Population density affects sexual selection in the red flour beetle

Analyses on body mass of focal individuals

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Last updated: 2022-07-24

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Knit directory: Density_and_sexual_selection_2022/

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Supplementary material reporting R code for the manuscript ‘Population density affects sexual selection in the red flour beetle’.

Load and prepare data

Before we started the analyses, we loaded all necessary packages and data.

#load packages
rm(list = ls())
library(ggeffects)
library(ggplot2)
library(gridExtra)
library(lme4)
library(lmerTest)
library(readr)
library(dplyr)
library(EnvStats)
library(cowplot)
library(gridGraphics)
library(car)
library(RColorBrewer)
library(boot)
library(data.table)
library(base)
library(tidyr)
library(ICC)

#load data
DB_data=read_delim("./data/DB_AllData_V04.CSV",";", escape_double = FALSE, trim_ws = TRUE)

#Set factors and level factors
DB_data$Week=as.factor(DB_data$Week)

DB_data$Date=as.factor(DB_data$Date)

DB_data$Sex=as.factor(DB_data$Sex)

DB_data$Gr_size=as.factor(DB_data$Gr_size)
DB_data$Gr_size <- factor(DB_data$Gr_size, levels=c("SG","LG"))

DB_data$Area=as.factor(DB_data$Area)

#Load Body mass data
DB_BM_female <- read_delim("./data/DB_mass_focals_female.CSV", 
                           ";", escape_double = FALSE, trim_ws = TRUE)

DB_BM_male <- read_delim("./data/DB_mass_focals_males.CSV", 
                         ";", escape_double = FALSE, trim_ws = TRUE)

DB_data_m=merge(DB_data,DB_BM_male,by.x = 'Well_ID',by.y = 'ID_male_focals')
DB_data_f=merge(DB_data,DB_BM_female,by.x = 'F1_ID',by.y = 'ID_female_focals')
DB_data=rbind(DB_data_m,DB_data_f)

###Exclude incomplete data
DB_data=DB_data[DB_data$excluded!=1,]


#Calculate total offspring number ####

DB_data$Total_N_MTP1=colSums(rbind(DB_data$N_MTP1_1,DB_data$N_MTP1_2,DB_data$N_MTP1_3,DB_data$N_MTP1_4,DB_data$N_MTP1_5,DB_data$N_MTP1_6), na.rm = T)
DB_data$Total_N_Rd=colSums(rbind(DB_data$N_RD_1,DB_data$N_RD_2,DB_data$N_RD_3,DB_data$N_RD_4,DB_data$N_RD_5,DB_data$N_RD_6), na.rm = T)/DB_data$N_comp

#Calculate proportional RS ####
#Percentage focal offspring
DB_data$m_prop_RS=NA
DB_data$m_prop_RS=(DB_data$Total_N_MTP1/(DB_data$Total_N_MTP1+DB_data$Total_N_Rd))*100
DB_data$m_prop_RS[DB_data$Sex=='F']=NA
DB_data$f_prop_RS=NA
DB_data$f_prop_RS=(DB_data$Total_N_MTP1/(DB_data$Total_N_MTP1+DB_data$Total_N_Rd))*100
DB_data$f_prop_RS[DB_data$Sex=='M']=NA

#Calculate proportion of successful matings ####
DB_data$Prop_MS=NA
DB_data$Prop_MS=DB_data$Matings_number/(DB_data$Attempts_number+DB_data$Matings_number)
DB_data$Prop_MS[DB_data$Prop_MS==0]=NA

#Calculate total encounters ####
DB_data$Total_Encounters=NA
DB_data$Total_Encounters=DB_data$Attempts_number+DB_data$Matings_number

# Treatment identifier for each density ####
n=1
DB_data$Treatment=NA
for(n in 1:length(DB_data$Sex)){if(DB_data$Gr_size[n]=='SG' && DB_data$Area[n]=='Large'){DB_data$Treatment[n]='D = 0.26'
}else if(DB_data$Gr_size[n]=='LG' && DB_data$Area[n]=='Large'){DB_data$Treatment[n]='D = 0.52'
}else if(DB_data$Gr_size[n]=='SG' && DB_data$Area[n]=='Small'){DB_data$Treatment[n]='D = 0.67'
}else if(DB_data$Gr_size[n]=='LG' && DB_data$Area[n]=='Small'){DB_data$Treatment[n]='D = 1.33'
}else{DB_data$Treatment[n]=NA}}

DB_data$Treatment=as.factor(DB_data$Treatment)

# Exclude Incubator 3 data #### -> poor performance 
DB_data_clean=DB_data[DB_data$Incu3!=1,]

# Calculate genetic MS ####
# Only clean data
DB_data_clean$gMS=NA 
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_1[i]>=1 & !is.na (DB_data_clean$N_MTP1_1[i])){
  DB_data_clean$gMS[i]=1
}else{DB_data_clean$gMS[i]=0}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_2[i]>=1 & !is.na (DB_data_clean$N_MTP1_2[i])){
  DB_data_clean$gMS[i]=DB_data_clean$gMS[i]+1
}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_3[i]>=1 & !is.na (DB_data_clean$N_MTP1_3[i])){
  DB_data_clean$gMS[i]=DB_data_clean$gMS[i]+1}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_4[i]>=1 & !is.na (DB_data_clean$N_MTP1_4[i])){
  DB_data_clean$gMS[i]=DB_data_clean$gMS[i]+1}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_5[i]>=1 & !is.na (DB_data_clean$N_MTP1_5[i])){
  DB_data_clean$gMS[i]=DB_data_clean$gMS[i]+1}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_6[i]>=1 & !is.na (DB_data_clean$N_MTP1_6[i])){
  DB_data_clean$gMS[i]=DB_data_clean$gMS[i]+1}else{}}

# All data
DB_data$gMS=NA 
for(i in 1:length(DB_data$Sex)) {if (DB_data$N_MTP1_1[i]>=1 & !is.na (DB_data$N_MTP1_1[i])){
  DB_data$gMS[i]=1
}else{DB_data$gMS[i]=0}}
for(i in 1:length(DB_data$Sex)) {if (DB_data$N_MTP1_2[i]>=1 & !is.na (DB_data$N_MTP1_2[i])){
  DB_data$gMS[i]=DB_data$gMS[i]+1
}else{}}
for(i in 1:length(DB_data$Sex)) {if (DB_data$N_MTP1_3[i]>=1 & !is.na (DB_data$N_MTP1_3[i])){
  DB_data$gMS[i]=DB_data$gMS[i]+1}else{}}
for(i in 1:length(DB_data$Sex)) {if (DB_data$N_MTP1_4[i]>=1 & !is.na (DB_data$N_MTP1_4[i])){
  DB_data$gMS[i]=DB_data$gMS[i]+1}else{}}
for(i in 1:length(DB_data$Sex)) {if (DB_data$N_MTP1_5[i]>=1 & !is.na (DB_data$N_MTP1_5[i])){
  DB_data$gMS[i]=DB_data$gMS[i]+1}else{}}
for(i in 1:length(DB_data$Sex)) {if (DB_data$N_MTP1_6[i]>=1 & !is.na (DB_data$N_MTP1_6[i])){
  DB_data$gMS[i]=DB_data$gMS[i]+1}else{}}

#Calculate Rd competition RS ####
DB_data_clean$m_RS_Rd_comp=NA
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_1[i]>=1 & !is.na (DB_data_clean$N_MTP1_1[i])){
  DB_data_clean$m_RS_Rd_comp[i]=DB_data_clean$N_RD_1[i]
}else{DB_data_clean$m_RS_Rd_comp[i]=0}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_2[i]>=1 & !is.na (DB_data_clean$N_MTP1_2[i])){
  DB_data_clean$m_RS_Rd_comp[i]=DB_data_clean$m_RS_Rd_comp[i]+DB_data_clean$N_RD_2[i]
}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_3[i]>=1 & !is.na (DB_data_clean$N_MTP1_3[i])){
  DB_data_clean$m_RS_Rd_comp[i]=DB_data_clean$m_RS_Rd_comp[i]+DB_data_clean$N_RD_3[i]
}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_4[i]>=1 & !is.na (DB_data_clean$N_MTP1_4[i])){
  DB_data_clean$m_RS_Rd_comp[i]=DB_data_clean$m_RS_Rd_comp[i]+DB_data_clean$N_RD_4[i]
}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_5[i]>=1 & !is.na (DB_data_clean$N_MTP1_5[i])){
  DB_data_clean$m_RS_Rd_comp[i]=DB_data_clean$m_RS_Rd_comp[i]+DB_data_clean$N_RD_5[i]
}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_6[i]>=1 & !is.na (DB_data_clean$N_MTP1_6[i])){
  DB_data_clean$m_RS_Rd_comp[i]=DB_data_clean$m_RS_Rd_comp[i]+DB_data_clean$N_RD_6[i]
}else{}}

# Check matings of males #### -> add copulations where offspring found but no copulation registered

for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_1[i]>=1 && DB_data_clean$Cop_Fe_1[i]==0 & !is.na (DB_data_clean$Cop_Fe_1[i])& !is.na (DB_data_clean$N_MTP1_1[i])){
  DB_data_clean$Cop_Fe_1[i]=1}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_2[i]>=1 && DB_data_clean$Cop_Fe_2[i]==0 & !is.na (DB_data_clean$Cop_Fe_2[i])& !is.na (DB_data_clean$N_MTP1_2[i])){
  DB_data_clean$Cop_Fe_2[i]=1}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_3[i]>=1 && DB_data_clean$Cop_Fe_3[i]==0 & !is.na (DB_data_clean$Cop_Fe_3[i])& !is.na (DB_data_clean$N_MTP1_3[i])){
  DB_data_clean$Cop_Fe_3[i]=1}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_4[i]>=1 && DB_data_clean$Cop_Fe_4[i]==0 & !is.na (DB_data_clean$Cop_Fe_4[i])& !is.na (DB_data_clean$N_MTP1_4[i])){
  DB_data_clean$Cop_Fe_4[i]=1}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_5[i]>=1 && DB_data_clean$Cop_Fe_5[i]==0 & !is.na (DB_data_clean$Cop_Fe_5[i])& !is.na (DB_data_clean$N_MTP1_5[i])){
  DB_data_clean$Cop_Fe_5[i]=1}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$N_MTP1_6[i]>=1 && DB_data_clean$Cop_Fe_6[i]==0 & !is.na (DB_data_clean$Cop_Fe_6[i])& !is.na (DB_data_clean$N_MTP1_6[i])){
  DB_data_clean$Cop_Fe_6[i]=1}else{}}

# Calculate Rd competition RS of all copulations with potential sperm competition with the  focal ####
DB_data_clean$m_RS_Rd_comp_full=NA
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$Cop_Fe_1[i]>=1 & !is.na (DB_data_clean$Cop_Fe_1[i])){
  DB_data_clean$m_RS_Rd_comp_full[i]=DB_data_clean$N_RD_1[i]
}else{DB_data_clean$m_RS_Rd_comp_full[i]=0}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$Cop_Fe_2[i]>=1 & !is.na (DB_data_clean$Cop_Fe_2[i])){
  DB_data_clean$m_RS_Rd_comp_full[i]=DB_data_clean$m_RS_Rd_comp_full[i]+DB_data_clean$N_RD_2[i]
}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$Cop_Fe_3[i]>=1 & !is.na (DB_data_clean$Cop_Fe_3[i])){
  DB_data_clean$m_RS_Rd_comp_full[i]=DB_data_clean$m_RS_Rd_comp_full[i]+DB_data_clean$N_RD_3[i]
}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$Cop_Fe_4[i]>=1 & !is.na (DB_data_clean$Cop_Fe_4[i])){
  DB_data_clean$m_RS_Rd_comp_full[i]=DB_data_clean$m_RS_Rd_comp_full[i]+DB_data_clean$N_RD_4[i]
}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$Cop_Fe_5[i]>=1 & !is.na (DB_data_clean$Cop_Fe_5[i])){
  DB_data_clean$m_RS_Rd_comp_full[i]=DB_data_clean$m_RS_Rd_comp_full[i]+DB_data_clean$N_RD_5[i]
}else{}}
for(i in 1:length(DB_data_clean$Sex)) {if (DB_data_clean$Cop_Fe_6[i]>=1 & !is.na (DB_data_clean$Cop_Fe_6[i])){
  DB_data_clean$m_RS_Rd_comp_full[i]=DB_data_clean$m_RS_Rd_comp_full[i]+DB_data_clean$N_RD_6[i]
}else{}}

# Calculate trait values ####
# Males ####
# Total number of matings (all data)
DB_data$m_TotMatings=NA
DB_data$m_TotMatings=DB_data$Matings_number
DB_data$m_TotMatings[DB_data$Sex=='F']=NA

