Supplementary material
Text S1. Behavioural measurements in nestlings before and after 2011
Just before fledging (day 16), morphometric and behavioural measurements were taken on all the
nestlings. Handling aggression has been measured from 2006 and 2007 onwards in adults and
nestlings respectively and breath rates from 2007 onwards. Until 2010, nestlings were taken out of
their box and placed individually in a small paper bag, the order of these being then randomized and
nestlings were measured and assayed. From 2011 onwards, nestlings were taken out of the box and
placed jointly in a large paper bag and taken from there individually to be measured and assayed.
We tested whether changes in the protocol used to assay behaviours of nestlings had consequences
for genetic variances. We estimated the genetic correlation for each trait contrasting measures
before and after 2011. We used animal models for HA and BR separately, with sex, observer, year
and order of measurement as fixed effects and nest of rearing as additional random effect. We
obtained genetic correlations close to 1 (0.99±0.01 for BR, 0.88±0.32 for HA). We concluded that
these measurements are reflecting the same nestling traits independently of the details of how they
were measured.
Text S2. R script used for the simulation of extra-pair paternities and for the estimation of the
quantitative genetic parameters based on the resulting pedigrees.
library(pedantics)
library(asreml)
#Import files
young<-read.csv("young_2003_2013_25042014.csv",header=T,sep=",",
na.strings= c(""," ","-99","-999"))
basic<-read.csv("Basic_data_2003_2013.csv",header=T,sep=",",
na.strings= c("-999",""," ","-99","0"))
Data<-read.table("ontoData2013.txt", header=T,na.strings=c("-999") )
basic<-subset(basic,basic$species=="BT")
#Create data frames for nestlings and adults containing brood IDs
#that can be merged
basic.parents<-data.frame("NestID"=basic$NestID,"Mother"=basic$fem_MATLAB,
"Father"=basic$mal_MATLAB)
young.rings<-data.frame("Ring"=young$Ring, "NestID"=young$GeneticID, "Year"=young$Year)
young.rings<-subset(young.rings,is.na(young.rings$Ring)==FALSE)
young.rings<-unique(young.rings)
Pedigree<-merge(young.rings,basic.parents,all=T)
# remove the nest IDs where no nestlings ringed
Pedigree<-subset(Pedigree, is.na(Pedigree$Ring)==FALSE)
Pedigree<-Pedigree[order(Pedigree$NestID),]
#Only take broods where Father is known.
Ped_red<-subset(Pedigree, is.na(Pedigree$Father)==FALSE)
broodsize<-aggregate(Ped_red$Ring, list(Ped_red$NestID), length)
colnames(broodsize)<-c("NestID", "Size")
###############################################################################
################Simulation part
Data$YEAR<-as.factor(Data$YEAR)
Data$RearID<-as.factor(Data$RearID)
Data$GeneticID<-as.factor(Data$GeneticID)
