With the internet, a massive amount of information on species abundance can be collected by citizen science programs. However, these data are often difficult to use directly in statistical inference, as their collection is generally opportunistic, and the distribution of the sampling effort is often not known. In this article, we develop a general statistical framework to combine such "opportunistic data" with data collected using schemes characterized by a known sampling effort. Under some structural assumptions regarding the sampling effort and detectability, our approach makes it possible to estimate the relative abundance of several species in different sites. It can be implemented through a simple generalized linear model. We illustrate the framework with typical bird datasets from the Aquitaine region in south-western France. We show that, under some assumptions, our approach provides estimates that are more precise than the ones obtained from the dataset with a known sampling effort alone. When the opportunistic data are abundant, the gain in precision may be considerable, especially for rare species. We also show that estimates can be obtained even for species recorded only in the opportunistic scheme. Opportunistic data combined with a relatively small amount of data collected with a known effort may thus provide access to accurate and precise estimates of quantitative changes in relative abundance over space and/or time.

Abstract. Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial points of view, and differ only by their mating preference: two individuals with the same genotype have a higher probability to mate and produce a viable offspring. The population is subdivided in several patches and individuals may migrate between them. We show that mating preferences by themselves, even if they are very small, are enough to entail reproductive isolation between patches, and we provide the time needed for this isolation to occur as a function of the population size. Our results rely on a fine study of the stochastic process and of its deterministic limit in large population, which is given by a system of coupled nonlinear differential equations. Besides, we propose several generalisations of our model, and prove that our findings are robust for those generalisations.