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Figure 4 | BMC Evolutionary Biology

Figure 4

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

Figure 4

Detailed dynamics explaining the seemingly counterintuitive result of the high fixation probability of Host allele 1 in spite of the high prevalence of Parasite allele 1 (in Figure3top middle panel) due to the inclusion of Lotka-Volterra dynamics. In this figure we depict the dynamics that occur at the initial conditions with a low H1 frequency and a high P1 frequency. In this particular case, the low initial frequency of H1 means that H2 is initially common, which in turn favours P2. This parasite allele thus rapidly increases in frequency, subsequently causing highly pronounced H2 and P2 frequency oscillations that show larger amplitudes than the interacting H1 and P1 alleles. If low H2 frequencies coincide with a Lotka-Volterra bottleneck in the hosts, then the associated stochastic effects lead to a higher likelihood of H2 going extinct, resulting in an overall higher fixation probability of H1. The top panel shows the average population dynamics, whereas the bottom panel shows the frequency changes for the indicated host and parasite alleles across the ten independent simulations. The vertical lines in the bottom panel denote the time points where the simulation is terminated due to a loss of an allele. Out of the 10 simulation runs 9 are stopped due to the allele H2 going extinct and only one due to H1 going extinct. The interaction parameters are a=5, c=2.5, b=10/Navg=0.01.

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