Data$Sex<-as.factor(Data$Sex)
Data$HAa<-as.numeric(Data$HAa)
Data$HAn<-as.numeric(Data$HAn)
#Pin function will be used to calculate genetic correlations and heritabilities
pin<-function (object, transform)
{
pframe <- as.list(object$gammas)
names(pframe) <- paste("V", seq(1, length(pframe)), sep = "")
tvalue <- eval(deriv(transform[[length(transform)]], names(pframe)),
pframe)
X <- as.vector(attr(tvalue, "gradient"))
X[object$gammas.type == 1] <- 0
tname <- if (length(transform) == 3)
transform[[2]]
else ""
n <- length(pframe)
i <- rep(1:n, 1:n)
j <- sequence(1:n)
k <- 1 + (i > j)
Vmat <- object$ai
se <- sqrt(sum(Vmat * X[i] * X[j] * k))
data.frame(row.names = tname, Estimate = tvalue, SE = se)
}
#Prepare the data frames
Sim_EPP<-data.frame("LogL1"=NA, "LogL2"=NA, "Convergence M1"=NA,
"Convergence M2"=NA, "EPO Broods"=NA, "EPO prop"= NA)
VA_sim<-data.frame("HAn"=NA, "HAa"=NA, "BRn"=NA, "BRa"=NA,"HAnHAa"=NA, "BRnBRa"=NA,
"BRaHAa"=NA, "BRnHAn"=NA, "BRnHAa"=NA, "BRaHAn"=NA)
VPE_sim<-data.frame( "HAa"=NA,"BRa"=NA, "BRaHAa"=NA)
VB_sim<-data.frame("HAn"=NA, "BRn"=NA, "BRnHAn"=NA)
VR_sim<-data.frame("HAn"=NA, "HAa"=NA, "BRn"=NA, "BRa"=NA,"BRnHAn"=NA,"BRaHAa"=NA )
#Run the loop
for (i in 1:1000){
#Generate pedigrees where paternal links are removed
#Attribute a number of EPY for each brood
n.broods=805
n.EPC<-rpois(n.broods,0.8751)
s=0.1555
f.per.brood=n.EPC*s/(n.EPC*s+(1-s))
broodsize$EPY.per.brood<-rbinom(n.broods,broodsize$Size,f.per.brood)
#Number of broods with EPO will be saved in a table
broodsize$EPO<-ifelse(broodsize$EPY.per.brood >=1, 1, 0)
Ped_red.size<-merge(Ped_red, broodsize, all=T)
Ped.EPP<-Pedigree
#Choose randomly which offspring are EPY in each brood
for (y in 1:805){
Brood<-subset(Ped_red.size, Ped_red.size$NestID==as.character(broodsize[y,1]))
EPY.Ring<-sample(Brood$Ring,Brood$EPY.per.brood)
#Delete information on father for these rings
Ped.EPP[Ped.EPP$Ring %in% EPY.Ring,5]<-NA
}
##Add the founders to the pedigree
Females<-basic.parents$Mother[!is.na(basic.parents$Mother)]
Females<-unique(Females)
Females<-Females[-which(Females %in% Ped.EPP$Ring)]
Males<-basic.parents$Father[!is.na(basic.parents$Father)]
Males<-unique(Males)
Males<-Males[-which(Males %in% Ped.EPP$Ring)]
Femalesped<-data.frame("Ring"=Females, "Year"=NA,"Mother"=NA,"Father"=NA)
Malesped<-data.frame("Ring"=Males, "Year"=NA,"Mother"=NA,"Father"=NA)
Pedigreetot<-rbind(Femalesped, Malesped,Ped.EPP[,c(2:5)])
Pedigreetot$Mother<-as.factor(Pedigreetot$Mother)
Pedigreetot$Father<-as.factor(Pedigreetot$Father)
Ped<-Pedigreetot[,c(1,4,3)]
Ped<-fixPedigree(Ped=Ped)
colnames(Ped)<-c("Ring", "Father", "Mother")
#Run the animal models
#create the inverse of the relationship matrix from the pedigree file
ainv<-asreml.Ainverse(Ped)$ginv
#starting values are needed.