# Avarage mating duration (all data)
DB_data$MatingDuration_av[DB_data$MatingDuration_av==0]=NA
DB_data$m_MatingDuration_av=NA
DB_data$m_MatingDuration_av=DB_data$MatingDuration_av
DB_data$m_MatingDuration_av[DB_data$Sex=='F']=NA
DB_data$MatingDuration_av[DB_data$MatingDuration_av==0]=NA

# Total number of mating attempts (all data)
DB_data$m_Attempts_number=NA
DB_data$m_Attempts_number=DB_data$Attempts_number
DB_data$m_Attempts_number[DB_data$Sex=='F']=NA

# Proportional mating success (all data)
DB_data$m_Prop_MS=NA
DB_data$m_Prop_MS=DB_data$Prop_MS
DB_data$m_Prop_MS[DB_data$Sex=='F']=NA

#Total encounters (all data)
DB_data$m_Total_Encounters=NA
DB_data$m_Total_Encounters=DB_data$Total_Encounters
DB_data$m_Total_Encounters[DB_data$Sex=='F']=NA

# Reproductive success
DB_data_clean$m_RS=NA
DB_data_clean$m_RS=DB_data_clean$Total_N_MTP1
DB_data_clean$m_RS[DB_data_clean$Sex=='F']=NA

# Mating success (number of different partners)
# Clean data
DB_data_clean$m_cMS=NA
DB_data_clean$m_cMS=DB_data_clean$MatingPartners_number
DB_data_clean$m_cMS[DB_data_clean$Sex=='F']=NA
for(i in 1:length(DB_data_clean$m_cMS)) {if (DB_data_clean$gMS[i]>DB_data_clean$m_cMS[i] & !is.na (DB_data_clean$m_cMS[i])){
  DB_data_clean$m_cMS[i]=DB_data_clean$gMS[i]}else{}}

# All data
DB_data$m_cMS=NA
DB_data$m_cMS=DB_data$MatingPartners_number
DB_data$m_cMS[DB_data$Sex=='F']=NA
for(i in 1:length(DB_data$m_cMS)) {if (DB_data$gMS[i]>DB_data$m_cMS[i] & !is.na (DB_data$m_cMS[i])){
  DB_data$m_cMS[i]=DB_data$gMS[i]}else{}}

# Insemination success
DB_data_clean$m_InSuc=NA
DB_data_clean$m_InSuc=DB_data_clean$gMS/DB_data_clean$m_cMS
for(i in 1:length(DB_data_clean$m_InSuc)) {if (DB_data_clean$m_cMS[i]==0 & !is.na (DB_data_clean$m_cMS[i])){
  DB_data_clean$m_InSuc[i]=NA}else{}}

# Fertilization success
DB_data_clean$m_feSuc=NA
DB_data_clean$m_feSuc=DB_data_clean$m_RS/(DB_data_clean$m_RS+DB_data_clean$m_RS_Rd_comp)
for(i in 1:length(DB_data_clean$m_feSuc)) {if (DB_data_clean$m_InSuc[i]==0 | is.na (DB_data_clean$m_InSuc[i])){
  DB_data_clean$m_feSuc[i]=NA}else{}}

# Fecundicty of partners
DB_data_clean$m_pFec=NA
DB_data_clean$m_pFec=(DB_data_clean$m_RS+DB_data_clean$m_RS_Rd_comp)/DB_data_clean$gMS
for(i in 1:length(DB_data_clean$m_pFec)) {if (DB_data_clean$gMS[i]==0){
  DB_data_clean$m_pFec[i]=NA}else{}}

# Paternity success
DB_data_clean$m_PS=NA
DB_data_clean$m_PS=DB_data_clean$m_RS/(DB_data_clean$m_RS+DB_data_clean$m_RS_Rd_comp_full)
for(i in 1:length(DB_data_clean$m_PS)) {if (DB_data_clean$m_RS[i]==0 & !is.na (DB_data_clean$m_RS[i])){
  DB_data_clean$m_PS[i]=NA}else{}}

# Fecundity of partners in all females the focal copulated with
DB_data_clean$m_pFec_compl=NA
DB_data_clean$m_pFec_compl=(DB_data_clean$m_RS+DB_data_clean$m_RS_Rd_comp_full)/DB_data_clean$m_cMS
for(i in 1:length(DB_data_clean$m_pFec)) {if (DB_data_clean$m_cMS[i]==0 & !is.na (DB_data_clean$m_cMS[i])){
  DB_data_clean$m_pFec[i]=NA}else{}}

# Females ####
# Total number of matings (all data)
DB_data$f_TotMatings=NA
DB_data$f_TotMatings=DB_data$Matings_number
DB_data$f_TotMatings[DB_data$Sex=='M']=NA

# Avarage mating duration (all data)
DB_data$f_MatingDuration_av=NA
DB_data$f_MatingDuration_av=DB_data$MatingDuration_av
DB_data$f_MatingDuration_av[DB_data$Sex=='M']=NA
DB_data$MatingDuration_av[DB_data$MatingDuration_av==0]=NA

# Total number of mating attempts (all data)
DB_data$f_Attempts_number=NA
DB_data$f_Attempts_number=DB_data$Attempts_number
DB_data$f_Attempts_number[DB_data$Sex=='M']=NA

# Proportional mating success (all data)
DB_data$f_Prop_MS=NA
DB_data$f_Prop_MS=DB_data$Prop_MS
DB_data_clean$f_Prop_MS[DB_data_clean$Sex=='M']=NA

#Total encounters (all data)
DB_data$f_Total_Encounters=NA
DB_data$f_Total_Encounters=DB_data$Total_Encounters
DB_data$f_Total_Encounters[DB_data$Sex=='M']=NA

# Reproductive success
DB_data_clean$f_RS=NA
DB_data_clean$f_RS=DB_data_clean$Total_N_MTP1
DB_data_clean$f_RS[DB_data_clean$Sex=='M']=NA

# Mating success (number of different partners)
# Clean data
DB_data_clean$f_cMS=NA
DB_data_clean$f_cMS=DB_data_clean$MatingPartners_number
DB_data_clean$f_cMS[DB_data_clean$Sex=='M']=NA
for(i in 1:length(DB_data_clean$f_cMS)) {if (DB_data_clean$gMS[i]>DB_data_clean$f_cMS[i] & !is.na (DB_data_clean$f_cMS[i])){
  DB_data_clean$f_cMS[i]=DB_data_clean$gMS[i]}else{}}

# All data
DB_data$f_cMS=NA
DB_data$f_cMS=DB_data$MatingPartners_number
DB_data$f_cMS[DB_data$Sex=='M']=NA
for(i in 1:length(DB_data$f_cMS)) {if (DB_data$gMS[i]>DB_data$f_cMS[i] & !is.na (DB_data$f_cMS[i])){
  DB_data$f_cMS[i]=DB_data$gMS[i]}else{}}

# Fecundity per mating partner
DB_data_clean$f_fec_pMate=NA
DB_data_clean$f_fec_pMate=DB_data_clean$f_RS/DB_data_clean$f_cMS
for(i in 1:length(DB_data_clean$f_fec_pMate)) {if (DB_data_clean$f_RS[i]==0 & !is.na (DB_data_clean$f_RS[i])){
  DB_data_clean$f_fec_pMate[i]=0}else{}}
for(i in 1:length(DB_data_clean$f_fec_pMate)) {if (DB_data_clean$f_cMS[i]==0 & !is.na (DB_data_clean$f_cMS[i])){
  DB_data_clean$f_fec_pMate[i]=NA}else{}}

# Relativize data per treatment and sex ####
# Small group + large Area
DB_data_clean_0.26=DB_data_clean[DB_data_clean$Treatment=='D = 0.26',]

DB_data_clean_0.26$rel_m_RS=NA
DB_data_clean_0.26$rel_m_prop_RS=NA
DB_data_clean_0.26$rel_m_cMS=NA
DB_data_clean_0.26$rel_m_InSuc=NA
DB_data_clean_0.26$rel_m_feSuc=NA
DB_data_clean_0.26$rel_m_pFec=NA
DB_data_clean_0.26$rel_m_PS=NA
DB_data_clean_0.26$rel_m_pFec_compl=NA

DB_data_clean_0.26$rel_f_RS=NA
DB_data_clean_0.26$rel_f_prop_RS=NA
DB_data_clean_0.26$rel_f_cMS=NA
DB_data_clean_0.26$rel_f_fec_pMate=NA

DB_data_clean_0.26$rel_m_RS=DB_data_clean_0.26$m_RS/mean(DB_data_clean_0.26$m_RS,na.rm=T)
DB_data_clean_0.26$rel_m_prop_RS=DB_data_clean_0.26$m_prop_RS/mean(DB_data_clean_0.26$m_prop_RS,na.rm=T)
DB_data_clean_0.26$rel_m_cMS=DB_data_clean_0.26$m_cMS/mean(DB_data_clean_0.26$m_cMS,na.rm=T)
DB_data_clean_0.26$rel_m_InSuc=DB_data_clean_0.26$m_InSuc/mean(DB_data_clean_0.26$m_InSuc,na.rm=T)
DB_data_clean_0.26$rel_m_feSuc=DB_data_clean_0.26$m_feSuc/mean(DB_data_clean_0.26$m_feSuc,na.rm=T)
DB_data_clean_0.26$rel_m_pFec=DB_data_clean_0.26$m_pFec/mean(DB_data_clean_0.26$m_pFec,na.rm=T)
DB_data_clean_0.26$rel_m_PS=DB_data_clean_0.26$m_PS/mean(DB_data_clean_0.26$m_PS,na.rm=T)
DB_data_clean_0.26$rel_m_pFec_compl=DB_data_clean_0.26$m_pFec_compl/mean(DB_data_clean_0.26$m_pFec_compl,na.rm=T)

DB_data_clean_0.26$rel_f_RS=DB_data_clean_0.26$f_RS/mean(DB_data_clean_0.26$f_RS,na.rm=T)
DB_data_clean_0.26$rel_f_prop_RS=DB_data_clean_0.26$f_prop_RS/mean(DB_data_clean_0.26$f_prop_RS,na.rm=T)
DB_data_clean_0.26$rel_f_cMS=DB_data_clean_0.26$f_cMS/mean(DB_data_clean_0.26$f_cMS,na.rm=T)
DB_data_clean_0.26$rel_f_fec_pMate=DB_data_clean_0.26$f_fec_pMate/mean(DB_data_clean_0.26$f_fec_pMate,na.rm=T)

# Large group + large Area
DB_data_clean_0.52=DB_data_clean[DB_data_clean$Treatment=='D = 0.52',]
#Relativize data

DB_data_clean_0.52$rel_m_RS=NA
DB_data_clean_0.52$rel_m_prop_RS=NA
DB_data_clean_0.52$rel_m_cMS=NA
DB_data_clean_0.52$rel_m_InSuc=NA
DB_data_clean_0.52$rel_m_feSuc=NA
DB_data_clean_0.52$rel_m_pFec=NA
DB_data_clean_0.52$rel_m_PS=NA
DB_data_clean_0.52$rel_m_pFec_compl=NA

DB_data_clean_0.52$rel_f_RS=NA
DB_data_clean_0.52$rel_f_prop_RS=NA
DB_data_clean_0.52$rel_f_cMS=NA
DB_data_clean_0.52$rel_f_fec_pMate=NA

DB_data_clean_0.52$rel_m_RS=DB_data_clean_0.52$m_RS/mean(DB_data_clean_0.52$m_RS,na.rm=T)
DB_data_clean_0.52$rel_m_prop_RS=DB_data_clean_0.52$m_prop_RS/mean(DB_data_clean_0.52$m_prop_RS,na.rm=T)
DB_data_clean_0.52$rel_m_cMS=DB_data_clean_0.52$m_cMS/mean(DB_data_clean_0.52$m_cMS,na.rm=T)
DB_data_clean_0.52$rel_m_InSuc=DB_data_clean_0.52$m_InSuc/mean(DB_data_clean_0.52$m_InSuc,na.rm=T)
DB_data_clean_0.52$rel_m_feSuc=DB_data_clean_0.52$m_feSuc/mean(DB_data_clean_0.52$m_feSuc,na.rm=T)
DB_data_clean_0.52$rel_m_pFec=DB_data_clean_0.52$m_pFec/mean(DB_data_clean_0.52$m_pFec,na.rm=T)
DB_data_clean_0.52$rel_m_PS=DB_data_clean_0.52$m_PS/mean(DB_data_clean_0.52$m_PS,na.rm=T)
DB_data_clean_0.52$rel_m_pFec_compl=DB_data_clean_0.52$m_pFec_compl/mean(DB_data_clean_0.52$m_pFec_compl,na.rm=T)

