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 intraspecific 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.*schenk@evolbio.mpg.de 1 Background 1 Diversity, induced by continuous co-evolution can theoretically be maintained by the intense an-2 tagonistic relationship of hosts and parasites. This is the central part of the Red Queen hypothesis, 3 verbally first formulated by van Valen in 1973 [1]. The hypothesis has been mathematically formu-4 lated in many models. However, owing to the modern usage of the term 'Red Queen' for different 5 but related phenomena [2,3,4,5,6,7,8,9], the models have diverging foci and many lack the 6 implementation of stochastic forces and ecological dynamics. A common synonym for the term 7 Red Queen dynamics is fluctuating selection dynamics (FSD). Such fluctuations can be induced by 8 co-evolving hosts and parasites and, as one possibility, be driven by negative frequency-dependent 9 selection (NFDS), wher...

Coevolution does not slow the rate of loss of heterozygosity in a stochastic host-parasite model with constant population size

“…(2009) found that genetic variation is not maintained at equilibrium except when mutation is very frequent. This is echoed in simulations in finite populations, where in the absence of mutation/migration, fixation in either the host or pathogen is vary rapid (Gokhale et al, 2013;Schenk et al, 2018). In addition to including mutation, there are several theoretical indications that, rather than being driven by NFDS, the emergent 45 effects of coevolution are dependent on the existence of heterozygote advantage in diploids.…”

“…Here we compare the maintenance of genetic variation in finite coevolving populations relative to that expected under neutral drift. Previous studies of finite coevolving populations have focused instead on the number of alleles maintained by mutation and coevolution (Borghans et al, 2004), the time until loss 55 of alleles (Gokhale et al, 2013), and the impact of different model assumptions on the time until loss (Schenk et al, 2018). A direct comparison with the neutral expectation is, however, only possible analytically in simple models of host-parasite coevolution.…”