Stochastic population growth in spatially heterogeneous environments

Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. To understand the interactive effects of environmental stochasticity, spatial heterogeneity, and dispersal on population growth, we study the following model for population abundances in $n$ patches: the conditional law of $X_{t+dt}$ given $X_t=x$ is such that when $dt$ is small the conditional mean of $X_{t+dt}^i-X_t^i$ is approximately $[x^i\mu_i+\sum_j(x^j D_{ji}-x^i D_{ij})]dt$, where $X_t^i$ and $\mu_i$ are the abundance and per capita growth rate in the $i$-th patch respectivly, and $D_{ij}$ is the dispersal rate from the $i$-th to the $j$-th patch, and the conditional covariance of $X_{t+dt}^i-X_t^i$ and $X_{t+dt}^j-X_t^j$ is approximately $x^i x^j \sigma_{ij}dt$. We show for such a spatially extended population that if $S_t=(X_t^1+...+X_t^n)$ is the total population abundance, then $Y_t=X_t/S_t$, the vector of patch proportions, converges in law to a random vector $Y_\infty$ as $t\to\infty$, and the stochastic growth rate $\lim_{t\to\infty}t^{-1}\log S_t$ equals the space-time average per-capita growth rate \sum_i\mu_i\E[Y_\infty^i] experienced by the population minus half of the space-time average temporal variation \E[\sum_{i,j}\sigma_{ij}Y_\infty^i Y_\infty^j] experienced by the population. We derive analytic results for the law of $Y_\infty$, find which choice of the dispersal mechanism $D$ produces an optimal stochastic growth rate for a freely dispersing population, and investigate the effect on the stochastic growth rate of constraints on dispersal rates. Our results provide fundamental insights into "ideal free" movement in the face of uncertainty, the persistence of coupled sink populations, the evolution of dispersal rates, and the single large or several small (SLOSS) debate in conservation biology.Comment: 47 pages, 4 figure

The risk of cryptorchidism among sons of women working in horticulture in Denmark: a cohort study

<p>Abstract</p> <p>Background</p> <p>Androgens are crucial for normal testicular descent. Studies show that some pesticides have estrogenic or antiandrogenic effects, and that female workers exposed to pesticides have increased risk of having a boy with cryptorchidism. The main objective of the present study was to investigate whether pregnant women exposed to pesticides due to their work in horticulture experience excess risk of having sons with cryptorchidism.</p> <p>Methods</p> <p>We conducted a cohort study of pregnant women working in horticulture using four cohorts including one cohort established with data from the departments of occupational medicine in Jutland and Funen and three existing mother-child cohorts (n = 1,468). A reference group was established from the entire Danish population of boys born in the period of 1986-2007 (n = 783,817). Nationwide Danish health registers provided information on birth outcome, cryptorchidism diagnosis and orchiopexy. The level of occupational exposure to pesticides was assessed by expert judgment blinded towards outcome status. Risk of cryptorchidism among exposed horticulture workers compared to the background population and to unexposed horticulture workers was assessed by Cox regression models.</p> <p>Results</p> <p>Pesticide exposed women employed in horticulture had a hazard ratio (HR) of having cryptorchid sons of 1.39 (95% CI 0.84; 2.31) and a HR of orchiopexy of 1.34 (0.72; 2.49) compared to the background population. Analysis divided into separate cohorts revealed a significantly increased risk of cryptorchidism in cohort 2: HR 2.58 (1.07;6.20) and increased risk of orchiopexy in cohort 4: HR 2.76 (1.03;7.35), but no significant associations in the other cohorts. Compared to unexposed women working in horticulture, pesticide exposed women had a risk of having sons with cryptorchidism of 1.34 (0.30; 5.96) and of orchiopexy of 1.93 (0.24;15.4).</p> <p>Conclusions</p> <p>The data are compatible with a slightly increased risk of cryptorchidism in sons of women exposed to pesticides by working in horticulture.</p