Our analyses show that evolutionary biologists and ecologists working in natural systems should consider modeling fine-scale spatial processes if they want to fully understand the environmental drivers of phenotypic variation and accurately estimate quantitative genetic parameters. Accounting for shared environmental effects associated with either SAC or home range overlap, over and above effects of maternal identity, cohort and region of the study area, resulted in decreases in h2 of up to an order of magnitude (e.g., RHR, Table 2). Furthermore, both SAC and S matrix approaches provided new insight into the way spatial heterogeneity in resources influences key behavioral, life-history, and fitness traits. Interestingly, both the variance explained by SAC or the S matrix and their effects on h2 estimates varied markedly depending on the trait in question (Table 2; Fig. 3). Furthermore, the variance explained by SAC was greater than that explained by the S matrix in some traits (e.g., RHR, BW) but the opposite was true for others (e.g., SHR, LBS).
To our knowledge, only one study previous to ours has addressed the effects of SAC between trait values in related individuals in a wild animal population (van der Jeugd and McCleery 2002). That study suggested SAC resulted in overestimation of heritability of lay date in the great tit (although not clutch size), suggesting our findings are not specific to this study system. The extent of the effect of SAC on other traits and species remains however to be seen. In any system where there is incomplete or nonrandom dispersal of relatives and the habitat is heterogeneous, relatives are more likely to experience the same environment than would be expected by chance and this shared environmental experience will result in phenotypic resemblance that does not have a genetic basis (unless there is a genetic component to habitat choice itself, see below). However, the extent to which this biases estimates of heritability will vary with the amount to which related and nonrelated individuals are distributed within an environment, the extent to which the environment varies over the studied area, and the extent to which environmental and genetic factors determine trait values. Below, we discuss possible reasons for the differences we have found between female red deer traits in the effect of SAC on heritability estimates. We also consider the relative merits of the SAC and S matrix approaches, and highlight the potential for developing and implementing fitting additional covariance matrices within evolutionary ecology.
DIFFERENCES IN SPATIAL EFFECTS AMONG TRAITS
To our knowledge, this is the first study to estimate the heritability of home range size in a wild mammal. Quantitative genetic studies of traits associated with dispersal, ranging, and foraging behavior remain rare in wild mammals (e.g., Waser and Jones 1989), although they are the focus of increasing interest in birds (e.g., Doligez et al. 2009; Charmantier et al. 2011; Teplitsky et al. 2011). Although initial models suggested high VA and h2 in both RHR and SHR in red deer, and a moderate maternal effect in RHR, these effects all but disappear once either SAC or home range overlap have been accounted for (Fig. 1A, B). This starkly illustrates the potential pitfalls of failing to account for space or habitat sharing in an “animal model.” In both home range traits, substantial proportions of total variance were attributable to positive spatial autocorrelation or home range sharing, indicating that individuals with average lifetime locations in close proximity, or those that shared large proportions of their lifetime home range, had similar home range sizes. This is not surprising: home range size is likely to be closely associated with food availability, with individuals having to range further to meet energetic demands if they live in poor quality habitats (McNab 1963). Forage availability and quality varies markedly across our study area, and our results are likely to reflect increased home range sizes and reduced home range overlap among females living in regions of poorer vegetation in the south and east of the North Block (McLoughlin et al. 2006; Moyes 2007).
The importance of spatial effects on both BW and LBS were smaller than for home range sizes and estimates of h2 were accordingly less biased by their exclusion. Quantitative genetic estimates from the models accord well with previous studies: our BW estimates of VA and VPE are similar to those for maternal genetic and environmental variance from a study that treated this as an offspring trait (Kruuk and Hadfield 2007), although estimates for LBS were slightly higher than previous work that found zero heritability (Kruuk et al. 2000). The latter difference could be attributable to our larger present dataset, an improved pedigree, or the inclusion of a cohort random effect in our models. For both BW and LBS, we found that a substantial proportion of variance (around 20% and 30%, respectively) was attributable to either SAC or home range overlap. This suggests fine-scale spatial effects are important for life-history and fitness-correlated traits as well as those associated with ranging behavior. Previous work has identified significant spatial heterogeneity in fitness linked to the relationships between use of Agrostis/Festuca grassland, local population density, and lifetime reproductive success, and suggested this heterogeneity could be maintained by social constraints to dispersal preventing females from moving to more productive areas (McLoughlin et al. 2006, 2008). Although the mechanisms linking spatial location or home range overlap with BW and LBS variation remain to be determined, our results illustrate how estimation of SAC or S matrix effects could be used to provide insight into their relative importance for demographic variation and population dynamics in wild animals.
The contrasting relative importance of SAC versus home range overlap effects in some traits suggests differences in the processes linking resource heterogeneity and phenotype. For example, although both SAC and S matrix accounted for comparably large proportions of variation in RHR, the S matrix explained considerably more variation in SHR (Fig. 3A, B). SAC models of SHR were notably unstable (Table 2), so the difference here could be due an inability of the model to estimate the variance explained by SAC. However, there are biological reasons to expect differences: resource availability increases over the spring period but declines over the autumn, and female home ranges shrink substantially during the rut and may fall under some degree of influence of male rutting behavior (Clutton-Brock et al. 1982, although see Stopher et al. 2011). Interestingly, SAC but not home range overlap explained variation in BW but the reverse was true for LBS. Why spatial location per se rather than home range overlap should explain variance in BW is unclear; it could reflect the importance of the specific area a female tends to use during the gestation and lactation periods. This is supported by the fact that models including region as a fixed effect would not converge, and suggests a wider scale of resource variation may be important. The relative importance of home range sharing, rather than spatial location, for LBS variation may reflect fine-scale constraints associated with local competition in high-density and resource quality regions in the north of the study area, where home ranges are likely to overlap extensively (McLoughlin et al. 2006, 2008). There is tentative support for this in the SAC models that show nonsignificant negative autocorrelation in the column (east-west direction), but positive SAC in the row (south-north) direction (Table 2). In ecological studies, negative SAC is indicative of competition, such that individuals with high trait values depress the trait values of neighbors (Dutkowski et al. Dukowtski 2002, Haining 2004). The distribution of females in the study area means that the majority of column process information comes from the North, moving east from Kilmory to Shamhnan Insir (Figs. 1,2), where high local densities would be expected to drive greater competition for resources.
