Bridging the generation gap in plants: pollination, parental fecundity, and offspring demography

Despite extensive study of pollination and plant reproduction on the one hand, and of plant demography on the other, we know remarkably little about links between seed production in successive generations, and hence about long-term population consequences of variation in pollination success. We bridged this "generation gap" in Ipomopsis aggregata, a long-lived semelparous wildflower that is pollinator limited, by adding varying densities of seeds to natural populations and following resulting plants through their entire life histories. To determine whether pollen limitation of seed production constrains rate of population growth in this species, we sowed seeds into replicated plots at a density that mimics typical pollination success and spacing of flowering plants in nature, and at twice that density to mimic full pollination. Per capita offspring survival, flower production, and contribution to population increase (lambda) did not decline with sowing density in this experiment, suggesting that typical I. aggregata populations freed from pollen limitation will grow over the short term. In a second experiment we addressed whether density dependence would eventually erase the growth benefits of full pollination, by sowing a 10-fold range of seed densities that falls within extremes estimated for the natural "seed rain" that reaches the soil surface. Per capita survival to flowering and age at flowering were again unaffected by sowing density, but offspring size, per capita flower production, and lambda declined with density. Such density dependence complicates efforts to predict population dynamics over the longer term, because it changes components of the life history (in this case fecundity) as a population grows. A complete understanding of how constraints on seed production affect long-term population growth will hinge on following offspring fates at least through flowering of the first offspring generation, and doing so for a realistic range of population densities.     

Albatross populations in peril: a population trajectory for black-browed albatrosses at south Georgia.

Simulation modeling was used to reconstruct Black-browed Albatross (Diomedea melanophris) population trends. Close approximations to observed data were accomplished by annually varying survival rates, reproductive success, and probabilities of returning to breed given success in previous years. The temporal shift in annual values coincided with the start of longline fishing at South Georgia and potential changes in krill abundance. We used 23 years of demographic data from long-term studies of a breeding colony of this species at Bird Island, South Georgia, to validate our model. When we used annual parameter estimates for survival, reproductive success, and probabilities of returning to breed given success in previous years, our model trajectory closely followed the observed changes in breeding population size over time. Population growth rate was below replacement (lambda < 1) in most years and was most sensitive to changes in adult survival. This supports the recent IUCN uplisting of this species from "Vulnerable" to "Endangered." Comparison of pre-1988 and post-1988 demography (before and after the inception of a longline fishery in the breeding area) reveals a decrease in lambda from 0.963 to 0.910. A life table response experiment (LTRE) showed that this decline in lambda was caused mostly by declines in survival of adults. If 1988-1998 demographic rates are maintained, the model predicts a 98% chance of a population of fewer than 25 pairs within 78 years. For this population to recover to a status under which it could be "delisted," a 10% increase in survival of all age classes would be needed.     

Characterizing source-sink dynamics with genetic parentage assignments

Source-sink dynamics have been suggested to characterize the population structure of many species, but the prevalence of source-sink systems in nature is uncertain because of inherent challenges in estimating migration rates among populations. Migration rates are often difficult to estimate directly with demographic methods, and indirect genetic methods are subject to a variety of assumptions that are difficult to meet or to apply to evolutionary timescales. Furthermore, such methods cannot be rigorously applied to high-gene-flow species. Here, we employ genetic parentage assignments in conjunction with demographic simulations to infer the level of immigration into a putative sink population. We use individual-based demographic models to estimate expected distributions of parent-offspring dyads under competing sink and closed-population models. By comparing the actual number of parent-offspring dyads (identified from multilocus genetic profiles) in a random sample of individuals taken from a population to expectations under these two contrasting demographic models, it is possible to estimate the rate of immigration and test hypotheses related to the role of immigration on population processes on an ecological timescale. The difference in the expected number of parent-offspring dyads between the two population models was greatest when immigration into the sink population was high, indicating that unlike traditional population genetic inference models, the highest degree of statistical power is achieved for the approach presented here when migration rates are high. We used the proposed genetic parentage approach to demonstrate that a threatened population of Marbled Murrelets (Braclhyrarmphus marmotus) appears to be supplemented by a low level of immigration (approximately 2-6% annually) from other populations.     

