New approaches of source-sink metapopulations decoupling the roles of demography and dispersal

Source-sink systems are metapopulations of habitat patches with different, and possibly temporally varying, habitat qualities, which are commonly used in ecology to study the fate of spatially extended natural populations. We propose new techniques that allow to disentangle the respective contributions of demography and dispersal to the dynamics and fate of a single species in a source-sink metapopulation. Our approach is valid for a general class of stochastic, individual-based, stepping-stone models, with density-independent demography and dispersal, provided the metapopulation is finite or else enjoys some transitivity property. We provide 1) a simple criterion of persistence, by studying the motion of a single random disperser until it returns to its initial position; 2) a joint characterization of the long-term growth rate and of the asymptotic occupancy frequencies of the ancestral lineage of a random survivor, by using large deviations theory. Both techniques yield formulae decoupling demography and dispersal, and can be adapted to the case of periodic or random environments, where habitat qualities are autocorrelated in space and possibly in time. In this last case, we display examples of coupled time-averaged sinks allowing survival, as was previously known in the absence of demographic stochasticity for fully mixing (Jansen and Yoshimura, 1998) and even partially mixing (Evans et al., 2012; Schreiber, 2010) metapopulations.Comment: arXiv admin note: substantial text overlap with arXiv:1111.253

Simple yet effective: historical proximity variables improve the species distribution models for invasive giant hogweed (Heracleum mantegazzianum s.l.) in Poland

Species distribution models are scarcely applicable to invasive species because of their breaking of the models’ assumptions. So far, few mechanistic, semi-mechanistic or statistical solutions like dispersal constraints or propagule limitation have been applied. We evaluated a novel quasi-semi-mechanistic approach for regional scale models, using historical proximity variables (HPV) representing a state of the population in a given moment in the past. Our aim was to test the effects of addition of HPV sets of different minimal recentness, information capacity and the total number of variables on the quality of the species distribution model for Heracleum mantegazzianum on 116000 km2 in Poland. As environmental predictors, we used fragments of 103 1×1 km, world- wide, free-access rasters from WorldGrids.org. Single and ensemble models were computed using BIOMOD2 package 3.1.47 working in R environment 3.1.0. The addition of HPV improved the quality of single and ensemble models from poor to good and excellent. The quality was the highest for the variants with HPVs based on the distance from the most recent past occurrences. It was mostly affected by the algorithm type, but all HPV traits (minimal recentness, information capacity, model type or the number of the time periods) were significantly important determinants. The addition of HPVs improved the quality of current projections, raising the occurrence probability in regions where the species had occurred before. We conclude that HPV addition enables semi-realistic estimation of the rate of spread and can be applied to the short-term forecasting of invasive or declining species, which also break equal-dispersal probability assumptions

Stochastic population growth in spatially heterogeneous environments: The density-dependent case

This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is spread throughout $n$ patches whose population abundances are modelled as the solutions of a system of nonlinear stochastic differential equations living on $[0,\infty)^n$. We prove that $r$, the stochastic growth rate of the total population in the absence of competition, determines the long-term behaviour of the population. The parameter $r$ can be expressed as the Lyapunov exponent of an associated linearized system of stochastic differential equations. Detailed analysis shows that if $r>0$, the population abundances converge polynomially fast to a unique invariant probability measure on $(0,\infty)^n$, while when $r<0$, the population abundances of the patches converge almost surely to $0$ exponentially fast. This generalizes and extends the results of Evans et al (2014 J. Math. Biol.) and proves one of their conjectures. Compared to recent developments, our model incorporates very general density-dependent growth rates and competition terms. Furthermore, we prove that persistence is robust to small, possibly density dependent, perturbations of the growth rates, dispersal matrix and covariance matrix of the environmental noise. Our work allows the environmental noise driving our system to be degenerate. This is relevant from a biological point of view since, for example, the environments of the different patches can be perfectly correlated. As an example we fully analyze the two-patch case, $n=2$, and show that the stochastic growth rate is a decreasing function of the dispersion rate. In particular, coupling two sink patches can never yield persistence, in contrast to the results from the non-degenerate setting treated by Evans et al.Comment: 43 pages, 1 figure, edited according to the suggestion of the referees, to appear in Journal of Mathematical Biolog