DB_data_clean_0.52$rel_f_RS=DB_data_clean_0.52$f_RS/mean(DB_data_clean_0.52$f_RS,na.rm=T)
DB_data_clean_0.52$rel_f_prop_RS=DB_data_clean_0.52$f_prop_RS/mean(DB_data_clean_0.52$f_prop_RS,na.rm=T)
DB_data_clean_0.52$rel_f_cMS=DB_data_clean_0.52$f_cMS/mean(DB_data_clean_0.52$f_cMS,na.rm=T)
DB_data_clean_0.52$rel_f_fec_pMate=DB_data_clean_0.52$f_fec_pMate/mean(DB_data_clean_0.52$f_fec_pMate,na.rm=T)

# Small group + small Area
DB_data_clean_0.67=DB_data_clean[DB_data_clean$Treatment=='D = 0.67',]
#Relativize data
DB_data_clean_0.67$rel_m_RS=NA
DB_data_clean_0.67$rel_m_prop_RS=NA
DB_data_clean_0.67$rel_m_cMS=NA
DB_data_clean_0.67$rel_m_InSuc=NA
DB_data_clean_0.67$rel_m_feSuc=NA
DB_data_clean_0.67$rel_m_pFec=NA
DB_data_clean_0.67$rel_m_PS=NA
DB_data_clean_0.67$rel_m_pFec_compl=NA

DB_data_clean_0.67$rel_f_RS=NA
DB_data_clean_0.67$rel_f_prop_RS=NA
DB_data_clean_0.67$rel_f_cMS=NA
DB_data_clean_0.67$rel_f_fec_pMate=NA

DB_data_clean_0.67$rel_m_RS=DB_data_clean_0.67$m_RS/mean(DB_data_clean_0.67$m_RS,na.rm=T)
DB_data_clean_0.67$rel_m_prop_RS=DB_data_clean_0.67$m_prop_RS/mean(DB_data_clean_0.67$m_prop_RS,na.rm=T)
DB_data_clean_0.67$rel_m_cMS=DB_data_clean_0.67$m_cMS/mean(DB_data_clean_0.67$m_cMS,na.rm=T)
DB_data_clean_0.67$rel_m_InSuc=DB_data_clean_0.67$m_InSuc/mean(DB_data_clean_0.67$m_InSuc,na.rm=T)
DB_data_clean_0.67$rel_m_feSuc=DB_data_clean_0.67$m_feSuc/mean(DB_data_clean_0.67$m_feSuc,na.rm=T)
DB_data_clean_0.67$rel_m_pFec=DB_data_clean_0.67$m_pFec/mean(DB_data_clean_0.67$m_pFec,na.rm=T)
DB_data_clean_0.67$rel_m_PS=DB_data_clean_0.67$m_PS/mean(DB_data_clean_0.67$m_PS,na.rm=T)
DB_data_clean_0.67$rel_m_pFec_compl=DB_data_clean_0.67$m_pFec_compl/mean(DB_data_clean_0.67$m_pFec_compl,na.rm=T)

DB_data_clean_0.67$rel_f_RS=DB_data_clean_0.67$f_RS/mean(DB_data_clean_0.67$f_RS,na.rm=T)
DB_data_clean_0.67$rel_f_prop_RS=DB_data_clean_0.67$f_prop_RS/mean(DB_data_clean_0.67$f_prop_RS,na.rm=T)
DB_data_clean_0.67$rel_f_cMS=DB_data_clean_0.67$f_cMS/mean(DB_data_clean_0.67$f_cMS,na.rm=T)
DB_data_clean_0.67$rel_f_fec_pMate=DB_data_clean_0.67$f_fec_pMate/mean(DB_data_clean_0.67$f_fec_pMate,na.rm=T)

# Large group + small Area
DB_data_clean_1.33=DB_data_clean[DB_data_clean$Treatment=='D = 1.33',]
#Relativize data

DB_data_clean_1.33$rel_m_RS=NA
DB_data_clean_1.33$rel_m_prop_RS=NA
DB_data_clean_1.33$rel_m_cMS=NA
DB_data_clean_1.33$rel_m_InSuc=NA
DB_data_clean_1.33$rel_m_feSuc=NA
DB_data_clean_1.33$rel_m_pFec=NA
DB_data_clean_1.33$rel_m_PS=NA
DB_data_clean_1.33$rel_m_pFec_compl=NA

DB_data_clean_1.33$rel_f_RS=NA
DB_data_clean_1.33$rel_f_prop_RS=NA
DB_data_clean_1.33$rel_f_cMS=NA
DB_data_clean_1.33$rel_f_fec_pMate=NA

DB_data_clean_1.33$rel_m_RS=DB_data_clean_1.33$m_RS/mean(DB_data_clean_1.33$m_RS,na.rm=T)
DB_data_clean_1.33$rel_m_prop_RS=DB_data_clean_1.33$m_prop_RS/mean(DB_data_clean_1.33$m_prop_RS,na.rm=T)
DB_data_clean_1.33$rel_m_cMS=DB_data_clean_1.33$m_cMS/mean(DB_data_clean_1.33$m_cMS,na.rm=T)
DB_data_clean_1.33$rel_m_InSuc=DB_data_clean_1.33$m_InSuc/mean(DB_data_clean_1.33$m_InSuc,na.rm=T)
DB_data_clean_1.33$rel_m_feSuc=DB_data_clean_1.33$m_feSuc/mean(DB_data_clean_1.33$m_feSuc,na.rm=T)
DB_data_clean_1.33$rel_m_pFec=DB_data_clean_1.33$m_pFec/mean(DB_data_clean_1.33$m_pFec,na.rm=T)
DB_data_clean_1.33$rel_m_PS=DB_data_clean_1.33$m_PS/mean(DB_data_clean_1.33$m_PS,na.rm=T)
DB_data_clean_1.33$rel_m_pFec_compl=DB_data_clean_1.33$m_pFec_compl/mean(DB_data_clean_1.33$m_pFec_compl,na.rm=T)

DB_data_clean_1.33$rel_f_RS=DB_data_clean_1.33$f_RS/mean(DB_data_clean_1.33$f_RS,na.rm=T)
DB_data_clean_1.33$rel_f_prop_RS=DB_data_clean_1.33$f_prop_RS/mean(DB_data_clean_1.33$f_prop_RS,na.rm=T)
DB_data_clean_1.33$rel_f_cMS=DB_data_clean_1.33$f_cMS/mean(DB_data_clean_1.33$f_cMS,na.rm=T)
DB_data_clean_1.33$rel_f_fec_pMate=DB_data_clean_1.33$f_fec_pMate/mean(DB_data_clean_1.33$f_fec_pMate,na.rm=T)

# Set colors for figures
colpal=brewer.pal(4, 'Dark2')
colpal2=brewer.pal(3, 'Set1')
colpal3=brewer.pal(4, 'Paired')
slava_ukrajini=(c('#0057B8','#FFD700'))
colorESEB=c('#01519c','#ffdf33')
colorESEB2=c('#1DA1F2','#ffec69')

# Merge data according to treatment #### -> Reduce treatments to area and population size
#Area
DB_data_clean_Large_area=rbind(DB_data_clean_0.26,DB_data_clean_0.52)
DB_data_clean_Small_area=rbind(DB_data_clean_0.67,DB_data_clean_1.33)

#Population size
DB_data_clean_Small_pop=rbind(DB_data_clean_0.26,DB_data_clean_0.67)
DB_data_clean_Large_pop=rbind(DB_data_clean_0.52,DB_data_clean_1.33)

# Merge data according to treatment full data set #### -> Reduce treatments to area and population size
DB_data_0.26=DB_data[DB_data$Treatment=='D = 0.26',]
DB_data_0.52=DB_data[DB_data$Treatment=='D = 0.52',]
DB_data_0.67=DB_data[DB_data$Treatment=='D = 0.67',]
DB_data_1.33=DB_data[DB_data$Treatment=='D = 1.33',]

#Area
DB_data_Large_area_full=rbind(DB_data_0.26,DB_data_0.52)
DB_data_Small_area_full=rbind(DB_data_0.67,DB_data_1.33)

#Population size
DB_data_Small_pop_full=rbind(DB_data_0.26,DB_data_0.67)
DB_data_Large_pop_full=rbind(DB_data_0.52,DB_data_1.33)

Repeatability

Repeatability of body mass measures.
Intra-class correlation coefficient:
- Males

ICCest(DB_data$Body_mass_mg_focal[DB_data$Sex=='M'], DB_data$Mass_reproducibility_mg_focal[DB_data$Sex=='M'])

NAs removed from rows:
 1 2 3 4 5 6 7 8 9 10 13 16 17 19 20 22 23 24 25 26 27 28 30 31 32 33 34 35 37 38 39 40 41 43 44 45 46 49 50 51 52 55 56 58 59 60 61 63 64 66 67 68 69 70 71 72 73 74 77 78 79 81 82 85 86 87 93 94 96 99 101 105 106 107 108 110 114 116 118 119 121 122 123 124 125 126 127 128 130 131 133 134 135 136 138 139 140 141 142 144 145 146 147 148 149 151 152 153 157 158 159 160 161 

$ICC
[1] 0.9742984

$LowerCI
[1] 0.9286547

$UpperCI
[1] 0.9888462

$N
[1] 35

$k
[1] 1.363971

$varw
[1] 0.0009358974

$vara
[1] 0.03547804

• Females

ICCest(DB_data$Body_mass_mg_focal[DB_data$Sex=='F'], DB_data$Mass_reproducibility_mg_focal[DB_data$Sex=='F'])

NAs removed from rows:
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19 20 21 24 25 26 27 28 29 30 31 32 34 35 36 37 38 39 41 45 47 48 49 51 53 54 61 63 66 75 76 77 78 79 80 82 83 84 86 87 91 92 93 94 95 96 97 98 99 100 101 103 104 105 107 108 109 110 111 112 113 114 115 116 117 118 119 121 123 124 125 126 127 128 129 130 132 133 134 137 138 141 142 143 144 145 147 149 150 151 152 153 

$ICC
[1] 0.9813802

$LowerCI
[1] 0.9479268

$UpperCI
[1] 0.9920222

$N
[1] 33

$k
[1] 1.384511

$varw
[1] 0.0007602564

$vara
[1] 0.0400702

Effect of body mass on reproductive success

Correlation between body mass and reproductive success (selection gradient).

# Effect of body mass on reproductive success - Selection gradient ####
#Male
DB_data_clean_M=DB_data_clean[DB_data_clean$Sex=='M',]
#Standardize body mass
DB_data_clean_M$stder_BM_focal=NA
DB_data_clean_M$stder_BM_focal=DB_data_clean_M$Body_mass_mg_focal-mean(DB_data_clean_M$Body_mass_mg_focal)
DB_data_clean_M$stder_BM_focal=DB_data_clean_M$stder_BM_focal/sd(DB_data_clean_M$Body_mass_mg_focal)

#Model treatment
treat1M=glm(m_RS~Gr_size*Area,data=DB_data_clean_M,family = quasipoisson)
DB_data_clean_M$res_RS=NA
DB_data_clean_M$res_RS=residuals(treat1M)

# Males
p3=ggplot(DB_data_clean_M, aes(x=stder_BM_focal, y=res_RS)) + 
  geom_point(size = 2)+xlab('Standardized male body mass')+ylab('Res. offspring number')+labs(tag = "A")+
  geom_smooth(method=lm,color="black")+ theme(axis.text=element_text(size=13),axis.title=element_text(size=14)) +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),panel.background = element_blank(), axis.line = element_line(colour = "black"))+
  xlim(-3,2.3)+ylim(-13,23)

#Females
DB_data_clean_F=DB_data_clean[DB_data_clean$Sex=='F',]
#Standardize body mass
DB_data_clean_F$stder_BM_focal=NA
DB_data_clean_F$stder_BM_focal=DB_data_clean_F$Body_mass_mg_focal-mean(DB_data_clean_F$Body_mass_mg_focal)
DB_data_clean_F$stder_BM_focal=DB_data_clean_F$stder_BM_focal/sd(DB_data_clean_F$Body_mass_mg_focal)

#Model treatment
treat1F=glm(f_RS~Gr_size*Area,data=DB_data_clean_F,family = quasipoisson)
DB_data_clean_F$res_RS=NA
DB_data_clean_F$res_RS=residuals(treat1F)

p4=ggplot(DB_data_clean_F, aes(x=stder_BM_focal, y=res_RS)) + 
geom_point(size = 2)+xlab('Standardized female body mass')+ylab('Res. offspring number')+labs(tag = "B")+
  geom_smooth(method=lm,color="black")+ theme(axis.text=element_text(size=13),axis.title=element_text(size=14)) +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),panel.background = element_blank(), axis.line = element_line(colour = "black"))+
  xlim(-3,2.3)+ylim(-13,23)

grid.arrange(p3,p4, nrow = 1,ncol=2)

Figure 1: Scatter plots of relationship between standardized body mass and residual offspring number for males (A) and females (B).

