Resource heterogeneity influences home range area in the swamp wallaby Wallabia bicolor

Home range area is influenced by the spatio-temporal distribution of multiple resources, but current theoretical frameworks such as the habitat productivity and resource dispersion hypotheses fail to account for this adequately. We propose a conceptual framework for quantifying the influence of multiple resources on home range area where separate resources interact to form a continuous, multi-dimensional resource surface exhibiting an emergent environmental pattern. We adopt the term resource heterogeneity to describe this pattern, and predict that home range area will be more closely correlated with resource heterogeneity than with simple additive or interactive effects of separate resources. Initially, we quantified resource heterogeneity as the geometric mean of resource abundance, and tested the performance of this index against simulated low, moderate and high heterogeneity scenarios. In all cases, the geometric mean reflected the modelled scenarios well, demonstrating its utility as a heterogeneity index. We then quantified shelter and food resources within the home ranges of swamp wallabies Wallabia bicolor, and used these data in a generalised linear mixed modelling framework to test our prediction. Based on Akaike's information criterion (AIC(c)), the best model included the main effect of sex and the heterogeneity index. Although model selection uncertainty was relatively high (largest Akaike weight=0.37), the AIC(c) value associated with the best model was 2.41 units less than the highest ranked model including shelter and food, indicating support for our prediction. Home range area was negatively correlated with resource heterogeneity, and males had larger home ranges than females (37.6 (28.5, 49.7) ha compared to 17.2 (13.6, 21.7) ha; mean and 95% CLs). We suggest that statistical models of home range area parameterised using an index of resource heterogeneity will often be superior to those that focus on a single resource, or fail to take the heterogeneity of multiple resources into account.