Eco-Evolutionary Dynamics of Populations in Fluctuating Environments

Summary

Understanding the origin of species diversity and the evolution of cooperation is a fundamental puzzle resonating with societal concerns, like the rise of antimicrobial resistance and the loss of biodiversity. Population dynamics traditionally ignores fluctuations and considers static or homogeneous environments. However, fluctuations from random birth and death events and changing environmental conditions play a crucial role in understanding the population eco-evolutionary dynamics, i.e. how its size and composition co-evolve. We will focus on the poorly understood situations where the population eco-evolutionary dynamics is shaped by the coupling of demographic noise and environmental variability. This is particularly relevant to understand the evolution of antimicrobial resistance, and poses interesting mathematical challenges.

Two concrete objectives:
- Generalization of Phys. Rev. Lett. 119, 158301 (2017) and Phys. Rev. Lett. 125, 048105 (2020) in various evolutionary scenarios.
- Modelling of microbial life cycles in fluctuating environments.

Understanding the origin of species diversity and the evolution of cooperation is a major scientific riddle that resonates with numerous societal concerns, like the rise of antimicrobial resistance or the loss of biodiversity, and is even relevant to epidemiology. Population dynamics traditionally ignores fluctuations and considers static and homogeneous environments. However, fluctuations arising from randomly occurring birth and death events (demographic noise) and the change of environmental conditions (environmental variability), together with the spatial dispersal of species, play a crucial role in understanding how the size and composition of a population jointly evolve in time, i.e. the population eco-evolutionary dynamics. In this project, we focus on the ubiquitous situation where the eco-evolutionary dynamics of fluctuating populations is shaped by the coupling of demographic noise and environmental variability. As an example, we can consider population consisting of a two strains of bacteria, with a “free-rider” strain having a constant selective advantage over the other (cooperators) that produces a public good. While free riders always prevail in the absence of randomness, the probability that cooperators take over is greatly enhanced when the population size is driven by a carrying capacity that randomly switches from a state of abundance in which the population size is large to a state of scarcity in which the population shrinks.

The interdependence of environmental variability and demographic noise is poorly understood but of great importance in microbial communities, which are often subject to sudden and extreme environmental changes, and is crucial for understanding the evolution of microbial antibiotic resistance. Evolutionary game theory (EGT) describes the dynamics of populations in which the success of one type depends on the actions of the others, and provides a suitable framework to model the evolution of cooperation. While EGT models have been extensively studied in static and homogeneous environments, little is known about the joint effect of coupled environmental and demographic randomness on cooperation, and even less is known about their effects in spatial settings.

This research is related to the interdisciplinary project Eco-Evolutionary Dynamics of Fluctuating Populations, an international collaboration funded by the EPSRC in the UK and the NSF in the USA.

Some concrete objectives of this project are:

- Generalization of the approaches of Physical Review Letters 119, 158301 (2017), Journal of the Royal Society Interface 15, 20180343:1-12 (2018), Physical Review Letters 125, 048105 (2020), and analysis of how environmental randomness affects the evolution of EGT under various competition and cooperation scenarios. We will consider paradigmatic EGT models and public goods games in finite populations of fluctuating size with a varying carrying capacity.

- Study of the spatially-extended counterparts of EGT competition and cooperation scenarios, with the population is arranged on lattices of interconnected patches of fluctuating size between which individuals can migrate. The circumstances under which space favours/hinders the evolution of cooperation will be analysed.

Keywords: population dynamics, stochastic processes, fluctuations, evolutionary games, complex systems, ecology, individual-based modelling, statistical mechanics, stochastic simulations, migration, structured populations.

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