The importance of space, time, and stochasticity to the demography and management of Alliaria petiolata

As population modeling is increasingly called upon to guide policy and management, it is important that we understand not only the central tendencies of our study systems, but the consequences of their variation in space and time as well. The invasive plant Alliaria petiolata (garlic mustard) is actively managed in the United States and is the focus of a developing biological control program. Two weevils (Coleoptera: Curculionidae: Ceutorhynchus) that reduce fecundity (C. alliariae) and rosette survival plus fecundity (C. scrobicollis) are under consideration for release pending host specificity testing. We used a demographic modeling approach to (1) quantify variability in A. petiolata growth and vital rates and (2) assess the potential for single- or multiple-agent biocontrol to suppress growth of 12 A. petiolata populations in Illinois and Michigan studied over three plant generations. We used perturbation analyses and simulation models with stochastic environments to estimate stochastic growth rates (lambda(S)) and predict the probability of successful management using either a single biocontrol agent or two agent species together. Not all populations exhibited invasive dynamics. Estimates of lambda(S) ranged from 0.78 to 2.21 across sites, while annual, deterministic growth (lambda) varied up to sevenfold within individual sites. Given our knowledge of the biocontrol agents, this analysis suggests that C. scrobicollis alone may control A. petiolata at up to 63% of our study sites where lambda >1, with the combination of both agents predicted to succeed at 88% of sites. Across sites and years, the elasticity rankings were dependent on lambda. Reductions of rosette survival, fecundity, or germination of new seeds are predicted to cause the greatest reduction of lambda in growing populations. In declining populations, transitions affecting seed bank survival have the greatest effect on lambda. This contrasts with past analyses that varied parameters individually in an otherwise constant matrix, which may yield unrealistic predictions by decoupling natural parameter covariances. Overall, comparisons of stochastic and deterministic growth rates illustrate how analyses of individual populations or years could misguide management or fail to characterize complex traits such as invasiveness that emerge as attributes of populations rather than species.     

Relating chronic toxicity responses to population-level effects: A comparison of population-level parameters for three salmon species as a function of low-level toxicity

Standard laboratory toxicity tests assess the physiological responses of individual organisms to exposure to toxic substances under controlled conditions. Time and space restrictions often prevent the assessment of population-level responses to a toxic substance. Contaminants can affect various biological functions (e.g. growth, fecundity or behavior), which may alter different demographic traits, leading to population-level impacts. In this study, immune suppression, reproductive dysfunction and somatic growth impairment were examined using life history matrix models for coho salmon (Oncorhynchus kisutch), sockeye salmon (Oncorhynchus nerka) and chinook salmon (Oncorhynchus tshawytscha). Our intent was to gauge the relative magnitude of response to toxic effects among species and between life history stages, not provide a specific estimate of population growth rate or abundance. Effects due to immune suppression were modeled as reductions in age-specific survival. Toxic impacts on reproductive function were modeled as a 10% reduction in reproductive contribution for all reproductively mature age groups. Model runs that examined the effect of somatic growth reduction on population parameters incorporated both survival and reproductive impacts. All impacts were modeled as 10% reductions in the affected population demographic parameters. First-year survival and reproductive impacts produced similar population growth rates (λ), but resulted in different sensitivity and stable age distributions. Modeled somatic growth reduction produced additive effects on survival and reproduction. Toxic stressors producing similar changes in λ did not necessarily produce similar changes in the age distributions. Sensitivity and elasticity analyses demonstrated that changes to the first-year survival rate produced the greatest per-unit effect on λ for each species. Alteration in abundance of mature females also strongly influenced λ. Differences observed between species showed that the number of reproductive ages and time to reproductive maturity were important components for population-level responses. These results emphasize the importance of linking toxicity responses at low concentrations to the demographic traits they affect, and help to highlight the toxicity tests that are more suitable for assessing impacts on the focal species. Additionally, life history modeling is a useful tool for developing testable hypotheses regarding impacts on specific populations as well as for conducting comparisons between populations.     

