Demographic Heterogeneity by Bruce Kendall
Theoretical Ecology, 2012
Among-individual variation in vital parameters such as birth and death rates that is unrelated to... more Among-individual variation in vital parameters such as birth and death rates that is unrelated to age, stage, sex, or environmental fluctuations is referred to as demographic heterogeneity. This kind of heterogeneity is prevalent in ecological populations, but is almost always left out of models. Demographic heterogeneity has been shown to affect demographic stochasticity in small populations and to increase growth rates for density-independent populations. The latter is due to “cohort selection,” where the most frail individuals die out first, lowering the cohort’s average mortality as it ages. The importance of cohort selection to population dynamics has only recently been recognized. We use a continuous-time model with density dependence, based on the logistic equation, to study the effects of demographic heterogeneity in mortality and reproduction. Reproductive heterogeneity is introduced in three ways: parent fertility, offspring viability, and parent–offspring correlation. We find that both the low-density growth rate and the equilibrium population size increase as the magnitude of mortality heterogeneity increases or as parent–offspring phenotypic correlation increases. Population dynamics are affected by complex interactions among the different types of heterogeneity, and trade-off scenarios are examined which can sometimes reverse the effect of increased heterogeneity. We show that there are a number of different homogeneous approximations to heterogeneous models, but all fail to capture important parts of the dynamics of the full model.
FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/2361s1fd . . . Demographic heterogenei... more FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/2361s1fd . . . Demographic heterogeneity—variation among individuals in survival and reproduction—is ubiquitous in natural populations. Structured population models address heterogeneity due to age, size, or major developmental stages. However, other important sources of demographic heterogeneity, such as genetic variation, spatial heterogeneity in the environment, maternal effects, and differential exposure to stressors, are often not easily measured and hence are modeled as stochasticity. Recent research has elucidated the role of demographic heterogeneity in changing the magnitude of demographic stochasticity in small populations. Here we demonstrate a previously unrecognized effect: heterogeneous survival in long-lived species can increase the long-term growth rate in populations of any size. We illustrate this result using simple models in which each individual's annual survival rate is independent of age but survival may differ among individuals within a cohort. Similar models, but with nonoverlapping generations, have been extensively studied by demographers, who showed that, because the more “frail” individuals are more likely to die at a young age, the average survival rate of the cohort increases with age. Within ecology and evolution, this phenomenon of “cohort selection” is increasingly appreciated as a confounding factor in studies of senescence. We show that, when placed in a population model with overlapping generations, this heterogeneity also causes the asymptotic population growth rate λ to increase, relative to a homogeneous population with the same mean survival rate at birth. The increase occurs because, even integrating over all the cohorts in the population, the population becomes increasingly dominated by the more robust individuals. The growth rate increases monotonically with the variance in survival rates, and the effect can be substantial, easily doubling the growth rate of slow-growing populations. Correlations between parent and offspring phenotype change the magnitude of the increase in λ, but the increase occurs even for negative parent–offspring correlations. The effect of heterogeneity in reproductive rate on λ is quite different: growth rate increases with reproductive heterogeneity for positive parent–offspring correlation but decreases for negative parent–offspring correlation. These effects of demographic heterogeneity on λ have important implications for population dynamics, population viability analysis, and evolution.
Using data on breeding birds from a 35-year study of Florida scrub-jays Aphelocoma coerulescens (... more Using data on breeding birds from a 35-year study of Florida scrub-jays Aphelocoma coerulescens (Bosc 1795), we show that survival probabilities are structured by age, birth cohort, and maternal family, but not by sex. Using both accelerated failure time (AFT) and Cox proportional hazard models, the data are best described by models incorporating variation among birth cohorts and greater mortality hazard with increasing age. AFT models using Weibull distributions with the shape parameter > 1 were always the best-fitting models.
Shared frailty models allowing for family structure greatly reduce model deviance. The best-fitting models included a term for frailty shared by maternal families.
To ask how long a data set must be to reach qualitatively the same conclusions, we repeated the analyses for all possible truncated data sets of 2 years in length or greater. Length of the data set affects the parameter estimates, but not the qualitative conclusions. In all but three of 337 truncated data sets the best-fitting models pointed to same conclusions as the full data set. Shared frailty models appear to be quite robust.
The data are not adequate for testing hypotheses as to whether variation in frailty is heritable.
