Kakapo Fertility Projpred modelling

set.seed(1111)
curr_dir <- setwd(dirname(rstudioapi::getSourceEditorContext()$path))
clutch_file <- file.path(curr_dir, "./Supplemental_Data_S1.csv")
kakapo_demog_file <- file.path(curr_dir, './Supplemental_Data_S2.csv')

outdir <- "./figure/"
ropeci <- 1.00 # proportion of posterior which intersects with ROPE. 
nchains <- 4
niter <- 30000 # iterations for brm

1 Credits

Markdown from readthedown template, from package rmdformats.
Code written by Alejandro Catalina and Andrew Digby.

2 Purpose

Code and results for the publication Hidden impacts of conservation management on fertility of the critically endangered kakapo. Model validation and diagnostics not included.

Use projected predictive variable selection package projpred to assess factors influencing kakapo fertility using a Bayesian model.
Compare multiple copulation frequency with kakapo density and sex ratio

3 Requirements

Requires the workflow branch of projpred.

4 Data

Input data:

Clutch fertility data frame from file Supplemental_Data_S1.csv.
Kakapo numbers per island per year from Supplemental_Data_S2.csv.

5 Fertility model

5.1 Load data

ref_predfun <- function(fit, newdata = NULL) {
  return(t(posterior_linpred(fit,
                             newdata = newdata,
                             transform = FALSE
  )))
}

# Retrieve model data
extract_model_data <- function(object, newdata = NULL, wrhs = NULL,
                               orhs = NULL, extract_y = TRUE) {
  if (!extract_y) {
    resp_form <- NULL
  } else {
    resp_form <- ~.y
  }
  
  if (is.null(newdata)) {
    newdata <- data
  }
  
  if (is.null(wrhs) && !is.null(object) &&
      !is.null(object$weights) && length(object$weights) != 0) {
    wrhs <- ~weights
    newdata <- cbind(newdata, weights = object$weights)
  }
  
  if (is.null(orhs) && !is.null(object) &&
      !is.null(object$offset) && length(object$offset) != 0) {
    orhs <- ~offset
    newdata <- cbind(newdata, offset = object$offset)
  }
  
  args <- nlist(object, newdata, wrhs, orhs, resp_form)
  return(do_call(projpred:::.extract_model_data, args))
}

# For more readable parameter names in plots
fn_labels <- function(string){
  string <- sub('b_','',string)
  string <- gsub('scmother_age','Mother age',string)
  string <- gsub('scfather_age','Father age',string)
  string <- gsub('schandrear.mother','Mother HR',string)
  string <- gsub('schandrear.father','Father HR',string)
  string <- gsub('handrear.mother','Mother HR',string)
  string <- gsub('handrear.father','Father HR',string)
  string <- gsub('HRTRUE', 'HR', string)
  string <- gsub('scnumber.of.copulations','No. copulations',string)
  string <- gsub('scnumber.of.males','No. males',string)
  string <- gsub('sccopulations.mates','Mother copulations: ',string)
  string <- gsub('copulations.mates','Mother copulations: ',string)
  string <- gsub('Intercept','Intercept',string)
  string <- gsub('Differentmales','Different males',string)
  string <- gsub('2Pcopulations','1 male, >1 copulation',string)
  string <- gsub('2\\+ copulations','1 male, >1 copulation',string)
  string <- gsub('sckin','Mother/father kinship',string)
  string <- gsub("scprev.male.copulations", "Father previous copulations", string)
  string <- gsub("scprev.female.copulations", "Mother previous copulations", string)
  string <- gsub("sd_mother__Intercept", "SD(Mother intercept)", string)
  string <- gsub("sd_father__Intercept", "SD(Father intercept)", string)
  string <- gsub("sd_year__Intercept", "SD(Year intercept)", string)
  string <- gsub(": $","",string) # remove colon at end of string (to remove "Mating:" if no subsequent variable)
  
  return(string)

}

Remove observations with missing values
Scale and centre continuous predictors to mean of zero and SD=0.5 (see http://www.stat.columbia.edu/~gelman/research/published/priors11.pdf)

# Read clutch data file:
full_data <- read.csv(clutch_file, header = T, stringsAsFactors = T) %>%
  mutate(year = as.factor(year),
         handrear.mother = as.factor(handrear.mother),
         handrear.father = as.factor(handrear.father)) %>%
  rename_with(~ gsub("\\.","_", .x)) 
cat(sprintf("Loaded %d records from %s\n", nrow(full_data), basename(clutch_file)))

Loaded 225 records from Supplemental_Data_S1.csv

# Retain only variables of interest and drop rows with missing values
data <- full_data %>%  dplyr::select(clutch_fert, mother_age, handrear_mother, father_age,
         handrear_father, copulations_mates, prev_male_copulations, prev_female_copulations, kin, father, mother, year) %>%
  tidyr::drop_na()

# Scale and centre inputs to mean of zero & SD = 0.5
data <- data %>% mutate(
  scmother_age = 0.5*scale(mother_age, center=T, scale=T) ,
  scfather_age = 0.5*scale(father_age, center=T, scale=T),
  scprev_male_copulations = 0.5*scale(prev_male_copulations, center=T, scale=T),
  scprev_female_copulations = 0.5*scale(prev_female_copulations, center=T, scale=T),
  sckin = 0.5*scale(kin, center=T, scale=T),
)

# Convert matrix columns to vectors (result of using scale)
data <- data %>% mutate(scmother_age = as.vector(scmother_age),
                        scfather_age = as.vector(scfather_age),
                        sckin = as.vector(sckin),
                        scprev_male_copulations = as.vector(scprev_male_copulations),
                        scprev_female_copulations = as.vector(scprev_female_copulations))

Show predictor distributions for numeric variables

facetlabs <- c('mother_age'='Mother age (years)', 'father_age' = 'Father age (years)', 'prev_male_copulations' = 'Father previous copulations', 'prev_female_copulations' = 'Mother previous copulations', 'kin' = 'Mother/father kinship')
df <- data %>%  dplyr::select(mother_age, father_age, prev_male_copulations, prev_female_copulations, kin)
dfl <- df %>% pivot_longer(everything(), names_to='variable') %>% 
  mutate(variable = factor(variable, levels=c('mother_age', 'father_age', 'prev_male_copulations', 'prev_female_copulations', 'kin')))
fill_col1 <- brewer.pal(name='Set2',n=3)[1]
fill_col2 <- brewer.pal(name='Set2',n=3)[2]
fill_col3 <- brewer.pal(name='Set2',n=3)[3]
ggplot(dfl, aes(x=value)) + 
#  geom_histogram(data=subset(dfl, variable %in% c('mother_age', 'father_age', 'prev_male_copulations')), binwidth = 2, closed = 'left') +
  geom_histogram(data=subset(dfl, variable %in% c('mother_age', 'father_age')), breaks = seq(0, 50, 2), closed = 'right', fill = fill_col1, colour = 'black' ) +
  geom_histogram(data=subset(dfl, variable %in% c('prev_male_copulations')), breaks = seq(0,40,2), closed = 'right', fill = fill_col2, colour = 'black'  ) +
  geom_histogram(data=subset(dfl, variable %in% c('prev_female_copulations')), breaks = seq(0,20,1), closed = 'right', fill = fill_col2, colour = 'black'  ) +
  geom_histogram(data=subset(dfl, variable %in% c('kin')), breaks = seq(0, 0.3, 0.01), closed = 'right', fill = fill_col3, colour = 'black'  ) + 
  facet_wrap(~variable, scales='free', labeller=labeller(variable=facetlabs), ncol=2) +
    scale_x_continuous(expand = c(0.01,0)) +
  labs(y = 'Frequency', x = '') + 
  guides(fill = 'none')

 ggsave("./figure/figure_s2_predictor_distributions.pdf", height = 7, width = 8)

# Random variables:
grouping_variables <- c("father", "mother", "year")

# Predictors:
predictors <- c(
  "scmother_age", "handrear_mother", "scfather_age",
  "handrear_father", "copulations_mates", "scprev_male_copulations",
  "scprev_female_copulations", "sckin"
)

5.2 Reference model

Fit full reference model

# Formula for model
formula <- paste(
  "clutch_fert ~", paste0(predictors, collapse = " + "), " + ",
  paste(paste0("(1 | ", grouping_variables, ")"), collapse = " + "),
  "+ handrear_mother:handrear_father"
) %>%
  as.formula()

# Fit original model with {brms}
fit_original <- brm(formula,
  data = data, family = bernoulli(),
  prior = set_prior(horseshoe()),
  iter = niter, 
  chains = nchains,
  seed = 1111,
  control = list(adapt_delta = 0.99)
)
fit_original

 Family: bernoulli 
  Links: mu = logit 
Formula: clutch_fert ~ scmother_age + handrear_mother + scfather_age + handrear_father + copulations_mates + scprev_male_copulations + scprev_female_copulations + sckin + (1 | father) + (1 | mother) + (1 | year) + handrear_mother:handrear_father 
   Data: data (Number of observations: 217) 
  Draws: 4 chains, each with iter = 30000; warmup = 15000; thin = 1;
         total post-warmup draws = 60000

Group-Level Effects: 
~father (Number of levels: 50) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     1.31      0.47     0.45     2.34 1.00    11905    11570

~mother (Number of levels: 60) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.66      0.43     0.03     1.64 1.00     9430    17488

~year (Number of levels: 16) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.65      0.51     0.03     1.91 1.00    13467    22681

Population-Level Effects: 
                                        Estimate Est.Error l-95% CI u-95% CI
Intercept                                   0.34      0.50    -0.67     1.33
scmother_age                               -0.11      0.37    -1.01     0.58
handrear_motherTRUE                        -0.18      0.42    -1.21     0.52
scfather_age                                0.25      0.46    -0.47     1.39
handrear_fatherTRUE                        -0.54      0.66    -2.10     0.36
copulations_mates2Pcopulations              0.50      0.53    -0.19     1.70
copulations_matesDifferentmales             1.04      0.60    -0.01     2.23
scprev_male_copulations                    -0.18      0.40    -1.20     0.46
scprev_female_copulations                  -0.24      0.41    -1.26     0.37
sckin                                      -0.21      0.34    -1.03     0.30
handrear_motherTRUE:handrear_fatherTRUE    -0.25      0.58    -1.69     0.73
                                        Rhat Bulk_ESS Tail_ESS
Intercept                               1.00    26170    34085
scmother_age                            1.00    54597    52449
handrear_motherTRUE                     1.00    47172    54689
scfather_age                            1.00    41212    47335
handrear_fatherTRUE                     1.00    29749    48986
copulations_mates2Pcopulations          1.00    24999    48199
copulations_matesDifferentmales         1.00    22274    14814
scprev_male_copulations                 1.00    35644    47661
scprev_female_copulations               1.00    40404    51617
sckin                                   1.00    33317    45872
handrear_motherTRUE:handrear_fatherTRUE 1.00    51141    53152

Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

5.3 Restricted variable selection

# Set up variable selection
## run variable selection on the unconstrained latent space
ref_original <- brms:::get_refmodel.brmsfit(fit_original, seed = 1111)
f_latent <- colMeans(posterior_linpred(fit_original, transform = FALSE))
data[[".y"]] <- f_latent
dis_latent <- rep(1, 2*niter)

# Get reference model
ref <- init_refmodel(fit_original,
 data = data, formula = formula, family = gaussian(),
 ref_predfun = ref_predfun, div_minimizer = projpred:::linear_multilevel_mle,
 proj_predfun = projpred:::linear_multilevel_proj_predfun, dis = dis_latent,
 extract_model_data = extract_model_data, cvfun = ref_original$cvfun,
 seed = 1111
)

Constrain the variable selection to select the fixed terms first, then the random terms.

