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Maintenance of sexual reproduction and genetic recombination imposes physiological costs when compared to parthenogenic reproduction, most prominently: for maintaining the corresponding (molecular) machinery, for finding a mating partner,…
We exhibit a stochastic discrete time model that has exactly the Eigen model as its deterministic continuous limit. Such model can be divided into two phases: reproduction followed by neutral selection. This result suggests that Eigen model…
Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. We focus on a single locus, any number of alleles in a two-gender dioecious population, for a large class of systems within population…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…
We consider an exponentially growing population of cells undergoing mutations and ask about the effect of reproductive fluctuations (genetic drift) on its long-term evolution. We combine first step analysis with the stochastic dynamics of a…
Sweepstakes reproduction may be generated by chance matching of reproduction with favorable environmental conditions. Gene genealogies generated by sweepstakes reproduction are in the domain of attraction of multiple-merger coalescents…
Crossover and mutation are the two main operators that lead to new solutions in evolutionary approaches. In this article, a new method of performing the crossover phase is presented. The problem of choice is evolutionary decision tree…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
Conventional population genetics considers the evolution of a limited number of genotypes corresponding to phenotypes with different fitness. As model phenotypes, in particular RNA secondary structure, have become computationally tractable,…
Recruitment dynamics, or the distribution of the number of offspring among individuals, is central for understanding ecology and evolution. Sweepstakes reproduction (heavy right-tailed offspring number distribution) is central for…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
Cells with the same genome can exist in different phenotypes. and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during development, reprogramming…
A probability model is presented for the dynamics of mutation-selection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full age-specific demographic schedules. The…
We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a 3-type…
We introduce an evolutionary algorithm called recombinator-$k$-means for optimizing the highly non-convex kmeans problem. Its defining feature is that its crossover step involves all the members of the current generation, stochastically…
It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with…
Genomic evolution can be viewed as string-editing processes driven by mutations. An understanding of the statistical properties resulting from these mutation processes is of value in a variety of tasks related to biological sequence data,…