Spatial Models for Ecological Communities

Equilibrium-based and large-population deterministic approaches, often formulated in well-mixed settings, are widely used in theoretical ecology, yet many ecologically relevant outcomes are shaped by transient amplification, long-lived metastable regimes, and stochastic effects that are not captured by mean-field steady states and linear stability alone. Within this context, this thesis addresses theoretical models of spatially distributed populations that extend beyond these baseline descriptions by relaxing selected underlying assumptions. Across distinct modeling frameworks, it adopts a mechanism-oriented perspective to derive population-level behavior from elementary microscopic processes – such as reproduction, dispersal, colonization-extinction events, and threshold-driven interactions. On this basis, the analysis develops tractable reduced descriptions and minimal models that retain key mechanistic features, enabling the characterization of dynamical regimes and transitions, ranging from survival–extinction thresholds to the onset of outbreak dynamics. Three case studies are developed here. In stochastic metapopulations, finite local carrying capacities replace deterministic persistence with metastable survival, yielding extinction-time statistics and finite-size scaling near the persistence threshold. In discrete-time models of dispersal evolution, demographic fluctuations coupled to nonlinear updates reshape invasion thresholds and long-run outcomes beyond mean-field predictions. Finally, bark-beetle outbreaks in spruce forests provide a biologically motivated setting, where disturbances trigger rapid transient amplification and recurrent outbreak regimes arise from ecological feedbacks. A spatial extension of this minimal model is outlined to study localized outbreak waves and emergent aggregation. Overall, this work presents a dynamical-systems perspective on ecological populations shaped by dispersal, finite-size fluctuations, and nonlinear feedbacks, drawing on tools from statistical physics to analyze population behavior.