sv<-asreml(cbind(HAn,BRn,HAa,BRa)~trait+YEAR+ at(trait,3):Sex+at(trait,4):Sex +
at(trait,3):OBSa +at(trait,4):OBSa+ at(trait,1):OBSn+at(trait,2):OBSn
,random=~us(trait):ped(Ring)+us(trait):ide(Ring)+us(trait):RearID
,rcov= ~ units:us(trait)
,data=Data
,ginverse=list(Ring=ainv)
, na.method.X="include", na.method.Y ="include"
,maxiter=20, start.values=TRUE)
gam<-sv$gammas.table
gam$fac<-factor(c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41))
#No constraint in this model
M<-asreml.constraints(~fac, gammas=gam)
gam$Value[c(1:10)]=c(0.3,0,0.03,0.1,0,3,0,0,0,0.03)
gam$Value[c(11:20)]=c(0.7,0.01,0.01,0,0,0.1,0,0,0.1,0.1)
gam$Value[c(21:30)]=c(0.3,0.001,0.03,0,0,0.001,0,0,0,0.001)
gam$Value[c(32:41)]=c(0.001,0,0.001,0,0,7,0,0,0.05,0.1)
gam$Constraint[c(14,15,17,18,24,25,26,27,28,29,30,32,33,34,35,36,38,39)]="F"
gam$Constraint[c(1:13,16,19,20:23,37,40,41)]="U"
model.1<-asreml(cbind(HAn,BRn,HAa,BRa)~trait+YEAR+at(trait,3):Sex+
at(trait,4):Sex + at(trait,3):OBSa +at(trait,4):OBSa+ at(trait,1):OBSn+at(trait,2):OBSn
,random=~us(trait):ped(Ring)+us(trait):ide(Ring)+us(trait):RearID
,rcov= ~ units:us(trait)
,data=Data
,ginverse=list(Ring=ainv)
, na.method.X="include", na.method.Y ="include"
,maxiter=100,constraints=M,G.param=gam,R.param=gam)
#HABR (parameter 2) constrained over the ontogeny for model 2
gam$fac<-factor(c(1,2,3,4,5,6,7,8,2,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41))
M<-asreml.constraints(~fac, gammas=gam)
model.2<-asreml(cbind(HAn,BRn,HAa,BRa)~trait+YEAR+at(trait,3):Sex+
at(trait,4):Sex + at(trait,3):OBSa +at(trait,4):OBSa+ at(trait,1):OBSn+at(trait,2):OBSn
,random=~us(trait):ped(Ring)+us(trait):ide(Ring)+us(trait):RearID
,rcov= ~ units:us(trait)
,data=Data
,ginverse=list(Ring=ainv)
, na.method.X="include", na.method.Y ="include"
,maxiter=20,constraints=M,G.param=gam,R.param=gam)
Sim_EPP[i,1]<-summary(model.1)$loglik
Sim_EPP[i,2]<-summary(model.2)$loglik
Sim_EPP[i,3]<-model.1$conv
Sim_EPP[i,4]<-model.2$conv
Sim_EPP[i,5]<-sum(broodsize$EPO)
Sim_EPP[i,6]<-mean(broodsize[,3]/broodsize[,2])
VA_sim[i,1]<-pin(model.1, va.HAn ~ V1 / (V1+V11+V21))[1]
VA_sim[i,2]<-pin(model.1, va.HAa ~ V6 / (V6+V16+V37))[1]
VA_sim[i,3]<-pin(model.1, va.BRn ~ V3 / (V3+V13+V23))[1]
VA_sim[i,4]<-pin(model.1, va.BRa ~ V10 / (V10+V20+V41))[1]
VA_sim[i,5]<-pin(model.1, ra.HAn.HAa ~ V4 / sqrt(V1*V6))[1]
VA_sim[i,6]<-pin(model.1, ra.BRn.BRa ~ V8 / sqrt(V3*V10))[1]
VA_sim[i,7]<-pin(model.1, ra.BRa.HAa ~ V9 / sqrt(V6*V10))[1]
VA_sim[i,8]<-pin(model.1, ra.BRn.HAn ~ V2 / sqrt(V3*V1))[1]
VA_sim[i,9]<-pin(model.1, ra.BRn.HAa ~ V5 / sqrt(V3*V6))[1]
VA_sim[i,10]<-pin(model.1, ra.BRa.HAn ~ V7 / sqrt(V1*V10))[1]
VPE_sim[i,1]<-pin(model.1, vpe.HAa ~ V16 / (V6+V16+V37))[1]
VPE_sim[i,2]<-pin(model.1, vpe.BRa ~ V20 / (V10+V20+V41))[1]
VPE_sim[i,3]<-pin(model.1, rpe.HAa.BRa ~ V19 / sqrt(V20*V16))[1]
VB_sim[i,1]<-pin(model.1, vb.HAn ~ V21/ (V1+V11+V21))[1]
VB_sim[i,2]<-pin(model.1, vb.BRn ~ V23 / (V3+V13+V23))[1]
VB_sim[i,3]<-pin(model.1, rb.HAn.BRn ~ V22 / sqrt(V21*V23))[1]
VR_sim[i,1]<-pin(model.1,
