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

TL;DR

This paper introduces an inference method to distinguish between birth and death processes and their interactions in stochastic heterogeneous populations, revealing insights from population time series data that are not accessible through deterministic models.

Contribution

The paper presents a novel inference approach for identifying birth-death dynamics and interactions from population data, including stochastic fluctuations, in heterogeneous ecological systems.

Findings

Different birth-death rate pairs with same net growth produce distinct time series.

The method accurately infers interaction types and parameters from simulated data.

Stochastic fluctuations enable estimation of parameters unidentifiable in deterministic models.

Abstract

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.