Amaury Lambert

ABGD, Automatic Barcode Gap Discovery for primary species delimitation

Within uncharacterized groups, DNA barcodes, short DNA sequences that are present in a wide range of species, can be used to assign organisms into species. We propose an automatic procedure that sorts the sequences into hypothetical species based on the barcode gap, which can be observed whenever the divergence among organisms belonging to the same species is smaller than divergence among organisms from different species. We use a range of prior intraspecific divergence to infer from the data a model‐based one‐sided confidence limit for intraspecific divergence. The method, called Automatic Barcode Gap Discovery (ABGD), then detects the barcode gap as the first significant gap beyond this limit and uses it to partition the data. Inference of the limit and gap detection are then recursively applied to previously obtained groups to get finer partitions until there is no further partitioning. Using six published data sets of metazoans, we show that ABGD is computationally efficient and performs well for standard prior maximum intraspecific divergences (a few per cent of divergence for the five data sets), except for one data set where less than three sequences per species were sampled. We further explore the theoretical limitations of ABGD through simulation of explicit speciation and population genetics scenarios. Our results emphasize in particular the sensitivity of the method to the presence of recent speciation events, via (unrealistically) high rates of speciation or large numbers of species. In conclusion, ABGD is fast, simple method to split a sequence alignment data set into candidate species that should be complemented with other evidence in an integrative taxonomic approach.

The contour of splitting trees is a Lévy process

Splitting trees are those random trees where individuals give birth at a constant rate during a lifetime with general distribution, to i.i.d. copies of themselves. The width process of a splitting tree is then a binary, homogeneous Crump-Mode-Jagers (CMJ) process, and is not Markovian unless the lifetime distribution is exponential (or a Dirac mass at {∞}). Here, we allow the birth rate to be infinite, that is, pairs of birth times and life spans of newboms form a Poisson point process along the lifetime of their mother, with possibly infinite intensity measure. A splitting tree is a random (so-called) chronological tree. Each element of a chronological tree is a (so-called) existence point (ν, τ) of some individual ν (vertex) in a discrete tree where τ is a nonnegative real number called chronological level (time). We introduce a total order on existence points, called linear order, and a mapping ϕ from the tree into the real line which preserves this order. The inverse of ϕ is called the exploration process, and the projection of this inverse on chronological levels the contour process. For splitting trees truncated up to level r, we prove that a thus defined contour process is a Levy process reflected below τ and killed upon hitting 0. This allows one to derive properties of (i) splitting trees: conceptual proof of Le Gall-Le Jans theorem in the finite variation case, exceptional points, coalescent point process and age distribution; (ii) CMJ processes: one-dimensional marginals, conditionings, limit theorems and asymptotic numbers of individuals with infinite versus finite descendances.

The branching process with logistic growth

In order to model random density-dependence in population dynamics, we construct the random analogue of the well-known logistic process in the branching processes’ framework. This density-dependence corresponds to intraspecific competition pressure, which is ubiquitous in ecology, and translates mathematically into a quadratic death rate. The logistic branching process, or LB-process, can thus be seen as (the mass of) a fragmentation process (corresponding to the branching mechanism) combined with constant coagulation rate (the death rate is proportional to the number of possible coalescing pairs). In the continuous state-space setting, the LB-process is a time-changed (in Lamperti’s fashion) Ornstein-Uhlenbeck type process. We obtain similar results for both constructions: when natural deaths do not occur, the LB-process converges to a specified distribution; otherwise, it goes extinct a.s. In the latter case, we provide the expectation and the Laplace transform of the absorption time, as a function of the solution of a Riccati dierential equation. We also show that the quadratic regulatory term allows the LB-process to start at infinity, despite the fact that births occur infinitely often as the initial state goes to 1. This result can be viewed as an extension of the pure death process starting from infinity associated to Kingman’s coalescent, when some fragmentation is added.

Quasi-stationary distributions and diffusion models in population dynamics

In this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to

Population Dynamics and Random Genealogies

- \infty

Proof(s) of the Lamperti representation of continuous-state branching processes ∗

at the origin, and the diffusion to have an entrance boundary at

Mass extinction in poorly known taxa

+\infty

Completely asymmetric Lévy processes confined in a finite interval

. These diffusions arise as images, by a deterministic map, of generalized Feller diffusions, which themselves are obtained as limits of rescaled birth--death processes. Generalized Feller diffusions take nonnegative values and are absorbed at zero in finite time with probability

ADAPTIVE RADIATION DRIVEN BY THE INTERPLAY OF ECO‐EVOLUTIONARY AND LANDSCAPE DYNAMICS

1

Coalescence times for the branching process

. An important example is the logistic Feller diffusion. We give sufficient conditions on the drift near