Finite metapopulation models with density-dependent migration and stochastic local dynamics

The effects of small density-dependent migration on the dynamics of a metapopulation are studied in a model with stochastic local dynamics. We use a diffusion approximation to study how changes in the migration rate and habitat occupancy affect the rates of local colonization and extinction. If the emigration rate increases or if the immigration rate decreases with local population size, a positive expected rate of change in habitat occupancy is found for a greater range of habitat occupancies than when the migration is density-independent. In contrast, the reverse patterns of density dependence in respective emigration and immigration reduce the range of habitat occupancies where the metapopulation will be viable. This occurs because density-dependent migration strongly influences both the establishment and rescue effects in the local dynamics of metapopulations.     

Probability of fixation in a heterogeneous environment

We investigate the probability of fixation of a new mutation arising in a metapopulation that ranges over a heterogeneous selective environment. Using simulations, we test the performance of several approximations of this probability, including a new analytical approximation based on separation of the timescales of selection and migration. We extend all approximations to multideme metapopulations with arbitrary population structure. Our simulations show that no single approximation produces accurate predictions of fixation probabilities for all cases of potential interest. At the limits of low and high migration, previously published approximations are found to be highly accurate. The new separation-of-timescales approach provides the best approximations for intermediate rates of migration among habitats, provided selection is not too intense. For nonzero migration and relatively strong selection, all approximations perform poorly. However, the probability of fixation is bounded above and below by the approximations based on low and high migration limits. Surprisingly, in our simulations with symmetric migration, heterogeneous selection in a metapopulation never decreased-and sometimes substantially increased-the probability of fixation of a new allele compared to metapopulations experiencing homogeneous selection with the same mean selection intensity.     

Developmental stability across the breeding distribution of the scissor-tailed flycatcher (Tyrannus forficatus)

A central question in ecology is how individual fitness interacts with the spatial variation in population density and habitat characteristics across species' ranges. We used fluctuating asymmetry (FA) as a measure of developmental stability (DS) in individuals of Tyrannus forficatus to estimate the suitability of sites of varying abundance and position within the species' range. FA in the inner-tail feathers of males and females is not spatially correlated across the species' range. FA in males increases towards the centre of the range and is not correlated with abundance. FA in females is not correlated with position in the range or abundance. Our results suggest that optimal sites are found throughout the range of the species, whereas suboptimal sites are mainly found towards the centre of the range. Additionally, our results suggest that abundance may not reflect the suitability of sites across species' ranges.     

From individual behavior to metapopulation dynamics: unifying the patchy population and classic metapopulation models

Spatially structured populations in patchy habitats show much variation in migration rate, from patchy populations in which individuals move repeatedly among habitat patches to classic metapopulations with infrequent migration among discrete populations. To establish a common framework for population dynamics in patchy habitats, we describe an individual-based model (IBM) involving a diffusion approximation of correlated random walk of individual movements. As an example, we apply the model to the Glanville fritillary butterfly (Melitaea cinxia) inhabiting a highly fragmented landscape. We derive stochastic patch occupancy model (SPOM) approximations for the IBMs assuming pure demographic stochasticity, uncorrelated environmental stochasticity, or completely correlated environmental stochasticity in local dynamics. Using realistic parameter values for the Glanville fritillary, we show that the SPOMs mimic the behavior of the IBMs well. The SPOMs derived from IBMs have parameters that relate directly to the life history and behavior of individuals, which is an advantage for model interpretation and parameter estimation. The modeling approach that we describe here provides a unified framework for patchy populations with much movements among habitat patches and classic metapopulations with infrequent movements.     

