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The stellar encounter rate Gamma has been shown to be strongly correlated with the number of X-ray binaries in clusters and also to the number of radio pulsars. However, the pulsar populations in different clusters show remarkably different…
Since steep declines in a population's size also typically alter its composition, population bottlenecks are considered highly important for evolution. However, despite such significance, the mechanisms governing the impact of a given…
We consider the evolution of an asexually reproducing population in an uncorrelated random fitness landscape in the limit of infinite genome size, which implies that each mutation generates a new fitness value drawn from a probability…
While evolutionary algorithms are known to be very successful for a broad range of applications, the algorithm designer is often left with many algorithmic choices, for example, the size of the population, the mutation rates, and the…
We study the evolutionary dynamics of a haploid population of infinite size recombining with a probability $r$ in a two locus model. Starting from a low fitness locus, the population is evolved under mutation, selection and recombination…
Linked beneficial and deleterious mutations are known to decrease the fixation probability of a favorable mutation in large asexual populations. While the hindering effect of strongly deleterious mutations on adaptive evolution has been…
We simultaneously study the dynamics of the growth of errors and the question of the faithfulness of simulations of $N$-body systems. The errors are quantified through the numerical reversibility of small-$N$ spherical systems, and by…
Classical population genetics a priori assigns fitness to alleles without considering molecular or functional properties of proteins that these alleles encode. Here we study population dynamics in a model where fitness can be inferred from…
In 1995 I wrote a paper: "A Speed Limit for Evolution" whose main result was that evolution must proceed rather slowly, in accordance with the earlier views and intuitions of many authors. The abstract of the paper said: "The genetic…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…
We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and…
We consider a branching-selection particle system on the real line. In this model the total size of the population at time $n$ is limited by $\exp\left(a n^{1/3}\right)$. At each step $n$, every individual dies while reproducing…
A model is presented relating the evolution of genomic GC content over time to AT$\rightarrow$GC and GC$\rightarrow$AT mutation rates. By employing It\^o calculus it is shown that if mutation rates in asexually reproducing organisms are…
A new approach to understanding evolution [Val09], namely viewing it through the lens of computation, has already started yielding new insights, e.g., natural selection under sexual reproduction can be interpreted as the Multiplicative…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Here we develop a general approach to modeling heterogeneous populations with discrete…
The Luria-Delbr\"uck distribution is a classical model of mutations in cell kinetics. It is obtained as a limit when the probability of mutation tends to zero and the number of divisions to infinity. It can be interpreted as a compound…
We present results from an experiment similar to one performed by Packard (1988), in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task. Packard examined the frequency of evolved CA…
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…
We consider a stochastic individual-based model for the evolution of a haploid, asexually reproducing population. The space of possible traits is given by the vertices of a (possibly directed) finite graph $G=(V,E)$. The evolution of the…
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…