Generalized Lotka-Volterra Model with Species Turnover in a Variable-Basis State Space

TL;DR

This paper introduces a novel variable-base state space for the generalized Lotka-Volterra model, enabling better modeling of species turnover and applying it to gut microbiota dynamics post-antibiotics.

Contribution

It extends the classical gLV model by incorporating a variable-base state space, reformulating it as a hybrid dynamical system for more realistic ecological modeling.

Findings

The new model captures species addition, removal, and mutation effects.

Application to gut microbiota demonstrates improved modeling of species dynamics.

Framework accommodates species turnover in ecological systems.

Abstract

The state space is a fundamental concept for describing the trajectory of a dynamic system. Depending on its form, it can highlight certain changes over time while ignoring others. This is particularly the case for the spaces associated with theoretical ecology models, notably the generalized Lotka-Volterra (gLV) model, which allows the modeling of interacting populations. The fixed-dimension state space classically used in gLV models does not account for the effective renewal of species through addition, removal, or mutation. To address this limitation, we propose a new variable-base state space, introduced in a previous study. This framework leads to a reformulation of the gLV model within the context of hybrid dynamical systems. To illustrate the approach, we apply the proposed model to the gut microbiota, particularly in the context of bacteriotherapy following antibiotic treatment.