Inferring Density-Dependent Population Dynamics Mechanisms through Rate Disambiguation for Logistic Birth-Death Processes

TL;DR

This paper introduces a method to distinguish birth and death processes in stochastic population dynamics using cell number fluctuations, aiding understanding of mechanisms behind density-dependent growth in microbial and cancer cells.

Contribution

The paper presents a novel approach to identify underlying birth and death rates from net growth data, validated through stochastic process analysis and applied to drug resistance scenarios.

Findings

Successfully disambiguated birth and death processes in logistic growth models.

Validated method's accuracy with respect to discretization bin size.

Provided an alternative maximum likelihood approach for limited data scenarios.

Abstract

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can manifest in birth processes, death processes, or both. Therefore, we utilize the mean and variance of cell number fluctuations to separately identify birth and death rates from time series that follow stochastic birth-death processes with logistic growth. Our method provides a novel perspective on stochastic parameter identifiability, which we validate by analyzing the accuracy in terms of the discretization bin size. We apply our method to the scenario where a homogeneous cell population goes through three stages: (1) grows naturally to its carrying capacity, (2) is treated with a drug that reduces its carrying capacity, and (3) overcomes the drug effect to restore its original carrying capacity. In each stage, we disambiguate whether it happens through the birth process, death process, or some combination of the two, which contributes to understanding drug resistance mechanisms. In the case of limited data sets, we provide an alternative method based on maximum likelihood and solve a constrained nonlinear optimization problem to identify the most likely density dependence parameter for a given cell number time series. Our methods can be applied to other biological systems at different scales to disambiguate density-dependent mechanisms underlying the same net growth rate.