DEVELOPING THE MULTIMATRIX APPROACH IN EVOLUTIONARY ECOLOGY
Our results suggest that exploring SAC and home range overlap effects side-by-side could be biologically informative, and other studies may also wish to explore the wider range of statistical methods developed for accounting for SAC (see for example Dutkowski et al. 2002). However, we would argue that fitting the matrix of home range overlap is the more appropriate way to deal with causes of environmental similarity between relatives. This is because patterns of space use, as indicated by home range overlap, are more likely to accurately describe the similarity of the environment two individuals experience, in terms of available food and shelter, and the energy they have to expend to acquire these. Because we used a home range overlap index that included information on the utilization distribution of home ranges (i.e., the amount individuals actually use different parts of the home range), our S matrix gives a very accurate measure of extent to which individuals experience similar environmental conditions. In contrast, using an average location is a cruder measure of the environment an individual experiences, not least because the error on the estimate of average location is likely to vary between individuals, depending upon the differences in the extent to which animals range around that average location. A comparison of model AICs shows that models including home range overlap performed better than models including SAC processes for three of four traits. Further, we found that models including SAC were not necessarily stable in the parameters they estimated, or in their likelihood of converging. In contrast, models using the double-matrix approach were straightforward to fit and converged. These considerations imply that, faced with a choice, ecologists and evolutionary biologists should favor the use of home range overlap or resource-sharing matrices rather than SAC functions.
It is striking that we found such strong effects of home range overlap on the traits considered despite the existence of certain limitations in our S matrix approach. For example, the matrix uses lifetime home ranges, and includes no information about when individuals existed: it therefore assumes individuals with identical home ranges separated by as much as 30 years experience the same environmental conditions. Ideally therefore, temporal information on overlap of individuals in time as well as space would be incorporated, or the matrix could be constructed on an annual basis. However, producing home range overlap matrices for large populations is not trivial and incorporating temporal variation in these matrices into animal models is not going to be straightforward.
Further, it is important to exercise caution when interpreting the results of this, or any similar study, to not assume that estimated heritabilities are free from bias even if shared environment effects are accounted for. For example, if there exists a genetic component to habitat choice, such that individuals choose habitats according to their genotypes, variance apparently explained by shared environmental effects may have an underlying genetic component. Accounting for shared environment effects may therefore result in underestimation of genetic variance. In this study, this may not be a problem, as females do not disperse and therefore have little opportunity to “choose” an environment, but were there a genetic component to the location of home range such a bias could exist, and future studies using such techniques should be aware of the issue. In general, as we begin to think about ways to more fully account for environmental similarity between relatives, it will be important to question whether additive genetic variance is to some extent absorbed by the environmental term and therefore downwardly biased. In this study, the pedigree, although imperfect, is more complete than the fitted S matrix, implying that this is unlikely. However, it may be a problem for other systems, particularly where the pedigree is shallow. In light of these limitations, future studies (including simulation studies) that examine how home range overlap matrices and other environmental similarity matrices could be best computed, the factors that affect the ability to separate genetic and environmental variance using such models, and what additional biological insight they could bring, would certainly be worthwhile in light of our results.
In general, this “double matrix” technique—fitting both genetic relatedness and environmental similarity—offers exciting possibilities for separating the causes of similarity between individuals. Fitting additional covariance matrices is a common practice in animal breeding to dissect different genetic contributions to phenotypic variation (e.g., additive, dominance, and epistatic effects: e.g., Smith and Maki-Tanila 1990; Palucci et al. 2007). A recent review has strongly advocated the separation of transmissible nongenetic effects using additional matrices capturing shared resources or social interactions (Danchin et al. 2011). To our knowledge, ours is the first study to empirically implement such an approach and it clearly highlights both the potential for confounding effects of fine-scale shared environmental effects on VA and h2, as well as the ecological importance of such effects on phenotypic variation.
Beyond spatial analysis, additional covariance matrices could be fitted to animal models to assess the variance explained in traits by association between individuals. The use of social network analysis has recently become very popular in behavioral ecology to identify and quantify the interactions between individuals and the extent to which individuals associate (Wey et al. 2008). The approach has been used to describe social structure and predict patterns of cooperation in guppies (Croft et al. 2004, 2006), and spatial-association networks in bats are thought to be important in not just in social life but also in epidemiology (Rhodes et al. 2006; Wey et al. 2008). Furthermore, the fitness correlates of social relationships are not well known (but see Silk et al. 2003, 2010). Methods to incorporate social association information into quantitative genetic analysis are currently an area of much endeavor (see Walsh and Lynch 2009). However, a recent study stated that matrices of genetic relatedness and social interactions could not be fitted simultaneously within an “animal model” (Frere et al. 2010), yet our study shows that this should be perfectly possible, given a data structure that allows the separation of genetic and social variance, by fitting a matrix of interactions between individuals, that is, an association matrix (Whitehead 2008), to an “animal model” of a fitness trait. Should sufficient data be available, with sufficient independence between the matrices to allow their separation, this could potentially even be extended to a model in which similarity between individuals in wild populations was separated into relatedness, shared environment, and social associations.