# Order variables for selection: first fixed terms, then random terms
search_terms <- c(
  "1",
  "handrear_mother + handrear_father + handrear_mother:handrear_father",
  "scmother_age",
  "handrear_mother",
  "scfather_age",
  "handrear_father",
  "copulations_mates",
  "scprev_male_copulations",
  "scprev_female_copulations",
  "sckin",
  paste(
    "scmother_age + handrear_mother + scfather_age + handrear_father +",
    "copulations_mates + scprev_male_copulations + scprev_female_copulations + sckin +",
    "handrear_mother:handrear_father + (1 | father)"
  ),
  paste(
    "scmother_age + handrear_mother + scfather_age + handrear_father +",
    "copulations_mates + scprev_male_copulations + scprev_female_copulations + sckin +",
    "handrear_mother:handrear_father + (1 | mother)"
  ),
  paste(
    "scmother_age + handrear_mother + scfather_age + handrear_father +",
    "copulations_mates + scprev_male_copulations + scprev_female_copulations + sckin +",
    "handrear_mother:handrear_father + (1 | year)"
  )
)

vs_restricted <- varsel(ref, search_terms = search_terms, seed=1111)

[1] "10% of terms selected."
[1] "20% of terms selected."
[1] "30% of terms selected."
[1] "40% of terms selected."
[1] "50% of terms selected."
[1] "60% of terms selected."
[1] "70% of terms selected."
[1] "80% of terms selected."
[1] "90% of terms selected."
[1] "100% of terms selected."

summary(vs_restricted, stats = c('elpd'), type = c('mean', 'se', 'lower', 'upper', 'diff', 'diff_se'), deltas = T)


Family: gaussian 
Link function: identity 

Formula: clutch_fert ~ scmother_age + handrear_mother + scfather_age + 
    handrear_father + copulations_mates + scprev_male_copulations + 
    scprev_female_copulations + sckin + (1 | father) + (1 | mother) + 
    (1 | year) + handrear_mother:handrear_father
<environment: 0x10e7435f0>
Observations: 217
Search method: forward, maximum number of terms 12
Draws used for selection: 20, in 20 clusters
Draws used for prediction: 400
Suggested Projection Size: 11

Selection Summary:
 size                  solution_terms   elpd  se  lower upper
    0                            <NA> -101.2 3.4 -104.6 -97.8
    1                 handrear_father  -79.3 2.9  -82.2 -76.4
    2               copulations_mates  -65.6 2.3  -67.9 -63.3
    3                 handrear_mother  -61.4 2.4  -63.8 -59.0
    4                    scfather_age  -59.6 2.5  -62.0 -57.1
    5       scprev_female_copulations  -57.7 2.6  -60.3 -55.1
    6 handrear_father:handrear_mother  -57.4 2.6  -60.0 -54.9
    7                    scmother_age  -57.3 2.5  -59.8 -54.8
    8         scprev_male_copulations  -57.2 2.5  -59.7 -54.7
    9                           sckin  -57.1 2.5  -59.7 -54.6
   10                    (1 | father)   -5.3 0.5   -5.9  -4.8
   11                    (1 | mother)   -0.1 0.4   -0.5   0.3
   12                      (1 | year)    0.0 0.3   -0.3   0.3

vs_binom <- vs_restricted

# Project onto latent space and then back to binomial: get better results than if just projecting original full model.
ll_fun <- ref_original$family$ll_fun
linkinv <- ref_original$family$linkinv
for (k in seq_along(vs_restricted$summaries$sub)) {
  vs_binom$summaries$sub[[k]]$mu <- linkinv(vs_restricted$summaries$sub[[k]]$mu)
  vs_binom$summaries$sub[[k]]$draws <-
    linkinv(vs_restricted$summaries$sub[[k]]$draws)
  lppd <- ll_fun(
    mu=vs_binom$summaries$sub[[k]]$draws,
    dis=NULL, y=as.numeric(as.matrix(data[, "clutch_fert"])),
    weights = ref$wobs
  )
  vs_binom$summaries$sub[[k]]$lppd <- apply(
    lppd, 1, projpred:::log_weighted_mean_exp, rep(1 / NCOL(lppd), NCOL(lppd))
  )
}

# Transform back to binomial space:
vs_binom$summaries$ref$mu <- linkinv(vs_restricted$summaries$ref$mu)
vs_binom$summaries$ref$draws <- linkinv(vs_restricted$summaries$ref$draws)
lppd <- ll_fun(
  vs_binom$summaries$ref$draws,
  NULL, as.numeric(as.matrix(data[, "clutch_fert"])),
  weights = ref$wobs
)
vs_binom$summaries$ref$lppd <- apply(
  lppd, 1, projpred:::log_weighted_mean_exp, ref$wsample
)

## Plot variable selection results
elpd_replace <- function(string){
  string <- paste(toupper(string), " difference vs reference model")
}
plot(vs_binom, stats = c('elpd'), deltas=T, alpha=0.32) +
  scale_x_continuous(breaks = c(0, seq_along(vs_restricted$solution_terms)),
                     labels = c("Intercept", fn_labels(vs_restricted$solution_terms))) +
  scale_y_continuous(expand = c(0,0)) +
  expand_limits(y=c(-60,1)) +
  facet_wrap(statistic ~ ., strip.position = "left", labeller = labeller(statistic=elpd_replace)) +
  theme(axis.text.x = element_text(angle = 30, hjust = 1, vjust = 1),
        axis.ticks = element_line(),
        panel.grid.major.x = element_blank(),
        panel.grid.minor.x = element_blank(),
        panel.grid.major.y = element_blank(),
        panel.grid.minor.y = element_blank(),
        strip.text = element_blank(), # no facet text
        strip.placement = "outside",
        strip.background = element_blank(),
      panel.border = element_rect(fill = NA, colour = 'black')) +
  labs(x='Terms in the submodel', y = 'ELPD difference from the reference model')

ggsave(file.path(outdir,"figure_1_varsel.pdf"), height = 6, width = 8)

# Makek table of variablel selection results
d <- summary(vs_binom, type=c('mean', 'se', 'diff', 'lower', 'upper'), stats=c('elpd'), deltas=T)

# Add contribution of difference to ELPD for each term, from the previous term:
tot_elpd <- d$selection$elpd[nrow(d$selection)] - d$selection$elpd[1]
dsel <- d$selection %>% mutate(elpd_diff = elpd - lag(elpd),
                       elpd_diff_pc = 100 * elpd_diff / tot_elpd)
format(dsel, digits=2)

   size                  solution_terms   elpd   se  lower upper elpd_diff
1     0                              NA -52.00 4.97 -56.95 -47.1        NA
2     1                 handrear_father -44.45 5.13 -49.55 -39.3    7.5529
3     2               copulations_mates -38.98 4.77 -43.73 -34.2    5.4651
4     3                 handrear_mother -37.76 4.60 -42.33 -33.2    1.2217
5     4                    scfather_age -37.52 4.54 -42.03 -33.0    0.2401
6     5       scprev_female_copulations -36.42 4.49 -40.88 -32.0    1.1045
7     6 handrear_father:handrear_mother -36.41 4.50 -40.89 -31.9    0.0035
8     7                    scmother_age -36.37 4.45 -40.80 -31.9    0.0427
9     8         scprev_male_copulations -36.35 4.41 -40.74 -32.0    0.0193
10    9                           sckin -36.20 4.40 -40.58 -31.8    0.1503
11   10                    (1 | father) -10.46 1.56 -12.01  -8.9   25.7451
12   11                    (1 | mother)  -4.30 0.92  -5.22  -3.4    6.1542
13   12                      (1 | year)  -0.16 0.27  -0.43   0.1    4.1392
   elpd_diff_pc
1            NA
2       14.5701
3       10.5425
4        2.3568
5        0.4631
6        2.1307
7        0.0068
8        0.0823
9        0.0373
10       0.2900
11      49.6639
12      11.8718
13       7.9848

# Random term contributions to ELPD:
cat(sprintf("Contribution of random model terms to ELPD difference = %.1f%%", dsel %>% filter(grepl("|", solution_terms, fixed=T)) %>% summarise(tot_elpd_diff_pc = sum(elpd_diff_pc)) %>% as.numeric()))

Contribution of random model terms to ELPD difference = 69.5%

5.3.1 Projection - full model

Projected marginals of the full model

# Set the solution terms - all terms
if (suggest_size(vs_binom) > length(vs_binom$solution_terms)){
  solution_terms <- vs_binom$solution_terms[seq_len(suggest_size(vs_binom)-1)]
} else {
  solution_terms <- vs_binom$solution_terms[seq_len(suggest_size(vs_binom))]
}
projection <- projpred::project(vs_restricted, solution_terms = solution_terms, seed=1111)

#Project onto latent space and then back to binomial: get better results than if just projecting original full model.
ll_fun <- ref_original$family$ll_fun
linkinv <- ref_original$family$linkinv
for (k in seq_along(projection$summaries$sub)) {
  projection$summaries$sub[[k]]$mu <- linkinv(projection$summaries$sub[[k]]$mu)
  projection$summaries$sub[[k]]$draws <-
    linkinv(projection$summaries$sub[[k]]$draws)
  lppd <- ll_fun(
    projection$summaries$sub[[k]]$draws,
    NULL, as.numeric(as.matrix(data[, "clutch_fert"])),
    weights = ref$wobs
  )
  projection$summaries$sub[[k]]$lppd <- apply(
    lppd, 1, projpred:::log_weighted_mean_exp, rep(1 / NCOL(lppd), NCOL(lppd))
  )
}

