Matrix community models for ecology and evolution.

Ecological communities are shaped by biotic interactions as well as environmental forces, and both must be incorporated to obtain models capable of forecasting realistic community dynamics. Many community models first specify pairwise biotic interactions and then secondarily examine how extrinsic factors such as abiotic conditions affect species abundances. A disadvantage of this approach is that the species interactions themselves are often environment and context specific, making parameterization difficult. We propose an alternative approach, matrix community models (MCMs), which are sets of matrix population models linked by an assumption of aggregate density dependence. MCMs incorporate detailed species autecology but are neutral with respect to pairwise species interactions, instead allowing interactions to be revealed within the model structure. These model-revealed species interactions, including competitive exclusion, facilitation, and interference competition, shape the distribution and abundance of species within communities and generate empirically testable predictions about species interactions. We develop a framework for building MCMs using vital rates in a stochastic, multispecies framework. Single-species matrix population models are connected via an assumption of aggregate density dependence, pairwise species interactions are estimated with sensitivity analysis, and community trajectories are analyzed under different environmental regimes using standard statistical tools and network analysis. MCMs have the advantage that pairwise species interactions need not be specified a priori, and that mechanistic demographic-environment linkages permit forecasting of community dynamics under novel, non-stationary environmental regimes. A challenge is that species' autecological vital rates, such as fecundity, growth and survivorship, must be measured under a diverse range of environmental conditions to parameterize the models. We illustrate the approach with examples and discuss prospects for future theoretical and empirical developments.