Chapter 2 Exploitation rate results

Here we present the results for best performances found by each selection scheme replicate on the exploitation rate diagnostic. Best performance found refers to the largest average trait score found in a given population. Note that performance values fall between 0.0 and 100.0.

2.1 Analysis dependencies

library(ggplot2)
library(cowplot)
library(dplyr)
library(PupillometryR)
library(sdamr)

2.2 Performance over time

Best performance in a population over time.

# data for lines and shading on plots
lines = filter(cc_over_time, diagnostic == 'exploitation_rate') %>%
  group_by(`Selection\nScheme`, gen) %>%
  dplyr::summarise(
    min = min(pop_fit_max) / DIMENSIONALITY,
    mean = mean(pop_fit_max) / DIMENSIONALITY,
    max = max(pop_fit_max) / DIMENSIONALITY
  )

## `summarise()` has grouped output by 'Selection Scheme'. You can override using
## the `.groups` argument.

ggplot(lines, aes(x=gen, y=mean, group = `Selection\nScheme`, fill =`Selection\nScheme`, color = `Selection\nScheme`, shape = `Selection\nScheme`)) +
  geom_ribbon(aes(ymin = min, ymax = max), alpha = 0.1) +
  geom_line(size = 0.5) +
  geom_point(data = filter(lines, gen %% 2000 == 0 & gen != 0), size = 1.5, stroke = 2.0, alpha = 1.0) +
  scale_y_continuous(
    name="Average trait score",
    limits=c(0, 100),
    breaks=seq(0,100, 20),
    labels=c("0", "20", "40", "60", "80", "100")
  ) +
  scale_x_continuous(
    name="Generations",
    limits=c(0, 50000),
    breaks=c(0, 10000, 20000, 30000, 40000, 50000),
    labels=c("0e+4", "1e+4", "2e+4", "3e+4", "4e+4", "5e+4")

  ) +
  scale_shape_manual(values=SHAPE)+
  scale_colour_manual(values = cb_palette) +
  scale_fill_manual(values = cb_palette) +
  ggtitle('Performance over time')+
  p_theme + theme(legend.title=element_blank(),legend.text=element_text(size=11)) +
  guides(
    shape=guide_legend(ncol=2, title.position = "bottom"),
    color=guide_legend(ncol=2, title.position = "bottom"),
    fill=guide_legend(ncol=2, title.position = "bottom")
  )

2.3 Best performance throughout

Best performance found throughout 50,000 generations.

### best performance throughout
filter(cc_best, col == 'pop_fit_max' & diagnostic == 'exploitation_rate') %>%
  ggplot(., aes(x = acron, y = val / DIMENSIONALITY, color = acron, fill = acron, shape = acron)) +
  geom_flat_violin(position = position_nudge(x = .2, y = 0), scale = 'width', alpha = 0.2) +
  geom_point(position = position_jitter(width = .1), size = 1.5, alpha = 1.0) +
  geom_boxplot(color = 'black', width = .2, outlier.shape = NA, alpha = 0.0) +
  scale_y_continuous(
    name="Average trait score",
    limits=c(-1, 101),
    breaks=seq(0,100, 20),
    labels=c("0", "20", "40", "60", "80", "100")
  ) +
  scale_x_discrete(
    name="Scheme"
  )+
  scale_shape_manual(values=SHAPE)+
  scale_colour_manual(values = cb_palette, ) +
  scale_fill_manual(values = cb_palette) +
  ggtitle('Best performance throughout')+
  p_theme + theme(legend.title=element_blank()) +
  guides(
    shape=guide_legend(nrow=2, title.position = "bottom"),
    color=guide_legend(nrow=2, title.position = "bottom"),
    fill=guide_legend(nrow=2, title.position = "bottom")
  )

## Warning: Using the `size` aesthietic with geom_polygon was deprecated in ggplot2 3.4.0.
## i Please use the `linewidth` aesthetic instead.

2.3.1 Stats

Summary statistics for the best performance.

