Recent empirical and theoretical work shows that intraspecific trait variation (ITV) is prevalent and ecologically important, and should thus be taken into account in ecological models. What is lacking, however, is a comprehensive understanding of the joint effects of ITV in two interacting species (two-dimensional ITV). Here we address this gap for the cases where interspecific individual-by-individual interactions are affected by the trait values of both participants. Using nonlinear averaging in two dimensions, we show for several interaction functions how ITV affects average predation rates or competition coefficients. We develop an intuition for the direction and magnitude of this effect by using a Taylor approximation based on the local curvatures of the interaction function, the trait means, and the trait variances and covariances. We then incorporate the estimated average interaction parameters into simple competition and predator-prey models to derive the expected population-dynamic consequences. We show that two-dimensional ITV can have quantitative effects on abundances, as well as qualitative effects, such as stabilizing or destabilizing coexistence. Our approach can straightforwardly be applied to other interaction functions and dynamical systems and thus provides a valuable tool for understanding the joint effect of trait variation in two interacting species.

Habitat loss (HL) is a major cause of species extinctions. Although effects of HL beyond the directly impacted area have been previously observed, they are not very well understood, especially in an eco-evolutionary context. To start filling this gap, we study a two-patch deterministic consumer-resource model, with one of the patches experiencing loss of resources. Our model allows foraging and mating within a patch as well as between patches. We then introduce heritable variation in consumer traits to investigate eco-evolutionary dynamics and compare results with constant or no trait variation scenarios. Our results show that HL indeed reduces consumer densities in the neighboring patch, but when the resources are overexploited, HL in one patch can increase the consumer densities in the neighbouring patch. Yet at the landscape scale, the effect of HL on consumer densities is consistently negative. In presence of HL, patch isolation has positive effects on consumer density in the patch experiencing HL and mostly negative effects on the neighbouring patch. The landscape level pattern depends on which of these effects are dominant at the local scale. Evolution always increased resistance of consumers in the affected patch to HL, with varied effects at the landscape level. Finally, we also show a possibility of landscape level consumer extinction due to HL in a local patch when the cross-patch dependence is high, and foraging and mating preferences are coupled. Eco-evolutionary dynamics can rescue consumers from such extinction in some cases if their death rates are sufficiently small. Our findings show that HL at a local scale can affect the neighbouring patch and the landscape as a whole, and that heritable trait variation can provide some resistance against HL. We thus suggest joint consideration of multiple spatial scales and trait variation when assessing and predicting the impacts of HL.