Invasion speeds for structured populations in fluctuating environments

We live in a time where climate models predict future increases in environmental variability and biological invasions are becoming increasingly frequent. A key to developing effective responses to biological invasions in increasingly variable environments will be estimates of their rates of spatial spread and the associated uncertainty of these estimates. Using stochastic, stage-structured, integro-difference equation models, we show analytically that invasion speeds are asymptotically normally distributed with a variance that decreases in time. We apply our methods to a simple juvenile-adult model with stochastic variation in reproduction and an illustrative example with published data for the perennial herb, \emph{Calathea ovandensis}. These examples buttressed by additional analysis reveal that increased variability in vital rates simultaneously slow down invasions yet generate greater uncertainty about rates of spatial spread. Moreover, while temporal autocorrelations in vital rates inflate variability in invasion speeds, the effect of these autocorrelations on the average invasion speed can be positive or negative depending on life history traits and how well vital rates ``remember'' the past

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

Neutrality and the Response of Rare Species to Environmental Variance

Neutral models and differential responses of species to environmental heterogeneity offer complementary explanations of species abundance distribution and dynamics. Under what circumstances one model prevails over the other is still a matter of debate. We show that the decay of similarity over time in rocky seashore assemblages of algae and invertebrates sampled over a period of 16 years was consistent with the predictions of a stochastic model of ecological drift at time scales larger than 2 years, but not at time scales between 3 and 24 months when similarity was quantified with an index that reflected changes in abundance of rare species. A field experiment was performed to examine whether assemblages responded neutrally or non-neutrally to changes in temporal variance of disturbance. The experimental results did not reject neutrality, but identified a positive effect of intermediate levels of environmental heterogeneity on the abundance of rare species. This effect translated into a marked decrease in the characteristic time scale of species turnover, highlighting the role of rare species in driving assemblage dynamics in fluctuating environments

The Tri-Trophic Interactions Hypothesis: Interactive Effects of Host Plant Quality, Diet Breadth and Natural Enemies on Herbivores

Several influential hypotheses in plant-herbivore and herbivore-predator interactions consider the interactive effects of plant quality, herbivore diet breadth, and predation on herbivore performance. Yet individually and collectively, these hypotheses fail to address the simultaneous influence of all three factors. Here we review existing hypotheses, and propose the tri-trophic interactions (TTI) hypothesis to consolidate and integrate their predictions. The TTI hypothesis predicts that dietary specialist herbivores (as compared to generalists) should escape predators and be competitively dominant due to faster growth rates, and that such differences should be greater on low quality (as compared to high quality) host plants. To provide a preliminary test of these predictions, we conducted an empirical study comparing the effects of plant (Baccharis salicifolia) quality and predators between a specialist (Uroleucon macolai) and a generalist (Aphis gossypii) aphid herbivore. Consistent with predictions, these three factors interactively determine herbivore performance in ways not addressed by existing hypotheses. Compared to the specialist, the generalist was less fecund, competitively inferior, and more sensitive to low plant quality. Correspondingly, predator effects were contingent upon plant quality only for the generalist. Contrary to predictions, predator effects were weaker for the generalist and on low-quality plants, likely due to density-dependent benefits provided to the generalist by mutualist ants. Because the TTI hypothesis predicts the superior performance of specialists, mutualist ants may be critical to A. gossypii persistence under competition from U. macolai. In summary, the integrative nature of the TTI hypothesis offers novel insight into the determinants of plant-herbivore and herbivore-predator interactions and the coexistence of specialist and generalist herbivores

Allocating HIV Prevention Funds in the United States: Recommendations from an Optimization Model

The Centers for Disease Control and Prevention (CDC) had an annual budget of approximately $327 million to fund health departments and community-based organizations for core HIV testing and prevention programs domestically between 2001 and 2006. Annual HIV incidence has been relatively stable since the year 2000 [1] and was estimated at 48,600 cases in 2006 and 48,100 in 2009 [2]. Using estimates on HIV incidence, prevalence, prevention program costs and benefits, and current spending, we created an HIV resource allocation model that can generate a mathematically optimal allocation of the Division of HIV/AIDS Prevention’s extramural budget for HIV testing, and counseling and education programs. The model’s data inputs and methods were reviewed by subject matter experts internal and external to the CDC via an extensive validation process. The model projects the HIV epidemic for the United States under different allocation strategies under a fixed budget. Our objective is to support national HIV prevention planning efforts and inform the decision-making process for HIV resource allocation. Model results can be summarized into three main recommendations. First, more funds should be allocated to testing and these should further target men who have sex with men and injecting drug users. Second, counseling and education interventions ought to provide a greater focus on HIV positive persons who are aware of their status. And lastly, interventions should target those at high risk for transmitting or acquiring HIV, rather than lower-risk members of the general population. The main conclusions of the HIV resource allocation model have played a role in the introduction of new programs and provide valuable guidance to target resources and improve the impact of HIV prevention efforts in the United States