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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…
A class of models for large-scale evolution and mass extinctions is presented. These models incorporate environmental changes on all scales, from influences on a single species to global effects. This is a step towards a unified picture of…
We present a stochastic model for the size of a taxon in paleobiology, in which we allow for the evolution of new taxon members, and both individual and catastrophic extinction events. The model uses ideas from the theory of birth and death…
Epidemic outbreaks of new pathogens, or known pathogens in new populations, cause a great deal of fear because they are hard to predict. For theoretical models of disease spreading, on the other hand, quantities characterizing the outbreak…
Habitat destruction threatens the viability of many populations, but its full consequences can take considerable time to unfold. Much of the discourse surrounding extinction debts--the number of species that persist transiently following…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
Established populations often exhibit oscillations in their sizes. If a population is isolated, intrinsic stochasticity of elemental processes can ultimately bring it to extinction. Here we study extinction of oscillating populations in a…
We consider epidemic extinction in finite networks with broad variation in local connectivity. Generalizing the theory of large fluctuations to random networks with a given degree distribution, we are able to predict the most probable, or…
A two-type two-sex branching process is introduced with the aim of describing the interaction of predator and prey populations with sexual reproduction and promiscuous mating. In each generation and in each species the total number of…
The fast diffusion equation is analyzed on a bounded domain with Dirichlet boundary conditions, for which solutions are known to extinct in finite time. We construct invariant manifolds that provide a finite-dimensional approximation near…
We discuss a simple model of co-evolution. In order to emphasise the effect of interaction between individuals the entire population is subjected to the same physical environment. Species are emergent structures and extinction, origination…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
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…
Given a branching random walk on a set $X$, we study its extinction probability vectors $\mathbf q(\cdot,A)$. Their components are the probability that the process goes extinct in a fixed $A\subseteq X$, when starting from a vertex $x\in…
A bit-string model for the evolution of a population of haploid organisms, subject to competition, reproduction with mutation and selection is studied, using mean field theory and Monte Carlo simulations. We show that, depending on…
We study the contact process on the configuration model with a power law degree distribution, when the exponent is smaller than or equal to two. We prove that the extinction time grows exponentially fast with the size of the graph and prove…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…
Despite tremendous interest in the topic and decades of research, the origins of the major losses of biodiversity in the history of life on Earth remain elusive. A variety of possible causes for these mass-extinction events have been…
Phylogenetic diversity is a measure for describing how much of an evolutionary tree is spanned by a subset of species. If one applies this to the (unknown) subset of current species that will still be present at some future time, then this…