Process noise distinguishes between indistinguishable population dynamics

Abstract

Model selection is becoming increasingly important in mathematical biology. Model selection often involves comparing a set of observations with predictions from a suite of continuum mathematical models and selecting the model that provides the best explanation of the data. In this work we consider the more challenging problem of model selection in a stochastic setting. We consider five different stochastic models describing population growth. Through simulation we show that all five stochastic models gives rise to classical logistic growth in the limit where we consider a large number of identically prepared realisations. Therefore, comparing mean data from each of the models gives indistinguishable predictions and model selection based on population-level information is impossible. To overcome this challenge we extract process noise from individual realisations of each model and identify properties in the process noise that differ between the various stochastic models. Using a Bayesian framework, we show how process noise can be used successfully to make a probabilistic distinction between the various stochastic models. The relative success of this approach depends upon the identification of appropriate summary statistics and we illustrate how increasingly sophisticated summary statistics can lead to improved model selection, but this improvement comes at the cost of requiring more detailed summary statistics.