#get data & summarize
performance = filter(cc_best, col == 'pop_fit_max' & diagnostic == 'exploitation_rate')
performance$acron = factor(performance$acron, levels = c('tru', 'tor', 'lex', 'gfs', 'pfs', 'nov', 'nds', 'ran'))
performance %>%
  group_by(acron) %>%
  dplyr::summarise(
    count = n(),
    na_cnt = sum(is.na(val)),
    min = min(val / DIMENSIONALITY, na.rm = TRUE),
    median = median(val / DIMENSIONALITY, na.rm = TRUE),
    mean = mean(val / DIMENSIONALITY, na.rm = TRUE),
    max = max(val / DIMENSIONALITY, na.rm = TRUE),
    IQR = IQR(val / DIMENSIONALITY, na.rm = TRUE)
  )

## # A tibble: 8 x 8
##   acron count na_cnt   min median  mean   max    IQR
##   <fct> <int>  <int> <dbl>  <dbl> <dbl> <dbl>  <dbl>
## 1 tru      50      0 100    100   100   100   0     
## 2 tor      50      0 100    100   100   100   0     
## 3 lex      50      0  99.9   99.9  99.9  99.9 0.0137
## 4 gfs      50      0  57.7   59.3  59.4  60.8 1.31  
## 5 pfs      50      0  58.0   59.5  59.5  61.4 0.908 
## 6 nov      50      0  15.9   19.2  19.3  22.3 1.34  
## 7 nds      50      0  17.9   18.4  18.5  19.5 0.516 
## 8 ran      50      0  13.5   15.9  15.9  18.7 1.15

Kruskal–Wallis test provides evidence of statistical differences.

kruskal.test(val ~ acron, data = performance)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  val by acron
## Kruskal-Wallis chi-squared = 384.91, df = 7, p-value < 2.2e-16

Results for post-hoc Wilcoxon rank-sum test with a Bonferroni correction.

pairwise.wilcox.test(x = performance$val, g = performance$acron, p.adjust.method = "bonferroni",
                     paired = FALSE, conf.int = FALSE, alternative = 'l')

## 
##  Pairwise comparisons using Wilcoxon rank sum test with continuity correction 
## 
## data:  performance$val and performance$acron 
## 
##     tru     tor     lex     gfs     pfs     nov     nds    
## tor 1e+00   -       -       -       -       -       -      
## lex < 2e-16 < 2e-16 -       -       -       -       -      
## gfs < 2e-16 < 2e-16 < 2e-16 -       -       -       -      
## pfs < 2e-16 < 2e-16 < 2e-16 1e+00   -       -       -      
## nov < 2e-16 < 2e-16 < 2e-16 < 2e-16 < 2e-16 -       -      
## nds < 2e-16 < 2e-16 < 2e-16 < 2e-16 < 2e-16 6e-04   -      
## ran < 2e-16 < 2e-16 < 2e-16 < 2e-16 < 2e-16 1.9e-15 7.9e-16
## 
## P value adjustment method: bonferroni

2.4 Generation satisfactory solution found

First generation a satisfactory solution is found throughout the 50,000 generations.

filter(cc_ssf, diagnostic == 'exploitation_rate') %>%
  ggplot(., aes(x = acron, y = Generations , color = acron, fill = acron, shape = acron)) +
  geom_flat_violin(position = position_nudge(x = .2, y = 0), scale = 'width', alpha = 0.2) +
  geom_point(position = position_jitter(width = .1), size = 1.5, alpha = 1.0) +
  geom_boxplot(color = 'black', width = .2, outlier.shape = NA, alpha = 0.0) +
  scale_y_continuous(
    name="Generation",
    limits=c(0, 60001),
    breaks=c(0, 10000, 20000, 30000, 40000, 50000, 60000),
    labels=c("0e+4", "1e+4", "2e+4", "3e+4", "4e+4", "5e+4", "Fail")
  ) +
  scale_x_discrete(
    name="Scheme"
  )+
  scale_shape_manual(values=SHAPE)+
  scale_colour_manual(values = cb_palette, ) +
  scale_fill_manual(values = cb_palette) +
  ggtitle('Generation satisfactory solution found')+
  p_theme + theme(legend.title=element_blank()) +
  guides(
    shape=guide_legend(nrow=2, title.position = "bottom"),
    color=guide_legend(nrow=2, title.position = "bottom"),
    fill=guide_legend(nrow=2, title.position = "bottom")
  )

2.4.1 Stats

Summary statistics for the first generation a satisfactory solution is found.

ssf = filter(cc_ssf, diagnostic == 'exploitation_rate'  & Generations < 60000)
ssf$acron = factor(ssf$acron, levels = c('tru', 'tor', 'lex'))
ssf %>%
  group_by(acron) %>%
  dplyr::summarise(
    count = n(),
    na_cnt = sum(is.na(Generations)),
    min = min(Generations, na.rm = TRUE),
    median = median(Generations, na.rm = TRUE),
    mean = mean(Generations, na.rm = TRUE),
    max = max(Generations, na.rm = TRUE),
    IQR = IQR(Generations, na.rm = TRUE)
  )

