Forecasting extinction risk with nonstationary matrix models.

Matrix population growth models are standard tools for forecasting population change and for managing rare species, but they are less useful for predicting extinction risk in the face of changing environmental conditions. Deterministic models provide point estimates of lambda, the finite rate of increase, as well as measures of matrix sensitivity and elasticity. Stationary matrix models can be used to estimate extinction risk in a variable environment, but they assume that the matrix elements are randomly sampled from a stationary (i.e., non-changing) distribution. Here we outline a method for using nonstationary matrix models to construct realistic forecasts of population fluctuation in changing environments. Our method requires three pieces of data: (1) field estimates of transition matrix elements, (2) experimental data on the demographic responses of populations to altered environmental conditions, and (3) forecasting data on environmental drivers. These three pieces of data are combined to generate a series of sequential transition matrices that emulate a pattern of long-term change in environmental drivers. Realistic estimates of population persistence and extinction risk can be derived from stochastic permutations of such a model. We illustrate the steps of this analysis with data from two populations of Sarracenia purpurea growing in northern New England. Sarracenia purpurea is a perennial carnivorous plant that is potentially at risk of local extinction because of increased nitrogen deposition. Long-term monitoring records or models of environmental change can be used to generate time series of driver variables under different scenarios of changing environments. Both manipulative and natural experiments can be used to construct a linking function that describes how matrix parameters change as a function of the environmental driver. This synthetic modeling approach provides quantitative estimates of extinction probability that have an explicit mechanistic basis.     

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.     

Local Population Dynamics in Metapopulation Models: Implications for Conservation

Abstract: Habitat fragmentation and the division of populations into spatially separated units have led to the increasing use of metapopulation models to characterize these populations. One prominent model that has served as a heuristic tool was introduced by Levins and is based on a collection of simplifying assumptions that exclude information on the dynamics and spatial distribution of local populations. Levins's and similar models predict the proportion of occupied habitat patches at equilibrium and the conditions needed to avoid total extinction. There are many obvious concerns about using such models, including how realistic alterations might change the predictions and whether occupancy has any relationship to population-level processes. Although many of the assumptions of these simple models are known to be unrealistic, we do not know how the assumptions affect model predictions. We simulated a metapopulation, and our results show that assumptions such as homogeneity of habitat patches, random migration among patches, equivalent extinction probabilities in all patches, and a large number of patches can lead to large overestimations of habitat occupancy. But when we explicitly modeled the underlying population dynamics within each patch, we found (1) that there was a strong correlation between proportion of occupied patches and total metapopulation size and (2) that the distribution of individuals among patches was relatively insensitive to model assumptions. Thus, our results show that although realistic modifications will change model predictions for occupancy, occupancy and population trends will be correlated. These correlations between occupancy and population size suggest that occupancy models may have some utility in conservation applications.     

Extinction of Mammal Populations in Western North American National Parks

Patterns of local extinction of mammal populations in western North American parks were examined in relation to current biogeographic and population lifetime models. The analysis was based on species sighting records as of 1989. While western North American parks are obviously not true isolates, patterns of mammal extinction in them are nonetheless consistent with two predictions of the land-bridge island hypothesis. First, the number of extinctions has exceeded the number of colonizations since park establishment, and, second, the rate of extinction is inversely related to park area. Factors influencing the lifetime of mammal populations were evaluated using a stepwise multivariate survival analysis procedure for censored data. Survival time for mammal populations was positively related to estimated initial population size. After accounting for population size, species within the order Lagomorpha were particularly prone to extinction. Finally, after controlling for population size and taxon variation, survival time was positively related to age of maturity, indicating that species with longer generation times—age of maturity and generation time are highly correlated in mammals—persist longer in absolute time.     

The unified neutral theory of biodiversity: do the numbers add up?