VR_sim[i,2]<-pin(model.1,
VR_sim[i,3]<-pin(model.1,
VR_sim[i,4]<-pin(model.1,
VR_sim[i,5]<-pin(model.1,
VR_sim[i,6]<-pin(model.1,
vr.HAn ~ V11
vr.HAa ~ V37
vr.BRn ~ V13
vr.BRa ~ V41
rr.HAn.BRn ~
rr.HAa.BRa ~
/ (V1+V11+V21))[1]#taken from ide matrix
/ (V6+V16+V37))[1]
/ (V3+V13+V23))[1]#taken from ide matrix
/ (V10+V20+V41))[1]
V12 / sqrt(V11*V13))[1]#taken from ide
V40 / sqrt(V37*V41))[1]
}
############################################################################
######################End of the simulation
#Estimate the genetic correlations
HAnHAa<-posterior.mode(as.mcmc((VA_sim[,5])))
CIHAnHAa<-HPDinterval(as.mcmc((VA_sim[,5])),0.95)
BRnBRa<-posterior.mode(as.mcmc((VA_sim[,6])))
CIBRnBRa<-HPDinterval(as.mcmc((VA_sim[,6])),0.95)
HAaBRa<-posterior.mode(as.mcmc((VA_sim[,7])))
CIHAaBRa<-HPDinterval(as.mcmc((VA_sim[,7])),0.95)
HAnBRn<-posterior.mode(as.mcmc((VA_sim[,8])))
CIHAnBRn<-HPDinterval(as.mcmc((VA_sim[,8])),0.95)
BRnHAa<-posterior.mode(as.mcmc((VA_sim[,9])))
CIBRnHAa<-HPDinterval(as.mcmc((VA_sim[,9])),0.95)
HAnBRa<-posterior.mode(as.mcmc((VA_sim[,10])))
CIHAnBRa<-HPDinterval(as.mcmc((VA_sim[,10])),0.95)
Text S3. R script used for the simulation of breeding values across ontogeny:
library(mvtnorm)
# Use the genetic variance-covariance matrix to simulate BV in nestlings
sigma <- matrix(c(0.38,-0.06,-0.06,0.04), ncol=2)
nestlings <- rmvnorm(n=1000, mean = rep(0, nrow(sigma)),sigma=sigma)
nestlings<-data.frame("BVHA"=nestlings[,1], "BVBR"=nestlings[,2])
cor.test(nestlings$BVHA,nestlings$BVBR)
# Simulate breeding values for adult traits based on the BV of nestling
## traits (X1) and the cross-ontogeny correlations (rho)
### using the function getBiCop
# Cross-trait-cross-ontogeny correlations are not modelled
# The function “getBiCop” was created by Dr. Felix Schönbrodt, Ludwig-Maximilian#University (LMU) Munich, Germany, and can be found at:
#http://stats.stackexchange.com/questions/15011/generate-a-random-variable-with-a#defined-correlation-to-an-existing-variable
getBiCop <- function(n, rho, X1 , sd) {
C <- matrix(rho, nrow = 2, ncol = 2)
diag(C) <- 1
C <- chol(C)
X2 <- rnorm(n, mean=0, sd)
X <- cbind(X1,X2)
# induce the correlation (does not change X1)
df <- X %*% C
return(df)
}
BVHA<-as.data.frame(getBiCop(10000,0.38,nestlings$BVHA,sd(nestlings$BVHA)))
colnames(BVHA)<-c("HAn", "HAa")
BVBR<-as.data.frame(getBiCop(10000,0.50,nestlings$BVBR,sd(nestlings$BVBR)))
colnames(BVBR)<-c("BRn", "BRa")
Correlations<-data.frame("HAnBRn"=NA,"HAnHAa"=NA,"BRnBRa"=NA,"HAnBRa"=NA,"BRnHAa"=NA,
"HAaBRa"=NA)
for (i in 1:1000){
BVHA<-as.data.frame(getBiCop(1000,0.38,nestlings$BVHA,0.56))
colnames(BVHA)<-c("HAn", "HAa")
BVBR<-as.data.frame(getBiCop(1000,0.5,nestlings$BVBR,0.2))
colnames(BVBR)<-c("BRn", "BRa")
Correlations[i,
Correlations[i,
Correlations[i,
Correlations[i,
Correlations[i,
Correlations[i,
1]<-cor.test(BVHA$HAn,BVBR$BRn)$estimate
2]<-cor.test(BVHA$HAn,BVHA$HAa)$estimate
3]<-cor.test(BVBR$BRn,BVBR$BRa)$estimate
4]<-cor.test(BVHA$HAn,BVBR$BRa)$estimate