# Project back to binomial space
projection$summaries$ref$mu <- linkinv(projection$summaries$ref$mu)
projection$summaries$ref$draws <- vs_binom$summaries$ref$draws
lppd <- ll_fun(
  projection$summaries$ref$draws,
  NULL, as.numeric(as.matrix(data[, "clutch_fert"])),
  weights = ref$wobs
)
projection$summaries$ref$lppd <- apply(
  lppd, 1, projpred:::log_weighted_mean_exp, ref$wsample
)

R^2 for original model:

# Compare with brms::bayes_R2 function
bayes_R2(fit_original)

    Estimate  Est.Error      Q2.5     Q97.5
R2 0.3124318 0.07100593 0.1709913 0.4513358

R^2 for full projection:

# Modified function to calculate R2 for projected model
# Modified from https://avehtari.github.io/bayes_R2/bayes_R2.html#1_Introduction
bayes_R2_res <- function(proj) {
  y <- get_y(proj$refmodel$fit)
  # Use proj_linpred instead of rstanarm::posterior_epred
  #   use $pred to get values in response space
  ypred_latent <- proj_linpred(proj, transform = T)$pred
  # Apply inverse link function to output of proj_linpred to convert from latent function
  ypred <- ref_original$family$linkinv(ypred_latent)

  if (proj$refmodel$fit$family$family == "binomial" && NCOL(y) == 2) {
    trials <- rowSums(y)
    y <- y[, 1]
    ypred <- ypred %*% diag(trials)
  }
  e <- -1 * sweep(ypred, 2, y)
  var_ypred <- apply(ypred, 1, var)
  var_e <- apply(e, 1, var)
  r2 <- var_ypred / (var_ypred + var_e)
    r2 %>% as.data.frame(.) %>%
    summarise(Mean = mean(r2), SD = sd(r2), Q2.5 = quantile(r2, 0.025), Q97.5 = quantile(r2, 0.975))

}
(R2_res <- bayes_R2_res(projection))

       Mean         SD      Q2.5     Q97.5
1 0.3114775 0.07144011 0.1651088 0.4516667

ROPE plot and posterior statistics. Use rope_range to specify range of ROPE, which is -0.1813799, 0.1813799 for logistic regression.

# Plot ROPE
mp <- as.data.frame(as.matrix(projection)) %>% 
  select(!starts_with("r_"), -sigma) # don't plot random factors or sigma

# Add median and HDI
gmp <- pivot_longer(mp %>% select(-b_Intercept), cols=everything(), names_to='variable')

# Retain order of variables for plot:
gmp$variable <- fct_relevel(gmp$variable, names(mp))
gmp$y <- gmp$variable
(p <- plot(rope(mp,ci=ropeci, range=rope_range(fit_original))) + 
    stat_pointinterval(data=gmp, aes(y=factor(variable, levels=names(mp)), x=value, height=NULL,fill=NULL), point_interval=median_hdi, .width=c(0.5, 0.95), normalize='xy',point_size=3, point_colour='black', interval_colour='blue', shape=21, point_fill='yellow', alpha=0.5) +
    scale_y_discrete(labels=fn_labels, expand = expansion(add = c(-0,1.2)))  +
    scale_x_continuous(labels = function(x)x/2) + # to convert posterior scale from 0.5 SD to SD
    labs(title='', y = 'Variable', x = "Possible values (SD)")  +
    guides(fill = 'none') 
)

ggsave(file.path(outdir, "figure_2_posterior_full.pdf"), height = 6, width = 8)

# Posterior statistics
names(mp) <- fn_labels(names(mp))
describe_posterior(mp, ci_method='hdi', ci=0.95, rope_ci=ropeci, rope_range=rope_range(fit_original), centrality = "median",test = c("p_direction", "p_significance", "rope", 'equivalence_test'))

Summary of Posterior Distribution

Parameter                                 | Median |        95% CI |     pd |   ps |          ROPE | % in ROPE | Equivalence (ROPE)
-----------------------------------------------------------------------------------------------------------------------------------
Intercept                                 |   0.43 | [-0.44, 1.25] | 85.25% | 0.73 | [-0.18, 0.18] |    19.25% |          Undecided
Father HR                                 |  -0.76 | [-2.00, 0.19] | 94.00% | 0.87 | [-0.18, 0.18] |    10.75% |          Undecided
Mother copulations: 1 male, >1 copulation |   0.35 | [-0.26, 1.64] | 81.75% | 0.61 | [-0.18, 0.18] |    35.25% |          Undecided
Mother copulations: Different males       |   1.11 | [-0.03, 2.05] | 96.25% | 0.90 | [-0.18, 0.18] |     9.50% |          Undecided
Mother HR                                 |  -0.16 | [-1.24, 0.56] | 71.00% | 0.48 | [-0.18, 0.18] |    39.00% |          Undecided
Father age                                |   0.11 | [-0.62, 1.16] | 64.75% | 0.43 | [-0.18, 0.18] |    43.75% |          Undecided
Mother previous copulations               |  -0.12 | [-1.06, 0.48] | 72.50% | 0.43 | [-0.18, 0.18] |    50.00% |          Undecided
Mother age                                |  -0.06 | [-0.98, 0.45] | 64.75% | 0.34 | [-0.18, 0.18] |    51.25% |          Undecided
Father previous copulations               |  -0.04 | [-1.00, 0.58] | 63.00% | 0.34 | [-0.18, 0.18] |    55.00% |          Undecided
Mother/father kinship                     |  -0.12 | [-1.01, 0.31] | 79.25% | 0.45 | [-0.18, 0.18] |    50.00% |          Undecided
Father HR:Mother HR                       |  -0.06 | [-1.48, 0.75] | 64.00% | 0.36 | [-0.18, 0.18] |    51.75% |          Undecided
SD(Mother intercept)                      |   0.53 | [ 0.00, 1.17] |   100% | 0.85 | [-0.18, 0.18] |    14.75% |          Undecided
SD(Father intercept)                      |   0.85 | [ 0.32, 1.67] |   100% | 0.99 | [-0.18, 0.18] |     1.00% |           Rejected
SD(Year intercept)                        |   0.41 | [ 0.00, 1.00] |   100% | 0.83 | [-0.18, 0.18] |    17.25% |          Undecided

5.3.2 Projection - reduced model

Project only the copulations and hand-rearing fixed predictors, since these contribute the most to the variance and have non-zero posteriors in the full model, plus the random terms

# Set solution terms: best two fixed terms and all random terms
solution_terms <- c(vs_binom$solution_terms[1:2],
                     vs_binom$solution_terms[10:12])
  projection <- projpred::project(vs_restricted, solution_terms = solution_terms, seed=1111)

# Project onto latent space and then back to binomial: get better results than if just projecting original full model.
ll_fun <- ref_original$family$ll_fun
linkinv <- ref_original$family$linkinv
for (k in seq_along(projection$summaries$sub)) {
  projection$summaries$sub[[k]]$mu <- linkinv(projection$summaries$sub[[k]]$mu)
  projection$summaries$sub[[k]]$draws <-
    linkinv(projection$summaries$sub[[k]]$draws)
  lppd <- ll_fun(
    projection$summaries$sub[[k]]$draws,
    NULL, as.numeric(as.matrix(data[, "clutch_fert"])),
    weights = ref$wobs
  )
  projection$summaries$sub[[k]]$lppd <- apply(
    lppd, 1, projpred:::log_weighted_mean_exp, rep(1 / NCOL(lppd), NCOL(lppd))
  )
}

# Project back to binomial
projection$summaries$ref$mu <- linkinv(projection$summaries$ref$mu)
projection$summaries$ref$draws <- vs_binom$summaries$ref$draws
lppd <- ll_fun(
  projection$summaries$ref$draws,
  NULL, as.numeric(as.matrix(data[, "clutch_fert"])),
  weights = ref$wobs
)
projection$summaries$ref$lppd <- apply(
  lppd, 1, projpred:::log_weighted_mean_exp, ref$wsample
)

R2 of projected reduced model:

(R2_res <- bayes_R2_res(projection))

       Mean         SD      Q2.5     Q97.5
1 0.3065322 0.07057051 0.1618977 0.4478909

ROPE plot and posterior statistics:

# Plot ROPE
mp <- as.data.frame(as.matrix(projection))%>% 
  select(!starts_with("r_"), -sigma) # don't plot random factors or sigma

# Add median and HDI
gmp <- pivot_longer(mp %>% select(-b_Intercept), cols=everything(), names_to='variable')

# Retain order of variables:
gmp$variable <- fct_relevel(gmp$variable, names(mp))
gmp$y <- gmp$variable
plot(rope(mp,ci=ropeci, range=rope_range(fit_original))) + 
  stat_pointinterval(data=gmp, aes(y=factor(variable, levels=names(mp)), x=value, height=NULL,fill=NULL), point_interval=median_hdi, .width=c(0.5, 0.95), normalize='xy',point_size=3, point_colour='black', interval_colour='blue', shape=21,point_fill='yellow', alpha=0.5) +
  scale_y_discrete(labels=fn_labels, expand = expansion(add = c(-0,1.2))) + 
      scale_x_continuous(labels = function(x)x/2) + # to convert posterior scale from 0.5 SD to SD
    labs(title='', y = 'Variable', x = "Possible values (SD)")  +
  guides(fill='none')

ggsave(file.path(outdir, "figure_3_posterior_reduced.pdf"), height = 6, width = 8)

# Posterior stats:
names(mp) <- fn_labels(names(mp))
describe_posterior(mp, ci_method='hdi', ci=0.95, rope_ci=ropeci, rope_range=rope_range(fit_original), centrality = "median",test = c("p_direction", "p_significance", "rope", 'equivalence_test'))

Summary of Posterior Distribution

Parameter                                 | Median |        95% CI |     pd |   ps |          ROPE | % in ROPE | Equivalence (ROPE)
-----------------------------------------------------------------------------------------------------------------------------------
Intercept                                 |   0.58 | [-0.22, 1.51] | 92.25% | 0.84 | [-0.18, 0.18] |    13.50% |          Undecided
Father HR                                 |  -1.03 | [-2.08, 0.16] | 97.50% | 0.93 | [-0.18, 0.18] |     6.50% |          Undecided
Mother copulations: 1 male, >1 copulation |   0.33 | [-0.24, 1.56] | 81.00% | 0.60 | [-0.18, 0.18] |    35.75% |          Undecided
Mother copulations: Different males       |   1.14 | [-0.03, 2.06] | 96.75% | 0.92 | [-0.18, 0.18] |     8.50% |          Undecided
SD(Mother intercept)                      |   0.65 | [ 0.05, 1.36] |   100% | 0.95 | [-0.18, 0.18] |     5.25% |          Undecided
SD(Father intercept)                      |   1.27 | [ 0.30, 2.18] |   100% | 1.00 | [-0.18, 0.18] |     0.25% |           Rejected
SD(Year intercept)                        |   0.63 | [ 0.00, 1.61] | 98.75% | 0.92 | [-0.18, 0.18] |     8.25% |          Undecided

5.3.2.1 Marginal means

Evaluate interaction plot of estimated marginal means from the projected posterior for hand-rearing and number of copulations combined:

# Create projection dataframe
mpb <- as.data.frame(as.matrix(projection)) %>% select(starts_with("b_")) %>% rename_with(.fn=function(x) gsub("b_","",x), .cols=everything())  %>% as.matrix(.)

