Resource-based modelling approach to studying evolutionary rescue

In this paper, we present an in-depth investigation into the dynamics of evolutionary rescue using a resource-based modelling approach. Utilizing classical consumer-resource models, we aim to understand how species can adapt to abrupt environmental changes that alter the availability of substitutable resources. Through both analytical solutions and simulation-based techniques, we explore the conditions under which populations can recover from critical sizes and avoid extinction. Our findings highlight the importance of minimum viable population sizes, mutation rates, and the adaptive capacity of metabolic strategies in influencing population resilience. We demonstrate that while increased mutation rates can facilitate faster recovery by enabling populations to evolve new metabolic strategies suited to the altered resource landscape, populations starting with smaller sizes or facing severe reductions in resource availability are more susceptible to extinction. This study offers valuable insights into the interplay between ecological dynamics and evolutionary mechanisms, providing a comprehensive framework for predicting population persistence and informing conservation strategies under changing environmental conditions.