The impact of invasive grasses on the population growth of Anemone patens, a long-lived native forb

Negative impacts of invasive plants on natives have been well documented, but much less is known about whether invasive plants can cause population level declines. We used demographic models to investigate the effects of two invasive grasses on the demography and population growth of Anemone patens, a long-lived native perennial of North American grasslands. Demographic data of A. patens growing in patches characterized by Bromus inermis, Poa pratensis, or native grasses were used to parameterize integral projection models. Models based on both average conditions and those allowing for environmental stochasticity indicate that A. patens is slowly increasing in patches of native grass (lambda = 1.02) and declining in patches of invasive grasses, particularly those dominated by B. inermis (lambda = 0.93). Extinction probabilities indicate that A. patens should persist in native grass patches, but has a much higher probability of extinction in Bromus patches compared to Poa patches. While sensitivity analyses showed that survival had the biggest effect on population growth rates in all habitats, results of a Life Table Response Experiment (LTRE) revealed that slower individual growth rates in patches of invasive grasses contributed the most to the observed reduction in population growth. These results suggest that invasive grasses may cause slow declines in A. patens, despite short-term coexistence, and that controlling B. inermis only would not be sufficient to ensure A. patens persistence.     

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.     

Conserving Slow-Growing, Long-Lived Tree Species: Input from the Demography of a Rare Understory Conifer, Taxus floridana

Abstract:  Although land preservation and promotion of successful regeneration are important conservation actions, their ability to increase population growth rates of slow-growing, long-lived trees is limited. We investigated the demography of Taxus floridana Nutt., a rare understory conifer, in three populations in different ravine forests spanning its entire geographic range along the Apalachicola River Bluffs in northern Florida (U.S.A.). We examined spatial and temporal patterns in demographic parameters and projected population growth rates by using four years of data on the recruitment and survival of seedlings and established stems, and on diameter growth from cross-sections of dead stems. All populations experienced a roughly 10-fold increase in seedling recruitment in 1996 compared with other years. The fates of seedlings and stems between 8 and 16 mm differed among populations. The fates of stems in two other size classes (the 2- to 4-mm class and the 4- to 8-mm class) differed among both populations and years. Individual stems in all populations exhibited similarly slow growth rates. Stochastic matrix models projected declines in all populations. Stochastic matrix analysis revealed the high elasticity of a measure of stochastic population growth rate to perturbations in the stasis of large reproductive stems for all populations. Additional analyses also indicated that occasional episodes of high recruitment do not greatly affect population growth rates. Conservation efforts directed at long-lived, slow-growing rare plants like Taxus floridana should both protect established reproductive individuals and further enhance survival of individuals in other life-history stages, such as juveniles, that often do not appear to contribute greatly to population growth rates.     

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.     

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.     

Age,stages, and the role of generation time in matrix models

The earliest matrix models, proposed in the 1940s, consider age classes, and were later proved to be equivalent to the discrete time version of the stable population theory. In this theory and models, besides the asymptotic growth rate, a very important characteristic is the turnover of individuals, measured in various ways by generation time. Models considering stages, on the contrary, do not take into account the age of individuals and seem largely preferable to age-structured models for many populations in which demographic characteristics are related to biological stages (such a seed, rosette, flowering plant, etc.) rather than to age per itself. These two kinds of models can be embedded as particular cases of stage by age models or multistate models. Theses general models can be used to develop a multistate stable population theory with many advantages. This general theory is reviewed with emphasis on general rules for sensitivity analyses in which generation time plays a central role.     

Demography of central and marginal populations of monkeyflowers (Mimulus cardinalis and M. lewisii)

Every species occupies a limited geographic area, but how spatiotemporal environmental variation affects individual and population fitness to create range limits is not well understood. Because range boundaries arise where, on average, populations are more likely to go extinct than to persist, range limits are an inherently population-level problem for which a demographic framework is useful. In this study, I compare demographic parameters and population dynamics between central and marginal populations of monkeyflowers, Mimulus cardinalis and M. lewisii, along an elevation gradient spanning both species' ranges. Central and marginal populations of both species differed in survival and fecundity. For M. lewisii, these components of fitness were higher in central than in marginal populations, but for M. cardinalis the converse was true. To assess spatiotemporal variation in population dynamics, I used transition matrix models to estimate asymptotic population growth rates (lambda) and found that population growth rates of M. lewisii were highest at the range center and reduced at the range margin. Population growth rates of M. cardinalis were highest at the range margin and greatly reduced at the range center. Life table response analysis decomposed spatiotemporal variation in lambda into contributions from each transition between life stages, finding that transitions from large nonreproductive and reproductive plants to the seed class and stasis in the reproductive class made the largest contributions to spatial differences in lambda. These transitions had only low to moderate sensitivities, indicating that differences in projected population growth rates resulted mainly from observed differences in transition matrix parameters and their underlying vital rates.     