# Grid for copulations_mates
grd_hr2 <- qdrg(~ copulations_mates + handrear_father , data=fit_original$data, mcmc=mpb[, c('Intercept','copulations_mates2+ copulations', 'copulations_matesDifferent males', 'handrear_fatherTRUE')], link='logit')


# Plot without data:
proj.int <- emmip(grd_hr2, formula("~copulations_mates  + handrear_father"), type='response', plotit=F) %>%
  mutate(father_rear= case_when(handrear_father=='TRUE' ~ 'Hand-reared',
                                 handrear_father=='FALSE' ~ 'Wild-reared'))
ghr_mate <- ggplot() + 
  geom_pointrange(data=proj.int, aes(x=copulations_mates, y=yvar, ymin=LCL, ymax=UCL, colour=father_rear, shape = father_rear), position=position_dodge(width=0.1))  + 
  labs(y='Probability of clutch fertility', x='', colour='Father rearing', shape = 'Father rearing') + 
  scale_x_discrete(labels=fn_labels) +
  scale_colour_brewer(palette = 'Set2', direction = -1) # colour-blind friendly

ggsave(file.path(outdir, "figure_4_predict.pdf"), ghr_mate, height = 6, width = 8)


# Plot with data:
ghr_mate + 
  geom_jitter(data=fit_original$data %>% 
                mutate(father_rear= case_when(
                  handrear_father=='TRUE' ~ 'Hand-reared',
                  handrear_father=='FALSE' ~ 'Wild-reared')), 
              aes(x=copulations_mates, y=clutch_fert, colour=father_rear, shape = father_rear), alpha=0.5, width=0.1, height=0.05)

ggsave(file.path(outdir, "figure_4_predict_data.pdf"), height = 6, width = 8)

# Results table:
proj.int %>% rename(clutch.fertility = yvar) %>%
  mutate(father_rear= case_when(handrear_father=='TRUE' ~ 'Hand-reared',
                                 handrear_father=='FALSE' ~ 'Wild-reared')) %>%
  select(copulations_mates, father_rear, clutch.fertility, LCL, UCL) %>%
  format(., digits=3)

  copulations_mates father_rear clutch.fertility   LCL   UCL
1      1 copulation Wild-reared            0.641 0.468 0.837
2    2+ copulations Wild-reared            0.718 0.524 0.924
3   Different males Wild-reared            0.842 0.666 0.972
4      1 copulation Hand-reared            0.385 0.154 0.732
5    2+ copulations Hand-reared            0.504 0.202 0.833
6   Different males Hand-reared            0.658 0.348 0.932

6 Multiple copulation and kakapo density

# Read number of kakapo per island per year
nk <- read.csv(kakapo_demog_file, header = T) 

# Number of copulations/males per island per year per number of matings/mates
tc <- table(full_data$Island, full_data$year, full_data$copulations_mates)
dtc <- data.frame(tc) %>% rename(Island = Var1, year = Var2, copulations = Var3) %>% mutate(year = as.numeric(as.character(year)))

# Total clutches per island:
dtc_tot <- dtc %>% group_by(year, Island) %>% summarise(totclutch=sum(Freq))
dtc <- left_join(dtc, dtc_tot, by=c('year', 'Island'))

# Combine dataframes: number of kakapo per island and copulations proportions
nk2 <- left_join(dtc, nk %>% filter(ageClass=='Adult'), by=c('year', 'Island'), suffix = c('.cop', '.kak')) %>%
  mutate(prop.kak = Freq.cop / Freq.kak,
         prop.clutch = Freq.cop / totclutch) %>%
  filter(!is.na(Sex) & !is.na(Freq.kak) & Freq.kak > 0)

Combine repeated copulations with the same male and copulations with different males to compare single vs multiple copulations.

Only consider Whenua Hou from 1990 onwards.

nk2 <- nk2 %>% mutate(copulations_comb = fct_collapse(copulations, 
                                              single = "1 copulation",
                                              multiple = c("2+ copulations", "Different males")))
# Totals:
nkg <- nk2 %>% 
  group_by(Island, year, Sex, copulations_comb) %>% 
  summarise(Freq.cop=sum(Freq.cop, na.rm=T), Freq.kak = mean(Freq.kak, na.rm = T), totclutch = mean(totclutch, na.rm = T)) %>%
  mutate(prop.clutch = Freq.cop / totclutch)

# Only Whenua Hou from 1990:
nkgsub <- nkg %>% filter(Island=='Whenua Hou' & year>=1990 & copulations_comb == 'multiple')

6.1 Number of copulations

Show table number of copulations vs number of mates

table(`Number of mates` = full_data$number_of_males, `Number of copulations` = full_data$number_of_copulations)

               Number of copulations
Number of mates   1   2   3   4
              1 105  46   4   0
              2   0  45  14   2
              3   0   0   1   1

6.2 Number of kakapo

Multiple copulation proportion vs number of males and females

# Calculate correlation:
(cor <- nkgsub %>% ungroup(.) %>% dplyr::select(Sex, Freq.kak, prop.clutch) %>% group_by( Sex) %>% correlation())

# Correlation Matrix (pearson-method)

Group  | Parameter1 |  Parameter2 |    r |        95% CI | t(8) |         p
---------------------------------------------------------------------------
Female |   Freq.kak | prop.clutch | 0.93 | [ 0.74, 0.98] | 7.44 | < .001***
Male   |   Freq.kak | prop.clutch | 0.61 | [-0.02, 0.90] | 2.20 | 0.059    

p-value adjustment method: Holm (1979)
Observations: 10

cor$p

[1] 7.319028e-05 5.875909e-02

# Base plot:
col <- brewer.pal(name='Set1',n=3)[2]
gwh1990_comb <- ggplot(nkgsub %>% filter(!is.na(prop.clutch)), aes(x= Freq.kak, y = prop.clutch)) + 
  geom_point(size=2, colour=col) + 
  geom_smooth(aes(shape=NULL), fill=col, method=lm, alpha=0.2) + 
  labs(y = "Proportion of clutches with multiple copulations", x = 'Number of adult kakapo')  + 
  facet_wrap(~Sex, scales='free_x')

6.3 Sex ratio

Multiple copulation proportion vs sex ratio:

# Calculate sex ratio
srg <- nkgsub %>% 
  pivot_wider(id_cols = c(Island, year, copulations_comb, Freq.cop, totclutch, prop.clutch), names_from = 'Sex', values_from="Freq.kak") %>%
  mutate(sex.ratio = Female/Male)

# Calculation correlation:
(corsex <- srg %>% ungroup(.) %>% dplyr::select(sex.ratio, prop.clutch)  %>% correlation(bayesian=F))

# Correlation Matrix (pearson-method)

Parameter1 |  Parameter2 |    r |       95% CI | t(8) |         p
-----------------------------------------------------------------
sex.ratio  | prop.clutch | 0.92 | [0.71, 0.98] | 6.88 | < .001***

p-value adjustment method: Holm (1979)
Observations: 10

corsex$p

[1] 0.0001274216

col <- brewer.pal(name='Set1',n=3)[1]
# Plot of multiple copulation frequency vs sex ratio
gswh1990comb <- ggplot(srg %>% filter(copulations_comb=='multiple'), aes(x= sex.ratio, y=prop.clutch)) + 
  geom_point(size=2, colour=col) + geom_smooth(aes(shape=NULL), method=lm, alpha=0.2, colour=col, fill=col) + 
  labs(y = "Prop. of clutches with multiple copulations", x = 'Female:male sex ratio')

6.4 Number and sex ratio combined

Combine number of male/female and sex ratio plots:

# Separate panels for females, males and sex ratio
# Multiple copulation frequency vs number of females
col <- brewer.pal(name='Set2',n=3)[1] # colour-blind friendly
gwh1990_female <- ggplot(nkgsub %>% filter(!is.na(prop.clutch) & Sex == 'Female'), aes(x= Freq.kak, y = prop.clutch)) + 
  geom_point(size=2, colour=col) + 
  geom_smooth(aes(shape=NULL), colour = col, fill=col, method=lm, alpha=0.2) + 
  labs(y = "Proportion of clutches", x = 'Number of females') +
  coord_cartesian(ylim = c(0,1)) + 
  expand_limits(x=40)

# Multiple copulation frequency vs number of males
col <- brewer.pal(name='Set2',n=3)[2]
gwh1990_male <- ggplot(nkgsub %>% filter(!is.na(prop.clutch) & Sex == 'Male'), aes(x= Freq.kak, y = prop.clutch)) + 
  geom_point(size=2, colour=col) + 
  geom_smooth(aes(shape=NULL), fill=col, method=lm, alpha=0.2, colour=col, fill=col) + 
  labs(y = "", x = 'Number of males')  +
  coord_cartesian(ylim = c(0,1)) + 
  expand_limits(x=c(15,30))

# Multiple copulation frequency vs sex ratio
col <- brewer.pal(name='Set2',n=3)[3]
gwh1990_sexratio <- ggplot(srg %>% filter(copulations_comb=='multiple'), aes(x= sex.ratio, y=prop.clutch)) + 
  geom_point(size=2, colour=col) + 
  geom_smooth(aes(shape=NULL), method=lm, alpha=0.2, colour=col, fill=col) + 
  labs(y = "", x = 'Female:male sex ratio') +
  coord_cartesian(ylim = c(0,1)) + 
  expand_limits(x=0.4) 

ggarrange(gwh1990_female,
          gwh1990_male,
          gwh1990_sexratio,
          common.legend = T , 
          labels = c("A", "B", "C"),
          label.x = 0.25,
          label.y = 0.98,
          ncol = 3,
          nrow = 1,
          widths=c(1,1,1))

# For publication:
ggsave(filename = file.path(outdir, 'figure_5_copulation_sex_ratio.pdf'), plot=last_plot(), device = 'pdf', width=10, height=6 )

6.5 Change over time

Show the change in Whenua Hou population and sex ratio over time (note that these data include some years in which there was no breeding):

# Total population
ggplot(srg %>% filter(!is.na(sex.ratio))  , aes(x = year, y = Female + Male)) +
         geom_point() + 
         geom_line() +
    scale_x_continuous(breaks = seq(min(srg$year), max(srg$year), 5), minor_breaks = c(min(srg$year): max(srg$year))) + 
  scale_y_continuous(breaks = seq(0,1,0.2)) +
  labs(y = 'Number of adult kakapo')

