Related papers: Error-induced extinction in a multi-type critical …
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
Populations are often subject to catastrophes that cause mass removal of individuals. Many stochastic growth models have been considered to explain such dynamics. Among the results reported, it has been considered whether dispersion…
We investigate how a catastrophic event (modeled as a temporary fall of the reproduction rate) increases the extinction probability of an isolated self-regulated stochastic population. Using a variant of the Verhulst logistic model as an…
Multiple-type branching processes that model the spread of infectious diseases are investigated. In these stochastic processes, the disease goes through multiple stages before it eventually disappears. We mostly focus on the critical…
In population biology, the Allee dynamics refer to negative growth rates below a critical population density. In this Letter, we study a reaction-diffusion (RD) model of population growth and dispersion in one dimension, which incorporates…
We study the extinction risk of a fragmented population residing on a network of patches coupled by migration, where the local patch dynamics include the Allee effect. We show that mixing between patches dramatically influences the…
Birth-death processes form a natural class where ideas and results on large deviations can be tested. In this paper, we derive a large deviation principle under the assumption that the rate of a jump down (death) is growing asymptotically…
We study the extinction of epidemics in a simplicial susceptible-infected-susceptible model, where each susceptible individual becomes infected either by two-body interactions ($S+I \to 2I$) with a rate $\beta$ or by three-body interactions…
I study a population model in which the reproduction rate lambda 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…
In a new type of percolation phase transition, which was observed in a set of non-equilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential…
The main substance of the paper concerns the growth rate and the classification (ergodicity, transience) of a family of random trees. In the basic model, new edges appear according to a Poisson process of parameter $\lambda$ and leaves can…
Quasispecies theory predicts that there is a critical mutation probability above which a viral population will go extinct. Above this threshold the virus loses the ability to replicate the best adapted genotype, leading to a population…
When computing the expected value of time till extinction of a Birth and Death process, the usual textbook approach results in an extreme case of numerical ill-conditioning, which prevents us from getting accurate answers beyond the first…
The asymptotic behavior, as $n\rightarrow \infty $ of the probability of the event that a decomposable critical branching process $\mathbf{Z}(m)=(Z_{1}(m),...,Z_{N}(m)),$ $m=0,1,2,...,$ with $N$ types of particles dies at moment $n$ is…
Cancer progression is an evolutionary process that is driven by mutation and selection in a population of tumor cells. We discuss mathematical models of cancer progression, starting from traditional multistage theory. Each stage is…
We establish connections between the absorption probabilities of a class of birth-death processes with killing, and the stationary tail of a related class of birth-death processes with catastrophes. The major ingredients of the proofs are a…
Environmental noise can cause an exponential reduction in the mean time to extinction (MTE) of an isolated population. We study this effect on an example of a stochastic birth-death process with rates modulated by a colored Gaussian noise.…
The causes of major and rapid transitions observed in biological macroevolution as well as in the evolution of social systems are a subject of much debate. Here we identify the proximate causes of crashes and recoveries that arise…
Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore it is reasonable to expect mutation rates will evolve downwards. However, we find this…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…