Allee effects, invasion pinning, and species' borders

All species' ranges are the result of successful past invasions. Thus, models of species' invasions and their failure can provide insight into the formation of a species' geographic range. Here, we study the properties of invasion models when a species cannot persist below a critical population density known as an "Allee threshold." In both spatially continuous reaction-diffusion models and spatially discrete coupled ordinary-differential-equation models, the Allee effect can cause an invasion to fail. In patchy landscapes (with dynamics described by the spatially discrete model), range limits caused by propagation failure (pinning) are stable over a wide range of parameters, whereas, in an uninterrupted habitat (with dynamics described by a spatially continuous model), the zero velocity solution is structurally unstable and thus unlikely to persist in nature. We derive conditions under which invasion waves are pinned in the discrete space model and discuss their implications for spatially complex dynamics, including critical phenomena, in ecological landscapes. Our results suggest caution when interpreting abrupt range limits as stemming either from competition between species or a hard environmental limit that cannot be crossed: under a wide range of plausible ecological conditions, species' ranges may be limited by an Allee effect. Several example systems appear to fit our general model.     

The relation of density regulation to habitat specialization, evolution of a species' range, and the dynamics of biological invasions

Prior studies of the evolution of species' niches and ranges have identified the importance of within-population genetic variance, migration rate, and environmental heterogeneity in determining evolutionarily stable patterns of species' range and habitat use. Different combinations of these variables can produce either habitat specialists or generalists and cause either stable range limits or unbounded expansion. We examine the effect of density regulation on a species' range and habitat use within a landscape comprised of two discrete habitats and along continuous environmental gradients. Using the theta-logistic formulation, we demonstrate the following. (1) Spatially uniform density regulation generally weakens gene swamping and opposes habitat specialization and range limitation. (2) The form of density regulation should play an important role in determining whether the equilibrium species' range is limited by gene flow. (3) Even when no long-term limited-range equilibrium occurs, quasi-stable (or even contracting) range limits may be maintained for a long period during the initial phases of an invasion; the length of this period depends on the form of density regulation. (4) The steady state invasion speed in heterogeneous environments depends on the form of density regulation. Implications for the study of biological invasions are discussed, and directions for further exploration are sketched.     

A general modeling framework for describing spatially structured population dynamics

Variation in movement across time and space fundamentally shapes the abundance and distribution of populations. Although a variety of approaches model structured population dynamics, they are limited to specific types of spatially structured populations and lack a unifying framework. Here, we propose a unified network‐based framework sufficiently novel in its flexibility to capture a wide variety of spatiotemporal processes including metapopulations and a range of migratory patterns. It can accommodate different kinds of age structures, forms of population growth, dispersal, nomadism and migration, and alternative life‐history strategies. Our objective was to link three general elements common to all spatially structured populations (space, time and movement) under a single mathematical framework. To do this, we adopt a network modeling approach. The spatial structure of a population is represented by a weighted and directed network. Each node and each edge has a set of attributes which vary through time. The dynamics of our network‐based population is modeled with discrete time steps. Using both theoretical and real‐world examples, we show how common elements recur across species with disparate movement strategies and how they can be combined under a unified mathematical framework. We illustrate how metapopulations, various migratory patterns, and nomadism can be represented with this modeling approach. We also apply our network‐based framework to four organisms spanning a wide range of life histories, movement patterns, and carrying capacities. General computer code to implement our framework is provided, which can be applied to almost any spatially structured population. This framework contributes to our theoretical understanding of population dynamics and has practical management applications, including understanding the impact of perturbations on population size, distribution, and movement patterns. By working within a common framework, there is less chance that comparative analyses are colored by model details rather than general principles.     

