Related papers: Phase Transition in an Exactly Solvable Extinction…
Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra…
We propose a variation of the GMS model of evolution of species. In this version, as in the GMS model, at each birth, the new species in the system is labeled with a random fitness mark, but in our variation, to each extinction event is…
The effect of diffusively correlated spatial fluctuations on the proliferation-extinction transition of autocatalytic agents is investigated numerically. Reactants adaptation to spatio-temporal active regions is shown to lead to…
The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a…
Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of…
A simple evolutionary model for biological ageing is modified such that it requires a minimum population for survival, like in human society. This social effect leads to a transition between extinction and survival of the species.
We present a quantitative model for the biological evolution of species body masses within large groups of related species, e.g., terrestrial mammals, in which body mass M evolves according to branching (speciation), multiplicative…
In models for the evolution of predation from initially purely competitive species interactions, the propensity of predation is most often assumed to be a direct consequence of the relative morphological and physiological traits of…
We introduce and study the mutating contact process, a variant of the multitype contact process, where one type mutates at a constant rate to the other type. We prove that on $\mathbb{Z}$ a single mutant cannot survive while on…
The basic mechanics of evolution have been understood since Darwin. But debate continues over whether macroevolutionary phenomena are driven primary by the fitness structure of genotype space or by ecological interaction. In this paper we…
A one dimensional stochastic exclusion process with two species of particles, $+$ and $-$, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show…
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…
Simulations of the coevolution of many interacting species are performed using the Webworld model. The model has a realistic set of predator-prey equations that describe the population dynamics of the species for any structure of the food…
Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…
Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where a fixed point is always reached and a dynamically-fluctuating phase have been found. The dynamics when…
We propose a simple model for genetic adaptation to a changing environment, describing a fitness landscape characterized by two maxima. One is associated with "specialist" individuals that are adapted to the environment; this maximum moves…
Three solvable models are set out in some detail in reviewing different types of phase transitions. Two of these relate directly to emergent critical phenomena, viz. melting and magnetic transitions in heavy rare-earth metals, and secondly,…
Introducing the effect of extinction into the so-called replicator equations in mathematical biology, we construct a general model of ecosystems. The present model shows mass extinction by its own extinction dynamics when the system…
Is evolution always gradual or can it make leaps? We examine a mathematical model of an evolutionary process on a fitness landscape and obtain analytic solutions for the probability of multi-mutation leaps, that is, several mutations…
We investigate the evolutionary rescue of a microbial population in a gradually deteriorating environment, through a combination of analytical calculations and stochastic simulations. We consider a population destined for extinction in the…