Related papers: Conditions for the Trivers-Willard hypothesis to b…
The management of endangered species as metapopulations is becoming increasingly common. Diverse aspects of metapopulation dynamics and management have received attention in recent years. In particular, translocation of individuals between…
In evolution theory the concept of a fitness landscape has played an important role, evolution itself being portrayed as a hill-climbing process on a rugged landscape. In this article it is shown that in general, in the presence of other…
A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of…
The Wright-Fisher model is the most popular population model for describing the behaviour of evolutionary systems with a finite population size. Approximations to the model have commonly been used for the analysis of time-resolved genome…
We consider a population organised hierarchically with respect to size in such a way that the growth rate of each individual depends only on the presence of larger individuals. As a concrete example one might think of a forest, in which the…
The concept of fitness is central to evolution, but it quantifies only the expected number of offspring an individual will produce. The actual number of offspring is also subject to noise, arising from environmental or demographic…
Deterministic evolutionary theory robustly predicts that populations displaying altruistic behaviours will be driven to extinction by mutant cheats that absorb common benefits but do not themselves contribute. Here we show that when…
Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the…
Modern developments in population dynamics emphasize the role of the turnover of individuals. In the new approaches stable population size is a dynamic equilibrium between different mortality and fecundity factors instead of an arbitrary…
In unicellular organisms such as bacteria and in most viruses, mutations mainly occur during reproduction. Thus, genotypes with a high birth rate should have a higher mutation rate. However, standard models of asexual adaptation such as the…
We consider the hypothesis that Evolution promotes population-wide genome patterns that, under randomization, ensures the External Validity of adaptations across population members. An adaptation is Externally Valid (EV) if its effect holds…
Consider an advantageous allele that arises in a haploid population of size $N$ evolving in continuous time according to a skewed reproduction mechanism, which generates under neutrality genealogies lying in the domain of attraction of a…
Biological evolution depends on the passing down to subsequent generations of genetic information encoding beneficial traits, and on the removal of unfit individuals by a selection mechanism. However, selection acts on phenotypes, and is…
We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as 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…
Our work was motivated by a recent study on birth defects of infants born to pregnant women exposed to a certain medication for treating chronic diseases. Outcomes such as birth defects are rare events in the general population, which often…
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,…
This work proves new probability bounds relating to the height, width, and size of Galton-Watson trees. For example, if $T$ is any Galton-Watson tree, and $H$, $W$, and $|T|$ are the height, width, and size of $T$, respectively, then $H/W$…
Identifying and quantifying the benefits of sex and recombination is a long standing problem in evolutionary theory. In particular, contradictory claims have been made about the existence of a benefit of recombination on high dimensional…
In sexual population, recombination reshuffles genetic variation and produces novel combinations of existing alleles, while selection amplifies the fittest genotypes in the population. If recombination is more rapid than selection,…