Related papers: A Relaxed Drift Diffusion Model for Phylogenetic T…
Understanding which phenotypic traits are consistently correlated throughout evolution is a highly pertinent problem in modern evolutionary biology. Here, we propose a multivariate phylogenetic latent liability model for assessing the…
The value of a continuous character evolving on a phylogenetic tree is commonly modelled as the location of a particle moving under one-dimensional Brownian motion with constant rate. The Brownian motion model is best suited to characters…
We study the large population limit of the Moran process, assuming weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuous model that may highlight the genetic-drift (neutral…
Relaxed random walk (RRW) models of trait evolution introduce branch-specific rate multipliers to modulate the variance of a standard Brownian diffusion process along a phylogeny and more accurately model overdispersed biological data.…
Comparative biologists are often interested in inferring covariation between multiple biological traits sampled across numerous related taxa. To properly study these relationships, we must control for the shared evolutionary history of the…
We investigate the nature of genetic drift acting at the leading edge of range expansions, building on recent results in [Hallatschek et al., Proc.\ Natl.\ Acad.\ Sci., \textbf{104}(50): 19926 - 19930 (2007)]. A well mixed population of two…
Inferring dependencies between complex biological traits while accounting for evolutionary relationships between specimens is of great scientific interest yet remains infeasible when trait and specimen counts grow large. The…
The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the…
The branching structure of biological evolution confers statistical dependencies on phenotypic trait values in related organisms. For this reason, comparative macroevolutionary studies usually begin with an inferred phylogeny that describes…
A central problem in biology is to understand how organisms evolve and adapt to their environment by acquiring variations in the observable characteristics or traits of species across the tree of life. With the growing availability of…
Inferring concerted changes among biological traits along an evolutionary history remains an important yet challenging problem. Besides adjusting for spurious correlation induced from the shared history, the task also requires sufficient…
Predicting Pandemic evolution involves complex modeling challenges, often requiring detailed discrete mathematics executed on large volumes of epidemiological data. Differential equations have the advantage of offering smooth, well-behaved…
Two stochastic models of susceptible/infected/removed (SIR) type are introduced for the spread of infection through a spatially-distributed population. Individuals are initially distributed at random in space, and they move continuously…
Phylogenetic comparative methods explore the relationships between quantitative traits adjusting for shared evolutionary history. This adjustment often occurs through a Brownian diffusion process along the branches of the phylogeny that…
We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
Influenza viruses undergo continual antigenic evolution allowing mutant viruses to evade host immunity acquired to previous virus strains. Antigenic phenotype is often assessed through pairwise measurement of cross-reactivity between…
We consider the question of the stability of evolutionary algorithms to gradual changes, or drift, in the target concept. We define an algorithm to be resistant to drift if, for some inverse polynomial drift rate in the target function, it…
A simple way to model phenotypic evolution is to assume that after splitting, the trait values of the sister species diverge as independent Brownian motions. Relying only on a prior distribution for the underlying species tree (conditioned…
We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold…