	2303.0	8.35e-03	0.4926500	ns	p = 0.49265	0.2410039	small
Lexicase	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1942.0	4.58e-01	1.0000000	ns	p = 1	0.0680369	small
Lexicase	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1432.0	5.37e-02	1.0000000	ns	p = 1	0.1763209	small
Lexicase	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1494.0	1.09e-01	1.0000000	ns	p = 1	0.1466157	small
Lexicase	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1753.0	8.07e-01	1.0000000	ns	p = 1	0.0225193	small
Lexicase	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1303.5	9.23e-03	0.5445700	ns	p = 0.54457	0.2378899	small
Lexicase	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1610.0	3.18e-01	1.0000000	ns	p = 1	0.0914490	small
Lexicase	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1774.0	8.93e-01	1.0000000	ns	p = 1	0.0125373	small
Lexicase	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1533.0	1.59e-01	1.0000000	ns	p = 1	0.1287479	small
Lexicase	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1231.0	2.67e-03	0.1575300	ns	p = 0.15753	0.2743729	small
Lexicase	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1792.0	9.60e-01	1.0000000	ns	p = 1	0.0049253	small
Lexicase	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1776.0	8.74e-01	1.0000000	ns	p = 1	0.0147759	small
Random	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1752.0	8.03e-01	1.0000000	ns	p = 1	0.0229984	small
Random	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	1764.0	8.52e-01	1.0000000	ns	p = 1	0.0172488	small
Random	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1435.0	5.57e-02	1.0000000	ns	p = 1	0.1748835	small
Random	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1717.0	6.25e-01	1.0000000	ns	p = 1	0.0449261	small
Random	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1811.5	9.48e-01	1.0000000	ns	p = 1	0.0062231	small
Random	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1714.5	5.42e-01	1.0000000	ns	p = 1	0.0560318	small
Random	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1848.0	8.03e-01	1.0000000	ns	p = 1	0.0229984	small
Random	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1754.0	8.11e-01	1.0000000	ns	p = 1	0.0220401	small
Random	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	940.0	6.50e-06	0.0003806	***	p = 0.00038055	0.4120544	moderate
Random	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	1949.0	4.36e-01	1.0000000	ns	p = 1	0.0713908	small
Random	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1645.0	4.17e-01	1.0000000	ns	p = 1	0.0742656	small
Random	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1736.0	7.39e-01	1.0000000	ns	p = 1	0.0306645	small
Tournament	Count Odds	10	value	Phenotypic	Phylogenetic	60	60	1534.0	1.63e-01	1.0000000	ns	p = 1	0.1274494	small
Tournament	Count Odds	100	value	Phenotypic	Phylogenetic	60	60	973.0	1.44e-05	0.0008496	***	p = 0.0008496	0.3962430	moderate
Tournament	Count Odds	1000	value	Phenotypic	Phylogenetic	60	60	1484.5	9.82e-02	1.0000000	ns	p = 1	0.1511756	small
Tournament	Logic-9	10	value	Phenotypic	Phylogenetic	60	60	1872.0	7.07e-01	1.0000000	ns	p = 1	0.0344982	small
Tournament	Logic-9	100	value	Phenotypic	Phylogenetic	60	60	1270.0	5.45e-03	0.3215500	ns	p = 0.32155	0.2539449	small
Tournament	Logic-9	1000	value	Phenotypic	Phylogenetic	60	60	1610.0	3.15e-01	1.0000000	ns	p = 1	0.0919101	small
Tournament	NK Landscape	10	value	Phenotypic	Phylogenetic	60	60	1789.0	9.26e-01	1.0000000	ns	p = 1	0.0089208	small
Tournament	NK Landscape	100	value	Phenotypic	Phylogenetic	60	60	1778.0	8.49e-01	1.0000000	ns	p = 1	0.0178416	small
Tournament	NK Landscape	1000	value	Phenotypic	Phylogenetic	60	60	1778.0	8.49e-01	1.0000000	ns	p = 1	0.0178416	small
Tournament	Sorting network	10	value	Phenotypic	Phylogenetic	60	60	2183.0	4.47e-02	1.0000000	ns	p = 1	0.1835086	small
Tournament	Sorting network	100	value	Phenotypic	Phylogenetic	60	60	1367.0	2.32e-02	1.0000000	ns	p = 1	0.2074646	small
Tournament	Sorting network	1000	value	Phenotypic	Phylogenetic	60	60	1787.0	9.44e-01	1.0000000	ns	p = 1	0.0067084	small

3.7.3 Transfer entropy between types of diversity

While we’re calculating transfer entropy, we might as well also calculate it between phenotypic diversity and phylogenetic diversity, as these could potentially also be in a feedback loop.