Hubbell's unified neutral theory is a zero-sum ecological drift model in which population sizes change at random in a process resembling genetic drift, eventually leading to extinction. Diversity is maintained within the community by speciation. Hubbell's model makes predictions about the distribution of species abundances within communities and the turnover of species from place to place (beta diversity). However, ecological drift cannot be tested adequately against these predictions without independent estimates of speciation rates, population sizes, and dispersal distances. A more practical prediction from ecological drift is that time to extinction of a population of size N is approximately 2N generations. I test this prediction here using data for passerine birds (Passeriformes). Waiting times to speciation and extinction were estimated from genetic divergence between sister populations and a lineage-through-time plot for endemic South American suboscine passerines. Population sizes were estimated from local counts of birds in two large forest plots extrapolated to the area of wet tropical forest in South America and from atlas data on European passerines. Waiting times to extinction (ca. 2 Ma) are much less than twice the product of average population size (4.0 and 14.4 x 10(6) individuals in South America and Europe) and generation length (five and three years) for songbirds, that is, 40 and 86 Ma, respectively. Thus, drift is too slow to account for turnover in regional avifaunas. Presumably, other processes, involving external drivers, such as climate and physiographic change, and internal drivers, such as evolutionary change in antagonistic interactions, predominate. Hubbell's model is historical and geographic, and his perspective importantly links local and regional process and pattern. Ecological reality can be added to the mix while retaining Hubbell's concept of continuity of communities in space and time.     

Small Populations and Offspring Sex-Ratio Deviations in Eagles

Abstract:  Stochastic variation of sex ratio has long been appreciated as a potential factor driving small populations to extinction, but it is not the only source of sex-ratio bias in small populations. We examined whether some consequences of sex allocation could affect extinction risk in small populations of size-dimorphic birds such as eagles. We report variations in sex ratio at fledging from a long-term study of a declining population of Spanish Imperial Eagles ( Aquila adalberti ). Nestling sex-ratio deviation apparently was mediated by age of breeders, whereas territory quality had no obvious effect. Adult–adult pairs produced the same proportion of both sexes in high- or low-density situations, but pairs with at least one member in nonadult plumage class produced more males. As the population declined over a period of years, the proportion of breeders with immature plumage increased; consequently, the proportion of fledgling males increased. However, when population density was high, the proportion of breeders with immature plumage decreased and more female offspring were produced. This relationship between population density, composition of breeder age, and fledgling sex ratios allowed us to make predictions of extinction risk due to nonstochastic deviations of sex ratio in small, declining populations. In the study population, on the basis of the Vortex simulation results, an estimated reduction of 42.5% in predicted mean time to extinction was attributed solely to biased sex ratio.     

Mutation and Conservation

Mutation can critically affect the viability of small populations by causing inbreeding depression, by maintaining potentially adaptive genetic variation in quantitative characters, and through the erosion of fitness by accumulation of mildly detrimental mutations. I review and integrate recent empirical and theoretical work on spontaneous mutation and its role in population viability and conservation planning. I analyze both the maintenance of potentially adaptive genetic variation in quantitative characters and the role of detrimental mutations in increasing the extinction risk of small populations. Recent experiments indicate that the rate of production of quasineutral, potentially adaptive genetic variance in quantitative characters is an order of magnitude smaller than the total mutational variance because mutations with large phenotypic effects tend to be strongly detrimental. This implies that, to maintain normal adaptive potential in quantitative characters under a balance between mutation and random genetic drift (or among mutation, drift, and stabilizing natural selection), the effective population size should be about 5000 rather than 500 (the Franklin-Soulé number). Recent theoretical results suggest that the risk of extinction due to the fixation of mildly detrimental mutations may be comparable in importance to environmental stochasticity and could substantially decrease the long-term viability of populations with effective sizes as large as a few thousand. These findings suggest that current recovery goals for many threatened and endangered species are inadequate to ensure long-term population viability.     

Population Viability Analysis for an Endangered Plant

Abstract: Demographic modeling is used to understand the population viability of Furbish's lousewort, Pedicularis furbishiae , a perennial plant species endemic to the St. John River Valley in northern Maine. Environment-specific summaries of demographic parameters (survivorship, growth, and fecundity) over four years, organized into stage-based projection matrices, provide predictions of future population dynamics given a deterministic extension of past conditions. Stochastic modeling, using (I) empirically observed variation in demographic parameters, and (2) estimated rates of natural catastrophes, leads to predictions of extinction probability.
P. furbishiae viability has varied widely over the study period Viable populations with finite rates of increase > 1 are found where cover is low, woody plants do not dominate, and disturbance does not occur. Rates of increase vary over time, suggesting that stochastic analyses would be realistic. Stochastic measures of population viability incorporating environmental variation suggest that early successional environments, especially wetter sites, can support viable populations in the absence of disturbance. However; observed rates of natural catastrophe dominate viability estimates of individual populations. Metapopulation dynamics feature extinction rates that are greater than recolonization rates, and may be affected by land use in the watershed Species management needs to consider a large-scale view of the riverine corridor.     