Stabilizing Spatially-Structured Populations through Adaptive Limiter Control

Stabilizing the dynamics of complex, non-linear systems is a major concern across several scientific disciplines including ecology and conservation biology. Unfortunately, most methods proposed to reduce the fluctuations in chaotic systems are not applicable to real, biological populations. This is because such methods typically require detailed knowledge of system specific parameters and the ability to manipulate them in real time; conditions often not met by most real populations. Moreover, real populations are often noisy and extinction-prone, which can sometimes render such methods ineffective. Here, we investigate a control strategy, which works by perturbing the population size, and is robust to reasonable amounts of noise and extinction probability. This strategy, called the Adaptive Limiter Control (ALC), has been previously shown to increase constancy and persistence of laboratory populations and metapopulations of Drosophila melanogaster. Here, we present a detailed numerical investigation of the effects of ALC on the fluctuations and persistence of metapopulations. We show that at high migration rates, application of ALC does not require a priori information about the population growth rates. We also show that ALC can stabilize metapopulations even when applied to as low as one-tenth of the total number of subpopulations. Moreover, ALC is effective even when the subpopulations have high extinction rates: conditions under which another control algorithm had previously failed to attain stability. Importantly, ALC not only reduces the fluctuation in metapopulation sizes, but also the global extinction probability. Finally, the method is robust to moderate levels of noise in the dynamics and the carrying capacity of the environment. These results, coupled with our earlier empirical findings, establish ALC to be a strong candidate for stabilizing real biological metapopulations.     

Evolutionarily accelerated invasions: the rate of dispersal evolves upwards during the range advance of cane toads

Human activities are changing habitats and climates and causing species' ranges to shift. Range expansion brings into play a set of powerful evolutionary forces at the expanding range edge that act to increase dispersal rates. One likely consequence of these forces is accelerating rates of range advance because of evolved increases in dispersal on the range edge. In northern Australia, cane toads have increased their rate of spread fivefold in the last 70 years. Our breeding trials with toads from populations spanning the species' invasion history in Australia suggest a genetic basis to dispersal rates and interpopulation genetic variation in such rates. Toads whose parents were from the expanding range front dispersed faster than toads whose parents were from the core of the range. This difference reflects patterns found in their field-collected mothers and fathers and points to heritable variance in the traits that have accelerated the toads' rate of invasion across tropical Australia over recent decades. Taken together with demonstrated spatial assortment by dispersal ability occurring on the expanding front, these results point firmly to ongoing evolution as a driving force in the accelerated expansion of toads across northern Australia.     

Interspecies physiological variation as a tool for cross-species assessments of global warming-induced endangerment: validation of an intrinsic determinant of macroecological and phylogeographic structure

Global warming is now recognized as the dominant threat to biodiversity because even protected populations and habitats are susceptible. Nonetheless, current criteria for evaluating species' relative endangerment remain purely ecological, and the accepted conservation strategies of habitat preservation and population management assume that species can mount ecological responses if afforded protection. The insidious threat from climate change is that it will attenuate or preclude ecological responses by species that are physiologically constrained; yet, quantitative, objective criteria for assessing relative susceptibility of diverse taxa to warming-induced stress are wanting. We explored the utility of using interspecies physiological variation for this purpose by relating species' physiological phenotypes to landscape patterns of ecological and genetic exchange. Using a salamander model system in which ecological, genetic and physiological diversity are well characterized, we found strong quantitative relationships of basal metabolic rates (BMRs) to both macroecological and phylogeographic patterns, with decreasing BMR leading to dispersal limitation (small contemporary ranges with marked phylogeographic structure). Measures of intrinsic physiological tolerance, which vary systematically with macroecological and phylogeographic patterns, afford objective criteria for assessing endangerment across a wide range of species and should be incorporated into conservation assessment criteria that currently rely exclusively upon ecological predictors.     

