Modelling population growth in stage-grouped organisms: a simple extension to the Leslie model

A simple method for decomposing a population's stage grouping into the underlying age structure is described. The population's dynamics can then be predicted using standard age-structured models, such as Leslie's matrix model. The method overcomes objections to previous attempts to use Leslie's procedure for modelling population growth in stage-grouped organisms. A hypothetical example is used to illustrate the new technique.     

Limited evolutionary rescue of locally adapted populations facing climate change

Dispersal is a key determinant of a population''s evolutionary potential. It facilitates the propagation of beneficial alleles throughout the distributional range of spatially outspread populations and increases the speed of adaptation. However, when habitat is heterogeneous and individuals are locally adapted, dispersal may, at the same time, reduce fitness through increasing maladaptation. Here, we use a spatially explicit, allelic simulation model to quantify how these equivocal effects of dispersal affect a population''s evolutionary response to changing climate. Individuals carry a diploid set of chromosomes, with alleles coding for adaptation to non-climatic environmental conditions and climatic conditions, respectively. Our model results demonstrate that the interplay between gene flow and habitat heterogeneity may decrease effective dispersal and population size to such an extent that substantially reduces the likelihood of evolutionary rescue. Importantly, even when evolutionary rescue saves a population from extinction, its spatial range following climate change may be strongly narrowed, that is, the rescue is only partial. These findings emphasize that neglecting the impact of non-climatic, local adaptation might lead to a considerable overestimation of a population''s evolvability under rapid environmental change.     

Allelic Richness following Population Founding Events – A Stochastic Modeling Framework Incorporating Gene Flow and Genetic Drift

Allelic richness (number of alleles) is a measure of genetic diversity indicative of a population''s long-term potential for adaptability and persistence. It is used less commonly than heterozygosity as a genetic diversity measure, partially because it is more mathematically difficult to take into account the stochastic process of genetic drift for allelic richness. This paper presents a stochastic model for the allelic richness of a newly founded population experiencing genetic drift and gene flow. The model follows the dynamics of alleles lost during the founder event and simulates the effect of gene flow on maintenance and recovery of allelic richness. The probability of an allele''s presence in the population was identified as the relevant statistical property for a meaningful interpretation of allelic richness. A method is discussed that combines the probability of allele presence with a population''s allele frequency spectrum to provide predictions for allele recovery. The model''s analysis provides insights into the dynamics of allelic richness following a founder event, taking into account gene flow and the allele frequency spectrum. Furthermore, the model indicates that the “One Migrant per Generation” rule, a commonly used conservation guideline related to heterozygosity, may be inadequate for addressing preservation of diversity at the allelic level. This highlights the importance of distinguishing between heterozygosity and allelic richness as measures of genetic diversity, since focusing merely on the preservation of heterozygosity might not be enough to adequately preserve allelic richness, which is crucial for species persistence and evolution.     

How many and when? Optimising targeted gene flow for a step change in the environment

Targeted gene flow is an emerging conservation strategy that involves introducing individuals with particular traits to places where these traits are of benefit. One obvious application is to adapt a recipient population to a known threat, but questions remain as to how best to achieve this. Here, we vary timing and size of the introduction to maximise our objective – survival of the recipient population's genome. We explore a generic population model as well as a specific example – the northern quoll, an Australian marsupial predator threatened by the toxic cane toad. We reveal a trade‐off between preserving the recipient genome and reducing population extinction risk, but key management levers can often optimise this so that nearly 100% of the recipient population's genome is preserved. Any action was better than none but the size of the benefit was sensitive to outbreeding depression, recombination rate, and the timing and size of the introduction.     

