The control of emigration and its consequences for the survival of populations

Dispersal is the key process enhancing the long-term persistence of metapopulations in heterogeneous and dynamic landscapes. However, any individual emigrating from a occupied patch also increases the risk of local population extinction. The consequences of this increase for metapopulation persistence likely depend on the control of emigration. In this paper, we present results of individual-based simulations to compare the consequences of density-independent (DIE) and density-dependent (DDE) emigration on the extinction risk of local populations and a two-patch metapopulation. (1) For completely isolated patches extinction risk increases linearly with realised emigration rates in the DIE scenario. (2) For the DDE scenario extinction risk is nearly insensitive to emigration as longs as emigration probabilities remain below ≈0.2. Survival chances are up to half an order of magnitude larger than for populations with DIE. (3) For low dispersal mortality both modes of emigration increase survival of a metapopulation by ca. one order of magnitude. (4) For high dispersal mortality only DDE can improve the global survival chances of the metapopulation. (5) With DDE individuals are only removed from a population at high population density and the risk of extinction due to demographic stochasticity is thus much smaller compared to the DIE scenario.With density-dependent emigration prospects of metapopulations survival may thus be much higher compared to a system with density-independent emigration. Consequently, the knowledge about the factors driving emigration may significantly affect our conclusions concerning the conservation status of species.     

A model for behavioral regulation of metapopulation dynamics

Habitat fragmentation can decrease local population persistence by reducing connectivity, which is a function of dispersal of individuals among habitat fragments. Dispersal is often treated as diffusion in population models, even though for many species it is a result of a series of behavioral decisions. We developed a metapopulation model to explore the potential importance of dispersal behaviors in driving metapopulation dynamics. We incorporated types of behavior that affect dispersal—colonization inhibiting, colonization enhancing, extinction inhibiting, extinction enhancing, rescue enhancing, rescue inhibiting—into Levins’ (1969) metapopulation model and projected occupancy rates for a variety of parameter values. Examples from the literature of behaviors associated with each of these parameters are provided. Our model simplifies into previously published metapopulation models that incorporate only a single behavior, and we present a density-dependent rescue function that leads to multiple non-zero equilibria. We found a variety of behavioral effects on metapopulations. Rescue enhancement fills patches faster than does colonization enhancement or extinction inhibition, and declines in patch occupancy are moderate with extinction enhancement, but colonization inhibition causes metapopulation extinction. We also found that with colonization and extinction inhibitions, equilibrium patch occupancy is inversely related to patch turnover rate. With density-dependent rescue, persistence depends not only on the strength of the strong rescue effect, but also on having a sufficient initial fraction of patches occupied; the stronger the rescue effect, the lower this fraction can be. This study suggests that dispersal behavior can have strong influences on metapopulation dynamics. It confirms the importance of understanding the relationship between landscape structure and dispersal behavior in understanding population persistence.     

Consistent scaling of persistence time in metapopulations

Recent theory and experimental work in metapopulations and metacommunities demonstrates that long-term persistence is maximized when the rate at which individuals disperse among patches within the system is intermediate; if too low, local extinctions are more frequent than recolonizations, increasing the chance of regional-scale extinctions, and if too high, dynamics exhibit region-wide synchrony, and local extinctions occur in near unison across the region. Although common, little is known about how the size and topology of the metapopulation (metacommunity) affect this bell-shaped relationship between dispersal rate and regional persistence time. Using a suite of mathematical models, we examined the effects of dispersal, patch number, and topology on the regional persistence time when local populations are subject to demographic stochasticity. We found that the form of the relationship between regional persistence time and the number of patches is consistent across all models studied; however, the form of the relationship is distinctly different among low, intermediate, and high dispersal rates. Under low and intermediate dispersal rates, regional persistence times increase logarithmically and exponentially (respectively) with increasing numbers of patches, whereas under high dispersal, the form of the relationship depends on local dynamics. Furthermore, we demonstrate that the forms of these relationships, which give rise to the bell-shaped relationship between dispersal rate and persistence time, are a product of recolonization and the region-wide synchronization (or lack thereof) of population dynamics. Identifying such metapopulation attributes that impact extinction risk is of utmost importance for managing and conserving the earth's evermore fragmented populations.     

