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Quantitative Biology; Populations and Evolution; q-bio.PE
Abstract:
The interplay between parasites and their hosts is found in all kinds of
species and plays an important role in understanding the principles of
evolution and coevolution. Usually, the different genotypes of hosts and
parasites oscillate in their abundances. The well-established theory of
oscillatory Red Queen dynamics proposes an ongoing change in frequencies of the
different types within each species. So far, it is unclear in which way Red
Queen dynamics persists with more than two types of hosts and parasites. In our
analysis, an arbitrary number of types within two species are examined in a
deterministic framework with constant or changing population size. This general
framework allows for analytical solutions for internal fixed points and their
stability. For more than two species, apparently chaotic dynamics has been
reported. Here we show that even for two species, once more than two types are
considered per species, irregular dynamics in their frequencies can be observed
in the long run. The nature of the dynamics depends strongly on the initial
configuration of the system; the usual regular Red Queen oscillations are only
observed in some parts of the parameter region.