Statistical tests
Selection gradient for males

mod2=glm(res_RS~stder_BM_focal,data=DB_data_clean_M,family = gaussian)
summary(mod2)

Call:
glm(formula = res_RS ~ stder_BM_focal, family = gaussian, data = DB_data_clean_M)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-11.394   -7.822    1.084    5.700   21.803  

Coefficients:
               Estimate Std. Error t value Pr(>|t|)  
(Intercept)     -1.4484     0.7408  -1.955   0.0533 .
stder_BM_focal   0.4628     0.7444   0.622   0.5355  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for gaussian family taken to be 57.07626)

    Null deviance: 5843.8  on 103  degrees of freedom
Residual deviance: 5821.8  on 102  degrees of freedom
AIC: 719.74

Number of Fisher Scoring iterations: 2

Selection gradient for females

mod3=glm(res_RS~stder_BM_focal,data=DB_data_clean_F,family = gaussian)
summary(mod3)

Call:
glm(formula = res_RS ~ stder_BM_focal, family = gaussian, data = DB_data_clean_F)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-12.723   -6.899    1.355    6.902   12.972  

Coefficients:
               Estimate Std. Error t value Pr(>|t|)   
(Intercept)     -1.6909     0.7503  -2.254  0.02647 * 
stder_BM_focal   2.2394     0.7541   2.970  0.00376 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for gaussian family taken to be 55.73024)

    Null deviance: 5897.3  on 98  degrees of freedom
Residual deviance: 5405.8  on 97  degrees of freedom
AIC: 682.96

Number of Fisher Scoring iterations: 2

Testing for a sex difference (sex x treatment interaction).

DB_data_clean_C=rbind(DB_data_clean_F,DB_data_clean_M)
mod4=glm(res_RS~stder_BM_focal*Sex,data=DB_data_clean_C,family = gaussian)
summary(mod4)

Call:
glm(formula = res_RS ~ stder_BM_focal * Sex, family = gaussian, 
    data = DB_data_clean_C)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-12.723   -7.614    1.355    6.488   21.803  

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)   
(Intercept)          -1.6909     0.7549  -2.240  0.02621 * 
stder_BM_focal        2.2394     0.7588   2.951  0.00354 **
SexM                  0.2425     1.0547   0.230  0.81839   
stder_BM_focal:SexM  -1.7766     1.0599  -1.676  0.09528 . 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for gaussian family taken to be 56.42016)

    Null deviance: 11744  on 202  degrees of freedom
Residual deviance: 11228  on 199  degrees of freedom
AIC: 1400.7

Number of Fisher Scoring iterations: 2

#Anova(mod4,type=3) #If the interactions are not significant, type II gives a more powerful test.
Anova(mod4,type=2)

Analysis of Deviance Table (Type II tests)

Response: res_RS
                   LR Chisq Df Pr(>Chisq)  
stder_BM_focal       6.2924  1    0.01213 *
Sex                  0.0529  1    0.81815  
stder_BM_focal:Sex   2.8095  1    0.09371 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Effect of body mass on reproductive behaviour

Correlation between body mass and reproductive behaviour:
- Number of matings
- Number of mating partners (mating success)
- Proportion of successful matings

Number of matings

Correlation between body mass and the number of matings.

# Effect of body mass on mating number ####
# Males
DB_data_M=DB_data[DB_data$Sex=='M',]
#Standardize body mass
DB_data_M$stder_BM_focal=NA
DB_data_M$stder_BM_focal=DB_data_M$Body_mass_mg_focal-mean(DB_data_M$Body_mass_mg_focal)
DB_data_M$stder_BM_focal=DB_data_M$stder_BM_focal/sd(DB_data_M$Body_mass_mg_focal)

#Model treatment
treat1M_MR=glm(m_TotMatings~Gr_size*Area,data=DB_data_M,family = quasipoisson)
DB_data_M$res_MR=NA
DB_data_M$res_MR=residuals(treat1M_MR)

p5=ggplot(DB_data_M, aes(x=stder_BM_focal, y=res_MR)) + 
  geom_point(size = 2)+xlab('Standardized male body mass')+ylab('Res. number of matings')+labs(tag = "A")+
  geom_smooth(method=lm,color="black")+ theme(axis.text=element_text(size=13),axis.title=element_text(size=14)) +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),panel.background = element_blank(), axis.line = element_line(colour = "black"))+
  xlim(-3.1,2.4)+ylim(-2.7,4.2)

#Females
DB_data_F=DB_data[DB_data$Sex=='F',]
#Standardize body mass
DB_data_F$stder_BM_focal=NA
DB_data_F$stder_BM_focal=DB_data_F$Body_mass_mg_focal-mean(DB_data_F$Body_mass_mg_focal)
DB_data_F$stder_BM_focal=DB_data_F$stder_BM_focal/sd(DB_data_F$Body_mass_mg_focal)

#Model treatment
treat1F_MR=glm(f_TotMatings~Gr_size*Area,data=DB_data_F,family = quasipoisson)
DB_data_F$res_MR=NA
DB_data_F$res_MR=residuals(treat1F_MR)

p6=ggplot(DB_data_F, aes(x=stder_BM_focal, y=res_MR)) + 
  geom_point(size = 2)+xlab('Standardized female body mass')+ylab('Res. number of matings')+labs(tag = "B")+
  geom_smooth(method=lm,color="black")+ theme(axis.text=element_text(size=13),axis.title=element_text(size=14)) +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),panel.background = element_blank(), axis.line = element_line(colour = "black"))+
  xlim(-3.1,2.4)+ylim(-2.7,4.2)

grid.arrange(p5,p6, nrow = 1,ncol=2)

Figure 2: Scatter plots of relationship between standardized body mass and residual number of matings for males (A) and females (B).

Statistical tests
Males

mod5=glm(res_MR~stder_BM_focal,data=DB_data_M,family = gaussian)
summary(mod5)

Call:
glm(formula = res_MR ~ stder_BM_focal, family = gaussian, data = DB_data_M)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.3383  -0.6797   0.0964   0.7216   3.3582  

Coefficients:
                Estimate Std. Error t value Pr(>|t|)
(Intercept)    -0.141687   0.089096  -1.590    0.114
stder_BM_focal -0.002149   0.089374  -0.024    0.981

(Dispersion parameter for gaussian family taken to be 1.278027)

    Null deviance: 203.21  on 160  degrees of freedom
Residual deviance: 203.21  on 159  degrees of freedom
AIC: 500.38

Number of Fisher Scoring iterations: 2

Females

mod6=glm(res_MR~stder_BM_focal,data=DB_data_F,family = gaussian)
summary(mod6)

Call:
glm(formula = res_MR ~ stder_BM_focal, family = gaussian, data = DB_data_F)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.3550  -1.0704  -0.0556   0.7454   4.3127  

Coefficients:
               Estimate Std. Error t value Pr(>|t|)   
(Intercept)     -0.2062     0.1035  -1.993   0.0481 * 
stder_BM_focal   0.3178     0.1038   3.061   0.0026 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for gaussian family taken to be 1.659158)

    Null deviance: 269.40  on 154  degrees of freedom
Residual deviance: 253.85  on 153  degrees of freedom
AIC: 522.34

Number of Fisher Scoring iterations: 2

Testing for a sex difference (sex x treatment interaction).

#Sex difference?
DB_data_clean_C=rbind(DB_data_F,DB_data_M)
mod4=glm(res_MR~stder_BM_focal*Sex,data=DB_data_clean_C,family = gaussian)
summary(mod4)

Call:
glm(formula = res_MR ~ stder_BM_focal * Sex, family = gaussian, 
    data = DB_data_clean_C)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.3550  -0.7234   0.0215   0.7283   4.3127  

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)   
(Intercept)         -0.20618    0.09722  -2.121  0.03472 * 
stder_BM_focal       0.31775    0.09753   3.258  0.00125 **
SexM                 0.06450    0.13620   0.474  0.63615   
stder_BM_focal:SexM -0.31990    0.13663  -2.341  0.01984 * 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for gaussian family taken to be 1.464928)

    Null deviance: 472.94  on 315  degrees of freedom
Residual deviance: 457.06  on 312  degrees of freedom
AIC: 1023.4

Number of Fisher Scoring iterations: 2

Anova(mod4,type=3) #If the interactions are not significant, type II gives a more powerful test.

Analysis of Deviance Table (Type III tests)

Response: res_MR
                   LR Chisq Df Pr(>Chisq)   
stder_BM_focal      10.6142  1   0.001122 **
Sex                  0.2242  1   0.635821   
stder_BM_focal:Sex   5.4819  1   0.019214 * 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#Anova(mod4,type=2)

Number of mating partners

Correlation between body mass and the number of mating partners.

# Effect of body mass on mating success ####
# Males
#Model treatment
treat1M_MS=glm(m_cMS~Gr_size*Area,data=DB_data_M,family = quasipoisson)
DB_data_M$res_MS=NA
DB_data_M$res_MS=residuals(treat1M_MS)

p7=ggplot(DB_data_M, aes(x=stder_BM_focal, y=res_MS)) + 
  geom_point(size = 2)+xlab('Standardized male body mass')+ylab('Res. number of mating partners')+labs(tag = "A")+
  geom_smooth(method=lm,color="black")+ theme(axis.text=element_text(size=13),axis.title=element_text(size=14)) +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),panel.background = element_blank(), axis.line = element_line(colour = "black"))+
  xlim(-3.1,2.4)+ylim(-2,2.5)

#Females
#Model treatment
treat1F_MS=glm(f_cMS~Gr_size*Area,data=DB_data_F,family = quasipoisson)
DB_data_F$res_MS=NA
DB_data_F$res_MS=residuals(treat1F_MS)

p8=ggplot(DB_data_F, aes(x=stder_BM_focal, y=res_MS)) + 
  geom_point(size = 2)+xlab('Standardized female body mass')+ylab('Res. number of mating partners')+labs(tag = "B")+
  geom_smooth(method=lm,color="black")+ theme(axis.text=element_text(size=13),axis.title=element_text(size=14)) +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),panel.background = element_blank(), axis.line = element_line(colour = "black"))+
  xlim(-3.1,2.4)+ylim(-2,2.5)

grid.arrange(p7,p8, nrow = 1,ncol=2)

Figure 3: Scatter plots of relationship between standardized body mass and residual number of mating partners for males (A) and females (B).

Statistical tests
Males

mod7=glm(res_MS~stder_BM_focal,data=DB_data_M,family = gaussian)
summary(mod7)

Call:
glm(formula = res_MS ~ stder_BM_focal, family = gaussian, data = DB_data_M)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.8428  -0.4506   0.2713   0.3866   2.2196  

Coefficients:
               Estimate Std. Error t value Pr(>|t|)
(Intercept)    -0.08519    0.06108  -1.395    0.165
stder_BM_focal -0.05431    0.06127  -0.886    0.377

(Dispersion parameter for gaussian family taken to be 0.6006104)

    Null deviance: 95.969  on 160  degrees of freedom
Residual deviance: 95.497  on 159  degrees of freedom
AIC: 378.81

Number of Fisher Scoring iterations: 2

Females

mod7=glm(res_MS~stder_BM_focal,data=DB_data_F,family = gaussian)
summary(mod7)

Call:
glm(formula = res_MS ~ stder_BM_focal, family = gaussian, data = DB_data_F)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.0623  -0.5118   0.1379   0.6399   2.1628  

Coefficients:
               Estimate Std. Error t value Pr(>|t|)   
(Intercept)    -0.12575    0.07105   -1.77  0.07872 . 
stder_BM_focal  0.23592    0.07128    3.31  0.00116 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for gaussian family taken to be 0.7823699)

    Null deviance: 128.27  on 154  degrees of freedom
Residual deviance: 119.70  on 153  degrees of freedom
AIC: 405.82

Number of Fisher Scoring iterations: 2

Testing for a sex difference (sex x treatment interaction).