Substantial structured heterogeneity for survival exists in this population. Such structured heterogeneity has been shown to have substantial effects in reducing demographic stochasticity.
FULL TEXT FREELY AVAILABLE AT https://escholarship.org/uc/item/8m35n1hz . . .
Demographic stoch... more FULL TEXT FREELY AVAILABLE AT https://escholarship.org/uc/item/8m35n1hz . . .
Demographic stochasticity increases the variance in the growth rate of small populations, and is an important factor to consider when predicting the fates of such populations. Unfortunately, the concept has been treated inconsistently. It is often defined verbally as representing chance variation among individuals in both traits (such as survival probability) and fates (such as whether the individual survived or not). In practice it is modeled as variation in fates only, with all individuals having identical underlying traits. In previous work we demonstrated that structured (but unmod- eled) individual variability in survival traits can reduce the variance in population survivorship associated with demographic stochasticity, but that unstructured random variability in survival traits has no such effect. We implicitly generalized the latter result to fecundity, without offering proof. Robert et al. (2003) have demonstrated, using simulations, that unstructured individual variability in fecundity traits can increase the extinction risk of a small population when demographic stochasticity in fecundity is modeled as following a Poisson distribution. In this paper we extend our earlier theory to correct our mistaken speculations and analyt- ically show the source of Robert et al.’s results. We also provide general predictions about the circumstances under which both structured and un- structured individual trait variation should either increase or decrease the magnitude of demographic stochasticity in the population.
Population viability analysis ( PVA) is a technique that employs stochastic demographic models to... more Population viability analysis ( PVA) is a technique that employs stochastic demographic models to predict extinction risk. All else being equal, higher variance in a demographic rate leads to a greater extinction risk. Demographic stochasticity represents variance due to differences among individuals. Current implementations of PVAs, however, assume that the expected fates of all individuals are identical. For example, demographic stochasticity in survival is modeled as a random draw from a binomial distribution. We developed a simple conceptual model showing that if there is variation among individuals in expected survival, then existing PVA models overestimate the variance due to demographic stochasticity in survival. This is a consequence of Jensen's inequality and the fact that the binomial demographic variance is a concave function of mean survival. The effect of variation among individuals on demographic stochasticity in fecundity depends on the mean-variance relationship for individual reproductive success, which is not presently known. If fecundity patterns mirror those of survival, then variation among individuals will reduce the extinction risk of small populations.
FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/06h8891s . . . Demographic stochastici... more FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/06h8891s . . . Demographic stochasticity is almost universally modeled as sampling variance in a homogeneous population, although it is defined as arising from random variation among individuals. This can lead to serious misestimation of the extinction risk in small populations. Here, we derive analytical expressions showing that the misestimation for each demographic parameter is exactly (in the case of survival) or approximately (in the case of fecundity) proportional to the among-individual variance in that parameter. We also show why this misestimation depends on systematic variation among individuals, rather than random variation. These results indicate that correctly assessing the importance of demographic stochasticity requires (1) an estimate of the variance in each demographic parameter; (2) information on the qualitative shape (convex or concave) of the mean–variance relationship; and (3) information on the mechanisms generating among-individual variation. An important consequence is that almost all population viability analyses (PVAs) overestimate the importance of demographic stochasticity and, therefore, the risk of extinction.
Environmental & Demographic Stochasticity by Bruce Kendall
Recent advances in stochastic demography provide unique insights into the probable effects of inc... more Recent advances in stochastic demography provide unique insights into the probable effects of increasing environmental variability on population dynamics, and these insights can be substantially different compared with those from deterministic models. Stochastic variation in structured population models influences estimates of population growth rate, persistence and resilience, which ultimately can alter community com- position, species interactions, distributions and harvest- ing. Here, we discuss how understanding these demographic consequences of environmental variation will have applications for anticipating changes in populations resulting from anthropogenic activities that affect the variance in vital rates. We also highlight new tools for anticipating the consequences of the magnitude and temporal patterning of environmental variability.
FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/07f27653 . . . Increased temporal vari... more FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/07f27653 . . . Increased temporal variance in life‐history traits is generally predicted to decrease individual fitness and population growth. We show that a widely used result of stochastic sensitivity analysis that bolsters this generality is flawed because it ignores the effects of correlations between vital rates. Considering the effects of these correlations (although ignoring autocorrelations), we show that the apparently simple relationship between vital rate variance and fitness can be considerably more complex than previously thought. In particular, the previously estimated negative sensitivities of fitness or population growth to variance in a vital rate can be either enhanced by positive correlations between rates or reversed by negative correlations, even to the point that variability in a rate can increase fitness or population growth. We apply this new sensitivity calculation to data from the desert tortoise and discuss its interpretation in light of the factors generating vital rate correlations.
FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/39b938pf . . . Demographic stochastici... more FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/39b938pf . . . Demographic stochasticity can have large effects on the dynamics of small populations as well as on the persistence of rare genotypes and lineages. Survival is sensibly modeled as a binomial process, but annual reproductive success (ARS) is more complex and general models for demographic stochasticity do not exist. Here we introduce a stochastic model framework for ARS and illustrate some of its properties. We model a sequence of stochastic events: nest completion, the number of eggs or neonates produced, nest predation, and the survival of individual offspring to independence. We also allow multiple nesting attempts within a breeding season. Most of these components can be described by Bernoulli or binomial processes; the exception is the distribution of offspring number. Using clutch and litter size distributions from 53 vertebrate species, we demonstrate that among-individual variability in offspring number can usually be described by the generalized Poisson distribution. Our model framework allows the demographic variance to be calculated from underlying biological processes and can easily be linked to models of environmental stochasticity or selection because of its parametric structure. In addition, it reveals that the distributions of ARS are often multimodal and skewed, with implications for extinction risk and evolution in small populations.
FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/6837k4gc . . . Both means and year-to-... more FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/6837k4gc . . . Both means and year-to-year variances of climate variables such as temperature and precipitation are predicted to change. However, the potential impact of changing climatic variability on the fate of populations has been largely unexamined. We analyzed multiyear demographic data for 36 plant and animal species with a broad range of life histories and types of environment to ask how sensitive their long-term stochastic population growth rates are likely to be to changes in the means and standard deviations of vital rates (survival, reproduction, growth) in response to changing climate. We quantified responsiveness using elasticities of the long-term population growth rate predicted by stochastic projection matrix models. Short-lived species (insects and annual plants and algae) are predicted to be more strongly (and negatively) affected by increasing vital rate variability relative to longer-lived species (perennial plants, birds, ungulates). Taxonomic affiliation has little power to explain sensitivity to increasing variability once longevity has been taken into account. Our results highlight the potential vulnerability of short-lived species to an increasingly variable climate, but also suggest that problems associated with short-lived undesirable species (agricultural pests, disease vectors, invasive weedy plants) may be exacerbated in regions where climate variability decreases.
FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/9kt8g5vj . . . Small populations are o... more FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/9kt8g5vj . . . Small populations are often at risk of extinction through processes that are effectively stochastic. Prediction of this extinction risk requires that the observed temporal variation in demographic rates be accurately partitioned between demographic stochasticity (variation among individuals) and environmental stochasticity (variation among years, correlated across individuals). However, studies of population viability analysis that include both forms of stochasticity parameterize the magnitude of environmental stochasticity incorrectly (they overestimate it). I describe and evaluate tests (1) to determine whether all the year-to-year variation in observed survivorship can be explained by demographic stochasticity alone, and (2) if not, to estimate the magnitude of environmental stochasticity in survival. The first issue can be resolved with a G test. I used simulated data to show that this test has an appropriate type I error rate, unless the individual survival probability is either very low or very high. Small amounts of environmental stochasticity often are not detected by the G test (type II error), but the hypothesis of demographic stochasticity alone is consistently rejected when environmental stochasticity is large. In contrast, estimating the magnitude of environmental stochasticity requires explicit hypotheses about the nature of the underlying variation, but I provide a flexible framework in which many such hypotheses can be examined. In particular, I show, using simulated data, that if the temporal variability in individual survival probabilities is distributed according to a beta distribution, then the maximum likelihood estimate of the variance of the survival probability is biased, but in a consistent and correctable way. The estimate obtained with my method is usually superior to an estimate that assumes that all of the variation in the observed survivorship is due to environmental stochasticity. I show how to include deterministic sources of variability, such as density dependence, and how to apply different assumptions about the underlying environmental stochasticity. I illustrate these tests with data from a population of Acorn Woodpeckers (Melanerpes formicivorus). With these data, I can determine that there is strong environmental stochasticity in juvenile survival, whereas variation in adult survival can be explained either by density dependence or by weak environmental stochasticity.
