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The mutation-selection mechanism of Darwinian evolution gives rise not only to adaptation to environmental conditions but also to the enhancement of robustness against mutations. When two or more phenotypes have the same fitness value, the…
Transient responses in disordered systems typically show a heavy-tail relaxation behavior: the decay time constant increases as time increases, revealing a spectral distribution of time constants. The asymptotic value of such transients is…
Statistical consistency in phylogenetics has traditionally referred to the accuracy of estimating phylogenetic parameters for a fixed number of species as we increase the number of characters. However, as sequences are often of fixed length…
The analysis of correlations of amino acid occurrences in globular proteins has led to the development of statistical tools that can identify native contacts -- portions of the chains that come to close distance in folded structural…
In the analysis of complex traits, genetic effects are frequently modelled as either fixed or random effects. Such assumptions serve as a foundation of defining heritability and relatedness using genome-wide single nucleotide polymorphism…
The theory of evolution states that the diversity of species can be explained by descent with modification. Therefore, all living beings are related through a common ancestor. This evolutionary process must have left traces in our molecular…
The recent explosion of genomic data has underscored the need for interpretable and comprehensive analyses that can capture complex phylogenetic relationships within and across species. Recombination, reassortment and horizontal gene…
We introduce a new model of evolution on a fitness landscape possessing a tunable degree of neutrality. The model allows us to study the general properties of molecular species undergoing neutral evolution. We find that a number of…
This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree based representation of stationary populations that holds both…
Recombinant Inbred Lines derived from divergent parental lines can display extensive segregation distortion and long-range linkage disequilibrium (LD) between distant loci. These genomic signatures are consistent with epistatic selection…
In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and…
GC-biased gene conversion (gBGC) is a recombination-associated process that favors the fixation of G/C alleles over A/T alleles. In mammals, gBGC is hypothesized to contribute to variation in GC content, rapidly evolving sequences, and the…
We consider a population model where individuals behave independently from each other and whose genealogy is described by a chronological tree called splitting tree. The individuals have i.i.d. (non-exponential) lifetime durations and give…
With advances in sequencing technologies, there are now massive amounts of genomic data from across all life, leading to the possibility that a robust Tree of Life can be constructed. However, "gene tree heterogeneity", which is when…
Speciation is fundamental to the huge diversity of life on Earth. Evidence suggests reproductive isolation arises most commonly in allopatry with a higher speciation rate in small populations. Current theory does not address this dependence…
We propose a minimal model to simulate long waiting times followed by evolutionary bursts on rugged landscapes. It combines point and inversions-like mutations as sources of genetic variation. The inversions are intended to simulate one of…
Species growing in environments that change in time and space will vary in their abundance across locations, even in the absence of persistent location preferences. Here we quantify this non-equilibrium effect by studying a minimal model of…
We propose a Markov chain approach for the evolution of a genealogical line of genomes. Our idealized genome has $N$ sites and each site can be in state $0$ or $1$. At each time step we pick a site at random. If the site is in state $0$ we…
Background: Continuous traits evolution of a group of taxa that are correlated through a phylogenetic tree is commonly modelled using parametric stochastic differential equations to represent deterministic change of trait through time,…
One of the first successes of neutral ecology was to predict realistically-broad distributions of rare and abundant species. However, it has remained an outstanding theoretical challenge to describe how this distribution of abundances…