Chaotic provinces in the kingdom of the Red Queen. (27th October 2017)

• Record Type: Journal Article
• Authors: Schenk, Hanna; Traulsen, Arne; Gokhale, Chaitanya S.
• Is Part Of: Journal of theoretical biology. Volume 431(2017)
• Page Start: 1
• Page End: 10
• Publication Date: 2017-10-27
• Subjects: Coevolution -- Multiple types -- Mathematical model -- Population size -- Red Queen -- Chaos; Biology -- Periodicals; Biological Science Disciplines -- Periodicals; Biology -- Periodicals; Biologie -- Périodiques; Theoretische biologie; Biology; Periodicals; 571.05
• DOI: 10.1016/j.jtbi.2017.07.027
• Languages: English
• ISSNs: 0022-5193

Abstract

Highlights: We study Red Queen host-parasite dynamics in a flexible deterministic framework. Population sizes (constant or changing) and interaction matrices are variable. Red Queen dynamics become irregular with more types of hosts and parasites. The dynamics depend strongly on the initial conditions. Besides stasis and cycling, chaos could be routine in Red Queen dynamics. 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 under what conditions Red Queen dynamics persists, especially when the number of types per species increases. Some models show that with many types of hosts and parasites or more species chaotic dynamics occur. In our analysis, an arbitrary number of types within two species are examined in a deterministic framework with constant or changing population size and very simple interactions. This general framework allows for analytical solutions for internal fixed points and their stability. The numerical analysis shows that 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 when all types initially have similar abundance.