Population Viability Analysis & Population Trends by Bruce Kendall
Simple population models are increasingly being used to predict extinction risk using historical ... more Simple population models are increasingly being used to predict extinction risk using historical abundance estimates. A very simple model, the stochastic exponential growth (SEG) model, is surprisingly robust. Extinction risk is commonly computed for this model using a mathematical approximation (the “diffusion approximation”) that assumes continuous breeding throughout the year, an assumption that is violated by many species. Here I show that, for an organism with seasonal breeding, the diffusion approximation systematically overestimates the extinction risk. I demonstrate the conditions generating large bias (high environmental variance, intermediate extinction risk), and reanalyze 100 populations of conservation concern. Analyzing several policy applications, I find that the bias may be most important when classifying the risk status of species. The SEG model is still sound, but associated risk estimates should be calculated by performing stochastic simulations (as with all other population viability models) rather than by evaluating the diffusion approximation.
Classifying species according to their risk of extinction is a common practice and underpins much... more Classifying species according to their risk of extinction is a common practice and underpins much conservation activity. The reliability of such classifications rests on the accuracy of threat categorizations, but very little is known about the magnitude and types of errors that might be expected. The process of risk classification involves combining information from many sources, and understanding the quality of each source is critical to evaluating the overall status of the species. One common criterion used to classify extinction risk is a decline in abundance. Because abundance is a direct measure of conservation status, counts of individuals are generally the preferred method of evaluating whether populations are declining. Using the thresholds from criterion A of the International Union for Conservation of Nature (IUCN) Red List (critically endangered, decline in abundance of >80% over 10 years or 3 generations; endangered, decline in abundance of 50–80%; vulnerable, decline in abundance of 30–50%; least concern or near threatened, decline in abundance of 0–30%), we assessed 3 methods used to detect declines solely from estimates of abundance: use of just 2 estimates of abundance; use of linear regression on a time series of abundance; and use of state-space models on a time series of abundance. We generated simulation data from empirical estimates of the typical variability in abundance and assessed the 3 methods for classification errors. The estimates of the proportion of falsely detected declines for linear regression and the state-space models were low (maximum 3–14%), but 33–75% of small declines (30–50% over 15 years) were not detected. Ignoring uncertainty in estimates of abundance (with just 2 estimates of abundance) allowed more power to detect small declines (95%), but there was a high percentage (50%) of false detections. For all 3 methods, the proportion of declines estimated to be >80% was higher than the true proportion. Use of abundance data to detect species at risk of extinction may either fail to detect initial declines in abundance or have a high error rate.
Estimating the abundance of migratory species is difficult because sources of variability differ ... more Estimating the abundance of migratory species is difficult because sources of variability differ substantially among species and populations. Recently developed state-space models address this variability issue by directly modeling both environmental and measurement error, although their efficacy in detecting declines is relatively untested for empirical data. We applied state-space modeling, generalized least squares (with autoregression error structure), and standard linear regression to data on abundance of wetland birds (shorebirds and terns) at Moreton Bay in southeast Queensland, Australia. There are internationally significant numbers of 8 species of waterbirds in the bay, and it is a major terminus of the large East Asian-Australasian Flyway. In our analyses, we considered 22 migrant and 8 resident species. State-space models identified abundances of 7 species of migrants as significantly declining and abundance of one species as significantly increasing. Declines in migrant abundance over 15 years were 43-79%. Generalized least squares with an autoregressive error structure showed abundance changes in 11 species, and standard linear regression showed abundance changes in 15 species. The higher power of the regression models meant they detected more declines, but they also were associated with a higher rate of false detections. If the declines in Moreton Bay are consistent with trends from other sites across the flyway as a whole, then a large number of species are in significant decline.
Shorebirds are one of the most well-monitored taxa in Australia. In this paper, we review the spa... more Shorebirds are one of the most well-monitored taxa in Australia. In this paper, we review the spatial and temporal coverage of the Australian shorebird monitoring count data currently administered by BirdLife Australia, and comment on the subset of those data likely to be of immediate use for comprehensive trend analysis. Of the 253 shorebird areas known in Australia, seventeen in the southern half of Australia had consistent survey coverage over the last 30 years, with summer counts available in over 80% of those years, and with each area holding nationally significant numbers of some shorebird species. Similarly consistent data were available for eight additional shorebird areas, but these generally held fewer birds. Another 21 shorebird areas with nationally important numbers of shorebirds had 15 to 30 years of data with some variation in spatial coverage or changes in methods over time. Our review suggests that Australian shorebird monitoring data are of sufficiently high quality and spatial coverage to permit robust analysis of shorebird population trends across much of Australia.