#Sex difference?
DB_data_clean_C=rbind(DB_data_F,DB_data_M)
mod4=glm(res_MS~stder_BM_focal*Sex,data=DB_data_clean_C,family = gaussian)
summary(mod4)

Call:
glm(formula = res_MS ~ stder_BM_focal * Sex, family = gaussian, 
    data = DB_data_clean_C)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.0623  -0.4644   0.2046   0.4252   2.2196  

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)         -0.12575    0.06671  -1.885 0.060342 .  
stder_BM_focal       0.23592    0.06692   3.525 0.000487 ***
SexM                 0.04056    0.09346   0.434 0.664594    
stder_BM_focal:SexM -0.29023    0.09375  -3.096 0.002142 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for gaussian family taken to be 0.6897425)

    Null deviance: 224.37  on 315  degrees of freedom
Residual deviance: 215.20  on 312  degrees of freedom
AIC: 785.37

Number of Fisher Scoring iterations: 2

#Anova(mod4,type=3) #If the interactions are not significant, type II gives a more powerful test.
Anova(mod4,type=2)

Analysis of Deviance Table (Type II tests)

Response: res_MS
                   LR Chisq Df Pr(>Chisq)   
stder_BM_focal       3.5281  1   0.060336 . 
Sex                  0.1883  1   0.664294   
stder_BM_focal:Sex   9.5830  1   0.001964 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Proportion of successful matings

Correlation between body mass and the proportion of successful matings.

# Effect of BM on proportion successful matings ####
# Males
#Model treatment
treat1M_Prop_MS=glm(Prop_MS~Gr_size*Area,data=DB_data_M,family = quasibinomial,na.action=na.exclude)
DB_data_M$res_Prop_MS=NA
DB_data_M$res_Prop_MS=residuals(treat1M_Prop_MS)

p9=ggplot(DB_data_M, aes(x=stder_BM_focal, y=res_Prop_MS)) + 
  geom_point(size = 2)+xlab('Standardized male body mass')+ylab('Res. prop. of successful matings')+labs(tag = "A")+
  geom_smooth(method=lm,color="black")+ theme(axis.text=element_text(size=13),axis.title=element_text(size=14)) +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),panel.background = element_blank(), axis.line = element_line(colour = "black"))+
  xlim(-3.1,2.4)+ylim(-0.8,1.6)

#Females
#Model treatment
treat1F_Prop_MS=glm(Prop_MS~Gr_size*Area,data=DB_data_F,family = quasibinomial,na.action=na.exclude)
DB_data_F$res_Prop_MS=NA
DB_data_F$res_Prop_MS=residuals(treat1F_Prop_MS)

p10=ggplot(DB_data_F, aes(x=stder_BM_focal, y=res_Prop_MS)) + 
  geom_point(size = 2)+xlab('Standardized female body mass')+ylab('Res. prop. of successful matings')+labs(tag = "B")+
  geom_smooth(method=lm,color="black")+ theme(axis.text=element_text(size=13),axis.title=element_text(size=14)) +
  theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(),panel.background = element_blank(), axis.line = element_line(colour = "black"))+
  xlim(-3.1,2.4)+ylim(-0.8,1.6)

grid.arrange(p9,p10, nrow = 1,ncol=2)

Figure 4: Scatter plots of relationship between standardized body mass and residual proportion of successful matings for males (A) and females (B).

Statistical tests
Males

mod7=glm(res_Prop_MS~stder_BM_focal,data=DB_data_M,family = gaussian)
summary(mod7)

Call:
glm(formula = res_Prop_MS ~ stder_BM_focal, family = gaussian, 
    data = DB_data_M)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-0.68186  -0.27630  -0.04741   0.22588   1.43708  

Coefficients:
               Estimate Std. Error t value Pr(>|t|)
(Intercept)    -0.01261    0.03208  -0.393    0.695
stder_BM_focal -0.03442    0.03238  -1.063    0.290

(Dispersion parameter for gaussian family taken to be 0.1521604)

    Null deviance: 22.387  on 147  degrees of freedom
Residual deviance: 22.215  on 146  degrees of freedom
  (13 observations deleted due to missingness)
AIC: 145.33

Number of Fisher Scoring iterations: 2

Females

mod7=glm(res_Prop_MS~stder_BM_focal,data=DB_data_F,family = gaussian)
summary(mod7)

Call:
glm(formula = res_Prop_MS ~ stder_BM_focal, family = gaussian, 
    data = DB_data_F)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-0.73785  -0.35714  -0.07916   0.23794   1.49479  

Coefficients:
                Estimate Std. Error t value Pr(>|t|)
(Intercept)    -0.003811   0.041903  -0.091    0.928
stder_BM_focal -0.031200   0.044334  -0.704    0.483

(Dispersion parameter for gaussian family taken to be 0.2254128)

    Null deviance: 28.964  on 129  degrees of freedom
Residual deviance: 28.853  on 128  degrees of freedom
  (25 observations deleted due to missingness)
AIC: 179.23

Number of Fisher Scoring iterations: 2

Testing for a sex difference (sex x treatment interaction).

#Sex difference?
DB_data_clean_C=rbind(DB_data_F,DB_data_M)
mod4=glm(res_Prop_MS~stder_BM_focal*Sex,data=DB_data_clean_C,family = gaussian)
summary(mod4)

Call:
glm(formula = res_Prop_MS ~ stder_BM_focal * Sex, family = gaussian, 
    data = DB_data_clean_C)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.7379  -0.3174  -0.0581   0.2367   1.4948  

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)
(Intercept)         -0.003811   0.038103  -0.100    0.920
stder_BM_focal      -0.031200   0.040313  -0.774    0.440
SexM                -0.008798   0.052083  -0.169    0.866
stder_BM_focal:SexM -0.003218   0.053939  -0.060    0.952

(Dispersion parameter for gaussian family taken to be 0.1863805)

    Null deviance: 51.355  on 277  degrees of freedom
Residual deviance: 51.068  on 274  degrees of freedom
  (38 observations deleted due to missingness)
AIC: 327.87

Number of Fisher Scoring iterations: 2

#Anova(mod4,type=3) #If the interactions are not significant, type II gives a more powerful test.
Anova(mod4,type=2)

Analysis of Deviance Table (Type II tests)

Response: res_Prop_MS
                   LR Chisq Df Pr(>Chisq)
stder_BM_focal      1.51780  1     0.2180
Sex                 0.03029  1     0.8618
stder_BM_focal:Sex  0.00356  1     0.9524

Density treatment and body mass

Here we tested the interaction of the density treatment and body mass. ## Reproductive success Males

#Males
#Model treatment
ModT1=glm(m_RS~stder_BM_focal*Gr_size*Area,data=DB_data_clean_M,family = quasipoisson)
summary(ModT1)

Call:
glm(formula = m_RS ~ stder_BM_focal * Gr_size * Area, family = quasipoisson, 
    data = DB_data_clean_M)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-12.9828   -9.2345   -0.1822    3.9908   19.7971  

Coefficients:
                                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)                         3.9365122  0.2752815  14.300   <2e-16 ***
stder_BM_focal                     -0.0201361  0.2598560  -0.077    0.938    
Gr_sizeLG                          -0.1123254  0.3462061  -0.324    0.746    
AreaSmall                           0.3657216  0.3223165   1.135    0.259    
stder_BM_focal:Gr_sizeLG            0.2210450  0.3246145   0.681    0.498    
stder_BM_focal:AreaSmall           -0.1194431  0.3108891  -0.384    0.702    
Gr_sizeLG:AreaSmall                -0.3239441  0.4473036  -0.724    0.471    
stder_BM_focal:Gr_sizeLG:AreaSmall  0.0007873  0.4426930   0.002    0.999    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for quasipoisson family taken to be 53.71862)

    Null deviance: 6253.5  on 103  degrees of freedom
Residual deviance: 5961.8  on  96  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 6

#Anova(ModT1,type=3) #If the interactions are not significant, type II gives a more powerful test.
Anova(ModT1,type=2)

Analysis of Deviance Table (Type II tests)

Response: m_RS
                            LR Chisq Df Pr(>Chisq)
stder_BM_focal               0.03629  1     0.8489
Gr_size                      2.49466  1     0.1142
Area                         1.18691  1     0.2760
stder_BM_focal:Gr_size       1.01929  1     0.3127
stder_BM_focal:Area          0.28702  1     0.5921
Gr_size:Area                 0.54260  1     0.4614
stder_BM_focal:Gr_size:Area  0.00000  1     0.9986

Females

#Females
#Model treatment
ModT2=glm(f_RS~stder_BM_focal*Gr_size*Area,data=DB_data_clean_F,family = quasipoisson)
summary(ModT2)

Call:
glm(formula = f_RS ~ stder_BM_focal * Gr_size * Area, family = quasipoisson, 
    data = DB_data_clean_F)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-12.919   -8.886   -1.206    5.387   11.193  

Coefficients:
                                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)                         4.051255   0.164331  24.653   <2e-16 ***
stder_BM_focal                      0.088055   0.181067   0.486    0.628    
Gr_sizeLG                          -0.350207   0.308144  -1.137    0.259    
AreaSmall                          -0.323725   0.285456  -1.134    0.260    
stder_BM_focal:Gr_sizeLG            0.255679   0.309906   0.825    0.412    
stder_BM_focal:AreaSmall            0.193118   0.283134   0.682    0.497    
Gr_sizeLG:AreaSmall                 0.481967   0.440290   1.095    0.277    
stder_BM_focal:Gr_sizeLG:AreaSmall -0.001952   0.441307  -0.004    0.996    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for quasipoisson family taken to be 48.60039)

    Null deviance: 6268.7  on 98  degrees of freedom
Residual deviance: 5669.3  on 91  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 6

#Anova(ModT2,type=3) #If the interactions are not significant, type II gives a more powerful test.
Anova(ModT2,type=2)

Analysis of Deviance Table (Type II tests)

Response: f_RS
                            LR Chisq Df Pr(>Chisq)   
stder_BM_focal                7.9202  1   0.004889 **
Gr_size                       0.0416  1   0.838310   
Area                          0.0658  1   0.797609   
stder_BM_focal:Gr_size        1.3502  1   0.245243   
stder_BM_focal:Area           0.7930  1   0.373205   
Gr_size:Area                  1.3528  1   0.244782   
stder_BM_focal:Gr_size:Area   0.0000  1   0.996471   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Number of matings

Males

#Males
#Model treatment
ModT1=glm(m_TotMatings~stder_BM_focal*Gr_size*Area,data=DB_data_M,family = quasipoisson)
summary(ModT1)

Call:
glm(formula = m_TotMatings ~ stder_BM_focal * Gr_size * Area, 
    family = quasipoisson, data = DB_data_M)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.4755  -0.8581  -0.1191   0.5468   3.2217  

Coefficients:
                                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)                         1.07096    0.12184   8.790 2.89e-15 ***
stder_BM_focal                     -0.02196    0.12344  -0.178   0.8591    
Gr_sizeLG                          -0.30669    0.16776  -1.828   0.0695 .  
AreaSmall                           0.03641    0.15782   0.231   0.8178    
stder_BM_focal:Gr_sizeLG           -0.12044    0.16544  -0.728   0.4677    
stder_BM_focal:AreaSmall            0.16486    0.16890   0.976   0.3306    
Gr_sizeLG:AreaSmall                -0.02603    0.23728  -0.110   0.9128    
stder_BM_focal:Gr_sizeLG:AreaSmall -0.03781    0.23897  -0.158   0.8745    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for quasipoisson family taken to be 1.28703)

    Null deviance: 219.60  on 160  degrees of freedom
Residual deviance: 202.24  on 153  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 5

#Anova(ModT1,type=3) #If the interactions are not significant, type II gives a more powerful test.
Anova(ModT1,type=2)

Analysis of Deviance Table (Type II tests)

Response: m_TotMatings
                            LR Chisq Df Pr(>Chisq)   
stder_BM_focal                0.0276  1   0.867939   
Gr_size                       6.9318  1   0.008468 **
Area                          0.0087  1   0.925775   
stder_BM_focal:Gr_size        1.3436  1   0.246400   
stder_BM_focal:Area           1.5029  1   0.220230   
Gr_size:Area                  0.0094  1   0.922607   
stder_BM_focal:Gr_size:Area   0.0250  1   0.874258   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Females

#Females
#Model treatment
ModT2=glm(f_TotMatings~stder_BM_focal*Gr_size*Area,data=DB_data_F,family = quasipoisson)
summary(ModT2)

Call:
glm(formula = f_TotMatings ~ stder_BM_focal * Gr_size * Area, 
    family = quasipoisson, data = DB_data_F)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.3335  -1.2043  -0.2771   0.4441   3.9971  

Coefficients:
                                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)                         1.15378    0.10889  10.596   <2e-16 ***
stder_BM_focal                      0.18056    0.11456   1.576   0.1171    
Gr_sizeLG                          -0.53957    0.21028  -2.566   0.0113 *  
AreaSmall                          -0.23530    0.18107  -1.299   0.1958    
stder_BM_focal:Gr_sizeLG           -0.08486    0.21438  -0.396   0.6928    
stder_BM_focal:AreaSmall           -0.09025    0.17444  -0.517   0.6057    
Gr_sizeLG:AreaSmall                 0.19895    0.30459   0.653   0.5147    
stder_BM_focal:Gr_sizeLG:AreaSmall  0.36257    0.30775   1.178   0.2406    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for quasipoisson family taken to be 1.819396)