3.7.3.1 Max pairwise distance and phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  phen_phylo_10 =      condinformation(discretize(phenotype_num_taxa), 
                                       discretize(lag(max_phenotype_pairwise_distance, 1)), 
                                       discretize(lag(phenotype_num_taxa, 1))),
  phen_phylo_100 =     condinformation(discretize(phenotype_num_taxa),
                                       discretize(lag(max_phenotype_pairwise_distance, 10)),
                                       discretize(lag(phenotype_num_taxa, 10))),
  pheno_phylo_1000 =   condinformation(discretize(phenotype_num_taxa),
                                       discretize(lag(max_phenotype_pairwise_distance, 100)),
                                       discretize(lag(phenotype_num_taxa, 100))),
  
  phylo_pheno_10 =     condinformation(discretize(max_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_num_taxa, 1)),
                                       discretize(lag(max_phenotype_pairwise_distance, 1))),
  phylo_pheno_100 =    condinformation(discretize(max_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_num_taxa, 10)),
                                       discretize(lag(max_phenotype_pairwise_distance, 10))),
  phylo_pheno_1000 =   condinformation(discretize(max_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_num_taxa, 100)),
                                       discretize(lag(max_phenotype_pairwise_distance, 100))))

# Turn Transfer Entropy columns into rows
res <- res %>% pivot_longer(cols=contains("phylo"))
# Pull lag into a column
res$offset <- str_extract(res$name, "[:digit:]*$")
# Make column indicating direction of transfer entropy
res$Type <- case_when(str_detect(res$name, "phylo_pheno") ~ "\nPhenotypic\n\t->\nPhylogenetic\n", TRUE ~ "\nPhylogenetic\n\t->\nPhenotypic\n")

ggplot(
  res, 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name* problem_name, ncol=4) + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	4.0	0.00e+00	0.0000000	****	p < 1e-04	0.8605228	large
Eco-EA	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	284.0	0.00e+00	0.0000000	****	p < 1e-04	0.7263656	large
Eco-EA	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	633.0	0.00e+00	0.0000001	****	p < 1e-04	0.5591482	large
Eco-EA	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1990.0	3.20e-01	1.0000000	ns	p = 1	0.0910353	small
Eco-EA	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2044.0	2.01e-01	1.0000000	ns	p = 1	0.1169084	small
Eco-EA	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1467.0	8.10e-02	1.0000000	ns	p = 1	0.1595513	small
Eco-EA	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	115.0	0.00e+00	0.0000000	****	p < 1e-04	0.8073391	large
Eco-EA	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	710.0	0.00e+00	0.0000006	****	p < 1e-04	0.5222549	large
Eco-EA	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1260.5	4.67e-03	0.2802000	ns	p = 0.2802	0.2584927	small
Eco-EA	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	115.0	0.00e+00	0.0000000	****	p < 1e-04	0.8073391	large
Eco-EA	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	996.0	2.47e-05	0.0014820	**	p = 0.001482	0.3852229	moderate
Eco-EA	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1135.0	4.87e-04	0.0292200		p = 0.02922	0.3186345	moderate
Fitness sharing	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	16.0	0.00e+00	0.0000000	****	p < 1e-04	0.8547732	large
Fitness sharing	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1617.0	3.38e-01	1.0000000	ns	p = 1	0.0876813	small
Fitness sharing	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1899.0	6.05e-01	1.0000000	ns	p = 1	0.0474342	small
Fitness sharing	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	867.0	1.00e-06	0.0000592	****	p < 1e-04	0.4470311	moderate
Fitness sharing	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1066.0	1.18e-04	0.0070800	**	p = 0.00708	0.3516836	moderate
Fitness sharing	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1445.0	6.28e-02	1.0000000	ns	p = 1	0.1700922	small
Fitness sharing	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Fitness sharing	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Fitness sharing	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	203.0	0.00e+00	0.0000000	****	p < 1e-04	0.7652019	large
Fitness sharing	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3.0	0.00e+00	0.0000000	****	p < 1e-04	0.8610020	large
Fitness sharing	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2733.0	1.00e-06	0.0000592	****	p < 1e-04	0.4470311	moderate
Fitness sharing	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2660.0	6.50e-06	0.0003870	***	p = 0.000387	0.4120544	moderate
Lexicase	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	22.0	0.00e+00	0.0000000	****	p < 1e-04	0.8518984	large
Lexicase	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	633.0	0.00e+00	0.0000001	****	p < 1e-04	0.5591676	large
Lexicase	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1402.0	3.69e-02	1.0000000	ns	p = 1	0.1906949	small
Lexicase	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1809.0	9.64e-01	1.0000000	ns	p = 1	0.0043122	small
Lexicase	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1545.0	1.82e-01	1.0000000	ns	p = 1	0.1221798	small
Lexicase	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	18.0	0.00e+00	0.0000000	****	p < 1e-04	0.8538150	large
Lexicase	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1134.0	4.78e-04	0.0286800		p = 0.02868	0.3191026	moderate
Lexicase	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2890.0	0.00e+00	0.0000006	****	p < 1e-04	0.5222640	large
Lexicase	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	30.0	0.00e+00	0.0000000	****	p < 1e-04	0.9099165	large
Random	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Random	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1.0	0.00e+00	0.0000000	****	p < 1e-04	0.8619602	large
Random	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	228.0	0.00e+00	0.0000000	****	p < 1e-04	0.7531970	large
Random	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	372.0	0.00e+00	0.0000000	****	p < 1e-04	0.6842019	large
Random	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	928.0	4.80e-06	0.0002868	***	p = 0.0002868	0.4178040	moderate
Random	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1227.0	2.66e-03	0.1596000	ns	p = 0.1596	0.2745451	small
Random	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Random	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Random	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	143.0	0.00e+00	0.0000000	****	p < 1e-04	0.7939371	large
Random	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	185.0	0.00e+00	0.0000000	****	p < 1e-04	0.7737998	large
Random	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	272.0	0.00e+00	0.0000000	****	p < 1e-04	0.7321152	large
Random	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	509.0	0.00e+00	0.0000000	****	p < 1e-04	0.6185607	large
Tournament	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1723.0	6.88e-01	1.0000000	ns	p = 1	0.0368932	small
Tournament	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2468.0	4.59e-04	0.0275400		p = 0.02754	0.3200608	moderate
Tournament	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2198.0	3.69e-02	1.0000000	ns	p = 1	0.1906949	small
Tournament	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2925.0	0.00e+00	0.0000002	****	p < 1e-04	0.5390246	large
Tournament	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2748.0	7.00e-07	0.0000395	****	p < 1e-04	0.4542181	moderate
Tournament	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1866.0	7.31e-01	1.0000000	ns	p = 1	0.0316230	small
Tournament	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	784.0	1.00e-07	0.0000059	****	p < 1e-04	0.4867991	moderate
Tournament	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1198.0	1.59e-03	0.0954000	ns	p = 0.0954	0.2884381	small
Tournament	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1630.5	3.75e-01	1.0000000	ns	p = 1	0.0812132	small
Tournament	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	686.0	0.00e+00	0.0000003	****	p < 1e-04	0.5337541	large
Tournament	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1272.0	5.63e-03	0.3378000	ns	p = 0.3378	0.2529822	small
Tournament	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1565.0	2.18e-01	1.0000000	ns	p = 1	0.1126002	small

3.7.3.2 Mean pairwise distance and phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  phen_phylo_10 =      condinformation(discretize(phenotype_num_taxa), 
                                       discretize(lag(mean_phenotype_pairwise_distance, 1)), 
                                       discretize(lag(phenotype_num_taxa, 1))),
  phen_phylo_100 =     condinformation(discretize(phenotype_num_taxa),
                                       discretize(lag(mean_phenotype_pairwise_distance, 10)),
                                       discretize(lag(phenotype_num_taxa, 10))),
  pheno_phylo_1000 =   condinformation(discretize(phenotype_num_taxa),
                                       discretize(lag(mean_phenotype_pairwise_distance, 100)),
                                       discretize(lag(phenotype_num_taxa, 100))),
  
  phylo_pheno_10 =     condinformation(discretize(mean_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_num_taxa, 1)),
                                       discretize(lag(mean_phenotype_pairwise_distance, 1))),
  phylo_pheno_100 =    condinformation(discretize(mean_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_num_taxa, 10)),
                                       discretize(lag(mean_phenotype_pairwise_distance, 10))),
  phylo_pheno_1000 =   condinformation(discretize(mean_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_num_taxa, 100)),
                                       discretize(lag(mean_phenotype_pairwise_distance, 100)))
)

# Turn Transfer Entropy columns into rows
res <- res %>% pivot_longer(cols=contains("phylo"))
# Pull lag into a column
res$offset <- str_extract(res$name, "[:digit:]*$")
# Make column indicating direction of transfer entropy
res$Type <- case_when(str_detect(res$name, "phylo_pheno") ~ "\nPhenotypic\n\t->\nPhylogenetic\n", TRUE ~ "\nPhylogenetic\n\t->\nPhenotypic\n")

ggplot(
  res, 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	310.0	0.00e+00	0.0000000	****	p < 1e-04	0.7139081	large
Eco-EA	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	822.0	3.00e-07	0.0000173	****	p < 1e-04	0.4685921	moderate
Eco-EA	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	984.0	1.87e-05	0.0011220	**	p = 0.001122	0.3909752	moderate
Eco-EA	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1530.0	1.57e-01	1.0000000	ns	p = 1	0.1293659	small
Eco-EA	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2183.0	4.47e-02	1.0000000	ns	p = 1	0.1835079	small
Eco-EA	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1983.0	3.38e-01	1.0000000	ns	p = 1	0.0876813	small
Eco-EA	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	117.0	0.00e+00	0.0000000	****	p < 1e-04	0.8063808	large
Eco-EA	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	775.0	1.00e-07	0.0000045	****	p < 1e-04	0.4911113	moderate
Eco-EA	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1562.5	2.14e-01	1.0000000	ns	p = 1	0.1137943	small
Eco-EA	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	73.0	0.00e+00	0.0000000	****	p < 1e-04	0.8274627	large
Eco-EA	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	518.0	0.00e+00	0.0000000	****	p < 1e-04	0.6142485	large
Eco-EA	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1393.0	3.29e-02	1.0000000	ns	p = 1	0.1950190	small
Fitness sharing	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3.0	0.00e+00	0.0000000	****	p < 1e-04	0.8610020	large
Fitness sharing	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1773.0	8.89e-01	1.0000000	ns	p = 1	0.0129366	small
Fitness sharing	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1935.0	4.80e-01	1.0000000	ns	p = 1	0.0646830	small
Fitness sharing	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	628.0	0.00e+00	0.0000000	****	p < 1e-04	0.5615439	large
Fitness sharing	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1010.0	3.42e-05	0.0020520	**	p = 0.002052	0.3785151	moderate
Fitness sharing	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1242.0	3.43e-03	0.2058000	ns	p = 0.2058	0.2673562	small
Fitness sharing	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Fitness sharing	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	30.0	0.00e+00	0.0000000	****	p < 1e-04	0.8480654	large
Fitness sharing	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	480.0	0.00e+00	0.0000000	****	p < 1e-04	0.6324555	large
Fitness sharing	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	6.0	0.00e+00	0.0000000	****	p < 1e-04	0.8595646	large
Fitness sharing	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2922.0	0.00e+00	0.0000002	****	p < 1e-04	0.5375872	large
Fitness sharing	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2862.0	0.00e+00	0.0000015	****	p < 1e-04	0.5088392	large
Lexicase	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	150.0	0.00e+00	0.0000000	****	p < 1e-04	0.7905694	large
Lexicase	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	931.0	5.10e-06	0.0003090	***	p = 0.000309	0.4163673	moderate
Lexicase	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1862.0	7.47e-01	1.0000000	ns	p = 1	0.0297062	small
Lexicase	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1835.0	8.56e-01	1.0000000	ns	p = 1	0.0167697	small
Lexicase	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1857.0	7.67e-01	1.0000000	ns	p = 1	0.0273106	small
Lexicase	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	4.0	0.00e+00	0.0000000	****	p < 1e-04	0.8605228	large
Lexicase	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1390.5	3.18e-02	1.0000000	ns	p = 1	0.1962803	small
Lexicase	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1955.0	4.17e-01	1.0000000	ns	p = 1	0.0742656	small
Lexicase	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1736.0	7.39e-01	1.0000000	ns	p = 1	0.0306647	small
Random	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Random	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	18.0	0.00e+00	0.0000000	****	p < 1e-04	0.8538150	large
Random	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	478.0	0.00e+00	0.0000000	****	p < 1e-04	0.6334138	large
Random	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	625.0	0.00e+00	0.0000000	****	p < 1e-04	0.5629813	large
Random	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1029.0	5.25e-05	0.0031500	**	p = 0.00315	0.3694115	moderate
Random	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1371.0	2.45e-02	1.0000000	ns	p = 1	0.2055480	small
Random	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Random	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	20.0	0.00e+00	0.0000000	****	p < 1e-04	0.8528567	large
Random	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	336.0	0.00e+00	0.0000000	****	p < 1e-04	0.7014507	large
Random	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	341.0	0.00e+00	0.0000000	****	p < 1e-04	0.6990550	large
Random	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	409.0	0.00e+00	0.0000000	****	p < 1e-04	0.6664740	large
Random	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	457.0	0.00e+00	0.0000000	****	p < 1e-04	0.6434756	large
Tournament	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	898.0	2.20e-06	0.0001338	***	p = 0.0001338	0.4321779	moderate
Tournament	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2480.0	3.62e-04	0.0217200		p = 0.02172	0.3258104	moderate
Tournament	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2402.0	1.59e-03	0.0954000	ns	p = 0.0954	0.2884381	small
Tournament	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1427.0	5.06e-02	1.0000000	ns	p = 1	0.1787166	small
Tournament	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2720.0	1.40e-06	0.0000834	****	p < 1e-04	0.4408023	moderate
Tournament	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1934.0	4.83e-01	1.0000000	ns	p = 1	0.0642038	small
Tournament	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	272.0	0.00e+00	0.0000000	****	p < 1e-04	0.7321152	large
Tournament	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	913.0	3.30e-06	0.0001962	***	p = 0.0001962	0.4249910	moderate
Tournament	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1765.0	8.56e-01	1.0000000	ns	p = 1	0.0167697	small
Tournament	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	314.0	0.00e+00	0.0000000	****	p < 1e-04	0.7119916	large
Tournament	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1160.0	7.89e-04	0.0473400		p = 0.04734	0.3066451	moderate
Tournament	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1766.0	8.60e-01	1.0000000	ns	p = 1	0.0162906	small

3.7.3.3 Mean pairwise distance and shannon diversity

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  phen_phylo_10 =      condinformation(discretize(phenotype_diversity), 
                                       discretize(lag(mean_phenotype_pairwise_distance, 1)), 
                                       discretize(lag(phenotype_diversity, 1))),
  phen_phylo_100 =     condinformation(discretize(phenotype_diversity),
                                       discretize(lag(mean_phenotype_pairwise_distance, 10)),
                                       discretize(lag(phenotype_diversity, 10))),
  pheno_phylo_1000 =   condinformation(discretize(phenotype_diversity),
                                       discretize(lag(mean_phenotype_pairwise_distance, 100)),
                                       discretize(lag(phenotype_diversity, 100))),
  phylo_pheno_10 =     condinformation(discretize(mean_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_diversity, 1)),
                                       discretize(lag(mean_phenotype_pairwise_distance, 1))),
  phylo_pheno_100 =    condinformation(discretize(mean_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_diversity, 10)),
                                       discretize(lag(mean_phenotype_pairwise_distance, 10))),
  phylo_pheno_1000 =   condinformation(discretize(mean_phenotype_pairwise_distance),
                                       discretize(lag(phenotype_diversity, 100)),
                                       discretize(lag(mean_phenotype_pairwise_distance, 100)))
  
)

# Turn Transfer Entropy columns into rows
res <- res %>% pivot_longer(cols=contains("phylo"))
# Pull lag into a column
res$offset <- str_extract(res$name, "[:digit:]*$")
# Make column indicating direction of transfer entropy
res$Type <- case_when(str_detect(res$name, "phylo_pheno") ~ "\nPhenotypic\n\t->\nPhylogenetic\n", TRUE ~ "\nPhylogenetic\n\t->\nPhenotypic\n")

ggplot(
  res, 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	557.0	0.00e+00	0.0000000	****	p < 1e-04	0.5955623	large
Eco-EA	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	898.0	2.20e-06	0.0001338	***	p = 0.0001338	0.4321779	moderate
Eco-EA	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	875.0	1.20e-06	0.0000732	****	p < 1e-04	0.4432011	moderate
Eco-EA	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1419.0	4.58e-02	1.0000000	ns	p = 1	0.1825497	small
Eco-EA	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1956.0	4.14e-01	1.0000000	ns	p = 1	0.0747447	small
Eco-EA	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1758.0	8.28e-01	1.0000000	ns	p = 1	0.0201236	small
Eco-EA	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1153.0	6.91e-04	0.0414600		p = 0.04146	0.3099990	moderate
Eco-EA	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1312.0	1.05e-02	0.6300000	ns	p = 0.63	0.2338169	small
Eco-EA	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1459.0	7.39e-02	1.0000000	ns	p = 1	0.1633843	small
Eco-EA	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	531.0	0.00e+00	0.0000000	****	p < 1e-04	0.6080198	large
Eco-EA	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2600.0	2.71e-05	0.0016260	**	p = 0.001626	0.3833064	moderate
Eco-EA	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1661.0	4.67e-01	1.0000000	ns	p = 1	0.0666060	small
Fitness sharing	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1.0	0.00e+00	0.0000000	****	p < 1e-04	0.8619602	large
Fitness sharing	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1695.0	5.83e-01	1.0000000	ns	p = 1	0.0503090	small
Fitness sharing	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2098.0	1.18e-01	1.0000000	ns	p = 1	0.1427816	small
Fitness sharing	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	588.0	0.00e+00	0.0000000	****	p < 1e-04	0.5807092	large
Fitness sharing	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1101.0	2.46e-04	0.0147600		p = 0.01476	0.3349140	moderate
Fitness sharing	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1411.0	4.14e-02	1.0000000	ns	p = 1	0.1863827	small
Fitness sharing	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Fitness sharing	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	40.0	0.00e+00	0.0000000	****	p < 1e-04	0.8432740	large
Fitness sharing	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	438.0	0.00e+00	0.0000000	****	p < 1e-04	0.6525791	large
Fitness sharing	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	5.0	0.00e+00	0.0000000	****	p < 1e-04	0.8600437	large
Fitness sharing	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2988.0	0.00e+00	0.0000000	****	p < 1e-04	0.5692100	large
Fitness sharing	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2871.0	0.00e+00	0.0000012	****	p < 1e-04	0.5131514	large
Lexicase	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	149.0	0.00e+00	0.0000000	****	p < 1e-04	0.7910485	large
Lexicase	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	871.0	1.10e-06	0.0000660	****	p < 1e-04	0.4451145	moderate
Lexicase	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1982.0	3.41e-01	1.0000000	ns	p = 1	0.0872022	small
Lexicase	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2120.0	9.36e-02	1.0000000	ns	p = 1	0.1533226	small
Lexicase	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1777.0	9.06e-01	1.0000000	ns	p = 1	0.0110201	small
Lexicase	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Lexicase	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	18.0	0.00e+00	0.0000000	****	p < 1e-04	0.8538150	large
Lexicase	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2118.5	9.23e-02	1.0000000	ns	p = 1	0.1539355	small
Lexicase	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2210.5	3.07e-02	1.0000000	ns	p = 1	0.1974746	small
Lexicase	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1859.0	7.59e-01	1.0000000	ns	p = 1	0.0282699	small
Random	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Random	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	51.0	0.00e+00	0.0000000	****	p < 1e-04	0.8380036	large
Random	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	455.0	0.00e+00	0.0000000	****	p < 1e-04	0.6444339	large
Random	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3394.0	0.00e+00	0.0000000	****	p < 1e-04	0.7637380	large
Random	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2548.0	8.73e-05	0.0052380	**	p = 0.005238	0.3583915	moderate
Random	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2370.0	2.80e-03	0.1680000	ns	p = 0.168	0.2731058	small
Random	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Random	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	39.0	0.00e+00	0.0000000	****	p < 1e-04	0.8437532	large
Random	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	456.0	0.00e+00	0.0000000	****	p < 1e-04	0.6439547	large
Random	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	562.0	0.00e+00	0.0000000	****	p < 1e-04	0.5931666	large
Random	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	369.0	0.00e+00	0.0000000	****	p < 1e-04	0.6856393	large
Random	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	608.0	0.00e+00	0.0000000	****	p < 1e-04	0.5711265	large
Tournament	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2065.0	1.65e-01	1.0000000	ns	p = 1	0.1269702	small
Tournament	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2459.0	5.48e-04	0.0328800		p = 0.03288	0.3157486	moderate
Tournament	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2074.5	1.50e-01	1.0000000	ns	p = 1	0.1315222	small
Tournament	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2035.0	2.18e-01	1.0000000	ns	p = 1	0.1125963	small
Tournament	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2437.0	8.35e-04	0.0501000	ns	p = 0.0501	0.3052077	moderate
Tournament	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1782.0	9.27e-01	1.0000000	ns	p = 1	0.0086244	small
Tournament	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1404.0	3.79e-02	1.0000000	ns	p = 1	0.1897367	small
Tournament	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1759.0	8.32e-01	1.0000000	ns	p = 1	0.0196445	small
Tournament	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1972.0	3.68e-01	1.0000000	ns	p = 1	0.0824109	small
Tournament	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	581.0	0.00e+00	0.0000000	****	p < 1e-04	0.5840631	large
Tournament	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1362.0	2.17e-02	1.0000000	ns	p = 1	0.2098602	small
Tournament	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1758.0	8.28e-01	1.0000000	ns	p = 1	0.0201237	small

