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Molecular phenotypes link genomic information with organismic functions, fitness, and evolution. Quantitative traits are complex phenotypes that depend on multiple genomic loci. In this paper, we study the adaptive evolution of a…
Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and…
We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been…
We consider an approximating sequence of interacting population models with branching, mutation and competition. Each individual is characterized by its trait and the traits of its ancestors. Birth- and death-events happen at exponential…
We consider an asexual population under strong selection-weak mutation conditions evolving on rugged fitness landscapes with many local fitness peaks. Unlike the previous studies in which the initial fitness of the population is assumed to…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing…
We show how concepts from statistical physics, such as order parameter, thermodynamic limit, and quantum phase transition, translate into biological concepts in mutation-selection models for sequence evolution and can be used there. The…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation. Biologically motivated by the influence of seasons or the variation of drug concentration during medical treatment,…
We consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its…
This work presents a population genetic model of evolution, which includes haploid selection, mutation, recombination, and drift. The mutation-selection equilibrium can be expressed exactly in closed form for arbitrary fitness functions…
Consider two ancestral lineages sampled from a system of two-dimensional branching random walks with logistic regulation in the stationary regime. We study the asymptotics of their coalescence time for large initial separation and find that…
We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly…
In the context of global warming, tree populations rely on two primary mechanisms of adaptation: phenotypic plasticity, which enables individuals to adjust their behavior in response to environmental stress, and genetic evolution, driven by…
Coevolutionary arms races form between interacting populations that constitute each other's environment and respond to mutual changes. This inherently far-from-equilibrium process finds striking manifestations in the adaptive immune system,…
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…
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…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
This Letter studies the quasispecies dynamics of a population capable of genetic repair evolving on a time-dependent fitness landscape. We develop a model that considers an asexual population of single-stranded, conservatively replicating…