Models of genetic drift as limiting forms of the Lotka-Volterra competition model

TL;DR

This paper compares the Moran and stochastic Lotka-Volterra models, showing their equivalence in neutral systems and advocating for SLVC's advantages in modeling population regulation and complex processes.

Contribution

It demonstrates the relationship between the Moran and SLVC models, highlighting SLVC's benefits in population regulation and handling complex evolutionary processes.

Findings

Moran and SLVC models are equivalent in neutral systems at long times.

SLVC's population regulation avoids ambiguities present in the Moran model.

SLVC is preferable for modeling systems with selection and complex processes.

Abstract

The relationship between the Moran model and stochastic Lotka-Volterra competition (SLVC) model is explored via timescale separation arguments. For neutral systems the two are found to be equivalent at long times. For systems with selective pressure, their behavior differs. It is argued that the SLVC is preferable to the Moran model since in the SLVC population size is regulated by competition, rather than arbitrarily fixed as in the Moran model. As a consequence, ambiguities found in the Moran model associated with the introduction of more complex processes, such as selection, are avoided.