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.

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−∞at the origin, and the diffusion to have an entrance boundary at +∞. 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 1. An important example is the logistic Feller diffusion. We give sufficient conditions on the drift near 0 and near +∞ for the existence of quasi-stationary distributions, as well as rate of convergence in the Yaglom limit and existence of the Q-process. We also show that, under these conditions, there is exactly one quasi-stationary distribution, and that this distribution attracts all initial distributions under the conditional evolution, if and only if +∞ is an entrance boundary. In particular, this gives a sufficient condition for the uniqueness of quasi-stationary distributions. In the proofs spectral theory plays an important role on L2 of the reference measure for the killed process

Splitting trees are those random trees where individuals give birth at 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 lifespans of newborns 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 (v, τ ) of some individual v (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 τ , we prove that thus defined contour process is a Lévy process reflected below τ and killed upon hitting 0. This allows to derive properties of (i) splitting trees: conceptual proof of Le Gall-Le Jan's theorem in the finite variation case, exceptional points, coalescent point process, age distribution; (ii) CMJ processes: onedimensional marginals, conditionings, limit theorems, asymptotic numbers of individuals with infinite vs finite descendances.Running head. The contour of splitting trees. AMS Subject Classification (2000). Primary 60J80; secondary 37E25, 60G51, 60G55, 60G70, 60J55, 60J75, 60J85, 92D25.

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In order to model random density-dependence in population dynamics, we construct the random analogue of the well-known logistic process in the branching process' 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 functional of the solution of a Riccati differential 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 \infty. This result can be viewed as an extension of the pure-death process starting from infinity associated to Kingman's coalescent, when some independent fragmentation is added.Comment: Published at http://dx.doi.org/10.1214/105051605000000098 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Since the 1980s, many have suggested we are in the midst of a massive extinction crisis, yet only 799 (0.04%) of the 1.9 million known recent species are recorded as extinct, questioning the reality of the crisis. This low figure is due to the fact that the status of very few invertebrates, which represent the bulk of biodiversity, have been evaluated. Here we show, based on extrapolation from a random sample of land snail species via two independent approaches, that we may already have lost 7% (130,000 extinctions) of the species on Earth. However, this loss is masked by the emphasis on terrestrial vertebrates, the target of most conservation actions. Projections of species extinction rates are controversial because invertebrates are essentially excluded from these scenarios. Invertebrates can and must be assessed if we are to obtain a more realistic picture of the sixth extinction crisis.

Summary 1.There exists a continuing dilemma in prioritizing conservation actions for large carnivores. Habitat loss, poaching, and prey depletion have often been cited as the three primary threats, but there is debate over the relative importance of each. 2. We assess the relative importance of poaching and prey depletion rates, and use existing information in the literature and multi-type branching process and deterministic felid population models to address four lines of evidence used to infer that tiger populations are inherently resilient to high mortality rates. 3. Our results suggest that tigers, more so than leopards or cougars, require large populations to persist, are quite susceptible to modest increases in mortality, and less likely to recover quickly after population declines. Demographic responses that would ensure population persistence with mortality rates that are sustainable for cougars or leopards are biologically unrealistic for tigers. 4. We propose alternative interpretations of evidence used to suggest that tigers are inherently resilient to high mortality rates. In contrast to other solitary felids, tigers breed later and their inter-birth interval is larger, making them less resilient to poaching. A model used to support the contention that prey depletion has greater impact on population persistence than poaching appears to be based on false premises. Camera-trapping data that suggest positive population growth despite low survival rate cannot differentiate mortality from emigration, and does not differentiate the impact of varying survival rate on different sex-age classes; for example, low survival rate of dispersers is tolerable if survival rate of adult breeding females is high. 5. Synthesis and applications. While high prey numbers are essential to sustain tiger populations, our results suggest prey recovery efforts will not be sufficient if mortality rates reach 15%. Extrapolating demographic responses from other, even closely related species to develop conservation strategies can be misleading. Reduction of human-caused mortality, especially of resident breeding females, appears to be the most essential short-term conservation effort that must be made. Since mortality rates are usually unknown and generally stochastic in nature, any management policy that might reduce survival rates should be firmly avoided.