Lotka–Volterra dynamics kills the Red Queen: population size fluctuations and associated stochasticity dramatically change host-parasite coevolution

Gokhale, C. S., Papkou, A., Traulsen, A., & Schulenburg, H. (2013). Lotka–Volterra dynamics kills the Red Queen: population size fluctuations and associated stochasticity dramatically change host-parasite coevolution. BMC Evolutionary Biology, 13(1), 254.

Coevolution between hosts and parasites, where a host’s defense against a parasite leads the parasite to develop a new attack mechanism, and vice versa, is well documented. However, while these coevolutionary dynamics have been observed in a wide variety of systems, the actual mechanisms of selection are not entirely clear. Understanding selection can reveal the drivers of fluctuations in host and parasite populations and how these populations are likely to change over time. In this paper, Gokhale et al. (2013) examine how population dynamics and environmental variation – and Lotka-Volterra cycles in particular – drive patterns in host-parasite coevolution.

The authors propose two alternative hypotheses for the patterns of host-parasite coevolution: recurrent selective sweeps and negative frequency-dependent selection. Ultimately, the difference between these two mechanisms is that under recurrent selective sweeps, a new allele emerges and then spreads to fixation, whereas negative frequency-dependent selection results in continuous oscillations (and no allele fixation). To address these hypotheses, the authors couple a deterministic Lotka-Volterra model of population sizes for host and parasite populations with a “matching allele” model, where parasites can only attack hosts with a “matching” genotype.

This simple model produces a few unexpected results, most notably that allele fixation is not necessarily dependent on initial conditions, but rather on the combination of initial conditions in both the host and parasite populations. Host alleles are more likely to go to fixation when their abundance is initially high, but can also fix equally readily when the abundance of the corresponding parasite allele is initially low. Fixation occurs much more rapidly when Lotka-Volterra dynamics are included than when they are ignored, since bottlenecks at low population sizes increase the probability of fixation due to stochasticity. Overall, the authors’ results indicate that environmental variability and population dynamics can actually have strong effects on coevolution.