Linking micro and macroevolution in the presence of migration.

Understanding macroevolutionary patterns is central to evolutionary biology. This involves the process of divergence within a species, which starts at the microevolutionary level, for instance, when two subpopulations evolve towards different phenotypic optima. The speed at which these optima are reached is controlled by the degree of stabilising selection, which pushes the mean trait towards different optima in the different subpopulations, and ongoing migration that pulls the mean phenotype away from that optimum. Traditionally, macro phenotypic evolution is modelled by directional selection processes, but these models usually ignore the role of migration within species. Here, our goal is to reconcile the processes of micro and macroevolution by modelling migration as part of the speciation process. More precisely, we introduce an Ornstein-Uhlenbeck (OU) model where migration happens between two subpopulations within a branch of a phylogeny and this migration decreases over time as it happens during speciation. We then use this model to study the evolution of trait means along a phylogeny, as well as the way phenotypic disparity between species changes with successive epochs. We show that ignoring the effect of migration in sampled time-series data biases significantly the estimation of the selective forces acting upon it. We also show that migration decreases the expected phenotypic disparity between species and we analyse the effect of migration in the particular case of niche filling. We further introduce a method to jointly estimate selection and migration from time-series data. Our model extends traditional quantitative genetics results of selection and migration from a microevolutionary time frame to multiple speciation events at a macroevolutionary scale. Our results further support that not accounting for gene flow has important consequences in inferences at both the micro and macroevolutionary scale.

Fitting Markovian binary trees using global and individual demographic data.

We consider a class of continuous-time branching processes called Markovian binary trees (MBTs), in which the individuals lifetime and reproduction epochs are modelled using a transient Markovian arrival process (TMAP). We develop methods for estimating the parameters of the TMAP by using either age-specific averages of reproduction and mortality rates, or age-specific individual demographic data. Depending on the degree of detail of the available information, we follow a weighted non-linear regression or a maximum likelihood approach. We discuss several criteria to determine the optimal number of states in the underlying TMAP. Our results improve the fit of an existing MBT model for human demography, and provide insights for the future conservation management of the threatened Chatham Island black robin population.

How old is this bird? The age distribution under some phase sampling schemes.

In this paper, we use a finite-state continuous-time Markov chain with one absorbing state to model an individual's lifetime. Under this model, the time of death follows a phase-type distribution, and the transient states of the Markov chain are known as phases. We then attempt to provide an answer to the simple question "What is the conditional age distribution of the individual, given its current phase"? We show that the answer depends on how we interpret the question, and in particular, on the phase observation scheme under consideration. We then apply our results to the computation of the age pyramid for the endangered Chatham Island black robin Petroica traversi during the monitoring period 2007-2014.

The Markovian binary tree applied to demography.

We apply matrix analytic methods and branching processes theory to a comparison of female populations in different countries. We show how the same mathematical model allows us to determine characteristics about individual women, such as the distribution of her lifetime, the time until her first and her last daughter, and the number of daughters, as well as to analyze properties of the whole female family generated by a first woman, such as the extinction probability of the family, the distributions of the time until extinction, of the family size at any given time and of the total progeny.