3.7.3.4 Mean evolutionary distinctiveness and phenotypic richness

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  phen_phylo_10 =      condinformation(
                          discretize(phenotype_num_taxa), 
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 1)), 
                          discretize(lag(phenotype_num_taxa, 1))),
  phen_phylo_100 =     condinformation(
                          discretize(phenotype_num_taxa),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 10)),
                          discretize(lag(phenotype_num_taxa, 10))),
  pheno_phylo_1000 =   condinformation(
                          discretize(phenotype_num_taxa),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 100)),
                          discretize(lag(phenotype_num_taxa, 100))),
  
  phylo_pheno_10 =     condinformation(
                          discretize(mean_phenotype_evolutionary_distinctiveness),
                          discretize(lag(phenotype_num_taxa, 1)),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 1))),
  phylo_pheno_100 =    condinformation(
                          discretize(mean_phenotype_evolutionary_distinctiveness),
                          discretize(lag(phenotype_num_taxa, 10)),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 10))),
  phylo_pheno_1000 =   condinformation(
                          discretize(mean_phenotype_evolutionary_distinctiveness),
                          discretize(lag(phenotype_num_taxa, 100)),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 100)))
)

# Turn Transfer Entropy columns into rows
res <- res %>% pivot_longer(cols=contains("phylo"))
# Pull lag into a column
res$offset <- str_extract(res$name, "[:digit:]*$")
# Make column indicating direction of transfer entropy
res$Type <- case_when(str_detect(res$name, "phylo_pheno") ~ "\nPhenotypic\n\t->\nPhylogenetic\n", TRUE ~ "\nPhylogenetic\n\t->\nPhenotypic\n")

ggplot(
  res, 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_y_continuous("Transfer Entropy") +  
  scale_color_discrete("")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	229.0	0.00e+00	0.0000000	****	p < 1e-04	0.7527179	large
Eco-EA	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1127.0	4.16e-04	0.0249600		p = 0.02496	0.3224565	moderate
Eco-EA	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1329.5	1.36e-02	0.8160000	ns	p = 0.816	0.2254325	small
Eco-EA	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	53.0	0.00e+00	0.0000000	****	p < 1e-04	0.8370453	large
Eco-EA	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1089.0	1.92e-04	0.0115200		p = 0.01152	0.3406635	moderate
Eco-EA	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1906.0	5.80e-01	1.0000000	ns	p = 1	0.0507881	small
Eco-EA	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	4.0	0.00e+00	0.0000000	****	p < 1e-04	0.8605228	large
Eco-EA	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	194.0	0.00e+00	0.0000000	****	p < 1e-04	0.7694876	large
Eco-EA	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	693.0	0.00e+00	0.0000004	****	p < 1e-04	0.5304002	large
Eco-EA	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Eco-EA	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Eco-EA	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	577.0	0.00e+00	0.0000000	****	p < 1e-04	0.5860000	large
Fitness sharing	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	447.0	0.00e+00	0.0000000	****	p < 1e-04	0.6482669	large
Fitness sharing	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1909.0	5.69e-01	1.0000000	ns	p = 1	0.0522255	small
Fitness sharing	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2119.0	9.46e-02	1.0000000	ns	p = 1	0.1528434	small
Fitness sharing	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1048.0	8.00e-05	0.0048000	**	p = 0.0048	0.3603080	moderate
Fitness sharing	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2263.0	1.52e-02	0.9120000	ns	p = 0.912	0.2218386	small
Fitness sharing	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2156.0	6.21e-02	1.0000000	ns	p = 1	0.1705713	small
Fitness sharing	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	80.0	0.00e+00	0.0000000	****	p < 1e-04	0.8241087	large
Fitness sharing	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	471.0	0.00e+00	0.0000000	****	p < 1e-04	0.6367677	large
Fitness sharing	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	946.0	7.50e-06	0.0004482	***	p = 0.0004482	0.4091796	moderate
Fitness sharing	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2089.0	1.30e-01	1.0000000	ns	p = 1	0.1384694	small
Fitness sharing	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3316.0	0.00e+00	0.0000000	****	p < 1e-04	0.7263656	large
Fitness sharing	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3011.0	0.00e+00	0.0000000	****	p < 1e-04	0.5802300	large
Lexicase	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	9.0	0.00e+00	0.0000000	****	p < 1e-04	0.8581272	large
Lexicase	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	155.0	0.00e+00	0.0000000	****	p < 1e-04	0.7881738	large
Lexicase	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	981.0	1.74e-05	0.0010440	**	p = 0.001044	0.3924106	moderate
Lexicase	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	856.0	7.00e-07	0.0000440	****	p < 1e-04	0.4523015	moderate
Lexicase	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2006.0	2.81e-01	1.0000000	ns	p = 1	0.0987014	small
Lexicase	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2615.0	1.91e-05	0.0011460	**	p = 0.001146	0.3904934	moderate
Lexicase	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3.0	0.00e+00	0.0000000	****	p < 1e-04	0.8610020	large
Lexicase	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	22.0	0.00e+00	0.0000000	****	p < 1e-04	0.8518984	large
Lexicase	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	167.0	0.00e+00	0.0000000	****	p < 1e-04	0.7824242	large
Lexicase	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624528	large
Lexicase	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	59.0	0.00e+00	0.0000000	****	p < 1e-04	0.8341705	large
Lexicase	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1576.0	2.41e-01	1.0000000	ns	p = 1	0.1073262	small
Random	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	324.0	0.00e+00	0.0000000	****	p < 1e-04	0.7072003	large
Random	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	852.0	7.00e-07	0.0000395	****	p < 1e-04	0.4542181	moderate
Random	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	994.0	2.36e-05	0.0014160	**	p = 0.001416	0.3861812	moderate
Random	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	166.0	0.00e+00	0.0000000	****	p < 1e-04	0.7829033	large
Random	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	653.0	0.00e+00	0.0000001	****	p < 1e-04	0.5495655	large
Random	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	529.0	0.00e+00	0.0000000	****	p < 1e-04	0.6089780	large
Random	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	77.0	0.00e+00	0.0000000	****	p < 1e-04	0.8255461	large
Random	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	415.0	0.00e+00	0.0000000	****	p < 1e-04	0.6635992	large
Random	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	599.0	0.00e+00	0.0000000	****	p < 1e-04	0.5754387	large
Random	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1578.0	2.45e-01	1.0000000	ns	p = 1	0.1063675	small
Random	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1711.0	6.42e-01	1.0000000	ns	p = 1	0.0426428	small
Random	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2147.0	6.90e-02	1.0000000	ns	p = 1	0.1662591	small
Tournament	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	277.0	0.00e+00	0.0000000	****	p < 1e-04	0.7297195	large
Tournament	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2039.0	2.11e-01	1.0000000	ns	p = 1	0.1145128	small
Tournament	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2142.0	7.31e-02	1.0000000	ns	p = 1	0.1638635	small
Tournament	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3.0	0.00e+00	0.0000000	****	p < 1e-04	0.8610020	large
Tournament	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	460.0	0.00e+00	0.0000000	****	p < 1e-04	0.6420382	large
Tournament	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1471.0	8.47e-02	1.0000000	ns	p = 1	0.1576348	small
Tournament	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624424	large
Tournament	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Tournament	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	20.0	0.00e+00	0.0000000	****	p < 1e-04	0.8536871	large
Tournament	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	4.0	0.00e+00	0.0000000	****	p < 1e-04	0.8605228	large
Tournament	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	54.0	0.00e+00	0.0000000	****	p < 1e-04	0.8365662	large
Tournament	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	932.0	5.30e-06	0.0003168	***	p = 0.0003168	0.4158874	moderate