Demographic Characteristics of Extinction in a Small, Insular Population of House Sparrows in Northern Norway

Abstract:  In conservation ecology there is an urgent need for indicators that can be used to predict the risk of extinction of populations. Identifying extinction-prone populations has been difficult because few data sets on the demographic characteristics of the final stage to extinction are available and because of problems in separating out stochastic effects from changes in the expected dynamics. We documented the demographic changes that occurred during the period prior to extinction of a small island population of House Sparrows ( Passer domesticus ) after the end of permanent human settlement. A mark-recapture analysis revealed that this decline to extinction was mainly due to increased mortality after closure of the last farm that resulted in a negative long-term-specific growth rate. No change occurred in either the structural composition (breeding sex ratio and age distribution) of the population or in female recruitment. No male, however, recruits were produced on the island after the farm closure. Based on a simple, stochastic, density-dependent model we constructed a population prediction interval (PPI) to estimate the time to extinction. The 95% PPI slightly overestimated the time to extinction with large uncertainty in predictions, especially due to the influence of demographic stochasticity and parameter drift. Our results strongly emphasize the importance of access to data on temporal variation that can be used to parameterize simple population models that allow estimation of critical parameters for credible prediction of time to extinction.     

Identifying key species in ecosystems with stochastic sensitivity analysis

The development of approaches to estimate the vulnerability of biological communities and ecosystems to extirpations and reductions of species is a central challenge of conservation biology. One key aim of this challenge is to develop quantitative approaches to estimate and rank interaction strengths and keystoneness of species and functional groups, i.e. to quantify the relative importance of species. Network analysis can be a powerful tool for this because certain structural aspects of ecological networks are good indicators of the mechanisms that maintain co-evolved, biotic interactions. A static view of ecological networks would lead us to focus research on highly-central species in food webs (topological key players in ecosystems). There are a variety of centrality indices, developed for several types of ecological networks (e.g. for weighted and un-weighted webs). However, truly understanding extinction and its community-wide effects requires the use of dynamic models. Deterministic dynamic models are feasible when population sizes are sufficiently large to minimize noise in the overall system. In models with small population sizes, stochasticity can be modelled explicitly. We present a stochastic simulation-based ecosystem model for identification of “dynamic key species” in situations where stochastic models are appropriate. To demonstrate this approach, we simulated ecosystem dynamics and performed sensitivity analysis using data from the Prince William Sound, Alaska ecosystem model. We then compare these results to those of purely topological analyses and deterministic dynamic (Ecosim) studies. We present the relationships between various topological and dynamic indices and discuss their biological relevance. The trophic group with the largest effect on others is nearshore demersals, the species mostly sensitive to others is halibut, and the group of both considerable effect on and sensitivity to others is juvenile herring. The most important trophic groups in our dynamical simulations appear to have intermediate trophic levels.     

Quantifying the importance of local niche-based and stochastic processes to tropical tree community assembly

Although niche-based and stochastic processes, including dispersal limitation and demographic stochasticity, can each contribute to community assembly, it is difficult to quantify the relative importance of each process in natural vegetation. Here, we extend Shipley's maxent model (Community Assembly by Trait Selection, CATS) for the prediction of relative abundances to incorporate both trait-based filtering and dispersal limitation from the larger landscape and develop a statistical decomposition of the proportions of the total information content of relative abundances in local communities that are attributable to trait-based filtering, dispersal limitation, and demographic stochasticity. We apply the method to tree communities in a mature, species-rich, tropical forest in French Guiana at 1-, 0.25- and 0.04-ha scales. Trait data consisted of species' means of 17 functional traits measured over both the entire meta-community and separately in each of nine 1-ha plots. Trait means calculated separately for each site always gave better predictions. There was clear evidence of trait-based filtering at all spatial scales. Trait-based filtering was the most important process at the 1-ha scale (34%), whereas demographic stochasticity was the most important at smaller scales (37-53%). Dispersal limitation from the meta-community was less important and approximately constant across scales (-9%), and there was also an unresolved association between site-specific traits and meta-community relative abundances. Our method allows one to quantify the relative importance of local niche-based and meta-community processes and demographic stochasticity during community assembly across spatial and temporal scales.     

