Lotka-Volterra and the Red Queen

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Gokhale, CS, Papkou, A., Traulsen, A., & Schulenburg, H.

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

BMC Evolutionary Biology,

13(1), 254


“Now here you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that” (The Red Queen) – Lewis Carroll (Through the Looking-Glass)

Host-parasite coevolution is generally believed to follow Red Queen dynamics consisting of ongoing oscillations in the frequencies of interacting host and parasite alleles. This belief is founded on previous theoretical work, which assumes infinite or constant population size. To what extent are such sustained oscillations realistic?

Acknowledging two critical pieces of realism we show that such Red Queen oscillations cannot be sustained over time: (i) population size fluctuations, caused by the antagonism of the interaction in concordance with the Lotka-Volterra relationship; and (ii) stochasticity, acting in any finite population. Together, these two factors cause fast allele fixation. Furthermore fixation is not restricted to common alleles, as expected from drift, but also seen for originally rare alleles under a wide parameter space, potentially facilitating spread of novel variants.

Our results call for a paradigm shift in our understanding of host-parasite coevolution, strongly suggesting that these are driven by recurrent selective sweeps rather than continuous allele oscillations.

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Lotka-Volterra and the Red Queen was last modified on Chaitanya S. Gokhale