# Male and female population
ggplot(srg %>% filter(!is.na(sex.ratio) & !is.nan(prop.clutch)) %>% pivot_longer(cols = Female:Male, names_to = 'variable') , aes(x = year, y = value, colour = variable)) +
         geom_point() + 
         geom_line() +
  facet_wrap(~variable, scales = 'fixed') + 
  guides(colour = 'none') + 
    scale_x_continuous(breaks = seq(min(srg$year), max(srg$year), 5), minor_breaks = c(min(srg$year): max(srg$year))) + 
  labs(y = 'Number of adult kakapo')

# Sex ratio
ggplot(srg %>% filter(!is.na(sex.ratio)& !is.nan(prop.clutch)) , aes(x = year, y = sex.ratio)) +
         geom_point() + 
         geom_line() +
    scale_x_continuous(breaks = seq(min(srg$year), max(srg$year), 5), minor_breaks = c(min(srg$year): max(srg$year))) + 
  labs(y = 'F:M adult sex ratio')

Change in multiple copulation rate over time:

# Sex ratio
ggplot(srg %>% filter(!is.na(sex.ratio)& !is.nan(prop.clutch)) , aes(x = year, y = prop.clutch)) +
         geom_point() + 
         geom_line() +
  scale_x_continuous(breaks = seq(min(srg$year), max(srg$year), 5), minor_breaks = c(min(srg$year): max(srg$year))) + 
  scale_y_continuous(breaks = seq(0,1,0.2)) +
  labs(y = 'Proportion of multiple copulations')

7 Session information

sessionInfo()

R version 4.1.2 (2021-11-01)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS Monterey 12.6.2

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.1-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.1-arm64/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] ggpubr_0.4.0         RColorBrewer_1.1-3   correlation_0.8.0   
 [4] emmeans_1.7.3        loo_2.5.1            brms_2.16.3         
 [7] Rcpp_1.0.9           doRNG_1.8.2          rngtools_1.5.2      
[10] doFuture_0.12.1      future_1.24.0        foreach_1.5.2       
[13] ggdist_3.1.1         see_0.6.9            bayestestR_0.11.5   
[16] bayesplot_1.9.0      lme4_1.1-29          Matrix_1.4-1        
[19] rstan_2.21.5         StanHeaders_2.21.0-7 forcats_0.5.1       
[22] stringr_1.4.0        dplyr_1.0.9          purrr_0.3.4         
[25] readr_2.1.1          tidyr_1.1.4          tibble_3.1.7        
[28] ggplot2_3.3.6        tidyverse_1.3.2      projpred_2.0.5.9000 

loaded via a namespace (and not attached):
  [1] readxl_1.3.1         backports_1.4.1      plyr_1.8.7          
  [4] igraph_1.2.11        splines_4.1.2        crosstalk_1.2.0     
  [7] listenv_0.8.0        optimx_2021-10.12    rstantools_2.2.0    
 [10] inline_0.3.19        digest_0.6.29        htmltools_0.5.2     
 [13] fansi_1.0.3          magrittr_2.0.3       checkmate_2.1.0     
 [16] googlesheets4_1.0.0  tzdb_0.2.0           globals_0.14.0      
 [19] modelr_0.1.8         RcppParallel_5.1.5   matrixStats_0.62.0  
 [22] xts_0.12.1           rmdformats_1.0.3     prettyunits_1.1.1   
 [25] colorspace_2.0-3     rvest_1.0.2          haven_2.4.3         
 [28] xfun_0.28            callr_3.7.0          crayon_1.5.1        
 [31] jsonlite_1.8.0       zoo_1.8-9            iterators_1.0.14    
 [34] glue_1.6.2           gtable_0.3.0         gargle_1.2.0        
 [37] distributional_0.3.0 car_3.0-12           pkgbuild_1.3.0      
 [40] abind_1.4-5          scales_1.2.0         mvtnorm_1.1-3       
 [43] DBI_1.1.1            rstatix_0.7.0        miniUI_0.1.1.1      
 [46] xtable_1.8-4         HDInterval_0.2.2     DT_0.20             
 [49] stats4_4.1.2         datawizard_0.4.0     htmlwidgets_1.5.4   
 [52] httr_1.4.2           threejs_0.3.3        posterior_1.2.1     
 [55] ellipsis_0.3.2       pkgconfig_2.0.3      farver_2.1.0        
 [58] sass_0.4.0           dbplyr_2.1.1         utf8_1.2.2          
 [61] labeling_0.4.2       reshape2_1.4.4       tidyselect_1.1.2    
 [64] rlang_1.0.2          later_1.3.0          munsell_0.5.0       
 [67] cellranger_1.1.0     tools_4.1.2          cli_3.3.0           
 [70] generics_0.1.2       broom_0.7.10         ggridges_0.5.3      
 [73] evaluate_0.15        fastmap_1.1.0        yaml_2.3.5          
 [76] processx_3.5.3       knitr_1.36           fs_1.5.2            
 [79] nlme_3.1-153         mime_0.12            xml2_1.3.3          
 [82] shinythemes_1.2.0    compiler_4.1.2       rstudioapi_0.13     
 [85] gamm4_0.2-6          ggsignif_0.6.3       reprex_2.0.1        
 [88] bslib_0.3.1          stringi_1.7.6        parameters_0.17.0   
 [91] highr_0.9            ps_1.7.0             Brobdingnag_1.2-8   
 [94] lattice_0.20-45      markdown_1.1         nloptr_2.0.0        
 [97] shinyjs_2.1.0        tensorA_0.36.2       vctrs_0.4.1         
[100] pillar_1.7.0         lifecycle_1.0.1      jquerylib_0.1.4     
[103] bridgesampling_1.1-2 estimability_1.3     cowplot_1.1.1       
[106] insight_0.17.0       httpuv_1.6.5         R6_2.5.1            
[109] bookdown_0.24        promises_1.2.0.1     gridExtra_2.3       
[112] parallelly_1.30.0    codetools_0.2-18     gtools_3.9.2        
[115] colourpicker_1.1.1   boot_1.3-28          MASS_7.3-54         
[118] assertthat_0.2.1     withr_2.5.0          shinystan_2.6.0     
[121] mgcv_1.8-38          parallel_4.1.2       hms_1.1.1           
[124] grid_4.1.2           coda_0.19-4          minqa_1.2.4         
[127] rmarkdown_2.11       carData_3.0-5        googledrive_2.0.0   
[130] numDeriv_2016.8-1.1  shiny_1.7.1          lubridate_1.8.0     
[133] base64enc_0.1-3      dygraphs_1.1.1.6

---
title: "Kakapo Fertility Projpred modelling"
author: "Alejandro Catalina and Andrew Digby"
date: "`r Sys.Date()`"
output: 
  rmdformats::readthedown:
     lightbox: true
     toc_depth: 5
     gallery: true
     fig_caption: true
     code_folding: hide
     code_download: true
     use_bookdown: true
editor_options: 
  chunk_output_type: inline
---

```{r setup, echo=FALSE, message=FALSE, include=FALSE}
knitr::opts_chunk$set(dev=c('png','pdf'), comment="", fig.width=10, echo=TRUE, warning=FALSE, cache=F, message=FALSE, fig.path='figure/')

# Requires workflow branch of projpred:
#library(devtools)
#install_github(repo = "stan-dev/projpred", ref = "workflow")

library(projpred)
library(tidyverse) 
library(rstan)
library(lme4)
library(bayesplot)
library(bayestestR)
library(see)
library(ggdist)
library(doFuture)
library(doRNG)
library(brms)
library(loo)
library(emmeans)
library(correlation)
library(RColorBrewer)
library(ggpubr)

rstan_options (auto_write=TRUE)
options (mc.cores=parallel::detectCores ()) # Run on multiple cores

theme_set(theme_minimal(base_size = 14) + theme(
        axis.ticks = element_line(),
      panel.grid.major.x = element_blank(),
      panel.grid.minor.x = element_blank(),
      panel.grid.minor.y = element_blank(),
      panel.grid.major.y = element_blank(),
      panel.border = element_rect(fill = NA, colour = 'black')))
```

```{r parameters}
set.seed(1111)
curr_dir <- setwd(dirname(rstudioapi::getSourceEditorContext()$path))
clutch_file <- file.path(curr_dir, "./Supplemental_Data_S1.csv")
kakapo_demog_file <- file.path(curr_dir, './Supplemental_Data_S2.csv')

outdir <- "./figure/"
ropeci <- 1.00 # proportion of posterior which intersects with ROPE. 
nchains <- 4
niter <- 30000 # iterations for brm
```

# Credits

-   Markdown from `readthedown` template, from package `rmdformats`.
-   Code written by Alejandro Catalina and Andrew Digby.

# Purpose

Code and results for the publication `Hidden impacts of conservation management on fertility of the critically endangered kakapo`. Model validation and diagnostics not included.

1.  Use projected predictive variable selection package `projpred` to assess factors influencing kakapo fertility using a Bayesian model.
2.  Compare multiple copulation frequency with kakapo density and sex ratio

# Requirements

 - Requires the `workflow` branch of `projpred`.
 
# Data

Input data:

-   Clutch fertility data frame from file `r basename(clutch_file)`.
-   Kakapo numbers per island per year from `r basename(kakapo_demog_file)`.