Effects of Social Structure and Prey Dynamics on Extinction Risk in Gray Wolves

Extinction models based on diffusion theory generally fail to incorporate two important aspects of population biology—social structure and prey dynamics. We include these aspects in an individual-based extinction model for small, isolated populations of the gray wolf (Canis lupus). Our model predicts mean times to extinction significantly longer than those predicted by more general (diffusion) models. According to our model, an isolated population of 50 wolves has a 95% chance of surviving just 9 years and only a 30% chance of surviving beyond 100 years. Reflecting the influence of social structure, a wolf population initially comprising 50 individuals is expected to persist only a few years longer, on average (71 years), than is a population initially comprising just a single reproductive pair (62 years). In contrast, substantially greater average prey abundance leads to dramatically longer expected persistence times. Autocorrelated prey dynamics result in a more complex distribution of extinction times than predicted by many extinction models. We contend that demographic stochasticity may pose the greatest threat to small, isolated wolf populations, although environmental stochasticity and genetic effects may compound this threat. Our work highlights the importance of considering social structure and resource dynamics in the development of population viability analyses.     

Predicting [corrected] extinction risk in spite of predator-prey oscillations.

Most population viability analyses (PVA) assume that the effects of species interactions are subsumed by population-level parameters. We examine how robust five commonly used PVA models are to violations of this assumption. We develop a stochastic, stage-structured predator-prey model and simulate prey population vital rates and abundance. We then use simulated data to parameterize and estimate risk for three demographic models (static projection matrix, stochastic projection matrix, stochastic vital rate matrix) and two time series models (diffusion approximation [DA], corrupted diffusion approximation [CDA]). Model bias is measured as the absolute deviation between estimated and observed quasi-extinction risk. Our results highlight three generalities about the application of single-species models to multi-species conservation problems. First, our collective model results suggest that most single-species PVA models overestimate extinction risk when species interactions cause periodic variation in abundance. Second, the DA model produces the most (conservatively) biased risk forecasts. Finally, the CDA model is the most robust PVA to population cycles caused by species interactions. CDA models produce virtually unbiased and relatively precise risk estimates even when populations cycle strongly. High performance of simple time series models like the CDA owes to their ability to effectively partition stochastic and deterministic sources of variation in population abundance.     

Extinction Dynamics in the American Marten (Martes americana)

We constructed a model of marten population dynamics and used it to investigate extinction processes across a wide range of parameter values. The model was based on rules governing the behavior and physiology of individual martens and focused on energy balance. Spatial dynamics and demographic and environmental stochasticity were incorporated. The outcome was the probability of extinction and quasiextinction (20 females remaining) over 500 years. Three qualitative forms of extinction were delineated. The first was deterministic extinction, associated with those parameter combinations leading to a negative population growth rate. The second was probabilistic extinction in systems with a strong positive growth rate but restricted population size due to habitat constraint. The transition from 100% persistence to 100% quasiextinction, as the input habitat size was decreased, was abrupt. The final form of extinction was in systems with a growth rate of approximately zero. Prey availability maintained an upper limit on these populations, but otherwise fluctuations in population size were essentially random, leading to nontrivial probabilities of extinction in even relatively large populations. A number of issues requiring further empirical research were identified. These included the relationship between habitat quality and marten reproduction, dispersal patterns and dispersal mortality, the effect of habitat edge on marten reproduction and mortality, and the characterization of the severity and frequency of catastrophic mortality as experienced by marten populations.     

Negative relationship between dispersal distance and demography in butterfly metapopulations

Little is known about the connection between demography and dispersal in metapopulations. The meta-analysis of the population time series of five butterfly species indicated that (meta)population dynamics are driven by density-dependent factors. Inter-specific comparison reveals a significant inverse relationship between population growth rate and the magnitude of dispersal distance. As the range of dispersal distances is constrained by the patch system, dispersing individuals moving too far away would (probably) get lost. This generates selective pressures on individuals with a high dispersal propensity, but favors individuals investing more in reproduction and results in a higher (meta)population growth rate. From a conservation perspective, individuals from (meta)populations and species sacrificing dispersal for the sake of reproductive performances are most vulnerable because of their higher sensitivity to stochastic events: the temporal variation of growth rate was much higher in the two metapopulations where dispersal was limited.     