3.7.3.5 Mean evolutionary distinctiveness and shannon diversity

res <- data %>% group_by(SEED, selection_name, problem_name) %>%
summarise(
  phen_phylo_10 =      condinformation(
                          discretize(phenotype_diversity), 
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 1)), 
                          discretize(lag(phenotype_diversity, 1))),
  phen_phylo_100 =     condinformation(
                          discretize(phenotype_diversity),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 10)),
                          discretize(lag(phenotype_diversity, 10))),
  pheno_phylo_1000 =   condinformation(
                          discretize(phenotype_diversity),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 100)),
                          discretize(lag(phenotype_diversity, 100))),
  
  phylo_pheno_10 =     condinformation(
                          discretize(mean_phenotype_evolutionary_distinctiveness),
                          discretize(lag(phenotype_diversity, 1)),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 1))),
  phylo_pheno_100 =    condinformation(
                          discretize(mean_phenotype_evolutionary_distinctiveness),
                          discretize(lag(phenotype_diversity, 10)),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 10))),
  phylo_pheno_1000 =   condinformation(
                          discretize(mean_phenotype_evolutionary_distinctiveness),
                          discretize(lag(phenotype_diversity, 100)),
                          discretize(lag(mean_phenotype_evolutionary_distinctiveness, 100)))
)

# Turn Transfer Entropy columns into rows
res <- res %>% pivot_longer(cols=contains("phylo"))
# Pull lag into a column
res$offset <- str_extract(res$name, "[:digit:]*$")
# Make column indicating direction of transfer entropy
res$Type <- case_when(str_detect(res$name, "phylo_pheno") ~ "\nPhenotypic\n\t->\nPhylogenetic\n", TRUE ~ "\nPhylogenetic\n\t->\nPhenotypic\n")

ggplot(
  res, 
  aes(
    x=as.factor(offset), 
    y=value, 
    color=Type
    )
  ) + 
  geom_boxplot() + 
  facet_wrap(~selection_name*problem_name, ncol=4) + 
  scale_y_continuous("Transfer Entropy") + 
  scale_color_discrete("")