# Fertility model

## Load data

```{r functions}

ref_predfun <- function(fit, newdata = NULL) {
  return(t(posterior_linpred(fit,
                             newdata = newdata,
                             transform = FALSE
  )))
}

# Retrieve model data
extract_model_data <- function(object, newdata = NULL, wrhs = NULL,
                               orhs = NULL, extract_y = TRUE) {
  if (!extract_y) {
    resp_form <- NULL
  } else {
    resp_form <- ~.y
  }
  
  if (is.null(newdata)) {
    newdata <- data
  }
  
  if (is.null(wrhs) && !is.null(object) &&
      !is.null(object$weights) && length(object$weights) != 0) {
    wrhs <- ~weights
    newdata <- cbind(newdata, weights = object$weights)
  }
  
  if (is.null(orhs) && !is.null(object) &&
      !is.null(object$offset) && length(object$offset) != 0) {
    orhs <- ~offset
    newdata <- cbind(newdata, offset = object$offset)
  }
  
  args <- nlist(object, newdata, wrhs, orhs, resp_form)
  return(do_call(projpred:::.extract_model_data, args))
}

# For more readable parameter names in plots
fn_labels <- function(string){
  string <- sub('b_','',string)
  string <- gsub('scmother_age','Mother age',string)
  string <- gsub('scfather_age','Father age',string)
  string <- gsub('schandrear.mother','Mother HR',string)
  string <- gsub('schandrear.father','Father HR',string)
  string <- gsub('handrear.mother','Mother HR',string)
  string <- gsub('handrear.father','Father HR',string)
  string <- gsub('HRTRUE', 'HR', string)
  string <- gsub('scnumber.of.copulations','No. copulations',string)
  string <- gsub('scnumber.of.males','No. males',string)
  string <- gsub('sccopulations.mates','Mother copulations: ',string)
  string <- gsub('copulations.mates','Mother copulations: ',string)
  string <- gsub('Intercept','Intercept',string)
  string <- gsub('Differentmales','Different males',string)
  string <- gsub('2Pcopulations','1 male, >1 copulation',string)
  string <- gsub('2\\+ copulations','1 male, >1 copulation',string)
  string <- gsub('sckin','Mother/father kinship',string)
  string <- gsub("scprev.male.copulations", "Father previous copulations", string)
  string <- gsub("scprev.female.copulations", "Mother previous copulations", string)
  string <- gsub("sd_mother__Intercept", "SD(Mother intercept)", string)
  string <- gsub("sd_father__Intercept", "SD(Father intercept)", string)
  string <- gsub("sd_year__Intercept", "SD(Year intercept)", string)
  string <- gsub(": $","",string) # remove colon at end of string (to remove "Mating:" if no subsequent variable)
  
  return(string)

}
```

-   Remove observations with missing values
-   Scale and centre continuous predictors to mean of zero and SD=0.5 (see http://www.stat.columbia.edu/~gelman/research/published/priors11.pdf)

```{r read_data}
# Read clutch data file:
full_data <- read.csv(clutch_file, header = T, stringsAsFactors = T) %>%
  mutate(year = as.factor(year),
         handrear.mother = as.factor(handrear.mother),
         handrear.father = as.factor(handrear.father)) %>%
  rename_with(~ gsub("\\.","_", .x)) 
cat(sprintf("Loaded %d records from %s\n", nrow(full_data), basename(clutch_file)))  

# Retain only variables of interest and drop rows with missing values
data <- full_data %>%  dplyr::select(clutch_fert, mother_age, handrear_mother, father_age,
         handrear_father, copulations_mates, prev_male_copulations, prev_female_copulations, kin, father, mother, year) %>%
  tidyr::drop_na()

# Scale and centre inputs to mean of zero & SD = 0.5
data <- data %>% mutate(
  scmother_age = 0.5*scale(mother_age, center=T, scale=T) ,
  scfather_age = 0.5*scale(father_age, center=T, scale=T),
  scprev_male_copulations = 0.5*scale(prev_male_copulations, center=T, scale=T),
  scprev_female_copulations = 0.5*scale(prev_female_copulations, center=T, scale=T),
  sckin = 0.5*scale(kin, center=T, scale=T),
)

# Convert matrix columns to vectors (result of using scale)
data <- data %>% mutate(scmother_age = as.vector(scmother_age),
                        scfather_age = as.vector(scfather_age),
                        sckin = as.vector(sckin),
                        scprev_male_copulations = as.vector(scprev_male_copulations),
                        scprev_female_copulations = as.vector(scprev_female_copulations))

```


Show predictor distributions for numeric variables

```{r moddata_distrib}
facetlabs <- c('mother_age'='Mother age (years)', 'father_age' = 'Father age (years)', 'prev_male_copulations' = 'Father previous copulations', 'prev_female_copulations' = 'Mother previous copulations', 'kin' = 'Mother/father kinship')
df <- data %>%  dplyr::select(mother_age, father_age, prev_male_copulations, prev_female_copulations, kin)
dfl <- df %>% pivot_longer(everything(), names_to='variable') %>% 
  mutate(variable = factor(variable, levels=c('mother_age', 'father_age', 'prev_male_copulations', 'prev_female_copulations', 'kin')))
fill_col1 <- brewer.pal(name='Set2',n=3)[1]
fill_col2 <- brewer.pal(name='Set2',n=3)[2]
fill_col3 <- brewer.pal(name='Set2',n=3)[3]
ggplot(dfl, aes(x=value)) + 
#  geom_histogram(data=subset(dfl, variable %in% c('mother_age', 'father_age', 'prev_male_copulations')), binwidth = 2, closed = 'left') +
  geom_histogram(data=subset(dfl, variable %in% c('mother_age', 'father_age')), breaks = seq(0, 50, 2), closed = 'right', fill = fill_col1, colour = 'black' ) +
  geom_histogram(data=subset(dfl, variable %in% c('prev_male_copulations')), breaks = seq(0,40,2), closed = 'right', fill = fill_col2, colour = 'black'  ) +
  geom_histogram(data=subset(dfl, variable %in% c('prev_female_copulations')), breaks = seq(0,20,1), closed = 'right', fill = fill_col2, colour = 'black'  ) +
  geom_histogram(data=subset(dfl, variable %in% c('kin')), breaks = seq(0, 0.3, 0.01), closed = 'right', fill = fill_col3, colour = 'black'  ) + 
  facet_wrap(~variable, scales='free', labeller=labeller(variable=facetlabs), ncol=2) +
    scale_x_continuous(expand = c(0.01,0)) +
  labs(y = 'Frequency', x = '') + 
  guides(fill = 'none')


 ggsave("./figure/figure_s2_predictor_distributions.pdf", height = 7, width = 8)

```

```{r model_setup}
# Random variables:
grouping_variables <- c("father", "mother", "year")

# Predictors:
predictors <- c(
  "scmother_age", "handrear_mother", "scfather_age",
  "handrear_father", "copulations_mates", "scprev_male_copulations",
  "scprev_female_copulations", "sckin"
)
```

## Reference model

Fit full reference model

```{r model_structure}
# Formula for model
formula <- paste(
  "clutch_fert ~", paste0(predictors, collapse = " + "), " + ",
  paste(paste0("(1 | ", grouping_variables, ")"), collapse = " + "),
  "+ handrear_mother:handrear_father"
) %>%
  as.formula()
```

```{r orig_fit, warnings = TRUE}
# Fit original model with {brms}
fit_original <- brm(formula,
  data = data, family = bernoulli(),
  prior = set_prior(horseshoe()),
  iter = niter, 
  chains = nchains,
  seed = 1111,
  control = list(adapt_delta = 0.99)
)
fit_original

```

## Restricted variable selection

```{r ref_model}
# Set up variable selection
## run variable selection on the unconstrained latent space
ref_original <- brms:::get_refmodel.brmsfit(fit_original, seed = 1111)
f_latent <- colMeans(posterior_linpred(fit_original, transform = FALSE))
data[[".y"]] <- f_latent
dis_latent <- rep(1, 2*niter)

# Get reference model
ref <- init_refmodel(fit_original,
 data = data, formula = formula, family = gaussian(),
 ref_predfun = ref_predfun, div_minimizer = projpred:::linear_multilevel_mle,
 proj_predfun = projpred:::linear_multilevel_proj_predfun, dis = dis_latent,
 extract_model_data = extract_model_data, cvfun = ref_original$cvfun,
 seed = 1111
)
```

Constrain the variable selection to select the fixed terms first, then the random terms.

```{r restrict_search_terms}
# Order variables for selection: first fixed terms, then random terms
search_terms <- c(
  "1",
  "handrear_mother + handrear_father + handrear_mother:handrear_father",
  "scmother_age",
  "handrear_mother",
  "scfather_age",
  "handrear_father",
  "copulations_mates",
  "scprev_male_copulations",
  "scprev_female_copulations",
  "sckin",
  paste(
    "scmother_age + handrear_mother + scfather_age + handrear_father +",
    "copulations_mates + scprev_male_copulations + scprev_female_copulations + sckin +",
    "handrear_mother:handrear_father + (1 | father)"
  ),
  paste(
    "scmother_age + handrear_mother + scfather_age + handrear_father +",
    "copulations_mates + scprev_male_copulations + scprev_female_copulations + sckin +",
    "handrear_mother:handrear_father + (1 | mother)"
  ),
  paste(
    "scmother_age + handrear_mother + scfather_age + handrear_father +",
    "copulations_mates + scprev_male_copulations + scprev_female_copulations + sckin +",
    "handrear_mother:handrear_father + (1 | year)"
  )
)
```

```{r varsel_restrict}
vs_restricted <- varsel(ref, search_terms = search_terms, seed=1111)
summary(vs_restricted, stats = c('elpd'), type = c('mean', 'se', 'lower', 'upper', 'diff', 'diff_se'), deltas = T)
vs_binom <- vs_restricted

# Project onto latent space and then back to binomial: get better results than if just projecting original full model.
ll_fun <- ref_original$family$ll_fun
linkinv <- ref_original$family$linkinv
for (k in seq_along(vs_restricted$summaries$sub)) {
  vs_binom$summaries$sub[[k]]$mu <- linkinv(vs_restricted$summaries$sub[[k]]$mu)
  vs_binom$summaries$sub[[k]]$draws <-
    linkinv(vs_restricted$summaries$sub[[k]]$draws)
  lppd <- ll_fun(
    mu=vs_binom$summaries$sub[[k]]$draws,
    dis=NULL, y=as.numeric(as.matrix(data[, "clutch_fert"])),
    weights = ref$wobs
  )
  vs_binom$summaries$sub[[k]]$lppd <- apply(
    lppd, 1, projpred:::log_weighted_mean_exp, rep(1 / NCOL(lppd), NCOL(lppd))
  )
}

# Transform back to binomial space:
vs_binom$summaries$ref$mu <- linkinv(vs_restricted$summaries$ref$mu)
vs_binom$summaries$ref$draws <- linkinv(vs_restricted$summaries$ref$draws)
lppd <- ll_fun(
  vs_binom$summaries$ref$draws,
  NULL, as.numeric(as.matrix(data[, "clutch_fert"])),
  weights = ref$wobs
)
vs_binom$summaries$ref$lppd <- apply(
  lppd, 1, projpred:::log_weighted_mean_exp, ref$wsample
)
```

```{r varsel_plot}
## Plot variable selection results
elpd_replace <- function(string){
  string <- paste(toupper(string), " difference vs reference model")
}
plot(vs_binom, stats = c('elpd'), deltas=T, alpha=0.32) +
  scale_x_continuous(breaks = c(0, seq_along(vs_restricted$solution_terms)),
                     labels = c("Intercept", fn_labels(vs_restricted$solution_terms))) +
  scale_y_continuous(expand = c(0,0)) +
  expand_limits(y=c(-60,1)) +
  facet_wrap(statistic ~ ., strip.position = "left", labeller = labeller(statistic=elpd_replace)) +
  theme(axis.text.x = element_text(angle = 30, hjust = 1, vjust = 1),
        axis.ticks = element_line(),
        panel.grid.major.x = element_blank(),
        panel.grid.minor.x = element_blank(),
        panel.grid.major.y = element_blank(),
        panel.grid.minor.y = element_blank(),
        strip.text = element_blank(), # no facet text
        strip.placement = "outside",
        strip.background = element_blank(),
      panel.border = element_rect(fill = NA, colour = 'black')) +
  labs(x='Terms in the submodel', y = 'ELPD difference from the reference model') 
ggsave(file.path(outdir,"figure_1_varsel.pdf"), height = 6, width = 8)
```

```{r varsel_summary, caption = "Contribution to expected log predictive density (elpd) for each term in the model. Column 'elpd' shows the difference in elpd from the reference model; 'elpd_diff' and 'elpd_diff_pc' give the difference and percentage difference in the elpd compared to the previous term. "}
# Makek table of variablel selection results
d <- summary(vs_binom, type=c('mean', 'se', 'diff', 'lower', 'upper'), stats=c('elpd'), deltas=T)

# Add contribution of difference to ELPD for each term, from the previous term:
tot_elpd <- d$selection$elpd[nrow(d$selection)] - d$selection$elpd[1]
dsel <- d$selection %>% mutate(elpd_diff = elpd - lag(elpd),
                       elpd_diff_pc = 100 * elpd_diff / tot_elpd)
format(dsel, digits=2)

# Random term contributions to ELPD:
cat(sprintf("Contribution of random model terms to ELPD difference = %.1f%%", dsel %>% filter(grepl("|", solution_terms, fixed=T)) %>% summarise(tot_elpd_diff_pc = sum(elpd_diff_pc)) %>% as.numeric()))
```