Effects of habitat heterogeneity and local adaptation on the body condition of a forest passerine at the edge of its distributional range

We studied fluctuating asymmetry and feather growth rates as indicators of fitness of blackcaps ( Sylvia atricapilla ) breeding at the border of their distribution range in the Iberian Peninsula. Iberian blackcaps increase their abundance with increasing rainfall and ground cover of brambles. In border habitats, they are sedentary and morphologically different from migrants, suggesting that they could be adapted to peripheral conditions. We tested whether juvenile body condition depends on (1) distance from the centre of the range, (2) mean precipitation or (3) bramble cover. Controlling for environmental variation, we tested for differences between migratory and sedentary populations. Body condition varied across the Iberian gradient in parallel with changes in precipitation. Controlling for this effect, sedentary populations were in better body condition than migratory populations. Our results support the idea that environmental heterogeneity causes fitness to fluctuate across species' ranges, and also that local adaptation may mean that peripheral populations are more than a 'tail end' of the species.  © 2003 The Linnean Society of London . Biological Journal of the Linnean Society , 2003, 78 , 479–488.     

IMPLICATIONS OF NON-LINEAR DENSITY DEPENDENCE

Abstract: Ranges of the ratio of maximum net productivity level (MNPL) to carrying capacity (K) are explored in general models for pinnipeds and odontocetes. MNPL/K is used in management of marine mammals but no empirical evidence exists to limit the range of values expected. Density dependent changes in age-specific birth and death rates have been used to infer MNPL/K. Non-linearities in these rates do not translate directly to population growth curves. The simple models demonstrate: (1) density dependence is likely to involve more than a single parameter (such as birth rate), (2) MNPL/K can be greatly reduced from that inferred from one strongly non-linear parameter when changes in other parameters are linear, (3) ranges of MNPL/K depend on biological limits on ranges of fecundity and survival rates, and (4) the magnitude and sign of bias incurred by inferring MNPL/K from functional forms of single parameters cannot be determined. Given current empirical evidence the range of MNPL/K for marine mammals as a group is large. Although MNPL/K should not be inferred from single parameter non-linearities, distributions of MNPL/K values can be generated through models which account for single species ranges for birth and death rates and maximum population growth rate.     

Malarial parasites as geographical markers in migratory birds?

We tested the hypothesis that malarial parasites (Plasmodium and Haemoproteus) of black-throated blue warblers (Dendroica caerulescens) provide sufficient geographical signal to track population movements between the warbler's breeding and wintering habitats in North America. Our results from 1083 warblers sampled across the species' breeding range indicate that parasite lineages are geographically widespread and do not provide site-specific information. The wide distribution of malarial parasites probably reflects postnatal dispersal of their hosts as well as mixing of breeding populations on the wintering range. When compared to geographically structured parasites of sedentary Caribbean songbirds, patterns of malarial infections in black-throated blue warblers suggest that host-malaria dynamics of migratory and sedentary bird populations may be subject to contrasting selection pressures.     

Species' borders: a unifying theme in ecology

Biologists have long been fascinated by species' borders, and with good reason. Understanding the ecological and evolutionary dynamics of species' borders may prove to be the key that unlocks new understanding across a wide range of biological phenomena. After all, geographic range limits are a point of entry into understanding the ecological niche and threshold responses to environmental change. Elucidating patterns of gene flow to, and returning from, peripheral populations can provide important insights into the nature of adaptation, speciation and coevolution. Species' borders form natural laboratories for the study of the spatial structure of species interactions. Comparative studies from the center to the margin of species' ranges allow us to explore species' demographic responses along gradients of increasing environmental stress. Range dynamics further permit investigation into invasion dynamics and represent bellwethers for a changing climate. This set of papers explores ecological and evolutionary dynamics of species' borders from diverse empirical and theoretical perspectives.     

A unifying framework for metapopulation dynamics

Many biologically important processes, such as genetic differentiation, the spread of disease, and population stability, are affected by the (natural or enforced) subdivision of populations into networks of smaller, partly isolated, subunits. Such "metapopulations" can have extremely complex dynamics. We present a new general model that uses only two functions to capture, at the metapopulation scale, the main behavior of metapopulations. We show how complex, structured metapopulation models can be translated into our generalized framework. The metapopulation dynamics arising from some important biological processes are illustrated: the rescue effect, the Allee effect, and what we term the "antirescue effect." The antirescue effect captures instances where high migration rates are deleterious to population persistence, a phenomenon that has been largely ignored in metapopulation conservation theory. Management regimes that ignore a significant antirescue effect will be inadequate and may actually increase extinction risk. Further, consequences of territoriality and conspecific attraction on metapopulation-level dynamics are investigated. The new, simplified framework can incorporate knowledge from epidemiology, genetics, and population biology in a phenomenological way. It opens up new possibilities to identify and analyze the factors that are important for the evolution and persistence of the many spatially subdivided species.     