Effects of directional environmental change on extinction dynamics in experimental microbial communities are predicted by a simple model

Global temperatures are expected to rise between 1.1 and 6.4°C over the next 100 years, although the exact rate will depend on future greenhouse emissions, and will vary spatially. Temperature can alter an individual's metabolic rate, and consequently birth and death rates. In declining populations, these alterations may manifest as changes in the rate of that population's decline, and subsequently the timing of extinction events. Predicting such events could therefore be of considerable use. We use a small‐scale experimental system to investigate how the rate of temperature change can alter a population's time to extinction, and whether it is possible to predict this event using a simple phenomenological model that incorporates information about population dynamics at a constant temperature, published scaling of metabolic rates, and temperature. In addition, we examine 1) the relative importance of the direct effects of temperature on metabolic rate, and the indirect effects (via temperature driven changes in body size), on predictive accuracy (defined as the proximity of the predicted date of extinction to the mean observed date of extinction), 2) the combinations of model parameters that maximise accuracy of predictions, and 3) whether substituting temperature change through time with mean temperature produces accurate predictions. We find that extinction occurs earlier in environments that warm faster, and this can be accurately predicted (R² > 0.84). Increasing the number of parameters that were temperature‐dependent increased the model's accuracy, as did scaling these temperature‐dependent parameters with either the direct effects of temperature alone, or with the direct and indirect effects. Using mean temperature through time instead of actual temperature produces less accurate predictions of extinction. These results suggest that simple phenomenological models, incorporating metabolic theory, may be useful in understanding how environmental change can alter a population's rate of extinction. Synthesis Understanding how populations will respond to future climatic change is a key goal in ecology, however the exact rate of future warming will vary both spatially and temporally. Consequently, mathematical models must be used to understand the potential range of future population dynamics under various warming scenarios. We use a combination of experimentation and modelling to show that the effects of varying rates of environmental change on population dynamics can be predicted by a simple model. However, the accuracy of these predictions depends upon, amongst other things, a detailed knowledge of how temperature will change over time, rather than approximating this change to mean temperature.     

Catastrophic events and recovery from low densities in populations of otariids: implications for risk of extinction

Two key factors in a population's risk of extinction are major population declines induced by natural or anthropogenic events (catastrophes) and whether the population's rate of growth increases or decreases at very low abundance levels. These two elements should be included in any population viability analysis (PVA), but estimates of the frequency and intensity of catastrophic events and data on the dynamics of low population densities are difficult to obtain. We examined the literature on population dynamics of otariids (fur seals and sea lions), to determine how frequently populations are subjected to major population declines, and to what extent depleted populations recover from low population size. We present frequency distributions for percentage declines for otariid life‐stages (pup, juvenile, adult female and male), and describe eight examples of events leading to a population decline of 50% or greater among otariids. We found that numerous otariid populations have been reduced to very low densities by exploitation (low enough to be thought extinct) and have recovered to levels where they are no longer at risk of extinction. This suggests that the reduction in population rate of increase at low densities in otariid populations may not be strong.     

Extracting spatial networks from capture–recapture data reveals individual site fidelity patterns within a marine mammal’s spatial range

1. Estimating the impacts of anthropogenic disturbances requires an understanding of the habitat‐use patterns of individuals within a population. This is especially the case when disturbances are localized within a population''s spatial range, as variation in habitat use within a population can drastically alter the distribution of impacts.
2. Here, we illustrate the potential for multilevel binomial models to generate spatial networks from capture–recapture data, a common data source used in wildlife studies to monitor population dynamics and habitat use. These spatial networks capture which regions of a population''s spatial distribution share similar/dissimilar individual usage patterns, and can be especially useful for detecting structured habitat use within the population''s spatial range.
3. Using simulations and 18 years of capture–recapture data from St. Lawrence Estuary (SLE) beluga, we show that this approach can successfully estimate the magnitude of similarities/dissimilarities in individual usage patterns across sectors, and identify sectors that share similar individual usage patterns that differ from other sectors, that is, structured habitat use. In the case of SLE beluga, this method identified multiple clusters of individuals, each preferentially using restricted areas within their summer range of the SLE.
4. Multilevel binomial models can be effective at estimating spatial structure in habitat use within wildlife populations sampled by capture–recapture of individuals, and can be especially useful when sampling effort is not evenly distributed. Our finding of a structured habitat use within the SLE beluga summer range has direct implications for estimating individual exposures to localized stressors, such as underwater noise from shipping or other activities.