### Projection - full model

Projected marginals of the full model

```{r project_full}
# Set the solution terms - all terms
if (suggest_size(vs_binom) > length(vs_binom$solution_terms)){
  solution_terms <- vs_binom$solution_terms[seq_len(suggest_size(vs_binom)-1)]
} else {
  solution_terms <- vs_binom$solution_terms[seq_len(suggest_size(vs_binom))]
}
projection <- projpred::project(vs_restricted, solution_terms = solution_terms, seed=1111)

#Project onto latent space and then back to binomial: get better results than if just projecting original full model.
ll_fun <- ref_original$family$ll_fun
linkinv <- ref_original$family$linkinv
for (k in seq_along(projection$summaries$sub)) {
  projection$summaries$sub[[k]]$mu <- linkinv(projection$summaries$sub[[k]]$mu)
  projection$summaries$sub[[k]]$draws <-
    linkinv(projection$summaries$sub[[k]]$draws)
  lppd <- ll_fun(
    projection$summaries$sub[[k]]$draws,
    NULL, as.numeric(as.matrix(data[, "clutch_fert"])),
    weights = ref$wobs
  )
  projection$summaries$sub[[k]]$lppd <- apply(
    lppd, 1, projpred:::log_weighted_mean_exp, rep(1 / NCOL(lppd), NCOL(lppd))
  )
}

# Project back to binomial space
projection$summaries$ref$mu <- linkinv(projection$summaries$ref$mu)
projection$summaries$ref$draws <- vs_binom$summaries$ref$draws
lppd <- ll_fun(
  projection$summaries$ref$draws,
  NULL, as.numeric(as.matrix(data[, "clutch_fert"])),
  weights = ref$wobs
)
projection$summaries$ref$lppd <- apply(
  lppd, 1, projpred:::log_weighted_mean_exp, ref$wsample
)
```

R^2 for original model:

```{r r2_original}
# Compare with brms::bayes_R2 function
bayes_R2(fit_original)
```

R^2 for full projection:

```{r r2_projection_full}
# Modified function to calculate R2 for projected model
# Modified from https://avehtari.github.io/bayes_R2/bayes_R2.html#1_Introduction
bayes_R2_res <- function(proj) {
  y <- get_y(proj$refmodel$fit)
  # Use proj_linpred instead of rstanarm::posterior_epred
  #   use $pred to get values in response space
  ypred_latent <- proj_linpred(proj, transform = T)$pred
  # Apply inverse link function to output of proj_linpred to convert from latent function
  ypred <- ref_original$family$linkinv(ypred_latent)

  if (proj$refmodel$fit$family$family == "binomial" && NCOL(y) == 2) {
    trials <- rowSums(y)
    y <- y[, 1]
    ypred <- ypred %*% diag(trials)
  }
  e <- -1 * sweep(ypred, 2, y)
  var_ypred <- apply(ypred, 1, var)
  var_e <- apply(e, 1, var)
  r2 <- var_ypred / (var_ypred + var_e)
    r2 %>% as.data.frame(.) %>%
    summarise(Mean = mean(r2), SD = sd(r2), Q2.5 = quantile(r2, 0.025), Q97.5 = quantile(r2, 0.975))

}
(R2_res <- bayes_R2_res(projection))

```


ROPE plot and posterior statistics. Use `rope_range` to specify range of ROPE, which is `r rope_range(fit_original)` for logistic regression.

```{r project_full_rope, eval=T, fig.height=8}
# Plot ROPE
mp <- as.data.frame(as.matrix(projection)) %>% 
  select(!starts_with("r_"), -sigma) # don't plot random factors or sigma

# Add median and HDI
gmp <- pivot_longer(mp %>% select(-b_Intercept), cols=everything(), names_to='variable')

# Retain order of variables for plot:
gmp$variable <- fct_relevel(gmp$variable, names(mp))
gmp$y <- gmp$variable
(p <- plot(rope(mp,ci=ropeci, range=rope_range(fit_original))) + 
    stat_pointinterval(data=gmp, aes(y=factor(variable, levels=names(mp)), x=value, height=NULL,fill=NULL), point_interval=median_hdi, .width=c(0.5, 0.95), normalize='xy',point_size=3, point_colour='black', interval_colour='blue', shape=21, point_fill='yellow', alpha=0.5) +
    scale_y_discrete(labels=fn_labels, expand = expansion(add = c(-0,1.2)))  +
    scale_x_continuous(labels = function(x)x/2) + # to convert posterior scale from 0.5 SD to SD
    labs(title='', y = 'Variable', x = "Possible values (SD)")  +
    guides(fill = 'none') 
)

ggsave(file.path(outdir, "figure_2_posterior_full.pdf"), height = 6, width = 8)

# Posterior statistics
names(mp) <- fn_labels(names(mp))
describe_posterior(mp, ci_method='hdi', ci=0.95, rope_ci=ropeci, rope_range=rope_range(fit_original), centrality = "median",test = c("p_direction", "p_significance", "rope", 'equivalence_test'))
```

### Projection - reduced model

Project only the `copulations` and `hand-rearing` fixed predictors, since these contribute the most to the variance and have non-zero posteriors in the full model, plus the random terms

```{r project_reduced, eval=T, cache=F}
# Set solution terms: best two fixed terms and all random terms
solution_terms <- c(vs_binom$solution_terms[1:2],
                     vs_binom$solution_terms[10:12])
  projection <- projpred::project(vs_restricted, solution_terms = solution_terms, seed=1111)

# Project onto latent space and then back to binomial: get better results than if just projecting original full model.
ll_fun <- ref_original$family$ll_fun
linkinv <- ref_original$family$linkinv
for (k in seq_along(projection$summaries$sub)) {
  projection$summaries$sub[[k]]$mu <- linkinv(projection$summaries$sub[[k]]$mu)
  projection$summaries$sub[[k]]$draws <-
    linkinv(projection$summaries$sub[[k]]$draws)
  lppd <- ll_fun(
    projection$summaries$sub[[k]]$draws,
    NULL, as.numeric(as.matrix(data[, "clutch_fert"])),
    weights = ref$wobs
  )
  projection$summaries$sub[[k]]$lppd <- apply(
    lppd, 1, projpred:::log_weighted_mean_exp, rep(1 / NCOL(lppd), NCOL(lppd))
  )
}

# Project back to binomial
projection$summaries$ref$mu <- linkinv(projection$summaries$ref$mu)
projection$summaries$ref$draws <- vs_binom$summaries$ref$draws
lppd <- ll_fun(
  projection$summaries$ref$draws,
  NULL, as.numeric(as.matrix(data[, "clutch_fert"])),
  weights = ref$wobs
)
projection$summaries$ref$lppd <- apply(
  lppd, 1, projpred:::log_weighted_mean_exp, ref$wsample
)
```

R2 of projected reduced model:

```{r r2_projection_reduced}
(R2_res <- bayes_R2_res(projection))
```


ROPE plot and posterior statistics:

```{r project_reduced_rope, eval=T, fig.height=8}
# Plot ROPE
mp <- as.data.frame(as.matrix(projection))%>% 
  select(!starts_with("r_"), -sigma) # don't plot random factors or sigma

# Add median and HDI
gmp <- pivot_longer(mp %>% select(-b_Intercept), cols=everything(), names_to='variable')

# Retain order of variables:
gmp$variable <- fct_relevel(gmp$variable, names(mp))
gmp$y <- gmp$variable
plot(rope(mp,ci=ropeci, range=rope_range(fit_original))) + 
  stat_pointinterval(data=gmp, aes(y=factor(variable, levels=names(mp)), x=value, height=NULL,fill=NULL), point_interval=median_hdi, .width=c(0.5, 0.95), normalize='xy',point_size=3, point_colour='black', interval_colour='blue', shape=21,point_fill='yellow', alpha=0.5) +
  scale_y_discrete(labels=fn_labels, expand = expansion(add = c(-0,1.2))) + 
      scale_x_continuous(labels = function(x)x/2) + # to convert posterior scale from 0.5 SD to SD
    labs(title='', y = 'Variable', x = "Possible values (SD)")  +
  guides(fill='none')

ggsave(file.path(outdir, "figure_3_posterior_reduced.pdf"), height = 6, width = 8)

# Posterior stats:
names(mp) <- fn_labels(names(mp))
describe_posterior(mp, ci_method='hdi', ci=0.95, rope_ci=ropeci, rope_range=rope_range(fit_original), centrality = "median",test = c("p_direction", "p_significance", "rope", 'equivalence_test'))