## # A tibble: 3 x 8
##   acron count na_cnt   min median   mean   max    IQR
##   <fct> <int>  <int> <int>  <dbl>  <dbl> <int>  <dbl>
## 1 tru      50      0  3357   3420  3421.  3481   34.2
## 2 tor      50      0  5403   5457  5453.  5519   51.8
## 3 lex      50      0 23514  25190 25857. 32980 1581

Kruskal–Wallis test provides evidence of difference amoung selection schemes.

kruskal.test(Generations ~ acron, data = ssf)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  Generations by acron
## Kruskal-Wallis chi-squared = 132.46, df = 2, p-value < 2.2e-16

Results for post-hoc Wilcoxon rank-sum test with a Bonferroni correction.

pairwise.wilcox.test(x = ssf$Generations, g = ssf$acron, p.adjust.method = "bonferroni",
                     paired = FALSE, conf.int = FALSE, alternative = 'g')

## 
##  Pairwise comparisons using Wilcoxon rank sum test with continuity correction 
## 
## data:  ssf$Generations and ssf$acron 
## 
##     tru    tor   
## tor <2e-16 -     
## lex <2e-16 <2e-16
## 
## P value adjustment method: bonferroni

2.5 Multi-valley crossing results

2.5.1 Performance over time

Best performance in a population over time.

# data for lines and shading on plots
lines = filter(cc_over_time_mvc, diagnostic == 'exploitation_rate') %>%
  group_by(`Selection\nScheme`, gen) %>%
  dplyr::summarise(
    min = min(pop_fit_max) / DIMENSIONALITY,
    mean = mean(pop_fit_max) / DIMENSIONALITY,
    max = max(pop_fit_max) / DIMENSIONALITY
  )

## `summarise()` has grouped output by 'Selection Scheme'. You can override using
## the `.groups` argument.

ggplot(lines, aes(x=gen, y=mean, group = `Selection\nScheme`, fill =`Selection\nScheme`, color = `Selection\nScheme`, shape = `Selection\nScheme`)) +
  geom_ribbon(aes(ymin = min, ymax = max), alpha = 0.1) +
  geom_line(size = 0.5) +
  geom_point(data = filter(lines, gen %% 2000 == 0 & gen != 0), size = 1.5, stroke = 2.0, alpha = 1.0) +
  scale_y_continuous(
    name="Average trait score",
    limits=c(0, 50),
    breaks=seq(0,50, 10),
    labels=c("0", "10", "20", "30", "40", "50")
  ) +
  scale_x_continuous(
    name="Generations",
    limits=c(0, 50000),
    breaks=c(0, 10000, 20000, 30000, 40000, 50000),
    labels=c("0e+4", "1e+4", "2e+4", "3e+4", "4e+4", "5e+4")

  ) +
  scale_shape_manual(values=SHAPE)+
  scale_colour_manual(values = cb_palette) +
  scale_fill_manual(values = cb_palette) +
  ggtitle('Performance over time')+
  p_theme + theme(legend.title=element_blank(),legend.text=element_text(size=11)) +
  guides(
    sh=guide_legend(ncol=2, title.position = "left"),
    color=guide_legend(ncol=2, title.position = "left"),
    fillape=guide_legend(ncol=2, title.position = "left")
  )

2.5.2 Best performance throughout

Best performance found throughout 50,000 generations.

### best performance throughout
filter(cc_best_mvc, col == 'pop_fit_max' & diagnostic == 'exploitation_rate') %>%
  ggplot(., aes(x = acron, y = val / DIMENSIONALITY, color = acron, fill = acron, shape = acron)) +
  geom_flat_violin(position = position_nudge(x = .2, y = 0), scale = 'width', alpha = 0.2) +
  geom_point(position = position_jitter(width = .1), size = 1.5, alpha = 1.0) +
  geom_boxplot(color = 'black', width = .2, outlier.shape = NA, alpha = 0.0) +
  scale_y_continuous(
    name="Average trait score",
    limits=c(0, 50),
    breaks=seq(0,50, 10),
    labels=c("0", "10", "20", "30", "40", "50")
  ) +
  scale_x_discrete(
    name="Scheme"
  )+
  scale_shape_manual(values=SHAPE)+
  scale_colour_manual(values = cb_palette, ) +
  scale_fill_manual(values = cb_palette) +
  ggtitle('Best performance throughout')+
  p_theme + theme(legend.title=element_blank()) +
  guides(
    shape=guide_legend(nrow=2, title.position = "bottom"),
    color=guide_legend(nrow=2, title.position = "bottom"),
    fill=guide_legend(nrow=2, title.position = "bottom")
  )

2.5.2.1 Stats

Summary statistics for the performance of the best performance.