Rapid Extinction of Mountain Sheep Populations Revisited

Abstract: Predicting extinction probabilities for populations of various sizes has been a primary focus of conservation biology. Berger (1990) presented an empirically based extinction model for mountain sheep ( Ovis canadensis ) populations in five southwestern states that predicted disappearance within 50 years of all populations estimated to number 50 sheep or fewer, but essentially no loss in that time period of populations estimated at over 100. The majority of the 122 populations he used in his analysis were from California, but his analysis did not use many of the historical size estimates for these populations. I tested Berger's (1990) model using the complete data set from California and found—contrary to his results—that, for all size classes of population estimates, at least 61% of the populations persisted for 50 years. Also, two predictions from Berger's model were not consistent with the data from California: (1) 10 populations have increased from estimates of 50 or fewer animals to over 100, whereas the Berger model predicted that these populations would only decline to extinction; and (2) of 27 extant populations with long enough records, 85% were estimated at least 50 years ago to be 50 individuals or fewer and should therefore be extinct by now. Berger's model has now failed tests in three states and therefore does not support the strong population size effect on extinction probability that it first appeared to provide, and it may serve conservation poorly through misdirected effort if it is used as the basis for setting policies or taking actions.     

Future distribution modelling: A stitch in time is not enough

The last two decades have seen an increasing number of studies assessing the impact of climate change upon biodiversity. A central assumption underpinning research into the potential future habitat of terrestrial biota is that species are presently in equilibrium with their environments and that quantitative climate models adequately represent the distribution of species. Recently, many alarming predictions have emerged concerning the extinction and redistribution of species. Here, we show that even large-scale models of the climatic niche dimensions of species are temporally variable. Distributional models were developed for Salix (willow) species occurring in the province of Ontario, Canada, using three historical climate data sets. Although historical data very accurately represented the distributions of willows, the inherent variability within the models of species based on different periods greatly influenced the direction and magnitude of projected distributional change. We expose a fundamental uncertainty with respect to predicting the responses of species to climate change.     

Extinction, recolonization, and dispersal through time in a planktonic crustacean

Dormant propagule banks are important reservoirs of biological and genetic diversity of local communities and populations and provide buffering mechanisms against extinction. Although dormant stages of various plant and animal species are known to remain viable for decades and even centuries, little is known about the effective influence of recolonization from such old sources on the genetic continuity of intermittent populations under natural conditions. Using recent and old dormant eggs recovered from a dated lake sediment core in Kenya, we traced the genetic composition of a local population of the planktonic crustacean Daphnia barbata through a sequence of extinction and recolonization events. This was combined with a phylogeographic and population-genetic survey of regional populations. Four successive populations, fully separated in time, inhabited Lake Naivasha from ca. 1330 to 1570 AD, from ca. 1610 to 1720 AD, from ca. 1840 to 1940 AD, and from 1995 to the present (2001 AD). Our results strongly indicate genetic continuity between the 1840-1940 and 1995-2001 populations, which are separated in time by at least 50 years, and close genetic relatedness of them both to the 1330-1580 population. A software tool (Colonize) was developed to find the most likely source population of the refounded 1995-2001 population and to test the number of colonists involved in the recolonization event. The results confirmed that the 1995-2001 population most probably developed out of a limited number of surviving local dormant eggs from the previous population, rather than out of individuals from regional (central and southern Kenya) or more distant (Ethiopia, Zimbabwe) populations that may have immigrated to Lake Naivasha through passive dispersal. These results emphasize the importance of prolonged dormancy for the natural long-term dynamics of crustacean zooplankton in fluctuating environments and suggest an important role of old local dormant egg banks in aquatic habitat restoration.     

Reconstructing the historic demography of an endangered seabird

Reducing extinction risk for threatened species requires determining which demographic parameters are depressed and causing population declines. Museum collections may constitute a unique, underutilized resource for measuring demographic changes over long time periods using age-ratio analysis. We reconstruct the historic demography of a U.S. federally endangered seabird, the Marbled Murrelet (Brachyramphus marmoratus), from specimens collected approximately 100 years ago for comparison with predictions from comparative analyses and with results from contemporary field studies using both age-ratio analysis and conventional demographic estimators. Reproduction in the late 1800s and early 1900s matched predictions from comparative analysis, but was 8-9 times greater than contemporary estimates, whereas adult survival was unchanged. Historic reproductive rates would support stable populations, but contemporary levels should result in population declines. Contemporary demographic estimates derived from age-ratio analysis were similar to estimates from conventional estimators. Using museum specimens to reconstruct historic demography provides a unique approach to identify causes of decline and to set demographic benchmarks for recovery of endangered species that meet most assumptions of age-ratio analysis.     