5]<-cor.test(BVBR$BRn,BVHA$HAa)$estimate
6]<-cor.test(BVHA$HAa,BVBR$BRa)$estimate
}
require(MCMCglmm)
posterior.mode(as.mcmc((Correlations[,1])))
HPDinterval(as.mcmc((Correlations[,1])),0.95)
posterior.mode(as.mcmc((Correlations[,2])))
HPDinterval(as.mcmc((Correlations[,2])),0.95)
posterior.mode(as.mcmc((Correlations[,3])))
HPDinterval(as.mcmc((Correlations[,3])),0.95)
posterior.mode(as.mcmc((Correlations[,4])))
HPDinterval(as.mcmc((Correlations[,4])),0.95)
posterior.mode(as.mcmc((Correlations[,5])))
HPDinterval(as.mcmc((Correlations[,5])),0.95)
posterior.mode(as.mcmc((Correlations[,6])))
HPDinterval(as.mcmc((Correlations[,6])),0.95)
Table S1: Data structure of the four behavioural traits measured. Handling aggression is a score
from 1 to 5 describing how aggressive an individual is during handling and is measured in nestlings
(HAn) and in adults (HAa). Breath rate is the number of breaths per second measured during
handling and is measured in nestlings (BRn) and in adults (BRa). For each trait, we present the total
number of observations (Nobs) and the number of individuals measured (Nind) with between
parentheses the number of individuals with 1, 2, 3, 4, or 5 repeated observations in the data. The
mean, standard deviation (SD) and range are provided.
Han
BRn
HAa
BRa
Nobs
Nindiv (1/2/3/4/5/6)
Mean
SD
Range
6149
5863
1633
1526
6149
5863
1103(766/209/79/36/10/3)
1031(720/182/89/28/9/3)
2.62
1.89
3.00
2.38
1.20
0.42
1.11
0.45
1-5
0.81 - 4.26
1-5
1.41 - 5.22
Table S2: Genetic correlations of handling aggression and breathing rate in adults of age 1, 2 and
3+ years old (n=1038 for HA, n=998 for BR). Age was estimated based on the colouration of the
greater coverts as either yearling or older. Hence, only individuals of known age such as recruits
and individuals caught for the first time at 1 year old were considered. Genetic correlations (upper
triangle) are represented as estimate ±SE and are derived from the matrix of additive genetic effects
estimated by a multivariate animal model, where HA and BR in different age classes are considered
as 3 different traits. Correlations were not significantly different from 1 as judged form a LRT (HA:
χ2= 0.33, d.f. = 3, P = 0.95; BR: χ2= 0.29,d.f=3, P=0.96).
Trait
Handling aggression:
Correlation ± SE
Age 2
Age 3
Age 1
0.99 ± n.e.
0.78 ± 0.33
Age 2
Age 3
Age 1
0.99 ± n.e.
0.86 ± 0.24
Age 2
0.99 ± n.e.
Breath rate:
Age 2
0.81 ± 0.38
Table S3: Proportion of the phenotypic variance (VP) due to different variance components (VA:
additive genetic variance, VB: common environment variance in nestlings due to being reared in the
same brood, VE: permanent environment variance, VR: residual variance). These variance
components have been estimated using the multivariate mixed-effects model for HA and BR in
adults and nestlings
Trait
Variance component
Proportion of VP ±SE
HAn
VA
VB
VR
0.26 ± 0.04
0.19 ± 0.02
0.54 ± 0.03
BRn
VA
VB
VR
0.28 ± 0.04
0.23± 0.02
0.50± 0.03
HAa
VA
VE
VR
0.29 ± 0.06
0.11 ± 0.06
0.60 ± 0.04
BRa
VA
VE
VR
0.27 ± 0.06
0.11± 0.06
0.63 ± 0.04
.