#get data & summarize
performance = filter(cc_best_mvc, col == 'pop_fit_max' & diagnostic == 'exploitation_rate')
performance$acron = factor(performance$acron, levels = c('gfs','pfs','tru','tor','nov', 'nds','lex', 'ran'))
performance %>%
  group_by(acron) %>%
  dplyr::summarise(
    count = n(),
    na_cnt = sum(is.na(val)),
    min = min(val / DIMENSIONALITY, na.rm = TRUE),
    median = median(val / DIMENSIONALITY, na.rm = TRUE),
    mean = mean(val / DIMENSIONALITY, na.rm = TRUE),
    max = max(val / DIMENSIONALITY, na.rm = TRUE),
    IQR = IQR(val / DIMENSIONALITY, na.rm = TRUE)
  )

## # A tibble: 8 x 8
##   acron count na_cnt   min median  mean   max   IQR
##   <fct> <int>  <int> <dbl>  <dbl> <dbl> <dbl> <dbl>
## 1 gfs      50      0  40.8   43.0  43.0  45.8 1.12 
## 2 pfs      50      0  40.9   43.1  43.1  45.3 1.30 
## 3 tru      50      0  17.8   18.0  18.0  18.2 0.118
## 4 tor      50      0  17.9   18.1  18.1  18.3 0.130
## 5 nov      50      0  16.5   18.3  18.3  21.5 1.19 
## 6 nds      50      0  14.7   15.4  15.3  16.0 0.318
## 7 lex      50      0  12.5   12.7  12.7  13.1 0.121
## 8 ran      50      0  10.3   13.2  13.1  14.6 1.25

Kruskal–Wallis test provides evidence of statistical differences.

kruskal.test(val ~ acron, data = performance)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  val by acron
## Kruskal-Wallis chi-squared = 366.01, df = 7, p-value < 2.2e-16

Results for post-hoc Wilcoxon rank-sum test with a Bonferroni correction.

pairwise.wilcox.test(x = performance$val, g = performance$acron, p.adjust.method = "bonferroni",
                     paired = FALSE, conf.int = FALSE, alternative = 'l')

## 
##  Pairwise comparisons using Wilcoxon rank sum test with continuity correction 
## 
## data:  performance$val and performance$acron 
## 
##     gfs    pfs    tru    tor    nov    nds    lex
## pfs 1      -      -      -      -      -      -  
## tru <2e-16 <2e-16 -      -      -      -      -  
## tor <2e-16 <2e-16 1      -      -      -      -  
## nov <2e-16 <2e-16 1      1      -      -      -  
## nds <2e-16 <2e-16 <2e-16 <2e-16 <2e-16 -      -  
## lex <2e-16 <2e-16 <2e-16 <2e-16 <2e-16 <2e-16 -  
## ran <2e-16 <2e-16 <2e-16 <2e-16 <2e-16 <2e-16 1  
## 
## P value adjustment method: bonferroni

2.5.3 Performance comparison

Best performances in the population at 40,000 and 50,000 generations.

dummy_df = filter(filter(cc_over_time_mvc, diagnostic == 'exploitation_rate' & (gen == 50000 | gen == 40000) & acron != 'ran'))
dummy_df$Generation <- factor(dummy_df$gen, levels = c(50000,40000))
p = ggplot(dummy_df, aes(x=gen, y=pop_fit_max / DIMENSIONALITY, group = acron, fill = acron, color = Generation, shape = Generation)) +
  geom_flat_violin(position = position_nudge(x = .2, y = 0), scale = 'width', alpha = 0.2) +
  geom_point(position = position_jitter(width = .03), size = 2, alpha = 1.0) +
  geom_boxplot(position = position_nudge(x = .13, y = 0), lwd = 1, width = .1, outlier.shape = NA, alpha = 0.0) +
  scale_shape_manual(values=c(0,1))+
  scale_colour_manual(values = mvc_col)+
  scale_fill_manual(values = cb_palette) + p_theme +
  guides(
    shape=guide_legend(ncol=2, title.position = "bottom"),
    color=guide_legend(ncol=2, title.position = "bottom"),
    fill='none')

legend <- cowplot::get_legend(
  p +
    guides(
      shape=guide_legend(ncol=2, title.position = "left"),
      color=guide_legend(ncol=2, title.position = "left"),
      fill='none'
    ) +
    theme(
      legend.position = "top",
      legend.box="verticle",
      legend.justification="center"
    )
)