# Determine which conditions are significantly different from each other
transfer_entropy_stats(res)

selection_name	problem_name	offset	.y.	group1	group2	n1	n2	statistic	p	p.adj	p.adj.signif	label	effsize	magnitude
Eco-EA	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	569.0	0.00e+00	0.0000000	****	p < 1e-04	0.5898127	large
Eco-EA	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1222.0	2.44e-03	0.1464000	ns	p = 0.1464	0.2769389	small
Eco-EA	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1062.5	1.10e-04	0.0066000	**	p = 0.0066	0.3533612	moderate
Eco-EA	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	101.0	0.00e+00	0.0000000	****	p < 1e-04	0.8140469	large
Eco-EA	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1068.0	1.23e-04	0.0073800	**	p = 0.00738	0.3507253	moderate
Eco-EA	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1639.0	4.00e-01	1.0000000	ns	p = 1	0.0771404	small
Eco-EA	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	108.0	0.00e+00	0.0000000	****	p < 1e-04	0.8106930	large
Eco-EA	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	269.0	0.00e+00	0.0000000	****	p < 1e-04	0.7335526	large
Eco-EA	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	717.0	0.00e+00	0.0000008	****	p < 1e-04	0.5189010	large
Eco-EA	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2.0	0.00e+00	0.0000000	****	p < 1e-04	0.8614811	large
Eco-EA	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	186.0	0.00e+00	0.0000000	****	p < 1e-04	0.7733206	large
Eco-EA	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	340.0	0.00e+00	0.0000000	****	p < 1e-04	0.6996022	large
Fitness sharing	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	345.0	0.00e+00	0.0000000	****	p < 1e-04	0.6971385	large
Fitness sharing	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1896.0	6.16e-01	1.0000000	ns	p = 1	0.0459968	small
Fitness sharing	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2291.0	1.00e-02	0.6000000	ns	p = 0.6	0.2352543	small
Fitness sharing	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1175.0	1.05e-03	0.0630000	ns	p = 0.063	0.2994581	small
Fitness sharing	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2410.0	1.38e-03	0.0828000	ns	p = 0.0828	0.2922711	small
Fitness sharing	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2203.0	3.46e-02	1.0000000	ns	p = 1	0.1930906	small
Fitness sharing	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	77.0	0.00e+00	0.0000000	****	p < 1e-04	0.8255461	large
Fitness sharing	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	578.0	0.00e+00	0.0000000	****	p < 1e-04	0.5855005	large
Fitness sharing	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	918.0	3.70e-06	0.0002232	***	p = 0.0002232	0.4225953	moderate
Fitness sharing	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1995.0	3.07e-01	1.0000000	ns	p = 1	0.0934309	small
Fitness sharing	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3322.0	0.00e+00	0.0000000	****	p < 1e-04	0.7292404	large
Fitness sharing	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3155.0	0.00e+00	0.0000000	****	p < 1e-04	0.6492252	large
Lexicase	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	9.0	0.00e+00	0.0000000	****	p < 1e-04	0.8581272	large
Lexicase	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	161.0	0.00e+00	0.0000000	****	p < 1e-04	0.7852990	large
Lexicase	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	840.0	5.00e-07	0.0000285	****	p < 1e-04	0.4599677	moderate
Lexicase	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1038.0	6.42e-05	0.0038520	**	p = 0.003852	0.3650993	moderate
Lexicase	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2118.0	9.56e-02	1.0000000	ns	p = 1	0.1523643	small
Lexicase	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2502.0	2.31e-04	0.0138600		p = 0.01386	0.3363514	moderate
Lexicase	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1.0	0.00e+00	0.0000000	****	p < 1e-04	0.8619602	large
Lexicase	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	12.0	0.00e+00	0.0000000	****	p < 1e-04	0.8566898	large
Lexicase	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	60.0	0.00e+00	0.0000000	****	p < 1e-04	0.8336914	large
Lexicase	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624633	large
Lexicase	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	83.0	0.00e+00	0.0000000	****	p < 1e-04	0.8226713	large
Lexicase	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1846.0	8.11e-01	1.0000000	ns	p = 1	0.0220402	small
Random	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	586.0	0.00e+00	0.0000000	****	p < 1e-04	0.5816674	large
Random	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	697.0	0.00e+00	0.0000004	****	p < 1e-04	0.5284837	large
Random	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	980.0	1.70e-05	0.0010200	**	p = 0.00102	0.3928890	moderate
Random	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	3146.0	0.00e+00	0.0000000	****	p < 1e-04	0.6449130	large
Random	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1327.0	1.31e-02	0.7860000	ns	p = 0.786	0.2266299	small
Random	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	691.0	0.00e+00	0.0000004	****	p < 1e-04	0.5313585	large
Random	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	44.0	0.00e+00	0.0000000	****	p < 1e-04	0.8413575	large
Random	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	354.0	0.00e+00	0.0000000	****	p < 1e-04	0.6928263	large
Random	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	749.0	0.00e+00	0.0000021	****	p < 1e-04	0.5035688	large
Random	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2339.0	4.71e-03	0.2826000	ns	p = 0.2826	0.2582527	small
Random	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1713.0	6.50e-01	1.0000000	ns	p = 1	0.0416846	small
Random	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	2121.0	9.25e-02	1.0000000	ns	p = 1	0.1538017	small
Tournament	Count Odds	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	626.0	0.00e+00	0.0000000	****	p < 1e-04	0.5625021	large
Tournament	Count Odds	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1787.0	9.48e-01	1.0000000	ns	p = 1	0.0062287	small
Tournament	Count Odds	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1727.0	7.04e-01	1.0000000	ns	p = 1	0.0349767	small
Tournament	Logic-9	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	54.0	0.00e+00	0.0000000	****	p < 1e-04	0.8365662	large
Tournament	Logic-9	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	496.0	0.00e+00	0.0000000	****	p < 1e-04	0.6247894	large
Tournament	Logic-9	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	1225.0	2.57e-03	0.1542000	ns	p = 0.1542	0.2755034	small
Tournament	NK Landscape	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	0.0	0.00e+00	0.0000000	****	p < 1e-04	0.8624394	large
Tournament	NK Landscape	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	32.0	0.00e+00	0.0000000	****	p < 1e-04	0.8471071	large
Tournament	NK Landscape	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	148.0	0.00e+00	0.0000000	****	p < 1e-04	0.7922984	large
Tournament	Sorting network	10	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	7.0	0.00e+00	0.0000000	****	p < 1e-04	0.8590854	large
Tournament	Sorting network	100	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	55.0	0.00e+00	0.0000000	****	p < 1e-04	0.8360870	large
Tournament	Sorting network	1000	value	Phenotypic -> Phylogenetic	Phylogenetic -> Phenotypic	60	60	217.0	0.00e+00	0.0000000	****	p < 1e-04	0.7584675	large