     

Scale‐dependent role of demography and dispersal on the distribution of populations in heterogeneous landscapes

Both dispersal and local demographic processes determine a population's distribution among habitats of varying quality, yet most theory, experiments, and field studies have focused on the former. We use a generic model to show how both processes contribute to a population's distribution, and how the relative importance of each mechanism depends on scale. In contrast to studies only considering habitat‐dependent dispersal, we show that predictions of ideal free distribution (IFD) theory are relevant even at landscape scales, where the assumptions of IFD theory are violated. This is because scales that inhibit one process, promote the other's ability to drive populations to the IFD. Furthermore, because multiple processes can generate IFDs, the pattern alone does not specify a causal mechanism. This is important because populations with IFDs generated by dispersal or demography respond much differently to shifts in resource distributions.     

Speedy speciation in a bacterial microcosm: new species can arise as frequently as adaptations within a species

Microbiologists are challenged to explain the origins of enormous numbers of bacterial species worldwide. Contributing to this extreme diversity may be a simpler process of speciation in bacteria than in animals and plants, requiring neither sexual nor geographical isolation between nascent species. Here, we propose and test a novel hypothesis for the extreme diversity of bacterial species—that splitting of one population into multiple ecologically distinct populations (cladogenesis) may be as frequent as adaptive improvements within a single population''s lineage (anagenesis). We employed a set of experimental microcosms to address the relative rates of adaptive cladogenesis and anagenesis among the descendants of a Bacillus subtilis clone, in the absence of competing species. Analysis of the evolutionary trajectories of genetic markers indicated that in at least 7 of 10 replicate microcosm communities, the original population founded one or more new, ecologically distinct populations (ecotypes) before a single anagenetic event occurred within the original population. We were able to support this inference by identifying putative ecotypes formed in these communities through differences in genetic marker association, colony morphology and microhabitat association; we then confirmed the ecological distinctness of these putative ecotypes in competition experiments. Adaptive mutations leading to new ecotypes appeared to be about as common as those improving fitness within an existing ecotype. These results suggest near parity of anagenesis and cladogenesis rates in natural populations that are depauperate of bacterial diversity.     

Using stage‐based system dynamics modeling for demographic management of captive populations

Management of captive populations relies on a complex synthesis of genetic and demographic analyses to guide populations toward sustainability. Demographic analyses of captive populations currently utilize age‐based matrix projections to predict a population's trajectory. An alternate approach is to use a stage‐based, system dynamics model for captive systems. Such models can more easily incorporate complex captive systems in which population dynamics are dependent on a combination of management and a species' biology. By linking these two areas, population managers can gain a more accurate understanding of how management decisions impact captive populations and which aspects of a species' demography should be of special concern in the future. We present a general stage‐based system dynamics model that has been developed for use with captive populations. The utility of the model is then illustrated by applying it to three captive bear populations: spectacled bears (Tremarctos ornatus), sloth bears (Melursus ursinus), and sun bears (Helarctos malayanus). Zoo Biol 22:45–64, 2003. © 2003 Wiley‐Liss, Inc.     

A plant toxin mediated mechanism for the lag in snowshoe hare population recovery following cyclic declines

A necessary condition for a snowshoe hare population to cycle is reduced reproduction after the population declines. But the cause of a cyclic snowshoe hare population's reduced reproduction during the low phase of the cycle, when predator density collapses, is not completely understood. We propose that moderate‐severe browsing by snowshoe hares upon preferred winter‐foods could increase the toxicity of some of the hare's best winter‐foods during the following hare low, with the result being a decline in hare nutrition that could reduce hare reproduction. We used a combination of modeling and experiments to explore this hypothesis. Using the shrub birch Betula glandulosa as the plant of interest, the model predicted that browsing by hares during a hare cycle peak, by increasing the toxicity B. glandulosa twigs during the following hare low, could cause a hare population to cycle. The model's assumptions were verified with assays of dammarane triterpenes in segments of B. glandulosa twigs and captive hare feeding experiments conducted in Alaska during February and March 1986. The model's predictions were tested with estimates of hare density and measurements of B. glandulosa twig growth made at Kluane, Yukon from 1988–2008. The empirical tests supported the model's predictions. Thus, we have concluded that a browsing‐caused increase in twig toxicity that occurs during the hare cycle's low phase could reduce hare reproduction during the low phase of the hare cycle.     