    Null deviance: 298.54  on 154  degrees of freedom
Residual deviance: 261.57  on 147  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 5

#Anova(ModT2,type=3) #If the interactions are not significant, type II gives a more powerful test.
Anova(ModT2,type=2)

Analysis of Deviance Table (Type II tests)

Response: f_TotMatings
                            LR Chisq Df Pr(>Chisq)   
stder_BM_focal                6.0743  1   0.013716 * 
Gr_size                       9.1006  1   0.002555 **
Area                          1.0495  1   0.305613   
stder_BM_focal:Gr_size        0.3787  1   0.538321   
stder_BM_focal:Area           0.0405  1   0.840530   
Gr_size:Area                  0.8158  1   0.366419   
stder_BM_focal:Gr_size:Area   1.3995  1   0.236807   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Number of mating partners

Males

#Males
#Model treatment
ModT1=glm(m_cMS~stder_BM_focal*Gr_size*Area,data=DB_data_M,family = quasipoisson)
summary(ModT1)

Call:
glm(formula = m_cMS ~ stder_BM_focal * Gr_size * Area, family = quasipoisson, 
    data = DB_data_M)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.9702  -0.5412   0.1364   0.2913   2.2159  

Coefficients:
                                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)                         0.514699   0.102225   5.035 1.33e-06 ***
stder_BM_focal                      0.026405   0.104501   0.253    0.801    
Gr_sizeLG                           0.031385   0.131187   0.239    0.811    
AreaSmall                          -0.028294   0.134223  -0.211    0.833    
stder_BM_focal:Gr_sizeLG           -0.180778   0.130773  -1.382    0.169    
stder_BM_focal:AreaSmall           -0.009218   0.143795  -0.064    0.949    
Gr_sizeLG:AreaSmall                 0.017297   0.185207   0.093    0.926    
stder_BM_focal:Gr_sizeLG:AreaSmall  0.093090   0.187605   0.496    0.620    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for quasipoisson family taken to be 0.5272771)

    Null deviance: 97.278  on 160  degrees of freedom
Residual deviance: 94.769  on 153  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 5

#Anova(ModT1,type=3) #If the interactions are not significant, type II gives a more powerful test.
Anova(ModT1,type=2)

Analysis of Deviance Table (Type II tests)

Response: m_cMS
                            LR Chisq Df Pr(>Chisq)
stder_BM_focal               1.75424  1     0.1853
Gr_size                      0.41253  1     0.5207
Area                         0.05590  1     0.8131
stder_BM_focal:Gr_size       2.07280  1     0.1499
stder_BM_focal:Area          0.24321  1     0.6219
Gr_size:Area                 0.00100  1     0.9748
stder_BM_focal:Gr_size:Area  0.24579  1     0.6201

Females

#Females
#Model treatment
ModT2=glm(f_cMS~stder_BM_focal*Gr_size*Area,data=DB_data_F,family = quasipoisson)
summary(ModT2)

Call:
glm(formula = f_cMS ~ stder_BM_focal * Gr_size * Area, family = quasipoisson, 
    data = DB_data_F)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-1.97428  -0.63095  -0.02418   0.50377   2.12530  

Coefficients:
                                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)                         0.603441   0.087773   6.875 1.65e-10 ***
stder_BM_focal                      0.128619   0.093958   1.369    0.173    
Gr_sizeLG                          -0.222851   0.152270  -1.464    0.145    
AreaSmall                          -0.238617   0.146523  -1.629    0.106    
stder_BM_focal:Gr_sizeLG           -0.022745   0.156456  -0.145    0.885    
stder_BM_focal:AreaSmall            0.007264   0.142895   0.051    0.960    
Gr_sizeLG:AreaSmall                 0.273617   0.221386   1.236    0.218    
stder_BM_focal:Gr_sizeLG:AreaSmall  0.190087   0.222670   0.854    0.395    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for quasipoisson family taken to be 0.6879626)

    Null deviance: 133.68  on 154  degrees of freedom
Residual deviance: 122.81  on 147  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 5

#Anova(ModT2,type=3) #If the interactions are not significant, type II gives a more powerful test.
Anova(ModT2,type=2)

Analysis of Deviance Table (Type II tests)

Response: f_cMS
                            LR Chisq Df Pr(>Chisq)   
stder_BM_focal                9.5920  1   0.001954 **
Gr_size                       0.6508  1   0.419842   
Area                          0.8286  1   0.362677   
stder_BM_focal:Gr_size        0.4145  1   0.519688   
stder_BM_focal:Area           0.6226  1   0.430078   
Gr_size:Area                  1.9817  1   0.159216   
stder_BM_focal:Gr_size:Area   0.7299  1   0.392910   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Proportion of successful matings

Males

#Males
#Model treatment
ModT1=glm(Prop_MS~stder_BM_focal*Gr_size*Area,data=DB_data_M,family = quasibinomial)
summary(ModT1)

Call:
glm(formula = Prop_MS ~ stder_BM_focal * Gr_size * Area, family = quasibinomial, 
    data = DB_data_M)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-0.74502  -0.28399  -0.04377   0.21477   1.44401  

Coefficients:
                                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)                         -0.7988     0.1573  -5.078  1.2e-06 ***
stder_BM_focal                      -0.2806     0.1794  -1.564    0.120    
Gr_sizeLG                            0.1350     0.2045   0.660    0.510    
AreaSmall                            0.1939     0.2020   0.960    0.339    
stder_BM_focal:Gr_sizeLG             0.2332     0.2154   1.083    0.281    
stder_BM_focal:AreaSmall             0.2863     0.2289   1.251    0.213    
Gr_sizeLG:AreaSmall                 -0.2348     0.2838  -0.827    0.409    
stder_BM_focal:Gr_sizeLG:AreaSmall  -0.2946     0.2940  -1.002    0.318    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for quasibinomial family taken to be 0.1493034)

    Null deviance: 22.477  on 147  degrees of freedom
Residual deviance: 21.992  on 140  degrees of freedom
  (13 observations deleted due to missingness)
AIC: NA

Number of Fisher Scoring iterations: 4

#Anova(ModT1,type=3) #If the interactions are not significant, type II gives a more powerful test.
Anova(ModT1,type=2)

Analysis of Deviance Table (Type II tests)

Response: Prop_MS
                            LR Chisq Df Pr(>Chisq)
stder_BM_focal               1.09858  1     0.2946
Gr_size                      0.00190  1     0.9653
Area                         0.15658  1     0.6923
stder_BM_focal:Gr_size       0.27316  1     0.6012
stder_BM_focal:Area          0.57881  1     0.4468
Gr_size:Area                 0.55361  1     0.4568
stder_BM_focal:Gr_size:Area  1.00959  1     0.3150

Females

#Females
#Model treatment
ModT2=glm(Prop_MS~stder_BM_focal*Gr_size*Area,data=DB_data_F,family = quasibinomial)
summary(ModT2)

Call:
glm(formula = Prop_MS ~ stder_BM_focal * Gr_size * Area, family = quasibinomial, 
    data = DB_data_F)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-0.74862  -0.35523  -0.06568   0.24476   1.49450  

Coefficients:
                                   Estimate Std. Error t value Pr(>|t|)  
(Intercept)                        -0.32710    0.13682  -2.391   0.0183 *
stder_BM_focal                     -0.07715    0.15674  -0.492   0.6235  
Gr_sizeLG                          -0.11339    0.23708  -0.478   0.6333  
AreaSmall                          -0.39009    0.22154  -1.761   0.0808 .
stder_BM_focal:Gr_sizeLG           -0.33245    0.26922  -1.235   0.2193  
stder_BM_focal:AreaSmall            0.12255    0.22951   0.534   0.5943  
Gr_sizeLG:AreaSmall                 0.38651    0.34511   1.120   0.2649  
stder_BM_focal:Gr_sizeLG:AreaSmall  0.38963    0.36727   1.061   0.2908  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for quasibinomial family taken to be 0.2073228)

    Null deviance: 29.610  on 129  degrees of freedom
Residual deviance: 28.089  on 122  degrees of freedom
  (25 observations deleted due to missingness)
AIC: NA

Number of Fisher Scoring iterations: 3

#Anova(ModT2,type=3) #If the interactions are not significant, type II gives a more powerful test.
Anova(ModT2,type=2)

Analysis of Deviance Table (Type II tests)

Response: Prop_MS
                            LR Chisq Df Pr(>Chisq)
stder_BM_focal               0.43199  1     0.5110
Gr_size                      0.13451  1     0.7138
Area                         1.51521  1     0.2183
stder_BM_focal:Gr_size       0.46389  1     0.4958
stder_BM_focal:Area          2.42000  1     0.1198
Gr_size:Area                 1.49477  1     0.2215
stder_BM_focal:Gr_size:Area  1.13236  1     0.2873

Selection coefficients

Finally, we used bootstrapping to estimate treatment specific selection coeficients on body mass.

# Selection coefficients ####
#All 
#Males
#Bootstrap
selDif_BW_males = function(dataFrame, indexVector) { 
  #Calculate relative fitness
  rel_fit_males=dataFrame[indexVector, match("m_RS",names(dataFrame))]/mean(dataFrame[indexVector, match("m_RS",names(dataFrame))],na.rm=T)
  #Calculate selection differential
  s = cov(dataFrame[indexVector, match("stder_BM_focal",names(dataFrame))],rel_fit_males,use="complete.obs",method = "pearson")
  return(s)
}

boot_BW_males = boot(DB_data_clean_M, selDif_BW_males, R = 10000)


#Females
selDif_BW_females = function(dataFrame, indexVector) { 
  #Calculate relative fitness
  rel_fit_females=dataFrame[indexVector, match("f_RS",names(dataFrame))]/mean(dataFrame[indexVector, match("f_RS",names(dataFrame))],na.rm=T)
  #Calculate selection differential
  s = cov(dataFrame[indexVector, match("stder_BM_focal",names(dataFrame))],rel_fit_females,use="complete.obs",method = "pearson")
  return(s)
}

boot_BW_females = boot(DB_data_clean_F, selDif_BW_females, R = 10000)


# Selection coefficients for treatments
#Males
#Group size
#Small group
boot_BW_males_group_size_small = boot(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',], selDif_BW_males, R = 10000)


#Large group
boot_BW_males_group_size_large = boot(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',], selDif_BW_males, R = 10000)


#Area
#Large Area
boot_BW_males_area_large = boot(DB_data_clean_M[DB_data_clean_M$Area=='Large',], selDif_BW_males, R = 10000)


#Small Area
boot_BW_males_area_small = boot(DB_data_clean_M[DB_data_clean_M$Area=='Small',], selDif_BW_males, R = 10000)


#Females
#Group size
#Small group
boot_BW_females_group_size_small = boot(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',], selDif_BW_females, R = 10000)


#Large group
boot_BW_females_group_size_large = boot(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',], selDif_BW_females, R = 10000)


#Area
#Large Area
boot_BW_females_area_large = boot(DB_data_clean_F[DB_data_clean_F$Area=='Large',], selDif_BW_females, R = 10000)


#Small Area
boot_BW_females_area_small = boot(DB_data_clean_F[DB_data_clean_F$Area=='Small',], selDif_BW_females, R = 10000)