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.     

Rates of Movement of Threatened Bird Species between IUCN Red List Categories and toward Extinction

Abstract:  In recent centuries bird species have been deteriorating in status and becoming extinct at a rate that may be 2–3 orders of magnitude higher than in prehuman times. We examined extinction rates of bird species designated critically endangered in 1994 and the rate at which species have moved through the IUCN (World Conservation Union) Red List categories of extinction risk globally for the period 1988–2004 and regionally in Australia from 1750 to 2000. For Australia we drew on historical accounts of the extent and condition of species habitats, spread of invasive species, and changes in sighting frequencies. These data sets permitted comparison of observed rates of movement through the IUCN Red List categories with novel predictions based on the IUCN Red List criterion E, which relates to explicit extinction probabilities determined, for example, by population viability analysis. The comparison also tested whether species listed on the basis of other criteria face a similar probability of moving to a higher threat category as those listed under criterion E. For the rate at which species moved from vulnerable to endangered, there was a good match between observations and predictions, both worldwide and in Australia. Nevertheless, species have become extinct at a rate that, although historically high, is 2 (Australia) to 10 (globally) times lower than predicted. Although the extinction probability associated with the critically endangered category may be too high, the shortfall in realized extinctions can also be attributed to the beneficial impact of conservation intervention. These efforts may have reduced the number of global extinctions from 19 to 3 and substantially slowed the extinction trajectory of 33 additional critically endangered species. Our results suggest that current conservation action benefits species on the brink of extinction, but is less targeted at or has less effect on moderately threatened species.     

Influence of Fragmentation and Bottlenecks on Genetic Divergence of Wild Turkey Populations

Abstract: There are few empirical studies of the effects of human-induced fragmentation and bottlenecks on the genetic structure of field populations. Assessment of these effects is necessary to evaluate the relevance of predictions obtained from simulation and theoretical models to the management of wild populations. The genetic structure of populations of the Wild Turkey (Meleagris gallopavo), which have been heavily influenced by human activities, was examined using allozyme electrophoresis Allele frequencies at four polymorphic loci were estimated for 27 localities using 461 turkeys The estimated proportion of genetic variation resulting from differences among populations (F_st= 0.102) was one of the highest reported for any avian species and was also much higher than that observed between turkey populations that had not passed through known bottlenecks Almost all of the variation (89%) among populations was accounted for by differences between groups of populations with different histories of manipulation Fragmented distributions and population bottlenecks due to human activities appear to have increased genetic differentiation among populations of wild turkeys. This observation agrees with theoretical predictions concerning the effects of isolation and bottlenecks on the genetic structure of field populations.     

The Reliability of Using Population Viability Analysis for Risk Classification of Species

I examine whether or not it is appropriate to use extinction probabilities generated by population viability analyses, based on best estimates for model parameters, as criteria for listing species in Red Data Book categories as recently proposed by the World Conservation Union. Such extinction probabilities are influenced by how accurately model parameters are estimated and by how accurately the models depict actual population dynamics. I evaluate the effect of uncertainty in parameter estimation through simulations. Simulations based on Steller sea lions were used to evaluate bias and precision in estimates of probability of extinction and to consider the performance of two proposed classification schemes. Extinction time estimates were biased (because of violation of the assumption of stable age distribution) and underestimated the variability of probability of extinction for a given time (primarily because of uncertainty in parameter estimation). Bias and precision in extinction probabilities are important when these probabilities are used to compare the risk of extinction between species. Suggestions are given for population viability analysis techniques that incorporate parameter uncertainty. I conclude that testing classification schemes with simulations using quantitative performance objectives should precede adoption of quantitative listing criteria.     

