A critical examination of models of annual-plant population dynamics and density-dependent fecundity

Abstract

Mathematical models serve many purposes in biology. Each and every model is a necessary simplification of reality, and, as simplifications, these models are also wrong by definition. And yet there are many ways to be wrong, and some of these are a much greater concern than others. For example, a paradoxical model-based prediction may simply be puzzling whereas unphysical variables (e.g. negative amounts of time or temperatures below absolute zero) and nonbiological variables (e.g. negative abundances or negative feeding rates) should be avoided altogether. Here I analyse a discrete-time model of annual-plant population dynamics and three phenomenological models for density-dependent fecundity. These phenomenological models are generally interchanged solely on the basis of their statistical fit to data. On the other hand, I highlight ways in which their phenomenological basis hampers our ability to capture known aspects of annual-plant biology. I then demonstrate how to specify a more flexible, biologically appropriate model and illustrate this model's behaviour and interpretation in single-species and multi-species contexts. By constructing this generative model for annual-plant population dynamics, I can also demonstrate how and why emergent phenomena, such as negative density dependence, emerge. Although my focus is on a model applied to annual plants, the biological implications extend to modelling any species with a discrete life cycle and nonoverlapping generations. More broadly, my exploration here showcases that there are many more criteria with which we could, and arguably should, ground-truth mathematical models across biology.