Estimating dispersal potential for marine larvae: dynamic models applied to scleractinian corals

Dispersal influences ecological dynamics, evolution, biogeography, and biodiversity conservation, but models of larval dispersal in marine organisms make simplifying assumptions that are likely to approximate poorly the temporal dynamics of larval survival and capacity for settlement. In particular, larval mortality rates are typically assumed to be constant throughout larval life; and all larvae are frequently assumed to acquire and lose competence at the same time. To improve upon these assumptions, we here develop simple models of dispersal potential that incorporate rates of mortality, and acquisition and loss of settlement competence. We fit these models to empirical competence and survival data for five scleractinian coral species, to test the models' ability to characterize empirical survival and competence patterns, and to estimate the dispersal potential implied by those patterns. The models fit the data well, incorporating qualitative features of competence and survival that traditional approaches to modeling dispersal do not, with important implications for dispersal potential. Most notably, there was high within-cohort variation in the duration of the competent period in all species, and this variation increases both self-recruitment and long-distance dispersal compared with models assuming a fixed competent period. These findings help to explain the seeming paradox of high genetic population structure, coupled with large geographic range size, observed in many coral species. More broadly, our approach offers a way to parsimoniously account for variation in competence dynamics in dispersal models, a phenomenon that our results suggest has important effects on patterns of connectivity in marine metapopulations.     

Consumptive and nonconsumptive effects of predators on metacommunities of competing prey

Although predators affect prey both via consumption and by changing prey migration behavior, the interplay between these two effects is rarely incorporated into spatial models of predator-prey dynamics and competition among prey. We develop a model where generalist predators have consumptive effects (i.e., altering the likelihood of local prey extinction) as well as nonconsumptive effects (altering the likelihood of colonization) on spatially separated prey populations (metapopulations). We then extend this model to explore the effects of predators on competition among prey. We find that generalist predators can promote persistence of prey metapopulations by promoting prey colonization, but predators can also hasten system-wide extinction by either increasing local extinction or reducing prey migration. By altering rates of prey migration, predators in one location can exert remote control over prey dynamics in another location via predator-mediated changes in prey flux. Thus, the effect of predators may extend well beyond the proportion of patches they visit. In the context of prey metacommunities, predator-mediated shifts in prey migration and mortality can shift the competition-colonization trade-off among competing prey, leading to changes in the prey community as well as changes in the susceptibility of prey species to habitat loss. Consequently, native prey communities may be susceptible to invasion not only by exotic prey species that experience reduced amounts of mortality from resident predators, but also by exotic prey species that exhibit strong dispersal in response to generalist native predators. Ultimately, our work suggests that the consumptive and nonconsumptive effects of generalist predators may have strong, yet potentially cryptic, effects on competing prey capable of mediating coexistence, fostering invasion, and interacting with anthropogenic habitat alteration.     

Demographic Viability of a Relict Population of the Critically Endangered Plant Borderea chouardii

Abstract:   In addition to human-caused changes in the environment, natural stochasticity may threaten species persistence, and its impact must be taken into account when priorities are established and management plans are designed. Borderea chouardii is a Tertiary relict at risk of extinction that occurs in only one location in the world, where the probability of human disturbance is low. Its persistence, therefore, is mainly linked to its response to natural threats such as stochasticity. Over 8 years I monitored up to 25% of this rupicolous small geophyte. The population had an unbalanced size structure and 90% failure in seed arrival at appropriate microhabitats, which suggests a problem with recruitment. I used matrix models to describe its population dynamics, conducted hand sowings, and performed stochastic simulations to investigate the effect of environmental stochasticity on population trend and viability. I modeled several scenarios to represent a variety of ecological situations, such as population reduction, episodic or persistent disease, and enhancement or decrease of recruitment. Population growth rate (λ) was never significantly different from unity over the study period. The risk of extinction was null over the next five centuries under current conditions. Increase of mortality and decrease of recruitment reduced stochastic population growth rate, but no factor except a persistent increase of 10% mortality resulted in extinction. These results are the consequence of the plant's extremely long life span (over 300 years) and low temporal variability of key vital rates. Even though hand sowing significantly increased the stochastic population growth rate, other approaches may be more important for the persistence of this species. The extremely slow capacity for recovery following disturbances renders habitat preservation essential. In addition, the founding of new populations would reduce the risk associated with habitat destruction.     