Association of Coloration Mode with Population Declines and Endangerment in Australian Frogs

Abstract: Successful protection of biodiversity requires increased understanding of the ecological characteristics that predispose some species to endangerment. Theory posits that species with polymorphic or variable coloration should have larger distributions, use more diverse resources, and be less vulnerable to population declines and extinctions, compared with taxa that do not vary in color. We used information from literature on 194 species of Australian frogs to search for associations of coloration mode with ecological variables. In general, species with variable or polymorphic color patterns had larger ranges, used more habitats, were less prone to have a negative population trend, and were estimated as less vulnerable to extinction compared with nonvariable species. An association of variable coloration with lower endangerment was also evident when we controlled statistically for the effects of range size. Nonvariable coloration was not a strong predictor of endangerment, and information on several characteristics is needed to reliably identify and protect species that are prone to decline and may become threatened by extinction in the near future. Analyses based on phylogenetic‐independent contrasts did not support the hypothesis that evolutionary transitions between nonvariable and variable or polymorphic coloration have been accompanied by changes in the ecological variables we examined. Irrefutable demonstration of a role of color pattern variation in amphibian decline and in the dynamics and persistence of populations in general will require a manipulative experimental approach.     

Prediction of extinction in plants: interaction of extrinsic threats and life history traits

The global extinction of species proceeds through the erosion of local populations. Using a 60-year time series of annual sighting records of plant species, we studied the correlates of local extinction risk associated with a risk of species extinction in the Park Grass Experiment where plants received long-term exposure to nutrient enrichment, soil acidification, and reductions in habitat size. We used multivariate linear models to assess how extrinsic threats and life history traits influence extinction risk. We investigated effects of four extrinsic threats (nitrogen enrichment, productivity, acidification, and plot size) as well as 11 life history traits (month of earliest flowering, flowering duration, stress tolerance, ruderalness [plant species' ability to cope with habitat disturbance], plant height, diaspore mass, seed bank, life form, dispersal mode, apomixis [the ability for a species to reproduce asexuall through seeds], and mating system). Extinction risk was not influenced by plant family. All of the 11 life history traits except life form and all threat variables influenced extinction risk but always via interactions which typically involved one threat variable and one life history trait. We detected comparatively few significant interactions between life history traits, and the interacting traits compensated for each other. These results suggest that simple predictions about extinction risk based on species' traits alone will often fail. In contrast, understanding the interactions between extrinsic threats and life history traits will allow us to make more accurate predictions of extinctions.     

Accuracy of Short‐Term Demographic Data in Projecting Long‐Term Fate of Populations

Short‐term surveys are useful in conservation of species if they can be used to reliably predict the long‐term fate of populations. However, statistical evaluations of reliability are rare. We studied how well short‐term demographic data (1999–2002) of tartar catchfly (Silene tatarica), a perennial riparian plant, projected the fate and growth of 23 populations of this species up to the year 2010. Surveyed populations occurred along a river with natural flood dynamics and along a regulated river. Riparian plant populations are affected by flooding, which maintains unvegetated shores, while forest succession proceeds in areas with little flooding. Flooding is less severe along the regulated river, and vegetation overgrowth reduces abundance of tartar catchfly on unvegetated shores. We built matrix models to calculate population growth rates and estimated times to population extinction in natural and in regulated rivers, 13 and 10 populations, respectively. Models predicted population survival well (model predictions matched observed survival in 91% of populations) and accurately predicted abundance increases and decreases in 65% of populations. The observed and projected population growth rates differed significantly in all but 3 populations. In most cases, the model overestimated population growth. Model predictions did not improve when data from more years were used (1999–2006). In the regulated river, the poorest model predictions occurred in areas where cover of other plant species changed the fastest. Although vegetation cover increased in most populations, it decreased in 4 populations along the natural river. Our results highlight the need to combine disturbance and succession dynamics in demographic models and the importance of habitat management for species survival along regulated rivers. Precisión de Datos Demográficos de Corto Plazo en la Proyección del Destino de Poblaciones a Largo Plazo     

Invading introduced species in insular heterogeneous environments

We are concerned with the development and analysis of a predator–prey system designed for heterogeneous insular environments; populations are native preys exposed to introduced and invading predators and competitor preys. We first look at the unstructured model; this yields a singular system of ordinary differential equations having interesting dynamical features, such as finite time extinction or persistence of populations. Next we build a spatially heterogeneous structured model upon developing a reaction–diffusion system; then, using numerical experiments we analyze some typical effects of spatial heterogeneities on the persistence or extinction of native or introduced and invading species. The case of Kerguelen sub-Antartic heterogeneous islands where both domestic cats and alien preys have been introduced is taken as an example.