Related papers: Extinction rate fragility in population dynamics
The extinction of species is a core process that affects the diversity of life on Earth. One way of investigating the causes and consequences of extinctions is to build conceptual ecological models, and to use the dynamical outcomes of such…
Species extinction is a core process that affects the diversity of life on Earth. Competition between species in a population is considered by ecological niche-based theories as a key factor leading to different severity of species…
Populations of species in ecosystems are often constrained by availability of resources within their environment. In effect this means that a growth of one population, needs to be balanced by comparable reduction in populations of others.…
In general, the rates of infection and removal (whether through recovery or death) are nonlinear functions of the number of infected and susceptible individuals. One of the simplest models for the spread of infectious diseases is the SIR…
We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…
There is empirical evidence from a range of disciplines that as the connectivity of a network increases, we observe an increase in the average fitness of the system. But at the same time, there is an increase in the proportion of…
Bacteria evolve in volatile environments and complex spatial structures. Migration, fluctuations and environmental variability therefore have a significant impact on the evolution of microbial populations. Here, we consider a class of…
This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between…
We introduce a model of biological evolution where species evolve in response to biotic interactions and a fluctuating environmental stress. The species may either become extinct or mutate to acquire a new fitness value when the effective…
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…
The extinction time of an isolated population can be exponentially reduced by a periodic modulation of its environment. We investigate this effect using, as an example, a stochastic branching-annihilation process with a time-dependent…
Aging is thought to be a consequence of intrinsic breakdowns in how genetic information is processed. But mounting experimental evidence suggests that aging can be slowed. To help resolve this mystery, I derive a mortality equation which…
A simple model of biological extinction with variable system size is presented that exhibits a power-law distribution of extinction event sizes. The model is a generalization of a model recently introduced by Newman (Proc. R. Soc. Lond.…
We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and…
Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been…
The fragility index is a clinically motivated metric designed to supplement the $p$ value during hypothesis testing. The measure relies on two pillars: selecting cases to have their outcome modified and modifying the outcomes. The measure…
The death toll for Covid-19 may be reduced by dividing the population into two classes, the vulnerable and the fit, with different lockdown regimes. Instead of one reproduction number there now are four parameters. These make it possible to…
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…
Population dynamics on a rugged landscape is studied analytically and numerically within a simple discrete model for evolution of N individuals in one-dimensional fitness space. We reduce the set of master equations to a single Fokker-Plank…
For a susceptible-infectious-susceptible (SIS) infection model in a heterogeneous population, we present simple formulae giving the leading-order asymptotic (large population) behaviour of the mean persistence time, from an endemic state to…