Population Viability Analysis of Spring Chinook Salmon in the South Umpqua River, Oregon

Run sizes of spring chinook salmon in the South Umpqua River in Oregon have declined dramatically since the early part of this century. Habitat degradation is thought to be an important factor contributing to the decline of this stock, and qualitative assessment suggests the stock is at moderate risk of extinction. We use data from this and similar stocks to develop an age-structured, density-dependent model of the population dynamics that incorporates both demographic and environmental stochasticity. Under the assumption of no further habitat destruction, the population is predicted to have a greater than 95% probability of persistence for 200 years. However, sensitivity analysis for the density-dependence estimated from historical run-return data shows that substantially lower predicted viabilities are also statistically consistent with the data. A model that simulates continued habitat degradation results in almost certain extinction within 100 years.     

Extinction times in experimental populations

Predicting population extinctions is a key element of quantitative conservation biology and population ecology. Although stochastic population theories have long been used to obtain theoretical distributions of population extinction times, model-based predictions have rarely been tested. Here I report results from a quantitative analysis of extinction time in 281 experimental populations of water fleas (Daphnia magna) in variable environments. To my knowledge, this is the first quantitative estimate of the shape of the distribution of population extinction times based on extinction data for any species. The finding that the distribution of population extinction times was extraordinarily peaked is consistent with theoretical predictions for density-independent populations, but inconsistent with predictions for density-dependent populations. The tail of the extinction time distribution was not exponential. These results imply that our current theories of extinction are inadequate. Future work should focus on how demographic stochasticity scales with population size and effects of nonrandom variable environments on population growth and decline.     

Predators, prey, and transient states in the assembly of spatially structured communities

Ecological theory suggests that both dispersal limitation and resource limitation can exert strong effects on community assembly. However, empirical studies of community assembly have focused almost exclusively on communities with a single trophic level. Thus, little is known about the combined effects of dispersal and resource limitation on assembly of communities with multiple trophic levels. We performed a landscape-scale experiment using spatially arranged mesocosms to study effects of dispersal and resource limitation on the assembly dynamics of aquatic invertebrate communities with two trophic levels. We found that interplay between dispersal and resource limitation regulated the assembly of predator and prey trophic levels in these pond communities. Early in assembly, predators and prey were strongly dispersal limited, and resource (i.e., prey) availability did not influence predator colonization. Later in assembly, after predators colonized, resource limitation was the strongest driver of predator abundance, and dispersal limitation played a negligible role. Thus, habitat isolation affected predators directly by reducing predator colonization rate, and indirectly through the effect of distance on prey availability. Dispersal and resource limitation of predators resulted in a transient period in which predators were absent or rare in isolated habitats. This period may be important for understanding population dynamics of vulnerable prey species. Our findings demonstrate that dispersal and resource limitation can jointly regulate assembly dynamics in multi-trophic systems. They also highlight the need to develop a temporal picture of the assembly process in multi-trophic communities because the availability and spatial distribution of limiting resources (i.e., prey) and the distribution of predators can shift radically over time.     

Extinction-effective population index: incorporating life-history variations in population viability analysis

Viability status of populations is a commonly used measure for decision-making in the management of populations. One of the challenges faced by managers is the need to consistently allocate management effort among populations. This allocation should in part be based on comparison of extinction risks among populations. Unfortunately, common criteria that use minimum viable population size or count-based population viability analysis (PVA) often do not provide results that are comparable among populations, primarily because they lack consistency in determining population size measures and threshold levels of population size (e.g., minimum viable population size and quasi-extinction threshold). Here I introduce a new index called the "extinction-effective population index," which accounts for differential effects of demographic stochasticity among organisms with different life-history strategies and among individuals in different life stages. This index is expected to become a new way of determining minimum viable population size criteria and also complement the count-based PVA. The index accounts for the difference in life-history strategies of organisms, which are modeled using matrix population models. The extinction-effective population index, sensitivity, and elasticity are demonstrated in three species of Pacific salmonids. The interpretation of the index is also provided by comparing them with existing demographic indices. Finally, a measure of life-history-specific effect of demographic stochasticity is derived.     