```

#### Marginal means

Evaluate interaction plot of estimated marginal means from the projected posterior for hand-rearing and number of copulations combined:

```{r project_reduced_marg_hr_mate}

# Create projection dataframe
mpb <- as.data.frame(as.matrix(projection)) %>% select(starts_with("b_")) %>% rename_with(.fn=function(x) gsub("b_","",x), .cols=everything())  %>% as.matrix(.)

# Grid for copulations_mates
grd_hr2 <- qdrg(~ copulations_mates + handrear_father , data=fit_original$data, mcmc=mpb[, c('Intercept','copulations_mates2+ copulations', 'copulations_matesDifferent males', 'handrear_fatherTRUE')], link='logit')


# Plot without data:
proj.int <- emmip(grd_hr2, formula("~copulations_mates  + handrear_father"), type='response', plotit=F) %>%
  mutate(father_rear= case_when(handrear_father=='TRUE' ~ 'Hand-reared',
                                 handrear_father=='FALSE' ~ 'Wild-reared'))
ghr_mate <- ggplot() + 
  geom_pointrange(data=proj.int, aes(x=copulations_mates, y=yvar, ymin=LCL, ymax=UCL, colour=father_rear, shape = father_rear), position=position_dodge(width=0.1))  + 
  labs(y='Probability of clutch fertility', x='', colour='Father rearing', shape = 'Father rearing') + 
  scale_x_discrete(labels=fn_labels) +
  scale_colour_brewer(palette = 'Set2', direction = -1) # colour-blind friendly

ggsave(file.path(outdir, "figure_4_predict.pdf"), ghr_mate, height = 6, width = 8)


# Plot with data:
ghr_mate + 
  geom_jitter(data=fit_original$data %>% 
                mutate(father_rear= case_when(
                  handrear_father=='TRUE' ~ 'Hand-reared',
                  handrear_father=='FALSE' ~ 'Wild-reared')), 
              aes(x=copulations_mates, y=clutch_fert, colour=father_rear, shape = father_rear), alpha=0.5, width=0.1, height=0.05)
ggsave(file.path(outdir, "figure_4_predict_data.pdf"), height = 6, width = 8)

# Results table:
proj.int %>% rename(clutch.fertility = yvar) %>%
  mutate(father_rear= case_when(handrear_father=='TRUE' ~ 'Hand-reared',
                                 handrear_father=='FALSE' ~ 'Wild-reared')) %>%
  select(copulations_mates, father_rear, clutch.fertility, LCL, UCL) %>%
  format(., digits=3)
```

# Multiple copulation and kakapo density

```{r density_data}
# Read number of kakapo per island per year
nk <- read.csv(kakapo_demog_file, header = T) 

# Number of copulations/males per island per year per number of matings/mates
tc <- table(full_data$Island, full_data$year, full_data$copulations_mates)
dtc <- data.frame(tc) %>% rename(Island = Var1, year = Var2, copulations = Var3) %>% mutate(year = as.numeric(as.character(year)))

# Total clutches per island:
dtc_tot <- dtc %>% group_by(year, Island) %>% summarise(totclutch=sum(Freq))
dtc <- left_join(dtc, dtc_tot, by=c('year', 'Island'))

# Combine dataframes: number of kakapo per island and copulations proportions
nk2 <- left_join(dtc, nk %>% filter(ageClass=='Adult'), by=c('year', 'Island'), suffix = c('.cop', '.kak')) %>%
  mutate(prop.kak = Freq.cop / Freq.kak,
         prop.clutch = Freq.cop / totclutch) %>%
  filter(!is.na(Sex) & !is.na(Freq.kak) & Freq.kak > 0)
```

Combine repeated copulations with the same male and copulations with different males to compare single vs multiple copulations.

Only consider Whenua Hou from 1990 onwards.

```{r density_combine, fig.width=18, fig.height=12}

nk2 <- nk2 %>% mutate(copulations_comb = fct_collapse(copulations, 
                                              single = "1 copulation",
                                              multiple = c("2+ copulations", "Different males")))
# Totals:
nkg <- nk2 %>% 
  group_by(Island, year, Sex, copulations_comb) %>% 
  summarise(Freq.cop=sum(Freq.cop, na.rm=T), Freq.kak = mean(Freq.kak, na.rm = T), totclutch = mean(totclutch, na.rm = T)) %>%
  mutate(prop.clutch = Freq.cop / totclutch)

# Only Whenua Hou from 1990:
nkgsub <- nkg %>% filter(Island=='Whenua Hou' & year>=1990 & copulations_comb == 'multiple')
```

## Number of copulations

Show table number of copulations vs number of mates

```{r tab_num_cop_mate}
table(`Number of mates` = full_data$number_of_males, `Number of copulations` = full_data$number_of_copulations)
```


## Number of kakapo

Multiple copulation proportion vs number of males and females

```{r density_mult_num}
# Calculate correlation:
(cor <- nkgsub %>% ungroup(.) %>% dplyr::select(Sex, Freq.kak, prop.clutch) %>% group_by( Sex) %>% correlation())
cor$p
# Base plot:
col <- brewer.pal(name='Set1',n=3)[2]
gwh1990_comb <- ggplot(nkgsub %>% filter(!is.na(prop.clutch)), aes(x= Freq.kak, y = prop.clutch)) + 
  geom_point(size=2, colour=col) + 
  geom_smooth(aes(shape=NULL), fill=col, method=lm, alpha=0.2) + 
  labs(y = "Proportion of clutches with multiple copulations", x = 'Number of adult kakapo')  + 
  facet_wrap(~Sex, scales='free_x')

```

## Sex ratio

Multiple copulation proportion vs sex ratio:

```{r density_mult_sex_ratio_data}
# Calculate sex ratio
srg <- nkgsub %>% 
  pivot_wider(id_cols = c(Island, year, copulations_comb, Freq.cop, totclutch, prop.clutch), names_from = 'Sex', values_from="Freq.kak") %>%
  mutate(sex.ratio = Female/Male)

# Calculation correlation:
(corsex <- srg %>% ungroup(.) %>% dplyr::select(sex.ratio, prop.clutch)  %>% correlation(bayesian=F))
corsex$p
```

```{r density_mult_sex_ratio, fig.keep=1}
col <- brewer.pal(name='Set1',n=3)[1]
# Plot of multiple copulation frequency vs sex ratio
gswh1990comb <- ggplot(srg %>% filter(copulations_comb=='multiple'), aes(x= sex.ratio, y=prop.clutch)) + 
  geom_point(size=2, colour=col) + geom_smooth(aes(shape=NULL), method=lm, alpha=0.2, colour=col, fill=col) + 
  labs(y = "Prop. of clutches with multiple copulations", x = 'Female:male sex ratio') 

```

## Number and sex ratio combined

Combine number of male/female and sex ratio plots:

```{r combine_number_sex_ratio}
# Separate panels for females, males and sex ratio
# Multiple copulation frequency vs number of females
col <- brewer.pal(name='Set2',n=3)[1] # colour-blind friendly
gwh1990_female <- ggplot(nkgsub %>% filter(!is.na(prop.clutch) & Sex == 'Female'), aes(x= Freq.kak, y = prop.clutch)) + 
  geom_point(size=2, colour=col) + 
  geom_smooth(aes(shape=NULL), colour = col, fill=col, method=lm, alpha=0.2) + 
  labs(y = "Proportion of clutches", x = 'Number of females') +
  coord_cartesian(ylim = c(0,1)) + 
  expand_limits(x=40)

# Multiple copulation frequency vs number of males
col <- brewer.pal(name='Set2',n=3)[2]
gwh1990_male <- ggplot(nkgsub %>% filter(!is.na(prop.clutch) & Sex == 'Male'), aes(x= Freq.kak, y = prop.clutch)) + 
  geom_point(size=2, colour=col) + 
  geom_smooth(aes(shape=NULL), fill=col, method=lm, alpha=0.2, colour=col, fill=col) + 
  labs(y = "", x = 'Number of males')  +
  coord_cartesian(ylim = c(0,1)) + 
  expand_limits(x=c(15,30))

# Multiple copulation frequency vs sex ratio
col <- brewer.pal(name='Set2',n=3)[3]
gwh1990_sexratio <- ggplot(srg %>% filter(copulations_comb=='multiple'), aes(x= sex.ratio, y=prop.clutch)) + 
  geom_point(size=2, colour=col) + 
  geom_smooth(aes(shape=NULL), method=lm, alpha=0.2, colour=col, fill=col) + 
  labs(y = "", x = 'Female:male sex ratio') +
  coord_cartesian(ylim = c(0,1)) + 
  expand_limits(x=0.4) 

ggarrange(gwh1990_female,
          gwh1990_male,
          gwh1990_sexratio,
          common.legend = T , 
          labels = c("A", "B", "C"),
          label.x = 0.25,
          label.y = 0.98,
          ncol = 3,
          nrow = 1,
          widths=c(1,1,1)) 


# For publication:
ggsave(filename = file.path(outdir, 'figure_5_copulation_sex_ratio.pdf'), plot=last_plot(), device = 'pdf', width=10, height=6 )

```

## Change over time

Show the change in Whenua Hou population and sex ratio over time (note that these data include some years in which there was no breeding):

```{r time_sex_ratio}
# Total population
ggplot(srg %>% filter(!is.na(sex.ratio))  , aes(x = year, y = Female + Male)) +
         geom_point() + 
         geom_line() +
    scale_x_continuous(breaks = seq(min(srg$year), max(srg$year), 5), minor_breaks = c(min(srg$year): max(srg$year))) + 
  scale_y_continuous(breaks = seq(0,1,0.2)) +
  labs(y = 'Number of adult kakapo') 
  

# Male and female population
ggplot(srg %>% filter(!is.na(sex.ratio) & !is.nan(prop.clutch)) %>% pivot_longer(cols = Female:Male, names_to = 'variable') , aes(x = year, y = value, colour = variable)) +
         geom_point() + 
         geom_line() +
  facet_wrap(~variable, scales = 'fixed') + 
  guides(colour = 'none') + 
    scale_x_continuous(breaks = seq(min(srg$year), max(srg$year), 5), minor_breaks = c(min(srg$year): max(srg$year))) + 
  labs(y = 'Number of adult kakapo')
  
# Sex ratio
ggplot(srg %>% filter(!is.na(sex.ratio)& !is.nan(prop.clutch)) , aes(x = year, y = sex.ratio)) +
         geom_point() + 
         geom_line() +
    scale_x_continuous(breaks = seq(min(srg$year), max(srg$year), 5), minor_breaks = c(min(srg$year): max(srg$year))) + 
  labs(y = 'F:M adult sex ratio')

```
Change in multiple copulation rate over time:

```{r time_mult_copulation}
# Sex ratio
ggplot(srg %>% filter(!is.na(sex.ratio)& !is.nan(prop.clutch)) , aes(x = year, y = prop.clutch)) +
         geom_point() + 
         geom_line() +
  scale_x_continuous(breaks = seq(min(srg$year), max(srg$year), 5), minor_breaks = c(min(srg$year): max(srg$year))) + 
  scale_y_continuous(breaks = seq(0,1,0.2)) +
  labs(y = 'Proportion of multiple copulations')

```

# Session information

```{r session}
sessionInfo()
```