Possible Extinction Vortex for a Population of Iberian Lynx on the Verge of Extirpation

Abstract: Theory suggests that demographic and genetic traits deteriorate (i.e., fitness and genetic diversity decrease) when populations become small, and that such deterioration could precipitate positive feedback loops called extinction vortices. We examined whether demographic attributes and genetic traits have changed over time in one of the 2 remaining small populations of the highly endangered Iberian lynx (Lynx pardinus) in Doñana, Spain. From 1983 to 2008, we recorded nontraumatic mortality rates, litter size, offspring survival, age at territory acquisition, and sex ratio. We combined these demographic attributes with measures of inbreeding and genetic diversity at neutral loci (microsatellites) and genes subjected to selection (major histocompatibility complex). Data on demographic traits were obtained through capture and radio tracking, checking dens during breeding, track surveys, and camera trapping. For genetic analyses, we obtained blood or tissue samples from captured or necropsied individuals or from museum specimens. Over time a female‐biased sex ratio developed, age of territory acquisition decreased, mean litter size decreased, and rates of nontraumatic mortality increased, but there were no significant changes in overall mortality rates, standardized individual heterozygosity declined steadily, and allelic diversity of exon 2 of class II major histocompatibility complex DRB genes remained constant (2 allelic variants present in all individuals analyzed). Changes in sex ratio and age of territory acquisition may have resulted from demographic stochasticity, whereas changes in litter size and nontraumatic mortality may be related to observed increases in inbreeding. Concomitant deterioration of both demographic attributes and genetic traits is consistent with an extinction vortex. The co‐occurrence, with or without interaction, of demographic and genetic deterioration may explain the lack of success of conservation efforts with the Doñana population of Iberian lynx.     

Sink populations in carnivore management: cougar demography and immigration in a hunted population.

Carnivores are widely hunted for both sport and population control, especially where they conflict with human interests. It is widely believed that sport hunting is effective in reducing carnivore populations and related human-carnivore conflicts, while maintaining viable populations. However, the way in which carnivore populations respond to harvest can vary greatly depending on their social structure, reproductive strategies, and dispersal patterns. For example, hunted cougar (Puma concolor) populations have shown a great degree of resiliency. Although hunting cougars on a broad geographic scale (> 2000 km2) has reduced densities, hunting of smaller areas (i.e., game management units, < 1000 km2), could conceivably fail because of increased immigration from adjacent source areas. We monitored a heavily hunted population from 2001 to 2006 to test for the effects of hunting at a small scale (< 1000 km2) and to gauge whether population control was achieved (lambda < or = 1.0) or if hunting losses were negated by increased immigration allowing the population to remain stable or increase (lambda > or = 1.0). The observed growth rate of 1.00 was significantly higher than our predicted survival/fecundity growth rates (using a Leslie matrix) of 0.89 (deterministic) and 0.84 (stochastic), with the difference representing an 11-16% annual immigration rate. We observed no decline in density of the total population or the adult population, but a significant decrease in the average age of independent males. We found that the male component of the population was increasing (observed male population growth rate, lambda(OM) = 1.09), masking a decrease in the female component (lambda(OF) = 0.91). Our data support the compensatory immigration sink hypothesis; cougar removal in small game management areas (< 1000 km2) increased immigration and recruitment of younger animals from adjacent areas, resulting in little or no reduction in local cougar densities and a shift in population structure toward younger animals. Hunting in high-quality habitats may create an attractive sink, leading to misinterpretation of population trends and masking population declines in the sink and surrounding source areas.     

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.     

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.     

Demographic stochasticity reduces the synchronizing effect of dispersal in predator-prey metapopulations

Dispersal may affect predator-prey metapopulations by rescuing local sink populations from extinction or by synchronizing population dynamics across the metapopulation, increasing the risk of regional extinction. Dispersal is likely influenced by demographic stochasticity, however, particularly because dispersal rates are often very low in metapopulations. Yet the effects of demographic stochasticity on predator-prey metapopulations are not well known. To that end, I constructed three models of a two-patch predator-prey system. The models constitute a hierarchy of complexity, allowing direct comparisons. Two models included demographic stochasticity (pure jump process [PJP] and stochastic differential equations [SDE]), and the third was deterministic (ordinary differential equations [ODE]). One stochastic model (PJP) treated population sizes as discrete, while the other (SDE) allowed population sizes to change continuously. Both stochastic models only produced synchronized predator-prey dynamics when dispersal was high for both trophic levels. Frequent dispersal by only predators or prey in the PJP and SDE spatially decoupled the trophic interaction, reducing synchrony of the non-dispersive species. Conversely, the ODE generated synchronized predator-prey dynamics across all dispersal rates, except when initial conditions produced anti-phase transients. These results indicate that demographic stochasticity strongly reduces the synchronizing effect of dispersal, which is ironic because demographic stochasticity is often invoked post hoc as a driver of extinctions in synchronized metapopulations.     