## Warning: The following aesthetics were dropped during statistical transformation:
## colour, shape
## i This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## i Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?
## The following aesthetics were dropped during statistical transformation:
## colour, shape
## i This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## i Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

rm(dummy_df, p)

# 80% and final generation comparison
end = filter(cc_over_time_mvc, diagnostic == 'exploitation_rate' & gen == 50000 & acron != 'ran')
end$Generation <- factor(end$gen)

mid = filter(cc_over_time_mvc, diagnostic == 'exploitation_rate' & gen == 40000 & acron != 'ran')
mid$Generation <- factor(mid$gen)

mvc_p = ggplot(mid, aes(x = acron, y=pop_fit_max / DIMENSIONALITY, group = acron, shape = Generation)) +
          geom_point(col = mvc_col[1] , position = position_jitternudge(jitter.width = .03, nudge.x = -0.05), size = 2, alpha = 1.0) +
          geom_boxplot(position = position_nudge(x = -.15, y = 0), lwd = 0.7, col = mvc_col[1], fill = mvc_col[1], width = .1, outlier.shape = NA, alpha = 0.0) +

          geom_point(data = end, aes(x = acron, y=pop_fit_max / DIMENSIONALITY), col = mvc_col[2], position = position_jitternudge(jitter.width = .03, nudge.x = 0.05), size = 2, alpha = 1.0) +
          geom_boxplot(data = end, aes(x = acron, y=pop_fit_max / DIMENSIONALITY), position = position_nudge(x = .15, y = 0), lwd = 0.7, col = mvc_col[2], fill = mvc_col[2], width = .1, outlier.shape = NA, alpha = 0.0) +

          scale_y_continuous(
          name="Average trait score",
          limits=c(0, 50),
          breaks=seq(0,50, 10),
          labels=c("0", "10", "20", "30", "40", "50")
          ) +
          scale_x_discrete(
          name="Scheme"
          )+
          scale_shape_manual(values=c(0,1))+
          scale_colour_manual(values = c(mvc_col[1],mvc_col[2])) +
          p_theme

plot_grid(
        mvc_p +
        ggtitle("Performance comparisons") +
        theme(legend.position="none"),
        legend,
        nrow=2,
        rel_heights = c(1,.05),
        label_size = TSIZE
      )

2.5.3.1 Stats

Summary statistics for the performance of the best performance at 40,000 and 50,000 generations.

### performance comparisons and generation slices 40K & 50K
slices = filter(cc_over_time_mvc, diagnostic == 'exploitation_rate' & (gen == 50000 | gen == 40000) & acron != 'ran')
slices$Generation <- factor(slices$gen, levels = c(50000,40000))
slices$acron = factor(slices$acron, levels = c('gfs','pfs','tru','tor','nov', 'nds','lex', 'ran'))
slices %>%
  group_by(acron, Generation) %>%
  dplyr::summarise(
    count = n(),
    na_cnt = sum(is.na(pop_fit_max  / DIMENSIONALITY)),
    min = min(pop_fit_max  / DIMENSIONALITY, na.rm = TRUE),
    median = median(pop_fit_max  / DIMENSIONALITY, na.rm = TRUE),
    mean = mean(pop_fit_max  / DIMENSIONALITY, na.rm = TRUE),
    max = max(pop_fit_max  / DIMENSIONALITY, na.rm = TRUE),
    IQR = IQR(pop_fit_max  / DIMENSIONALITY, na.rm = TRUE)
  )

