Population dynamics in the triplet annihilation model with a mutating reproduction rate

• Published in: Physica A Vol. 576; p. 126066
• Main Author: Dickman, Ronald
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.08.2021
• Subjects: Monte Carlo simulation; Nonequilibrium phase transitions; Population dynamics; Stochastic particle systems; Stochastic particle systems; Population dynamics; Monte Carlo simulation; Nonequilibrium phase transitions
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2021.126066

I study a population model in which the reproduction rate λ is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant of the triplet annihilation model introduced several decades ago Dickman (1989) in which organisms (“particles”) reproduce and diffuse on a lattice, subject to annihilation when (and only when) occupying three consecutive sites. For diffusion rates below a certain value, the population possesses two “survival strategies”: (i) rare reproduction (0<λ<λc,1), in which a low density of diffusing particles renders triplets exceedingly rare, and (ii) frequent reproduction (λ>λc,2). For λ between λc,1 and λc,2 there is no active steady state. In the rare-reproduction regime, a mutating λ leads to stochastic boom-and-bust cycles in which the reproduction rate fluctuates upward in certain regions, only to lead to extinction as the local value of λ becomes excessive. The global population can nevertheless survive due to the presence of other regions, with reproduction rates that have yet to drift upward. •Study of population dynamics under conflicting influences on reproduction rate.•Analysis of time series and spatiotemporal structure of complex evolutionary dynamics.•Event-driven Monte Carlo simulation of the model.