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

Persistence for stochastic difference equations: A mini-review

Understanding under what conditions populations, whether they be plants, animals, or viral particles, persist is an issue of theoretical and practical importance in population biology. Both biotic interactions and environmental fluctuations are key factors that can facilitate or disrupt persistence. One approach to examining the interplay between these deterministic and stochastic forces is the construction and analysis of stochastic difference equations $X_{t+1}=F(X_t,\xi_{t+1})$ where $X_t \in \R^k$ represents the state of the populations and $\xi_1,\xi_2,...$ is a sequence of random variables representing environmental stochasticity. In the analysis of these stochastic models, many theoretical population biologists are interested in whether the models are bounded and persistent. Here, boundedness asserts that asymptotically $X_t$ tends to remain in compact sets. In contrast, persistence requires that $X_t$ tends to be "repelled" by some "extinction set" $S_0\subset \R^k$. Here, results on both of these proprieties are reviewed for single species, multiple species, and structured population models. The results are illustrated with applications to stochastic versions of the Hassell and Ricker single species models, Ricker, Beverton-Holt, lottery models of competition, and lottery models of rock-paper-scissor games. A variety of conjectures and suggestions for future research are presented.Comment: Accepted for publication in the Journal of Difference Equations and Application

The Value of Information for Populations in Varying Environments

The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit where any information about future environmental variations is common to the members of the population, our model is equivalent to known models of financial investment. In this case, the population can be interpreted as a portfolio of financial assets and previous analyses have shown that a key quantity of Shannon's communication theory, the mutual information, sets a fundamental limit on the value of information. We show that this bound can be violated when accounting for features that are irrelevant in finance but inherent to biological systems, such as the stochasticity present at the individual level. This leads us to generalize the measures of uncertainty and information usually encountered in information theory

Negative Effects of Paternal Age on Children's Neurocognitive Outcomes Can Be Explained by Maternal Education and Number of Siblings

Background: Recent findings suggest advanced paternal age may be associated with impaired child outcomes, in particular, neurocognitive skills. Such patterns are worrisome given relatively universal trends in advanced countries toward delayed nuptiality and fertility. But nature and nurture are both important for child outcomes, and it is important to control for both when drawing inferences about either pathway. Methods and Findings: We examined cross-sectional patterns in six developmental outcome measures among children in the U.S. Collaborative Perinatal Project (n = 31,346). Many of these outcomes at 8 mo, 4 y, and 7 y of age (Bayley scales, Stanford Binet Intelligence Scale, Graham-Ernhart Block Sort Test, Wechsler Intelligence Scale for Children, Wide Range Achievement Test) are negatively correlated with paternal age when important family characteristics such as maternal education and number of siblings are not included as covariates. But controlling for family characteristics in general and mother’s education in particular renders the effect of paternal age statistically insignificant for most developmental measures. Conclusions: Assortative mating produces interesting relationships between maternal and paternal characteristics that can inject spurious correlation into observational studies via omitted variable bias. Controlling for both nature and nurture reveals little residual evidence of a link between child neurocognitive outcomes and paternal age in these data. Result

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

Demography and Life Histories of Sympatric Patas Monkeys, Erythrocebus patas, and Vervets, Cercopithecus aethiops, in Laikipia, Kenya

Mortality patterns are thought to be strong selective forces on life history traits, with high adult mortality and low immature mortality favoring early and rapid reproduction. Patas monkeys (Erythrocebus patas) have the highest potential rates of population increase for their body size of any haplorhine primate because they reproduce both earlier and more often. We report here 10 yr of comparative demographic data on a population of patas monkeys and a sympatric population of vervet monkeys (Cercopithecus aethiops), a closely related species differing in aspects of social system, ecology, and life history. The data reveal that 1) adult female patas monkeys have significantly higher mortality than adult female vervets; 2) infant mortality in patas monkeys is relatively low compared to the norm for mammals because it is not significantly different from that of adult female patas monkeys; and 3) infant mortality is significantly higher than adult female mortality in vervets. For both species, much of the mortality could be attributed to predation. An epidemic illness was also a major contributor to the mortality of adult female patas monkeys whereas chronic exposure to pathogens in a cold and damp microenvironment may have contributed to the mortality of infant vervets. Both populations experienced large fluctuations during the study period. Our results support the prediction from demographic models of life history evolution that high adult mortality relative to immature mortality selects for early maturation

A multi-metric approach to investigate the effects of weather conditions on the demographic of a terrestrial mammal, the European badger (Meles meles)

Models capturing the full effects of weather conditions on animal populations are scarce. Here we decompose yearly temperature and rainfall into mean trends, yearly amplitude of change and residual variation, using daily records. We establish from multi-model inference procedures, based on 1125 life histories (from 1987 to 2008), that European badger (Meles meles) annual mortality and recruitment rates respond to changes in mean trends and to variability in proximate weather components. Variation in mean rainfall was by far the most influential predictor in our analysis. Juvenile survival and recruitment rates were highest at intermediate levels of mean rainfall, whereas low adult survival rates were associated with only the driest, and not the wettest, years. Both juvenile and adult survival rates also exhibited a range of tolerance for residual standard deviation around daily predicted temperature values, beyond which survival rates declined. Life-history parameters, annual routines and adaptive behavioural responses, which define the badgers’ climatic niche, thus appear to be predicated upon a bounded range of climatic conditions, which support optimal survival and recruitment dynamics. That variability in weather conditions is influential, in combination with mean climatic trends, on the vital rates of a generalist, wide ranging and K-selected medium-sized carnivore, has major implications for evolutionary ecology and conservation

Species Interactions Alter Evolutionary Responses to a Novel Environment

Adaptation to a novel environment is altered by the presence of co-occurring species. Species in diverse communities evolved complementary resource use, which altered the functioning of the experimental ecosystems