How long do Red Queen dynamics survive under genetic drift? A comparative analysis of evolutionary and eco-evolutionary models

Abstract

Background: Red Queen dynamics are defined as long term co-evolutionary dynamics, often with oscillations of genotype abundances driven by fluctuating selection in host-parasite systems. Much of our current understanding of these dynamics is based on theoretical concepts explored in mathematical models that are mostly (i) deterministic, inferring an infinite population size and (ii) evolutionary, thus ecological interactions that change population sizes are excluded. Here, we recall the different mathematical approaches used in the current literature on Red Queen dynamics. We then compare models from game theory (evo) and classical theoretical ecology models (eco-evo), that are all derived from individual interactions and are thus intrinsically stochastic. We assess the influence of this stochasticity through the time to the first loss of a genotype within a host or parasite population. Results: The time until the first genotype is lost ("extinction time"), is shorter when ecological dynamics, in the form of a changing population size, is considered. Furthermore, when individuals compete only locally with other individuals extinction is even faster. On the other hand, evolutionary models with a fixed population size and competition on the scale of the whole population prolong extinction and therefore stabilise the oscillations. The stabilising properties of intra-specific competitions become stronger when population size is increased and the deterministic part of the dynamics gain influence. In general, the loss of genotype diversity can be counteracted with mutations (or recombination), which then allow the populations to recurrently undergo negative frequency-dependent selection dynamics and selective sweeps. Conclusion: Although the models we investigated are equal in their biological motivation and interpretation, they have diverging mathematical properties both in the derived deterministic dynamics and the derived stochastic dynamics. We find that models that do not consider intraspecific competition and that include ecological dynamics by letting the population size vary, lose genotypes -and thus Red Queen oscillations -faster than models with competition and a fixed population size.

Understanding evolutionary and ecological dynamics using a continuum limit

“…The fixation probability, mean extinction time, and stationary distribution are accessible by the same means as for the continuum limit. Applications of diffusion approximations are abundant and cover diverse topics (e.g., Assaf & Mobilia, 2011;Constable et al, 2016;Czuppon & Gokhale, 2018;Czuppon & Traulsen, 2018;Débarre & Otto, 2016;Houchmandzadeh, 2015;Kang & Park, 2017;Koopmann et al, 2017;McLeod & Day, 2019;Parsons et al, 2018;Reichenbach et al, 2007;Schenk et al, 2020;Serrao & Täuber, 2017;Traulsen et al, 2005).…”

Population size impacts host–pathogen coevolution

“…Consequently, large populations have a higher evolutionary potential than populations of finite size or subjected to bottlenecks, which are constrained by low genetic diversity and genetic drift [14]. Theoretical studies demonstrated that population size can change the rate of reciprocal adaptation [15], shift the outcome of antagonistic interactions in favour of the antagonist with a larger population size [16] and produce qualitatively distinct coevolutionary dynamics [17][18][19]. However, empirical evidence for these effects is scarce.…”

Viral mutation, contact rates and testing: a DCM study of fluctuations

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