Competitive intransitivity, population interaction structure, and strategy coexistence
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Date
2016-06-14
Authors
Laird, Robert A.
Schamp, Brandon S.
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Abstract
Intransitive competition occurs when competing strategies cannot be listed in a hierarchy, but rather
form loops – as in the game Rock-Paper-Scissors. Due to its cyclic competitive replacement, competitive
intransitivity promotes strategy coexistence, both in Rock-Paper-Scissors and in higher-richness communities. Previous work has shown that this intransitivity-mediated coexistence is strongly
influenced by spatially explicit interactions, compared to when populations are well mixed. Here, we
extend and broaden this line of research and examine the impact on coexistence of intransitive
competition taking place on a continuum of small-world networks linking spatial lattices and regular
random graphs. We use simulations to show that the positive effect of competitive intransitivity on
strategy coexistence holds when competition occurs on networks toward the spatial end of the
continuum. However, in networks that are sufficiently disordered, increasingly violent fluctuations in
strategy frequencies can lead to extinctions and the prevalence of monocultures. We further show that
the degree of disorder that leads to the transition between these two regimes is positively dependent
on population size; indeed for very large populations, intransitivity-mediated strategy coexistence may
even be possible in regular graphs with completely random connections. Our results emphasize the
importance of interaction structure in determining strategy dynamics and diversity.
Description
Sherpa Romeo green journal. Permission to archive accepted author manuscript
Keywords
Cyclical population dynamics , Evolutionary graph theory , Quenched randomness , Rock-paper-scissors , Small-world networks
Citation
Laird, R. A., & Schamp, B. S. (2015). Competitive intransitivity, population interaction structure, and strategy coexistence. Journal of Theoretical Biology, 365, 149-158. http://dx.doi.org/10.1016/j.jtbi.2014.10.010