Biological Conservation, 2009
Prescribed fire Matrix projection models Prairie restoration Population viability analysis Commun... more Prescribed fire Matrix projection models Prairie restoration Population viability analysis Community-level management Annual plant A B S T R A C T
Marine & Terrestrial Protected Areas by Bruce Kendall
Systematic conservation planning has a substantial theoretical underpinning that allows optimizat... more Systematic conservation planning has a substantial theoretical underpinning that allows optimization of tradeoffs between biodiversity conservation and other socioeconomic goals. However, this theory assumes perfect spatial information about the locations of biodiversity features (e.g., species distributions). In practice, planners represent well-known taxa and other biodiversity ‘‘surrogates’’ in protected area systems, hoping that unmapped species will also be conserved. However, empirical research finds that surrogates predict species presence imperfectly, and sometimes rather poorly, at scales relevant to planning, and existing theory provides no further guidance. We developed new theory, explicitly incorporating aspects of spatial scale, for the representation problem when the locations of species distributions are unknown. Using probability theory and simulated and real species distributions, we found that the probability of adequately representing an unmapped species in a protected area system will be low unless the total fraction of the region being protected is larger than the species representation target. Furthermore, successful conservation depended critically on the relative sizes of the species distribution and of the individual protected areas; fewer, larger protected areas allowed the entire species distribution to fall into an unprotected gap. This scale-dependence varied with the configuration of the protected area system, with the conservation objective most likely to be attained if the individual protected areas were hyperdispersed (evenly spaced across the planning region). Using these results, we developed three design principles for representing unmapped species in protected areas: (1) The fraction of the region placed in protected areas should be substantially larger than the species-level representation target; (2) Individual protected areas must be at least one to two orders of magnitude smaller than the unmapped species’ distribution; and (3) Protected areas should be evenly dispersed over geographic space. We also performed preliminary investigations of the effects of surrogates and socio-economic cost data on the probability of adequately representing unmapped species, finding that the primary effect of surrogates may simply be to promote hyperdispersion of protected areas across the planning region, and that seeking to minimize opportunity costs gives poorer conservation results than random protected area placement.
The establishment of marine protected areas is often viewed as a conflict between conservation an... more The establishment of marine protected areas is often viewed as a conflict between conservation and fishing. We considered consumptive and nonconsumptive interests of multiple stakeholders (i.e., fishers, scuba divers, conservationists, managers, scientists) in the systematic design of a network of marine protected areas along California's central coast in the context of the Marine Life Protection Act Initiative. With advice from managers, administrators, and scientists, a representative group of stakeholders defined biodiversity conservation and socioeconomic goals that accommodated social needs and conserved marine ecosystems, consistent with legal requirements. To satisfy biodiversity goals, we targeted 11 marine habitats across 5 depth zones, areas of high species diversity, and areas containing species of special status. We minimized adverse socioeconomic impacts by minimizing negative effects on fishers. We included fine-scale fishing data from the recreational and commercial fishing sectors across 24 fisheries. Protected areas designed with consideration of commercial and recreational fisheries reduced potential impact to the fisheries approximately 21% more than protected areas designed without consideration of fishing effort and resulted in a small increase in the total area protected (approximately 3.4%). We incorporated confidential fishing data without revealing the identity of specific fisheries or individual fishing grounds. We sited a portion of the protected areas near land parks, marine laboratories, and scientific monitoring sites to address nonconsumptive socioeconomic goals. Our results show that a stakeholder-driven design process can use systematic conservation-planning methods to successfully produce options for network design that satisfy multiple conservation and socioeconomic objectives.Marine protected areas that incorporate multiple stakeholder interests without compromising biodiversity conservation goals are more likely to protect marine ecosystems.
FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/3tx9b6s9 . . . Lively debate continues... more FULL TEXT FREELY AVAILABLE AT www.escholarship.org/uc/item/3tx9b6s9 . . . Lively debate continues over whether marine reserves can lead to increased fishery yields when compared to conventional, quota-based management, apparently driven by differences in the complexity and biological richness of the models being used. In an influential article, Hastings and Botsford used an analytically tractable, spatially implicit, non-age-structured model to assert that reserves are typically incapable of increasing yields relative to conventional management, regardless of the type (pre- or post-dispersal, involving adults and/or larvae) or functional form (Ricker or Beverton-Holt) of density dependence present. A recent numerical (simulation) model by Gaylord et al. concludes that reserves can enhance yield compared to conventional management, a result the authors attribute to their spatially-explicit evaluation of stage-structured adult growth, survivability and fecundity; and intercohort (adult-on-larvae) post-dispersal density dependent population dynamics. Here we demonstrate that the increased model complexity is not responsible for the different conclusions. We analyze a spatially-implicit model without stage structure that incorporates intercohort post-dispersal density dependence. In this simple model we still find annual extirpation of adult populations outside reserves due to fishing to enhance larval recruitment there, allowing for increased yields compared to those achieved when harvest is evenly spread across the entire domain under conventional management. Consideration of neither spatially-explicit dispersal dynamics nor stage-structure in adult demographics is required for reserves to substantially improve yield beyond that attainable under conventional management. In contrast, consideration of within cohort post-dispersal density dependence among larva during settlement in an otherwise identical model generates equivalence in yield between the two management strategies. These results recast a common message characterizing the relative benefit of reserve versus non-reserve management from “equivalence at best” to “potentially improved”.
Some studies suggest that fishery yields can be higher with reserves than under conventional mana... more Some studies suggest that fishery yields can be higher with reserves than under conventional management. However, the economic performance of fisheries depends on economic profit, not fish yield. The predictions of higher yields with reserves rely on intensive fishing pressures between reserves; the exorbitant costs of harvesting low-density populations erode profits. We incorporated this effect into a bioeconomic model to evaluate the economic performance of reserve-based management. Our results indicate that reserves can still benefit fisheries, even those targeting species that are expensive to harvest. However, in contrast to studies focused on yield, only a moderate proportion of the coast in reserves (with moderate harvest pressures outside reserves) is required to maximize profit. Furthermore, reserve area and harvest intensity can be traded off with little impact on profits, allowing for management flexibility while still providing higher profit than attainable under conventional management.Ecology Letters (2008) 11: 370–379
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Demographic Heterogeneity by Bruce Kendall
Shared frailty models allowing for family structure greatly reduce model deviance. The best-fitting models included a term for frailty shared by maternal families.
To ask how long a data set must be to reach qualitatively the same conclusions, we repeated the analyses for all possible truncated data sets of 2 years in length or greater. Length of the data set affects the parameter estimates, but not the qualitative conclusions. In all but three of 337 truncated data sets the best-fitting models pointed to same conclusions as the full data set. Shared frailty models appear to be quite robust.
The data are not adequate for testing hypotheses as to whether variation in frailty is heritable.
Substantial structured heterogeneity for survival exists in this population. Such structured heterogeneity has been shown to have substantial effects in reducing demographic stochasticity.
Demographic stochasticity increases the variance in the growth rate of small populations, and is an important factor to consider when predicting the fates of such populations. Unfortunately, the concept has been treated inconsistently. It is often defined verbally as representing chance variation among individuals in both traits (such as survival probability) and fates (such as whether the individual survived or not). In practice it is modeled as variation in fates only, with all individuals having identical underlying traits. In previous work we demonstrated that structured (but unmod- eled) individual variability in survival traits can reduce the variance in population survivorship associated with demographic stochasticity, but that unstructured random variability in survival traits has no such effect. We implicitly generalized the latter result to fecundity, without offering proof. Robert et al. (2003) have demonstrated, using simulations, that unstructured individual variability in fecundity traits can increase the extinction risk of a small population when demographic stochasticity in fecundity is modeled as following a Poisson distribution. In this paper we extend our earlier theory to correct our mistaken speculations and analyt- ically show the source of Robert et al.’s results. We also provide general predictions about the circumstances under which both structured and un- structured individual trait variation should either increase or decrease the magnitude of demographic stochasticity in the population.
Environmental & Demographic Stochasticity by Bruce Kendall
Population Viability Analysis & Population Trends by Bruce Kendall
Marine & Terrestrial Protected Areas by Bruce Kendall
Shared frailty models allowing for family structure greatly reduce model deviance. The best-fitting models included a term for frailty shared by maternal families.