Table S4: Estimates of the correlation between handling aggression and breathing rate in nestlings
and adults and their standard error for different components of variance. These correlations have
been estimated using the multivariate mixed-effects model for HA and BR in adults and nestlings.
Component
Nestlings
Additive genetic
-0.49 ±0.09
Permanent
environment
Adults
0.07 ± 0.16
-0.67 ± 0.49
Common
environment
-0.26 ±0.07
Residual
-0.19 ±0.03
0.18 ± 0.04
Phenotypic
-0.36 ±0.03
0.07 ± 0.03
Table S5: Estimates and conditional Wald-F tests of the fixed effects included in the multivariate
mixed effects model for HA and BR in adults and nestlings. The sex-specific contrast “male”
specifies the difference in trait value of a male relative to a female for adult traits.
Estimate ± SE
Fcond
df
P
2.68 ± 0.12
5294
22.62
2.895
1
3
7
<0.001
<0.001
0.005
1.78 ± 0.03
23900
47.67
17.6
1
3
6
<0.001
<0.001
<0.001
3.14 ± 0.29
0.46 ± 0.06
7800
57.49
9.701
4.221
1
1
6
6
<0.001
<0.001
<0.001
<0.001
2.58 ± 0.11
-0.31 ± 0.02
35840
187.8
31.96
8.368
1
1
6
5
<0.001
<0.001
<0.001
<0.001
HA in nestlings :
Intercept
Observer
Year
BR in nestlings :
Intercept
Observer
Year
HA in adults :
Intercept
Sex (male)
Observer
Year
BR in adults :
Intercept
Sex (male)
Observer
Year
Table S6: Genetic correlations and heritabilities of handling aggression (HA) and breath rate (BR)
in recruited nestlings, non-recruited nestlings and adults. Genetic correlations (upper triangle) and
heritabilities (diagonal) are represented as estimate ± 1SE and are derived from the fully
unconstrained matrix of additive genetic (co)variances (model I/I/I in Table 2). The genetic
correlations underlying the HA – BR behavioural syndrome in the recruited and non-recruited
nestlings are indicated in bold and these are reported in the main text.
HArec
BRrec
HAnonrec
BRnonrec
HAa
BRa
0.31± 0.09
-0.59 ± 0.27
0.21 ±0.1
1.00 ± n.e.
-0.56 ± 0.21
0.25± 0. 04
-0.50 ± 0.15
0.89 ± 0.18
-0.46 ± 0.09
0.30± 0.04
0.25 ± 0.17
-0.14 ± 0.21
0.37 ± 0.11
-0.19 ± 0.10
0.31 ±0.06
0.22 ± 0.20
0.21 ± 0.23
0.07 ± 0.12
0.53 ± 0.11
-0.11 ± 0.15
0.30± 0.06
Figure S1: Additive genetic correlations estimated by the animal model using the population’s
social pedigree (filled symbols) and simulated pedigrees with extra-pair paternity (open symbols).
Point estimates and SE of each correlation were calculated over all the simulations using highest
posterior density distributions. The point estimates of the genetic correlations obtained for the social
pedigree always fall within the range of the simulated correlations which confirms that the results
are robust to integration of uncertainty in pedigree links due to extra-pair paternity.
Figure S2: Distribution of the χ2 used to compare the models where HABR was unconstrained
across ontogeny to the models where HAnBRn and HAaBRa were constrained to the same value (2*(logL model1- logL model2) for all the simulated pedigrees with extra-pair paternity. The thick
black vertical line represents the χ2 value of 3.8 above which the difference between two models
differing by 1 degree of freedom is significant (P<0.05).