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Star-shaped branching patterns of genealogies are common in marine species. High-fecundity marine populations are characterized by low ratios of effective to actual population size, which reflect high variance in reproductive success among…
How natural selection acts to limit the proliferation of transposable elements (TEs) in genomes has been of interest to evolutionary biologists for many years. To describe TE dynamics in populations, many previous studies have used models…
In this work we model the dynamics of a population that evolves as a continuous time branching process with a trait structure and ecological interactions in form of mutations and competition between individuals. We generalize existing…
While Neutral Theory famously describes the number of discrete genetic differences in populations, we consider the number of genetic backgrounds under which such differences are observed - setting limits to the generalizability of their…
Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of…
Due to the conventional distinction between ecological (rapid) and evolutionary (slow)timescales, ecological and population models to date have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has…
The process of speciation, where an ancestral species divides in two or more new species, involves several geographic, environmental and genetic components that interact in a complex way. Understanding all these elements at once is…
Consider a branching process with a homogeneous reproduction law. Sampling a single cell uniformly from the population at a time $T > 0$ and looking along the sampled cell's ancestral lineage, we find that the reproduction law is…
Speciation is of fundamental importance to understanding the huge diversity of life on Earth. In contrast to current phenomenological models, we develop a biophysically motivated approach to study speciation involving the co-evolution of…
We consider a population of N individuals, whose dynamics through time is represented by a biparental Moran model with two types: an advantaged type and a disadvantaged type. The advantage is due to a mutation, transmitted in a Mendelian…
In a randomly-mating biparental population of size $N$ there are, with high probability, individuals who are genealogical ancestors of every extant individual within approximately $\log_2(N)$ generations into the past. We use this result of…
I review the evolutionary history of human populations in Europe with an emphasis on what has been learned in recent years through the study of ancient DNA. Human populations in Europe ~430-39kya (archaic Europeans) included Neandertals and…
Understanding the population structure and patterns of gene flow within species is of fundamental importance to the study of evolution. In the fields of population and evolutionary genetics, measures of genetic differentiation are commonly…
We study a class of Cannings models with population size $N$ having a mixed multinomial offspring distribution with random success probabilities $W_1,\ldots,W_N$ induced by independent and identically distributed positive random variables…
We develop Bayesian inference methods for a recently-emerging type of epigenetic data to study the transmission fidelity of DNA methylation patterns over cell divisions. The data consist of parent-daughter double-stranded DNA methylation…
The recently discovered correspondence between the distribution of rapidity gaps in electron-nucleus diffractive processes and the statistics of the height of genealogical trees in branching random walks is reviewed. In addition, a new…
Commonly recognized evolutionarily relevant effects of sexual reproduction include increased diversity, accelerated adaptation, and constrained accumulation of deleterious mutations, along with a secondary effect of species genotype…
The observation that phenotypic variability is ubiquitous in isogenic populations has led to a multitude of experimental and theoretical studies seeking to probe the causes and consequences of this variability. Whether it be in the context…
In this paper we propose a new mathematical model capable of merging Darwinian Evolution, Human History and SETI into a single mathematical scheme: 1) Darwinian Evolution over the last 3.5 billion years is defined as one particular…
This contribution is concerned with mathematical models for the dynamics of the genetic composition of populations evolving under recombination. Recombination is the genetic mechanism by which two parent individuals create the mixed type of…