Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0910.0219

The speed of evolution in large asexual populations

Su-Chan Park·Damien Simon·Joachim Krug
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider an asexual biological population of constant size $N$ evolving in discrete time under the influence of selection and mutation. Beneficial mutations appear at rate $U$ and their selective effects $s$ are drawn from a distribution $g(s)$. After introducing the required models and concepts of mathematical population genetics, we review different approaches to computing the speed of logarithmic fitness increase as a function of $N$, $U$ and $g(s)$. We present an exact solution of the infinite population size limit and provide an estimate of the population size beyond which it is valid. We then discuss approximate approaches to the finite population problem, distinguishing between the case of a single selection coefficient, $g(s) = δ(s - s_b)$, and a continuous distribution of selection coefficients. Analytic estimates for the speed are compared to numerical simulations up to population sizes of order $10^{300}$.

Explore related subjects

q-bio.PEcond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Su-Chan Park, Damien Simon, Joachim Krug. 2009-10-01. The speed of evolution in large asexual populations. https://doi.org/10.1007/s10955-009-9915-x

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Phase transitions in microbial lineage trees

Microbial populations exhibit high cell-to-cell variability, which fundamentally shapes population behavior. A striking consequence is the existence of phase transitions, where small genetic or environmental changes trigger abrupt shifts in population dynamics. While biological phase transitions have often been proposed, connecting observed behavior to the underlying physics has remained challenging. We combine population genetics with statistical physics to show how phase transitions arise naturally in microbial populations. We highlight the existence of a first-order transition in a model of bacterial plasmid engineering and find a strict lower bound on the number of plasmids that can be stably maintained in a population.

q-bio.PE↗
arXiv2026

Phylogenetic Inference and the Stickiness of Fréchet Means, via Precise Asymptotics of an Embedded Random Walk

A well-known phenomenon in statistical analyses of populations of phylogenetic trees in the Billera-Holmes-Vogtmann space is that the topology of the Fréchet mean tree can contain multifurcations (i.e., internal nodes with more than two children), which raises the practical question of whether this reflects a population-level branching structure (hard polytomy) or merely sampling variability in the data (soft polytomy). This is an instance of the more general phenomenon of "stickiness" in non-Euclidean statistics, whereby the sample Fréchet mean in certain non-positively curved stratified spaces becomes permanently trapped in a lower-dimensional stratum. In this work, we identify a particular multidimensional random walk embedded within the Fréchet mean process, and we show that the time at which stickiness occurs is determined by the largest last-passage time above zero of the coordinates of this random walk. Using this representation, we develop a fully nonparametric procedure for estimating the probability that trifurcations in a sample Fréchet mean tree will bifurcate at some future time if more observations are collected. Lastly, we apply our methodology to a problem in phylogenetics where we consider whether an observed trifurcation in the species tree of primates, glires, and tree shrews is genuinely trifurcated at the population level.

q-bio.PE↗
arXiv2026

Coexistence coalitions in propagule disperser quasi-communities

Many natural ecosystems harbor large numbers of coexisting species competing for far fewer distinct resources, in apparent defiance of the competitive exclusion principle. Various mechanisms have been proposed to explain this apparent paradox, often pertaining to organisms with a two-stage sessile--propagule life cycle. Here we develop a stochastic model class for such propagule disperser communities that combines competition--colonization trade-offs, spatial heterogeneity, demographic stochasticity, as well as inherited trait variation, and recover several classical models as special or limiting cases. Using bifurcation analysis, we classify equilibrium coalitions near the extinction threshold and give sufficient conditions for their realization by macroscopic equilibria away from the threshold, bypassing the costly numerical computation of the actual equilibrium states. Illustrative examples examine the resulting trait distributions and coalition patterns, demonstrating the interactive effects of different coexistence mechanisms.

q-bio.PE↗