Integral projection models for finite populations in a stochastic environment

Continuous types of population structure occur when continuous variables such as body size or habitat quality affect the vital parameters of individuals. These structures can give rise to complex population dynamics and interact with environmental conditions. Here we present a model for continuously structured populations with finite size, including both demographic and environmental stochasticity in the dynamics. Using recent methods developed for discrete age-structured models we derive the demographic and environmental variance of the population growth as functions of a continuous state variable. These two parameters, together with the expected population growth rate, are used to define a one-dimensional diffusion approximation of the population dynamics. Thus, a substantial reduction in complexity is achieved as the dynamics of the complex structured model can be described by only three population parameters. We provide methods for numerical calculation of the model parameters and demonstrate the accuracy of the diffusion approximation by computer simulation of specific examples. The general modeling framework makes it possible to analyze and predict future dynamics and extinction risk of populations with various types of structure, and to explore consequences of changes in demography caused by, e.g., climate change or different management decisions. Our results are especially relevant for small populations that are often of conservation concern.     

The transition from isolated patches to a metapopulation in the eastern collared lizard in response to prescribed fires

Habitat fragmentation often arises from human-induced alterations to the matrix that reduce or eliminate dispersal between habitat patches. Elimination of dispersal increases local extinction and decreases recolonization. These phenomena were observed in the eastern collared lizard (Crotaphytus collaris collaris), which lives in the mid-continental highland region of the Ozarks (Missouri, USA) on glades: habitats of exposed bedrock that form desert-like habitats imbedded in a woodland matrix. With the onset of woodland fire suppression, glade habitats degenerated and the woodland matrix was altered to create a strong barrier to dispersal. By 1980, lizard populations in the Ozarks were rapidly going extinct. In response to this decline, some glades were restored by clearing and burning. Starting in 1984, collared lizard populations were translocated onto these restored habitats. The translocated populations persisted but did not colonize nearby glades or disperse among one another. In 1994 prescribed woodland fires were initiated, which unleashed much dispersal and colonizing behavior. Dispersal was highly nonrandom by both intrinsic variables (age, gender) and extrinsic variables (overall demography, glade population sizes, glade areas, landscape features), resulting in different classes of lizards being dominant in creating demographic cohesiveness among glades, colonizing new glades on a mountain, and colonizing new mountain systems. A dramatic transition was documented from isolated fragments, to a nonequilibrium colonizing metapopulation, and finally to a stable metapopulation. This transition is characterized by the convergence of rates of extinction and recolonization and a major alteration of dispersal probabilities and pattern in going from the nonequilibrium to stable metapopulation states.     

A Behaviorally Explicit Demographic Model Integrating Habitat Selection and Population Dynamics in California Sea Lions

Abstract: Although there has been a call for the integration of behavioral ecology and conservation biology, there are few tools currently available to achieve this integration. Explicitly including information about behavioral strategies in population viability analyses may enhance the ability of conservation biologists to understand and estimate patterns of extinction risk. Nevertheless, most behavioral‐based PVA approaches require detailed individual‐based data that are rarely available for imperiled species. We present a mechanistic approach that incorporates spatial and demographic consequences of behavioral strategies into population models used for conservation. We developed a stage‐structured matrix model that includes the costs and benefits of movement associated with 2 habitat‐selection strategies (philopatry and direct assessment). Using a life table for California sea lions (Zalophus californianus), we explored the sensitivity of model predictions to the inclusion of these behavioral parameters. Including behavioral information dramatically changed predicted population sizes, model dynamics, and the expected distribution of individuals among sites. Estimated population sizes projected in 100 years diverged up to 1 order of magnitude among scenarios that assumed different movement behavior. Scenarios also exhibited different model dynamics that ranged from stable equilibria to cycles or extinction. These results suggest that inclusion of behavioral data in viability models may improve estimates of extinction risk for imperiled species. Our approach provides a simple method for incorporating spatial and demographic consequences of behavioral strategies into population models and may be easily extended to other species and behaviors to understand the mechanisms of population dynamics for imperiled populations.