A noninvasive demographic assessment of sea lions based on stage-specific abundances

A pressing need exists to develop new approaches for obtaining information on demographic rates without causing further threats to imperiled animal populations. In this paper, we illustrate and apply a data-fitting technique based on quadratic programming that uses stage-specific abundance data to estimate demographic rates and asymptotic population growth rates (lambda). We used data from seven breeding colonies of California sea lions (Zalophus californianus) in the Gulf of California, Mexico. Estimates of lambda were similar to those from previous studies relying on a diffusion approximation using trends in total abundance. On average, predicted abundances were within 24% of the observed value for the inverse estimation method and within 29% of the observed value for the diffusion approximation. Our results suggest that three of the seven populations are declining (lambda < 1), but as many as six may be at risk. Elasticity and sensitivity analyses suggest that population management in most sites should focus on the protection of adults, whose survival generally contributes the most to lambda. The quadratic programming approach is a promising noninvasive technique for estimating demographic rates and assessing the viability of populations of imperiled species.     

Stochastic population dynamics in populations of western terrestrial garter snakes with divergent life histories

Comparative evaluations of population dynamics in species with temporal and spatial variation in life-history traits are rare because they require long-term demographic time series from multiple populations. We present such an analysis using demographic data collected during the interval 1978-1996 for six populations of western terrestrial garter snakes (Thamnophis elegans) from two evolutionarily divergent ecotypes. Three replicate populations from a slow-living ecotype, found in mountain meadows of northeastern California, were characterized by individuals that develop slowly, mature late, reproduce infrequently with small reproductive effort, and live longer than individuals of three populations of a fast-living ecotype found at lakeshore locales. We constructed matrix population models for each of the populations based on 8-13 years of data per population and analyzed both deterministic dynamics based on mean annual vital rates and stochastic dynamics incorporating annual variation in vital rates. (1) Contributions of highly variable vital rates to fitness (lambda(s)) were buffered against the negative effects of stochastic variation, and this relationship was consistent with differences between the meadow (M-slow) and lakeshore (L-fast) ecotypes. (2) Annual variation in the proportion of gravid females had the greatest negative effect among all vital rates on lambda(s). The magnitude of variation in the proportion of gravid females and its effect on lambda(s) was greater in M-slow than L-fast populations. (3) Variation in the proportion of gravid females, in turn, depended on annual variation in prey availability, and its effect on lambda(s) was 4 23 times greater in M-slow than L-fast populations. In addition to differences in stochastic dynamics between ecotypes, we also found higher mean mortality rates across all age classes in the L-fast populations. Our results suggest that both deterministic and stochastic selective forces have affected the evolution of divergent life-history traits in the two ecotypes, which, in turn, affect population dynamics. M-slow populations have evolved life-history traits that buffer fitness against direct effects of variation in reproduction and that spread lifetime reproduction across a greater number of reproductive bouts. These results highlight the importance of long-term demographic and environmental monitoring and of incorporating temporal dynamics into empirical studies of life-history evolution.     

Modelling environmental stochasticity in adult survival for a long-lived species

Stochastic matrix population models are often used to help guide the management of animal populations. For a long-lived species, environmental stochasticity in adult survival will play an important role in determining outcomes from the model. One of the most common methods for modelling such stochasticity is to randomly select the value of adult survival for each year from a distribution with a specified mean and standard deviation. We consider four distributions that can provide realistic models for stochasticity in adult survival. For values of the mean and standard deviation that cover the range we would expect for long-lived species, all four distributions have similar shapes, with small differences in their skewness and kurtosis. This suggests that many of the outcomes from a population model will be insensitive to the choice of distribution, assuming that distribution provides a realistic model for environmental stochasticity in adult survival. For a generic age-structured model, the estimate of the long-run stochastic growth rate is almost identical for the four distributions, across this range of values for the mean and standard deviation. Model outcomes based on short-term projections, such as the probability of a decline over a 20-year period, are more sensitive to the choice of distribution.