Chaotic provinces in the kingdom of the Red Queen

TL;DR

This paper investigates how increasing the number of host and parasite types in Red Queen models leads to complex, often chaotic, evolutionary dynamics, extending understanding beyond traditional two-type oscillations.

Contribution

It provides a general analytical framework for multi-type Red Queen dynamics and demonstrates that chaos can arise even with two species when multiple types are considered.

Findings

More than two types per species can produce irregular, chaotic dynamics.

Regular Red Queen oscillations occur only in specific parameter regions.

Initial conditions significantly influence the long-term behavior.

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.