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 .