Inferring birth versus death dynamics for ecological interactions in stochastic heterogeneous populations

In this paper, we study the significance of ecological interactions and separation of birth and death dynamics in stochastic heterogeneous populations via general birth-death processes. Interactions can manifest through the birth dynamics, the death dynamics, or some combination of the two. The underlying microscopic mechanisms are important but often implicit in population-level data. We propose an inference method for disambiguating the types of interaction and the birth and death processes from population size time series data of a stochastic $n$-type heterogeneous population. The interspecies interactions considered can be competitive, antagonistic, or mutualistic. We show that different pairs of birth and death rates with the same net growth rate result in different time series statistics. Then, the inference method is validated in the example of a birth-death process inspired by the two-type Lotka-Volterra interaction dynamics. Utilizing stochastic fluctuations enables us to estimate additional parameters in this stochastic Lotka-Volterra model, which are not identifiable in a deterministic model.