Populations adapt to fluctuating selection using derived and ancestral allelic diversity

Populations can adapt to changing environments by using allelic diversity, yet whether diversity is recently derived or ancestral is often debated. Although evolution could productively use both types of diversity in a changing environment, their relative frequency has not been quantified. We address this question experimentally using budding yeast strains that harbor a tandem repeat containing URA3 gene, which we expose to cyclical selection and counterselection. We characterize and quantify the dynamics of frameshift events in the URA3 gene in eight populations over 12 cycles of selection and find that ancestral alleles account for 10–20% of all adaptive events. Using a general model of fluctuating selection, we determine how these results depend on mutation rates, population sizes, and fluctuation timescales. We quantify the contribution of derived alleles to the adaptation process using the de novo mutation rate along the population's ancestral lineage, a novel measure that is applicable in a wide range of settings. We find that the adaptive dynamics undergoes a sharp transition from selection on ancestral alleles to selection on derived alleles as fluctuation timescales increase. Our results demonstrate that fluctuations can select between different modes of adaptation over evolutionary timescales.     

Patterns of density dependence in measles dynamics.

An important question in metapopulation dynamics is the influence of external perturbations on the population''s long-term dynamic behaviour. In this paper we address the question of how spatiotemporal variations in demographic parameters affect the dynamics of measles populations in England and Wales. Specifically, we use nonparametric statistical methods to analyse how birth rate and population size modulate the negative density dependence between successive epidemics as well as their periodicity. For the observed spatiotemporal data from 60 cities, and for simulated model data, the demographic variables act as bifurcation parameters on the joint density of the trade-off between successive epidemics. For increasing population size, a transition occurs from an irregular unpredictable pattern in small communities towards a regular, predictable endemic pattern in large places. Variations in the birth rate parameter lead to a bifurcation from annual towards biennial cyclicity in both observed data and model data.     

Non-Linear Analysis Indicates Chaotic Dynamics and Reduced Resilience in Model-Based Daphnia Populations Exposed to Environmental Stress

In this study we present evidence that anthropogenic stressors can reduce the resilience of age-structured populations. Enhancement of disturbance in a model-based Daphnia population lead to a repression of chaotic population dynamics at the same time increasing the degree of synchrony between the population''s age classes. Based on the theory of chaos-mediated survival an increased risk of extinction was revealed for this population exposed to high concentrations of a chemical stressor. The Lyapunov coefficient was supposed to be a useful indicator to detect disturbance thresholds leading to alterations in population dynamics. One possible explanation could be a discrete change in attractor orientation due to external disturbance. The statistical analysis of Lyapunov coefficient distribution is proposed as a methodology to test for significant non-linear effects of general disturbance on populations. Although many new questions arose, this study forms a theoretical basis for a dynamical definition of population recovery.     

Preliminary Remediation Goals for Terrestrial Wildlife

Remediation of contaminated sites requires information on upper concentration limits of chemicals in environmental media that are protective of ecological receptors. These upper concentration limits can be considered ecological preliminary remediation goals (EcoPRGs). The motivation for developing EcoPRGs was to provide risk managers with a simple tool for evaluating remedial actions that would be protective of the environment. Hazard quotient calculations used to support ecological screening assessments were modified to derive soil EcoPRGs for terrestrial wildlife populations. The primary modification is a population area use factor that is the fraction of a terrestrial animal population potentially affected by the contaminated site. Wildlife assessment population boundaries are based on a receptor's dispersal distance; for mammals dispersal distance is strongly related to the linear dimension (square root) of home range. Assuming that wildlife are unlikely to disperse beyond some distance from their birth or natal site, dispersal distance can be thought of as the radius of the assessment population's boundaries. This general relationship is useful as a simple way to estimate assessment population areas for terrestrial animals and helps fill data gaps for wildlife without direct measurements of dispersal.     

