Mathematical models of biological populations and communities are the most common type of representation in ecology, with a wide array of functional forms and many different types of variables and parameters. This complexity and the uneasy relationship between theoretical and empirical work in ecology makes for fertile philosophical fodder. For example, most ecological models are highly idealized, incorporating unrealistic assumptions to make mathematical model analysis tractable. This is troubling in ecology as mathematical ecologists often uncritically emulate mathematically sophisticated models of physics to ensure their modeling is mathematically rigorous. Showing the characterization of ecological stability as Lyapunov stability as indefensible is one goal of this chapter. Another goal is assessing the ecological promise of individual-based models (IBMs) and the philosophical issues they pose. IBMs do not aggregate over, or abstract from, the details of interactions between individual organisms. This modeling strategy is part of a more general, well-vetted “methodologically-individualistic” approach to representing the world often employed in social sciences. Debates about methodological individualism in the social sciences reveal insights about how individual-based ecological modeling should be understood and indicate their reductive potential in ecology.