Evaluating the metapopulation consequences of ecological traps

Ecological traps occur when environmental changes cause maladaptive habitat selection. Despite their relevance to metapopulations, ecological traps have been studied predominantly at local scales. How these local impacts scale up to affect the dynamics of spatially structured metapopulations in heterogeneous landscapes remains unexplored. We propose that assessing the metapopulation consequences of traps depends on a variety of factors that can be grouped into four categories: the probability of encounter, the likelihood of selection, the fitness costs of selection and species-specific vulnerability to these costs. We evaluate six hypotheses using a network-based metapopulation model to explore the relative importance of factors across these categories within a spatial context. Our model suggests (i) traps are most severe when they represent a large proportion of habitats, severely reduce fitness and are highly attractive, and (ii) species with high intrinsic fitness will be most susceptible. We provide the first evidence that (iii) traps may be beneficial for metapopulations in rare instances, and (iv) preferences for natal-like habitats can magnify the effects of traps. Our study provides important insight into the effects of traps at landscape scales, and highlights the need to explicitly consider spatial context to better understand and manage traps within metapopulations.     

Population genetics and the evolution of geographic range limits in an annual plant

Abstract Theoretical models of species' geographic range limits have identified both demographic and evolutionary mechanisms that prevent range expansion. Stable range limits have been paradoxical for evolutionary biologists because they represent locations where populations chronically fail to respond to selection. Distinguishing among the proposed causes of species' range limits requires insight into both current and historical population dynamics. The tools of molecular population genetics provide a window into the stability of range limits, historical demography, and rates of gene flow. Here we evaluate alternative range limit models using a multilocus data set based on DNA sequences and microsatellites along with field demographic data from the annual plant Clarkia xantiana ssp. xantiana. Our data suggest that central and peripheral populations have very large historical and current effective population sizes and that there is little evidence for population size changes or bottlenecks associated with colonization in peripheral populations. Whereas range limit populations appear to have been stable, central populations exhibit a signature of population expansion and have contributed asymmetrically to the genetic diversity of peripheral populations via migration. Overall, our results discount strictly demographic models of range limits and more strongly support evolutionary genetic models of range limits, where adaptation is prevented by a lack of genetic variation or maladaptive gene flow.     

Distribution-wide effects of climate on population densities of a declining migratory landbird

1. Increases in global temperatures have created concern about effects of climatic variability on populations, and climate has been shown to affect population dynamics in an increasing number of species. Testing for effects of climate on population densities across a species' distribution allows for elucidation of effects of climate that would not be apparent at smaller spatial scales. 2. Using autoregressive population models, we tested for effects of the North Atlantic Oscillation (NAO) and the El Ni?o Southern Oscillation (ENSO) on annual population densities of a North American migratory landbird, the yellow-billed cuckoo Coccyzus americanus, across the species' breeding distribution over a 37-year period (1966-2002). 3. Our results indicate that both the NAO and ENSO have affected population densities of C. americanus across much of the species' breeding range, with the strongest effects of climate in regions in which these climate systems have the strongest effects on local temperatures. Analyses also indicate that the strength of the effect of local temperatures on C. americanus populations was predictive of long-term population decline, with populations that were more negatively affected by warm temperatures experiencing steeper declines. 4. Results of this study highlight the importance of distribution-wide analyses of climatic effects and demonstrate that increases in global temperatures have the potential to lead to additional population declines.