Dynamical facilitation of the ideal free distribution in nonideal populations

The ideal free distribution (IFD) requires that individuals can accurately perceive density‐dependent habitat quality, while failure to discern quality differences below a given perception threshold results in distributions approaching spatial uniformity. Here, we investigate the role of population growth in restoring a nonideal population to the IFD. We place a simple model of discrete patch choice under limits to the resolution by which patch quality is perceived and include population growth driven by that underlying quality. Our model follows the population's distribution through both breeding and dispersal seasons when perception limits differ in their likely influence. We demonstrate that populations of perception limited movers can approximate an IFD provided sufficient population growth; however, the emergent IFD would be temporally inconstant and correspond to reproductive events. The time to emergence of the IFD during breeding is shorter under exponential growth than under logistic growth. The IFD during early colonization of a community persists longer when more patches are available to individuals. As the population matures and dispersal becomes increasingly random, there is an oscillation in the observance of IFD, with peaks most closely approximating the IFD occurring immediately after reproductive events, and higher reproductive rates producing distributions closer to the IFD.     

The nature of nurture in a wild mammal's fitness

Genetic variation in fitness is required for the adaptive evolution of any trait but natural selection is thought to erode genetic variance in fitness. This paradox has motivated the search for mechanisms that might maintain a population''s adaptive potential. Mothers make many contributions to the attributes of their developing offspring and these maternal effects can influence responses to natural selection if maternal effects are themselves heritable. Maternal genetic effects (MGEs) on fitness might, therefore, represent an underappreciated source of adaptive potential in wild populations. Here we used two decades of data from a pedigreed wild population of North American red squirrels to show that MGEs on offspring fitness increased the population''s evolvability by over two orders of magnitude relative to expectations from direct genetic effects alone. MGEs are predicted to maintain more variation than direct genetic effects in the face of selection, but we also found evidence of maternal effect trade-offs. Mothers that raised high-fitness offspring in one environment raised low-fitness offspring in another environment. Such a fitness trade-off is expected to maintain maternal genetic variation in fitness, which provided additional capacity for adaptive evolution beyond that provided by direct genetic effects on fitness.     

Mate‐choice copying: A fitness‐enhancing behavior that evolves by indirect selection

A spatially explicit, individual‐based simulation model is used to study the spread of an allele for mate‐choice copying (MCC) through horizontal cultural transmission when female innate preferences do or do not coevolve with a male viability‐increasing trait. Evolution of MCC is unlikely when innate female preferences coevolve with the trait, as copier females cannot express a higher preference than noncopier females for high‐fitness males. However, if a genetic polymorphism for innate preference persists in the population, MCC can evolve by indirect selection through hitchhiking: the copying allele hitchhikes on the male trait. MCC can be an adaptive behavior—that is, a behavior that increases a population's average fitness relative to populations without MCC—even though the copying allele itself may be neutral or mildly deleterious.     

Quantifying Health Across Populations

In this article, I argue that as a theoretical matter, a population's health‐level is best quantified via averagism. Averagism asserts that the health of a population is the average of members’ health‐levels. This model is better because it does not fall prey to a number of objections, including the repugnant conclusion, and because it is not arbitrary. I also argue that as a practical matter, population health‐levels are best quantified via totalism. Totalism asserts that the health of a population is the sum of members’ health‐levels. Totalism is better here because it fits better with cost‐benefit analysis and such an analysis is the best practical way to value healthcare outcomes. The two results are compatible because the theoretical and practical need not always align, whether in general or in the context of population health.     

Heritable variation in garter snake color patterns in postglacial populations

Global climate change is expected to trigger northward shifts in the ranges of natural populations of plants and animals, with subsequent effects on intraspecific genetic diversity. Investigating how genetic diversity is patterned among populations that arose following the last Ice Age is a promising method for understanding the potential future effects of climate change. Theoretical and empirical work has suggested that overall genetic diversity can decrease in colonial populations following rapid expansion into postglacial landscapes, with potential negative effects on the ability of populations to adapt to new environmental regimes. The crucial measure of this genetic variation and a population''s overall adaptability is the heritable variation in phenotypic traits, as it is this variation that mediates the rate and direction of a population''s multigenerational response to selection. Using two large full-sib quantitative genetic studies (N_Manitoba = 144; N_{South Dakota} = 653) and a smaller phenotypic analysis from Kansas (N_Kansas = 44), we compared mean levels of pigmentation, genetic variation and heritability in three pigmentation traits among populations of the common garter snake, Thamnophis sirtalis, along a north-south gradient, including a postglacial northern population and a putative southern refuge population. Counter to our expectations, we found that genetic variance and heritability for the three pigmentation traits were the same or higher in the postglacial population than in the southern population.