## `summarise()` has grouped output by 'acron'. You can override using the
## `.groups` argument.

## # A tibble: 14 x 9
## # Groups:   acron [7]
##    acron Generation count na_cnt   min median  mean   max   IQR
##    <fct> <fct>      <int>  <int> <dbl>  <dbl> <dbl> <dbl> <dbl>
##  1 gfs   50000         50      0  40.7   42.8  42.8  45.7 1.21 
##  2 gfs   40000         50      0  34.9   36.4  36.6  39.3 1.15 
##  3 pfs   50000         50      0  40.7   43.0  42.8  45.0 1.30 
##  4 pfs   40000         50      0  34.4   36.7  36.6  38.1 1.01 
##  5 tru   50000         50      0  17.8   18.0  18.0  18.2 0.118
##  6 tru   40000         50      0  17.7   17.9  17.9  18.1 0.147
##  7 tor   50000         50      0  17.9   18.1  18.1  18.3 0.130
##  8 tor   40000         50      0  17.7   18.0  18.0  18.2 0.115
##  9 nov   50000         50      0  16.0   17.8  17.8  21.1 1.17 
## 10 nov   40000         50      0  14.3   16.1  16.3  18.1 1.39 
## 11 nds   50000         50      0  14.3   15.0  15.0  15.8 0.327
## 12 nds   40000         50      0  12.8   13.4  13.4  14.0 0.516
## 13 lex   50000         50      0  12.0   12.2  12.2  12.5 0.199
## 14 lex   40000         50      0  12.0   12.2  12.2  12.7 0.132

Truncation selection comparisons.

wilcox.test(x = filter(slices, acron == 'tru' & Generation == 50000)$pop_fit_max,
            y = filter(slices, acron == 'tru' & Generation == 40000)$pop_fit_max,
            alternative = 't')

## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  filter(slices, acron == "tru" & Generation == 50000)$pop_fit_max and filter(slices, acron == "tru" & Generation == 40000)$pop_fit_max
## W = 2037.5, p-value = 5.705e-08
## alternative hypothesis: true location shift is not equal to 0

Tournament selection comparisons.

wilcox.test(x = filter(slices, acron == 'tor' & Generation == 50000)$pop_fit_max,
            y = filter(slices, acron == 'tor' & Generation == 40000)$pop_fit_max,
            alternative = 't')

## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  filter(slices, acron == "tor" & Generation == 50000)$pop_fit_max and filter(slices, acron == "tor" & Generation == 40000)$pop_fit_max
## W = 2075, p-value = 1.301e-08
## alternative hypothesis: true location shift is not equal to 0

Lexicase selection comparisons.

wilcox.test(x = filter(slices, acron == 'lex' & Generation == 50000)$pop_fit_max,
            y = filter(slices, acron == 'lex' & Generation == 40000)$pop_fit_max,
            alternative = 't')

## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  filter(slices, acron == "lex" & Generation == 50000)$pop_fit_max and filter(slices, acron == "lex" & Generation == 40000)$pop_fit_max
## W = 1260.5, p-value = 0.945
## alternative hypothesis: true location shift is not equal to 0

Genotypic fitness sharing comparisons.

wilcox.test(x = filter(slices, acron == 'gfs' & Generation == 50000)$pop_fit_max,
            y = filter(slices, acron == 'gfs' & Generation == 40000)$pop_fit_max,
            alternative = 't')

## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  filter(slices, acron == "gfs" & Generation == 50000)$pop_fit_max and filter(slices, acron == "gfs" & Generation == 40000)$pop_fit_max
## W = 2500, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0

Phenotypic fitness sharing comparisons.

wilcox.test(x = filter(slices, acron == 'pfs' & Generation == 50000)$pop_fit_max,
            y = filter(slices, acron == 'pfs' & Generation == 40000)$pop_fit_max,
            alternative = 't')

## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  filter(slices, acron == "pfs" & Generation == 50000)$pop_fit_max and filter(slices, acron == "pfs" & Generation == 40000)$pop_fit_max
## W = 2500, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0

Nondominated sorting comparisons.

wilcox.test(x = filter(slices, acron == 'nds' & Generation == 50000)$pop_fit_max,
            y = filter(slices, acron == 'nds' & Generation == 40000)$pop_fit_max,
            alternative = 't')

## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  filter(slices, acron == "nds" & Generation == 50000)$pop_fit_max and filter(slices, acron == "nds" & Generation == 40000)$pop_fit_max
## W = 2500, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0

Novelty search comparisons.

wilcox.test(x = filter(slices, acron == 'nov' & Generation == 50000)$pop_fit_max,
            y = filter(slices, acron == 'nov' & Generation == 40000)$pop_fit_max,
            alternative = 't')

## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  filter(slices, acron == "nov" & Generation == 50000)$pop_fit_max and filter(slices, acron == "nov" & Generation == 40000)$pop_fit_max
## W = 2196, p-value = 7.119e-11
## alternative hypothesis: true location shift is not equal to 0