Shared environment effects
Phenotypic similarity between individuals in any quantitative trait may
be generated by individuals experiencing similar environmental
conditions, as well as by their shared genes . This may include, for
example, effects of variation in resources (e.g. habitat quality) or of
social networks (two individuals with spatial overlap will be more
likely to encounter the same conspecifics). We accounted for the
possible effects of shared environments by estimating individuals’
overlap in their spatial environments, using data on their home ranges
(see model details below). Home ranges were estimated as utilization
distributions using VHF radiotracking locations of collared koalas.
Tracking data was therefore collected after our measure of infection
(i.e. whether koalas tested positive at first capture). However, koala
home ranges are thought to be relatively stable through time, even when
disturbed by habitat changes . Utilization distributions describe the
frequency distribution of individuals’ location data, and estimate the
probability of an individual occurring across the study site . We
included all individuals with at least five sightings over the study
period (N = 342). The average number of sightings per individual was 186
(interquartile range = 48 – 346). Utilization distributions were
estimated using the adehabitatHR package in the R statistical
environment with a smoothing parameter of 100 meters and grid size of 50
meters. This smoothing parameter was selected to 1) standardize the
estimation of home ranges of all individuals, and 2) avoid over- or
under-smoothing in utilization distribution estimation for individuals
with few sightings. All utilization distributions were visually
inspected post estimation in order to ensure accuracy. Home range
overlap (abbreviated “HRO” in the results) between all pairs of
individuals was then measured using utilization distribution overlap
indices , from which a home-range overlap matrix was constructed. This
measures the extent to which koalas overlap spatially, although it does
not account for the possibility that some pairs of koalas may co-occur
spatially but not temporally.
Statistical Analysis.
We first tested whether our genetic dataset contained the power to
detect inbreeding (if present) using the R package inbreedR to
estimate identity disequilibrium (g 2 ).
Specifically, this tested for variance in inbreeding in the population,
which is required to detect inbreeding depression. Then, to investigate
whether there was evidence for inbreeding depression, additive genetic
effects, and/or shared environment effects, we ran a suite of
generalized linear mixed effects models using the MCMCglmm
package in the R statistical environment. In all models, our response
was a binary variable describing whether or not the koala tested
positive for C. pecorum at first capture (effectively a
case/control comparison), and all models were fit with the following
fixed effects: age in years at time of capture, season in which the
individual was caught (breeding vs non-breeding), sex, IR, and
the interaction between age and IR. The effect of IR tested for evidence
for inbreeding depression, predicting that if there was evidence for
inbreeding depression, more inbred individuals would have poorer health
outcomes and would therefore be more likely to test positive forC. pecorum . We also included an interaction between IR and age to
test whether the effect of inbreeding changes with age . Although it is
likely that the components of variance also change with age, our
data-set structure and size were not suitable for addressing this
question: of the 342 individuals in the dataset, only 20 individuals
were between 0-1 years old, and 81 between 1 – 2 years old, resulting
in very few observations of individuals prior to sexual maturity, making
estimating variances at different ages difficult using this dataset.
Fixed effects were given flat weakly informative priors, and random
effects were given a X12 prior,
following the advice of . In this paper, de Villemereuil and colleagues
found that when estimating heritability of binary traits, this prior was
less sensitive to the inclusion of multiple random effects than
alternative priors and performs best with small sample sizes. We ran
1,030,000 iterations per model with a burn in period of 30,000
iterations, sampling at intervals of 1000 iterations; this resulted in
low autocorrelation and a sufficient number of iterations for the model
to mix and converge. Convergence of models was assessed by examining
trace-plots to visualise sampling mixing and by assessing effective
sample sizes. Further, we plotted predicted random effect values to
visually check for normality. We considered estimates of fixed effects
to be different from zero when the 95% credible intervals of the
posterior distribution did not overlap with zero. These models were
fitted with a threshold distribution and a probit link. Residual
variance was fixed at one due to the use of binary data.
The first model we fitted used the full dataset including all
individuals for which we had disease, genetic, and spatial data (N=342),
and decomposed variance not accounted for by the fixed effects into two
components: additive genetic effects and shared-environment effects.
Additive genetic effects were estimated by fitting the relatedness
matrix as a covariance matrix. This was therefore an ‘animal model’,
which extends linear mixed effects models to incorporate relatedness
information, and partitions phenotypic variance into additive genetic
effects and other sources of variance . Shared-environment effects were
estimated by including the home range overlap matrix as an additional
covariance matrix, allowing us to estimate the variance associated with
individuals sharing the same environment. Prior to fitting the animal
model, we ensured that the relatedness matrix and the home range overlap
matrix were not correlated with each other and would not affect variance
partitioning. The Pearson’s correlation between the two matrices was
0.3, which we deemed low enough to not affect parameter estimates
derived from the model. Nevertheless, we also fitted the model without
the spatial overlap matrix and compared the deviance information
criterion (DIC) of the two models to further examine evidence for a
shared environment effect. Doing so also enabled us to ensure that
fitting the spatial overlap matrix did not influence our heritability
estimates. Fitting animal models requires positive definite matrices,
and as our relatedness matrix was not positive definite, we calculated
the nearest positive definite matrix to our observed relatedness matrix
using the corpcor package in R . We subsequently ensured that the
original information contained in the relatedness matrix was unchanged
by calculating and visualizing the correlation between the observed and
the new matrix (r2 = 0.98). The observed spatial
overlap matrix was positive definite and therefore did not require
transformation.
The second model we ran was used to investigate the extent to which the
probability that a koala tests positive for C. pecorum may be
caused by vertical transmission from mother to offspring (maternal
effects). This is necessary because heritability estimates may be
inflated when maternal effects are not accounted for (Kruuk and
Hadfield, 2007). To do this, we used a subset of the data used
for the first model that included only the individuals for which we knew
the mother (NIND = 195 of N = 106 mothers).
Although analytically possible, we considered this reduced sample size
too small and lacking in statistical power to fully partition variance
in disease status into additive genetic effects, maternal effects, and
shared environment effects. Instead, we aimed to (1) estimate the extent
of maternal effect variance, and (2) ensure that our heritability
estimates were not inflated by potential mother-offspring transmission
of disease. To do this, we again fitted the model with the relatedness
matrix (as explained above), but here included maternal ID as an
additional random effect (instead of the shared environment effect). The
maternal ID term estimates the phenotypic variance that is attributed to
individuals sharing the same mother, over and above that due to shared
additive genetic effects .