Related papers: Muller's ratchet with overlapping generations
In many statistical problems, a more coarse-grained model may be suitable for population-level behaviour, whereas a more detailed model is appropriate for accurate modelling of individual behaviour. This raises the question of how to…
We present an elementary model of random size varying population given by a stationary continuous state branching process. For this model we compute the joint distribution of: the time to the most recent common ancestor, the size of the…
The paper is devoted to the study of the asymptotic behaviour of Moran process in random environment, say random selection. In finite population, the Moran process may be degenerate in finite time, thus we will study its limiting process in…
When beneficial mutations are rare, they accumulate by a series of selective sweeps. But when they are common, many beneficial mutations will occur before any can fix, so there will be many different mutant lineages in the population…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
The stationary asymptotic properties of the diffusion limit of a multi-type branching process with neutral mutations are studied. For the critical and subcritical processes the interesting limits are those of quasi-stationary distributions…
The interrelationships of the fundamental biological processes natural selection, mutation, and stochastic drift are quantified by the entropy rate of Moran processes with mutation, measuring the long-run variation of a Markov process. The…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
A mutator is an allele that increases the mutation rate throughout the genome by disrupting some aspect of DNA replication or repair. Mutators that increase the mutation rate by the order of 100 fold have been observed to spontaneously…
Large language models can exhibit unexpected behavior in the blink of an eye. In a recent computer use demo, a language model switched from coding to Googling pictures of Yellowstone, and these sudden shifts in behavior have also been…
We consider the classical Wright-Fisher model with mutation and selection. Mutations occur independently in each locus, and selection is performed according to the sharp peak landscape. In the asymptotic regime studied in [3], a…
A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…
A simple one-dimensional cellular automaton model with threshold dynamics is introduced. The cumulative distribution of the size of the relaxations is analytically computed and behaves as a power law with an exponent equal to -1. This…
The importance of mutator clones in the adaptive evolution of asexual populations is not fully understood. Here we address this problem by using an ab initio microscopic model of living cells, whose fitness is derived directly from their…
Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic, such that the dynamics becomes deterministic…
Under natural assumptions a Feller type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, positively regular). Namely, it is proved…
Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…
Evolution occurs in populations of reproducing individuals. It is well known that population structure can affect evolutionary dynamics. Traditionally, natural selection is studied between mutants that differ in reproductive rate, but are…
Fluctuations due to a super-position of uncorrelated Lorentzian pulses with a random distribution of amplitudes and duration times are considered. These are demonstrated to be strongly intermittent in the limit of weak pulse overlap,…