Evolutionary invasion analysis for structured populations: a synthesis

Natural populations exhibit complex class structures that fundamentally shape evolutionary dynamics. Yet predicting adaptation in such systems remains a central challenge in ecology because ecological realism inherently generates high-dimensional models that obscure biological interpretation and hinder general evolutionary prediction. Here, we overcome this long-standing obstacle by developing structural evolutionary invasion analysis, a unifying theoretical framework integrating invasion determinants with the Projected Next-Generation Matrix (PNGM). The invasion determinant provides a general, closed-form algebraic condition for invasion, while the PNGM structurally compresses life-cycle graphs by eliminating non-focal classes. Crucially, this compression formally derives timescale separation, rigorously preserves Fishers reproductive values, and guarantees that the location, convergence, and evolutionary stability of equilibria remain identical to those of the full ecological system. By applying the framework to examples spanning evolutionary epidemiology, stage structure, and inclusive fitness, we show how to capture the direct impact of ecological complexity on evolutionary outcomes while retaining analytical tractability. Our results establish a general principle linking ecological structure to evolutionary prediction, enabling ecologists to analyze adaptation and eco-evolutionary dynamics in heterogeneous populations.