#Data table ####
boot_data_BW_males <- as.data.frame(cbind("Male", "Mass", "All", mean(boot_BW_males$t,na.rm=T), quantile(boot_BW_males$t,.025, names = FALSE,na.rm=T), quantile(boot_BW_males$t,.975, names = FALSE,na.rm=T)))
boot_data_BW_females <- as.data.frame(cbind("Female", "Mass", "All", mean(boot_BW_females$t,na.rm=T), quantile(boot_BW_females$t,.025, names = FALSE,na.rm=T), quantile(boot_BW_females$t,.975, names = FALSE,na.rm=T)))

boot_data_BW_males_group_size_small <- as.data.frame(cbind("Male", "Mass", "Small group", mean(boot_BW_males_group_size_small$t,na.rm=T), quantile(boot_BW_males_group_size_small$t,.025, names = FALSE,na.rm=T), quantile(boot_BW_males_group_size_small$t,.975, names = FALSE,na.rm=T)))
boot_data_BW_females_group_size_small <- as.data.frame(cbind("Female", "Mass", "Small group", mean(boot_BW_females_group_size_small$t,na.rm=T), quantile(boot_BW_females_group_size_small$t,.025, names = FALSE,na.rm=T), quantile(boot_BW_females_group_size_small$t,.975, names = FALSE,na.rm=T)))
boot_data_BW_males_group_size_large <- as.data.frame(cbind("Male", "Mass", "large group", mean(boot_BW_males_group_size_large$t,na.rm=T), quantile(boot_BW_males_group_size_large$t,.025, names = FALSE,na.rm=T), quantile(boot_BW_males_group_size_large$t,.975, names = FALSE,na.rm=T)))
boot_data_BW_females_group_size_large <- as.data.frame(cbind("Female", "Mass", "large group", mean(boot_BW_females_group_size_large$t,na.rm=T), quantile(boot_BW_females_group_size_large$t,.025, names = FALSE,na.rm=T), quantile(boot_BW_females_group_size_large$t,.975, names = FALSE,na.rm=T)))
boot_data_BW_males_area_small <- as.data.frame(cbind("Male", "Mass", "Small area", mean(boot_BW_males_area_small$t,na.rm=T), quantile(boot_BW_males_area_small$t,.025, names = FALSE,na.rm=T), quantile(boot_BW_males_area_small$t,.975, names = FALSE,na.rm=T)))
boot_data_BW_females_area_small <- as.data.frame(cbind("Female", "Mass", "Small area", mean(boot_BW_females_area_small$t,na.rm=T), quantile(boot_BW_females_area_small$t,.025, names = FALSE,na.rm=T), quantile(boot_BW_females_area_small$t,.975, names = FALSE,na.rm=T)))
boot_data_BW_males_area_large <- as.data.frame(cbind("Male", "Mass", "large area", mean(boot_BW_males_area_large$t,na.rm=T), quantile(boot_BW_males_area_large$t,.025, names = FALSE,na.rm=T), quantile(boot_BW_males_area_large$t,.975, names = FALSE,na.rm=T)))
boot_data_BW_females_area_large <- as.data.frame(cbind("Female", "Mass", "large area", mean(boot_BW_females_area_large$t,na.rm=T), quantile(boot_BW_females_area_large$t,.025, names = FALSE,na.rm=T), quantile(boot_BW_females_area_large$t,.975, names = FALSE,na.rm=T)))

SelDifBoot_Table <- as.table(as.matrix(rbind(boot_data_BW_males,boot_data_BW_females,boot_data_BW_males_group_size_small,boot_data_BW_females_group_size_small,
                                             boot_data_BW_males_group_size_large,boot_data_BW_females_group_size_large,
                                             boot_data_BW_males_area_small,boot_data_BW_females_area_small,
                                             boot_data_BW_males_area_large,boot_data_BW_females_area_large)))

is.table(SelDifBoot_Table)

colnames(SelDifBoot_Table)[1] <- "Sex"
colnames(SelDifBoot_Table)[2] <- "Trait"
colnames(SelDifBoot_Table)[3] <- "Treatment"
colnames(SelDifBoot_Table)[4] <- "Coefficient"
colnames(SelDifBoot_Table)[5] <- "l95_CI"
colnames(SelDifBoot_Table)[6] <- "u95_CI"
SelDifBoot_Table=as.data.frame.matrix(SelDifBoot_Table)
SelDifBoot_Table$Sex <- as.factor(as.character(SelDifBoot_Table$Sex))
SelDifBoot_Table$Trait <- as.factor(as.character(SelDifBoot_Table$Trait))
SelDifBoot_Table$Treatment <- as.factor(as.character(SelDifBoot_Table$Treatment))
SelDifBoot_Table$Coefficient <- as.numeric(as.character(SelDifBoot_Table$Coefficient))
SelDifBoot_Table$l95_CI <- as.numeric(as.character(SelDifBoot_Table$l95_CI))
SelDifBoot_Table$u95_CI <- as.numeric(as.character(SelDifBoot_Table$u95_CI))

SelDifBoot_Table_round=cbind(SelDifBoot_Table[,c(1,2,3)],round(SelDifBoot_Table[,c(4,5,6)],digit=3))

Figure of section coefficients on body mass for different density treatments.

#Figures ####
SelDifBoot_Table$Treatment <- factor(SelDifBoot_Table$Treatment, levels=c("All",'Small group','large group','large area','Small area'))
SelDifBoot_Table$Sex <- factor(SelDifBoot_Table$Sex, levels=c("Female",'Male'))

BarPlot_2<- ggplot(SelDifBoot_Table[3:6,], aes(x=Sex, y=Coefficient, fill=Treatment)) + 
  scale_y_continuous(limits = c(-.27, .75), expand = c(0 ,0)) + 
  geom_hline(yintercept=0, linetype="solid", color = "black", size=1) +
  geom_bar(stat="identity", color="black", position=position_dodge(), alpha=0.8) +
  geom_errorbar(aes(ymin=l95_CI, ymax=u95_CI), width=.3,size=1, position=position_dodge(.9)) +
  ylab(expression(paste("Standardized selection differential (",~italic("s'"),")"))) +xlab('Sex') +ggtitle('Group size')+labs(tag = "A")+
  scale_x_discrete(breaks=waiver(),labels = c("Female","Male"))+ 
  theme(panel.border = element_blank(),
        plot.margin = margin(0.1,2,0.1,0.2,"cm"),
        plot.title = element_text(hjust = 0.5),
        panel.background = element_blank(),
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        plot.tag.position=c(0.01,0.98),
        legend.position = c(1.05, 0.8),
        legend.text = element_text(colour="black", size=10),
        axis.line.x = element_line(colour = "black", size = 1),
        axis.line.y = element_line(colour = "black", size = 1),
        axis.text.x = element_text(face="plain", color="black", size=16, angle=0),
        axis.text.y = element_text(face="plain", color="black", size=16, angle=0),
        axis.title.x = element_text(size=16,face="plain", margin = margin(r=0,10,0,0)),
        axis.title.y = element_text(size=16,face="plain", margin = margin(r=10,0,0,0)),
        axis.ticks = element_line(size = 1),
        axis.ticks.length = unit(.3, "cm"))+
  scale_fill_manual(values=c(slava_ukrajini[1],slava_ukrajini[2]),name = "", labels = c("Small group",'Large group'))

BarPlot_3<- ggplot(SelDifBoot_Table[c(9,10,7,8),], aes(x=Sex, y=Coefficient, fill=Treatment)) + 
  scale_y_continuous(limits = c(-.27, .75), breaks = seq(-.3,.7,.15), expand = c(0 ,0)) + 
  geom_hline(yintercept=0, linetype="solid", color = "black", size=1) +
  geom_bar(stat="identity", color="black", position=position_dodge(), alpha=0.8) +
  geom_errorbar(aes(ymin=l95_CI, ymax=u95_CI), width=.3,size=1, position=position_dodge(.9)) +
  ylab('') +xlab('Sex') +ggtitle('Area')+labs(tag = "B")+
  scale_x_discrete(breaks=waiver(),labels = c("Female","Male"))+ 
  theme(panel.border = element_blank(),
        plot.margin = margin(0.1,2,0.1,0.2,"cm"),
        plot.title = element_text(hjust = 0.5),
        panel.background = element_blank(),
        panel.grid.major = element_blank(),
        panel.grid.minor = element_blank(),
        plot.tag.position=c(0.01,0.98),
        legend.position = c(1.05, 0.8),
        legend.text = element_text(colour="black", size=10),
        axis.line.x = element_line(colour = "black", size = 1),
        axis.line.y = element_line(colour = "black", size = 1),
        axis.text.x = element_text(face="plain", color="black", size=16, angle=0),
        axis.text.y = element_text(face="plain", color="black", size=16, angle=0),
        axis.title.x = element_text(size=16,face="plain", margin = margin(r=0,10,0,0)),
        axis.title.y = element_text(size=16,face="plain", margin = margin(r=10,0,0,0)),
        axis.ticks = element_line(size = 1),
        axis.ticks.length = unit(.3, "cm"))+
  scale_fill_manual(values=c(slava_ukrajini[1],slava_ukrajini[2]),name = "", labels = c("Large area",'Small area'))

plot1<-grid.arrange(BarPlot_2,BarPlot_3, nrow = 1,ncol=2)

Figure 5: Effect of density on sex-specific standardized selection differential (s’) for population size (A) and area treatment (B).

Permutation tests for differences in density dependent standardized selection differentials.

# Permutation test ####
# Sex bias ####
#population size ####
#Small
Sex_diff_Small_male_pop=c(boot_BW_males_group_size_small$t)-c(boot_BW_females_group_size_small$t)

t_Sex_diff_Small_male_pop=mean(Sex_diff_Small_male_pop,na.rm=TRUE)
t_Sex_diff_Small_male_pop_lower=quantile(Sex_diff_Small_male_pop,.025,na.rm=TRUE)
t_Sex_diff_Small_male_pop_upper=quantile(Sex_diff_Small_male_pop,.975,na.rm=TRUE)

#Permutation test to calculate p value
comb_data_RS=c(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS),
            DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS))
comb_data_BM=c(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$stder_BM_focal,
               DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$stder_BM_focal)

diff.observed_Small_pop = cov(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$stder_BM_focal,DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS),use="complete.obs",method = "pearson") - cov(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$stder_BM_focal,DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS),use="complete.obs",method = "pearson") 
diff.observed_Small_pop

[1] -0.2106987

number_of_permutations = 100000
diff.random_Small_pop = NULL
for (i in 1 : number_of_permutations) {
  
  # Sample from the combined dataset
  a.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS))), TRUE)
  b.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS))), TRUE)
  c.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS))), TRUE)
  d.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS))), TRUE)
  
  # Null (permuated) difference
  diff.random_Small_pop[i] = cov(b.random,a.random,use="complete.obs",method = "pearson") - cov(d.random,c.random,use="complete.obs",method = "pearson")
}

# P-value is the fraction of how many times the permuted difference is
# equal or more extreme than the observed difference

p_Sex_diff_Small_pop = sum((diff.random_Small_pop) >= as.numeric((diff.observed_Small_pop)))/   number_of_permutations
p_Sex_diff_Small_pop

[1] 0.85978

#population size ####
#Large
Sex_diff_large_male_pop=c(boot_BW_males_group_size_large$t)-c(boot_BW_females_group_size_large$t)

t_Sex_diff_large_male_pop=mean(Sex_diff_large_male_pop,na.rm=TRUE)
t_Sex_diff_large_male_pop_lower=quantile(Sex_diff_large_male_pop,.025,na.rm=TRUE)
t_Sex_diff_large_male_pop_upper=quantile(Sex_diff_large_male_pop,.975,na.rm=TRUE)

#Permutation test to calculate p value
comb_data_RS=c(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS),
               DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS/mean(DB_data_clean_M[DB_data_clean_F$Gr_size=='LG',]$f_RS))
comb_data_BM=c(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$stder_BM_focal,
               DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$stder_BM_focal)

diff.observed_large_pop = cov(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$stder_BM_focal,DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS),use="complete.obs",method = "pearson") - cov(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$stder_BM_focal,DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS),use="complete.obs",method = "pearson") 
diff.observed_large_pop

[1] -0.2786662

number_of_permutations = 100000
diff.random_large_pop = NULL
for (i in 1 : number_of_permutations) {
  
  # Sample from the combined dataset
  a.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS))), TRUE)
  b.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS))), TRUE)
  c.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS))), TRUE)
  d.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS))), TRUE)
  
  # Null (permuated) difference
  diff.random_large_pop[i] = cov(b.random,a.random,use="complete.obs",method = "pearson") - cov(d.random,c.random,use="complete.obs",method = "pearson")
}

# P-value is the fraction of how many times the permuted difference is
# equal or more extreme than the observed difference

p_Sex_diff_large_pop = sum(abs(diff.random_large_pop) >= as.numeric(abs(diff.observed_large_pop)))/   number_of_permutations
p_Sex_diff_large_pop

[1] 0.13493

#Area ####
#Large
Sex_diff_large_area=c(boot_BW_males_area_large$t)-c(boot_BW_females_area_large$t)

t_Sex_diff_large_area=mean(Sex_diff_large_area,na.rm=TRUE)
t_Sex_diff_large_area_lower=quantile(Sex_diff_large_area,.025,na.rm=TRUE)
t_Sex_diff_large_area_upper=quantile(Sex_diff_large_area,.975,na.rm=TRUE)

#Permutation test to calculate p value
comb_data_RS=c(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS),
               DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS))
comb_data_BM=c(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$stder_BM_focal,
               DB_data_clean_F[DB_data_clean_F$Area=='Large',]$stder_BM_focal)

diff.observed_large_area = cov(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$stder_BM_focal,DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS),use="complete.obs",method = "pearson") - cov(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$stder_BM_focal,DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS),use="complete.obs",method = "pearson") 
diff.observed_large_area