To ask how long a data set must be to reach qualitatively the same conclusions, we repeated the analyses for all possible truncated data sets of 2 years in length or greater. Length of the data set affects the parameter estimates, but not the qualitative conclusions. In all but three of 337 truncated data sets the best-fitting models pointed to same conclusions as the full data set. Shared frailty models appear to be quite robust.
The data are not adequate for testing hypotheses as to whether variation in frailty is heritable.
Substantial structured heterogeneity for survival exists in this population. Such structured heterogeneity has been shown to have substantial effects in reducing demographic stochasticity.
Demographic stochasticity increases the variance in the growth rate of small populations, and is an important factor to consider when predicting the fates of such populations. Unfortunately, the concept has been treated inconsistently. It is often defined verbally as representing chance variation among individuals in both traits (such as survival probability) and fates (such as whether the individual survived or not). In practice it is modeled as variation in fates only, with all individuals having identical underlying traits. In previous work we demonstrated that structured (but unmod- eled) individual variability in survival traits can reduce the variance in population survivorship associated with demographic stochasticity, but that unstructured random variability in survival traits has no such effect. We implicitly generalized the latter result to fecundity, without offering proof. Robert et al. (2003) have demonstrated, using simulations, that unstructured individual variability in fecundity traits can increase the extinction risk of a small population when demographic stochasticity in fecundity is modeled as following a Poisson distribution. In this paper we extend our earlier theory to correct our mistaken speculations and analyt- ically show the source of Robert et al.’s results. We also provide general predictions about the circumstances under which both structured and un- structured individual trait variation should either increase or decrease the magnitude of demographic stochasticity in the population.
Framework: We introduce an evolutionary framework that maps different levels of biological diversity onto one another. We provide (1) an overview of maps linking levels of biological organization and (2) a guideline of how to analyse the complexity of relationships from genes to population growth.
Method: We specify the appropriate levels of biological organization for responses to selection, for opportunities for selection, and for selection itself. We map between them and embed these maps into an ecological setting.
We use the distinction between compositional and aggregate variability to develop an organizational framework for describing patterns of community variability. At their extremes, compositional and aggregate variability combine in four different ways: (I) stasis, low compositional and low aggregate variability; (2) synchrony, low compositional and high aggregate variability; (3) asynchrony, high compositional and high aggregate variability; and (4) compensation, high compositional and low aggregate variability. Each of these patterns has been observed in natural communities, and can be linked to a suite of abiotic and biotic mechanisms. We give examples of the potential relevance of variability patterns to applied ecology, and describe the methodological developments needed to make meaningful comparisons of aggregate and compositional variability across communities. Finally, we provide two numerical examples of how our approach can be applied to natural communities.
Location: We include studies from both marine and terrestrial systems that encompass many geographic locations around the globe.
Methods: We first performed a literature search and analysis of marine and terrestrial SDMs in ISI Web of Science to assess trends and applications. Using knowledge from terrestrial applications, we critically evaluate the application of SDMs in marine systems in the context of ecological factors (dispersal, species interactions, aggregation and ontogenetic shifts) and practical considerations (data quality, alternative modelling approaches and model validation) that facilitate or create difficulties for model application.
Results: The relative importance of ecological factors to be considered when applying SDMs varies among terrestrial and marine organisms. Correctly incorporating dispersal is frequently considered an important issue for terrestrial models, but because there is greater potential for dispersal in the ocean, it is often less of a concern in marine SDMs. By contrast, ontogenetic shifts and feeding have received little attention in terrestrial SDM applications, but these factors are important to many marine SDMs. Opportunities also exist for applying more advanced SDM approaches in the marine realm, including mechanistic ecophysiological models, where water balance and heat transfer equations are simpler for some marine organisms relative to their terrestrial counterparts.
Main conclusions: SDMs have generally been under-utilized in the marine realm relative to terrestrial applications. Correlative SDM methods should be tested on a range of marine organisms, and we suggest further development of methods that address ontogenetic shifts and feeding interactions. We anticipate developments in, and cross-fertilization between, coupled correlative and process-based SDMs, mechanistic eco-physiological SDMs, and spatial population dynamic models for climate change and species invasion applications in particular. Comparisons of the outputs of different model types will provide insight that is useful for improved spatial management of marine species.