[1] -0.05780497

number_of_permutations = 100000
diff.random_large_area = NULL
for (i in 1 : number_of_permutations) {
  
  # Sample from the combined dataset
  a.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS))), TRUE)
  b.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS))), TRUE)
  c.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS))), TRUE)
  d.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS))), TRUE)
  
  # Null (permuated) difference
  diff.random_large_area[i] = cov(b.random,a.random,use="complete.obs",method = "pearson") - cov(d.random,c.random,use="complete.obs",method = "pearson")
}

# P-value is the fraction of how many times the permuted difference is
# equal or more extreme than the observed difference

p_Sex_diff_large_area = sum(abs(diff.random_large_area) >= as.numeric(abs(diff.observed_large_area)))/   number_of_permutations
p_Sex_diff_large_area

[1] 0.74254

#Small
Sex_diff_small_area=c(boot_BW_males_area_small$t)-c(boot_BW_females_area_small$t)

t_Sex_diff_small_area=mean(Sex_diff_small_area,na.rm=TRUE)
t_Sex_diff_small_area_lower=quantile(Sex_diff_small_area,.025,na.rm=TRUE)
t_Sex_diff_small_area_upper=quantile(Sex_diff_small_area,.975,na.rm=TRUE)

#Permutation test to calculate p value
comb_data_RS=c(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS),
               DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS))
comb_data_BM=c(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$stder_BM_focal,
               DB_data_clean_F[DB_data_clean_F$Area=='Small',]$stder_BM_focal)

diff.observed_small_area = cov(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$stder_BM_focal,DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS),use="complete.obs",method = "pearson") - cov(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$stder_BM_focal,DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS),use="complete.obs",method = "pearson") 
diff.observed_small_area

[1] -0.4511778

number_of_permutations = 100000
diff.random_small_area = NULL
for (i in 1 : number_of_permutations) {
  
  # Sample from the combined dataset
  a.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS))), TRUE)
  b.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS))), TRUE)
  c.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS))), TRUE)
  d.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS))), TRUE)
  
  # Null (permuated) difference
  diff.random_small_area[i] = cov(b.random,a.random,use="complete.obs",method = "pearson") - cov(d.random,c.random,use="complete.obs",method = "pearson")
}
# P-value is the fraction of how many times the permuted difference is
# equal or more extreme than the observed difference

p_Sex_diff_small_area = sum(abs(diff.random_small_area) >= as.numeric(abs(diff.observed_small_area)))/   number_of_permutations
p_Sex_diff_small_area

[1] 0.03397

# Treatment bias ####
# Group size ####
# Males
Treat_diff_male_pop=c(boot_BW_males_group_size_large$t)-c(boot_BW_males_group_size_small$t)

t_Treat_diff_male_pop=mean(Treat_diff_male_pop,na.rm=TRUE)
t_Treat_diff_male_pop_lower=quantile(Treat_diff_male_pop,.025,na.rm=TRUE)
t_Treat_diff_male_pop_upper=quantile(Treat_diff_male_pop,.975,na.rm=TRUE)

#Permutation test to calculate p value
comb_data_RS=c(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS),
               DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS))
comb_data_BM=c(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$stder_BM_focal,
               DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$stder_BM_focal)

diff.observed_male_pop = cov(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$stder_BM_focal,DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS),use="complete.obs",method = "pearson") - cov(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$stder_BM_focal,DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS),use="complete.obs",method = "pearson") 
diff.observed_male_pop

[1] 0.1803

number_of_permutations = 100000
diff.random_male_pop = NULL
for (i in 1 : number_of_permutations) {
  
  # Sample from the combined dataset
  a.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS))), TRUE)
  b.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='LG',]$m_RS))), TRUE)
  c.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS))), TRUE)
  d.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Gr_size=='SG',]$m_RS))), TRUE)
  
  # Null (permuated) difference
  diff.random_male_pop[i] = cov(b.random,a.random,use="complete.obs",method = "pearson") - cov(d.random,c.random,use="complete.obs",method = "pearson")
}

# P-value is the fraction of how many times the permuted difference is
# equal or more extreme than the observed difference

p_Treat_diff_male_pop = sum(abs(diff.random_male_pop) >= as.numeric(abs(diff.observed_male_pop)))/   number_of_permutations
p_Treat_diff_male_pop

[1] 0.34208

# Females
Treat_diff_female_pop=c(boot_BW_females_group_size_large$t)-c(boot_BW_females_group_size_small$t)

t_Treat_diff_female_pop=mean(Treat_diff_female_pop,na.rm=TRUE)
t_Treat_diff_female_pop_lower=quantile(Treat_diff_female_pop,.025,na.rm=TRUE)
t_Treat_diff_female_pop_upper=quantile(Treat_diff_female_pop,.975,na.rm=TRUE)

#Permutation test to calculate p value
comb_data_RS=c(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS),
               DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS))
comb_data_BM=c(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$stder_BM_focal,
               DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$stder_BM_focal)

diff.observed_female_pop = cov(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$stder_BM_focal,DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS),use="complete.obs",method = "pearson") - cov(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$stder_BM_focal,DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS),use="complete.obs",method = "pearson") 
diff.observed_female_pop

[1] 0.2482675

number_of_permutations = 100000
diff.random_female_pop = NULL
for (i in 1 : number_of_permutations) {
  
  # Sample from the combined dataset
  a.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS))), TRUE)
  b.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='LG',]$f_RS))), TRUE)
  c.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS))), TRUE)
  d.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Gr_size=='SG',]$f_RS))), TRUE)
  
  # Null (permuated) difference
  diff.random_female_pop[i] = cov(b.random,a.random,use="complete.obs",method = "pearson") - cov(d.random,c.random,use="complete.obs",method = "pearson")
}


# P-value is the fraction of how many times the permuted difference is
# equal or more extreme than the observed difference

p_Treat_diff_female_pop = sum(abs(diff.random_female_pop) >= as.numeric(abs(diff.observed_female_pop)))/   number_of_permutations
p_Treat_diff_female_pop

[1] 0.20807

# Area ####
# Males
Treat_diff_male_area=c(boot_BW_males_area_large$t)-c(boot_BW_males_area_small$t)

t_Treat_diff_male_area=mean(Treat_diff_male_area,na.rm=TRUE)
t_Treat_diff_male_area_lower=quantile(Treat_diff_male_area,.025,na.rm=TRUE)
t_Treat_diff_male_area_upper=quantile(Treat_diff_male_area,.975,na.rm=TRUE)

#Permutation test to calculate p value
comb_data_RS=c(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS),
               DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS))
comb_data_BM=c(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$stder_BM_focal,
               DB_data_clean_M[DB_data_clean_M$Area=='Large',]$stder_BM_focal)

diff.observed_male_area = cov(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$stder_BM_focal,DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS),use="complete.obs",method = "pearson") - cov(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$stder_BM_focal,DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS),use="complete.obs",method = "pearson") 
diff.observed_male_area

[1] -0.1190065

number_of_permutations = 100000
diff.random_male_area = NULL
for (i in 1 : number_of_permutations) {
  
  # Sample from the combined dataset
  a.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS))), TRUE)
  b.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Small',]$m_RS))), TRUE)
  c.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS))), TRUE)
  d.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS/mean(DB_data_clean_M[DB_data_clean_M$Area=='Large',]$m_RS))), TRUE)
  
  # Null (permuated) difference
  diff.random_male_area[i] = cov(b.random,a.random,use="complete.obs",method = "pearson") - cov(d.random,c.random,use="complete.obs",method = "pearson")
}

# P-value is the fraction of how many times the permuted difference is
# equal or more extreme than the observed difference

p_Treat_diff_male_area = sum(abs(diff.random_male_area) >= as.numeric(abs(diff.observed_male_area)))/   number_of_permutations
p_Treat_diff_male_area

[1] 0.52933

# Females
Treat_diff_female_area=c(boot_BW_females_area_large$t)-c(boot_BW_females_area_small$t)

t_Treat_diff_female_area=mean(Treat_diff_female_area,na.rm=TRUE)
t_Treat_diff_female_area_lower=quantile(Treat_diff_female_area,.025,na.rm=TRUE)
t_Treat_diff_female_area_upper=quantile(Treat_diff_female_area,.975,na.rm=TRUE)

#Permutation test to calculate p value
comb_data_RS=c(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS),
               DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS))
comb_data_BM=c(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$stder_BM_focal,
               DB_data_clean_F[DB_data_clean_F$Area=='Large',]$stder_BM_focal)

diff.observed_female_area = cov(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$stder_BM_focal,DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS),use="complete.obs",method = "pearson") - cov(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$stder_BM_focal,DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS),use="complete.obs",method = "pearson") 
diff.observed_female_area

[1] 0.2743663

number_of_permutations = 100000
diff.random_female_area = NULL
for (i in 1 : number_of_permutations) {
  
  # Sample from the combined dataset
  a.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS))), TRUE)
  b.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Small',]$f_RS))), TRUE)
  c.random = sample (na.omit(comb_data_RS), length(c(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS))), TRUE)
  d.random = sample (na.omit(comb_data_BM), length(c(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS/mean(DB_data_clean_F[DB_data_clean_F$Area=='Large',]$f_RS))), TRUE)
  
  # Null (permuated) difference
  diff.random_female_area[i] = cov(b.random,a.random,use="complete.obs",method = "pearson") - cov(d.random,c.random,use="complete.obs",method = "pearson")
}
# P-value is the fraction of how many times the permuted difference is
# equal or more extreme than the observed difference

p_Treat_diff_female_area = sum(abs(diff.random_female_area) >= as.numeric(abs(diff.observed_female_area)))/   number_of_permutations
p_Treat_diff_female_area

[1] 0.16343

Session information

sessionInfo()

R version 4.0.2 (2020-06-22)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19042)

Matrix products: default

locale:
[1] LC_COLLATE=German_Germany.1252  LC_CTYPE=German_Germany.1252   
[3] LC_MONETARY=German_Germany.1252 LC_NUMERIC=C                   
[5] LC_TIME=German_Germany.1252    

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

other attached packages:
 [1] ICC_2.4.0          tidyr_1.2.0        data.table_1.14.2  boot_1.3-25       
 [5] RColorBrewer_1.1-3 car_3.1-0          carData_3.0-5      gridGraphics_0.5-1
 [9] cowplot_1.1.1      EnvStats_2.7.0     dplyr_1.0.9        readr_2.1.2       
[13] lmerTest_3.1-3     lme4_1.1-30        Matrix_1.2-18      gridExtra_2.3     
[17] ggplot2_3.3.6      ggeffects_1.1.2    workflowr_1.7.0   

loaded via a namespace (and not attached):
 [1] httr_1.4.3          sass_0.4.1          bit64_4.0.5        
 [4] vroom_1.5.7         jsonlite_1.8.0      splines_4.0.2      
 [7] bslib_0.3.1         assertthat_0.2.1    getPass_0.2-2      
[10] highr_0.9           yaml_2.3.5          numDeriv_2016.8-1.1
[13] pillar_1.7.0        lattice_0.20-41     glue_1.6.2         
[16] digest_0.6.29       promises_1.2.0.1    minqa_1.2.4        
[19] colorspace_2.0-3    htmltools_0.5.2     httpuv_1.6.5       
[22] pkgconfig_2.0.3     purrr_0.3.4         scales_1.2.0       
[25] processx_3.7.0      whisker_0.4         later_1.3.0        
[28] tzdb_0.3.0          git2r_0.30.1        tibble_3.1.7       
[31] mgcv_1.8-31         farver_2.1.1        generics_0.1.3     
[34] ellipsis_0.3.2      withr_2.5.0         cli_3.3.0          
[37] magrittr_2.0.3      crayon_1.5.1        evaluate_0.15      
[40] ps_1.7.1            fs_1.5.2            fansi_1.0.3        
[43] nlme_3.1-148        MASS_7.3-51.6       tools_4.0.2        
[46] hms_1.1.1           lifecycle_1.0.1     stringr_1.4.0      
[49] munsell_0.5.0       callr_3.7.1         compiler_4.0.2     
[52] jquerylib_0.1.4     rlang_1.0.4         nloptr_2.0.3       
[55] rstudioapi_0.13     labeling_0.4.2      rmarkdown_2.14     
[58] gtable_0.3.0        abind_1.4-5         DBI_1.1.3          
[61] R6_2.5.1            knitr_1.39          bit_4.0.4          
[64] fastmap_1.1.0       utf8_1.2.2          rprojroot_2.0.3    
[67] stringi_1.7.6       parallel_4.0.2      Rcpp_1.0.9         
[70] vctrs_0.4.1         tidyselect_1.1.2    xfun_0.31