The diversity of population responses to environmental change.
ABSTRACT: The current extinction and climate change crises pressure us to predict population dynamics with ever-greater accuracy. Although predictions rest on the well-advanced theory of age-structured populations, two key issues remain poorly explored. Specifically, how the age-dependency in demographic rates and the year-to-year interactions between survival and fecundity affect stochastic population growth rates. We use inference, simulations and mathematical derivations to explore how environmental perturbations determine population growth rates for populations with different age-specific demographic rates and when ages are reduced to stages. We find that stage- vs. age-based models can produce markedly divergent stochastic population growth rates. The differences are most pronounced when there are survival-fecundity-trade-offs, which reduce the variance in the population growth rate. Finally, the expected value and variance of the stochastic growth rates of populations with different age-specific demographic rates can diverge to the extent that, while some populations may thrive, others will inevitably go extinct.
Project description:Populations in variable environments are described by both a mean growth rate and a variance of stochastic population growth. Increasing variance will increase the width of confidence bounds around estimates of population size, growth, probability of and time to quasi-extinction. However, traditional sensitivity analyses of stochastic matrix models only consider the sensitivity of the mean growth rate. We derive an exact method for calculating the sensitivity of the variance in population growth to changes in demographic parameters. Sensitivities of the variance also allow a new sensitivity calculation for the cumulative probability of quasi-extinction. We apply this new analysis tool to an empirical dataset on at-risk polar bears to demonstrate its utility in conservation biology We find that in many cases a change in life history parameters will increase both the mean and variance of population growth of polar bears. This counterintuitive behaviour of the variance complicates predictions about overall population impacts of management interventions. Sensitivity calculations for cumulative extinction risk factor in changes to both mean and variance, providing a highly useful quantitative tool for conservation management. The mean stochastic growth rate and its sensitivities do not fully describe the dynamics of population growth. The use of variance sensitivities gives a more complete understanding of population dynamics and facilitates the calculation of new sensitivities for extinction processes.
Project description:There is increasing evidence of indirect effects of hunting on populations. In species with sexually selected infanticide (SSI), hunting may decrease juvenile survival by increasing male turnover. We aimed to evaluate the relative importance of direct and indirect effects of hunting via SSI on the population dynamics of the Scandinavian brown bear (Ursus arctos). We performed prospective and retrospective demographic perturbation analyses for periods with low and high hunting pressures. All demographic rates, except yearling survival, were lower under high hunting pressure, which led to a decline in population growth under high hunting pressure (? = 0.975; 95% CI = 0.914-1.011). Hunting had negative indirect effects on the population through an increase in SSI, which lowered cub survival and possibly also fecundity rates. Our study suggests that SSI could explain 13.6% of the variation in population growth. Hunting also affected the relative importance of survival and fecundity of adult females for population growth, with fecundity being more important under low hunting pressure and survival more important under high hunting pressure. Our study sheds light on the importance of direct and indirect effects of hunting on population dynamics, and supports the contention that hunting can have indirect negative effects on populations through SSI.
Project description:Despite the observed distribution of variable individual phenotypes, survival and reproductive performance in wild populations, models of population dynamics often focus on mean demographic rates. Populations are constituted by individuals with different phenotypes and thus different performances. However, many models of population dynamics provide no understanding of the influence of this phenotypic variation on population dynamics. In this paper, we investigate how the relationships between demographic rates and phenotype distribution influence the transmission and the upholding of phenotypic variation, and population dynamics. We used integral projection models to measure associations between differences of phenotypic trait (size or mass) among individuals and demographic rates, growth and inheritance, and then quantify the influence of phenotypic variation on population dynamics. We build an analytical and general model resulting from simplifications assuming small phenotypic variance. We illustrate our model with two case studies: a short- and a long-lived life history. Population growth rate r is determined by a Lotka style equation in which survival and fertility are averaged over a phenotypic distribution that changes with age. Here, we further decomposed r to show how much it is affected by shifts in phenotypic average as well as variance. We derived the elasticities of r to the first and second derivative of each demographic rate. In particular, we show that the nonlinearity of change in selective pressure with phenotype matters more to population dynamics than the strength of this selection. In other words, the variance of a given trait will be most important when the strength of selection increases (or decreases) nonlinearly with that trait. Inheritance shapes the distribution of newborn phenotypes. Even if newborns have a fixed average phenotype, the variance among newborns increases with phenotypic variance among mothers, strength of inheritance and developmental variation. We explain how the components of inheritance can influence phenotypic variance and thus the demographic rates and population dynamics. In particular, when mothers of different ages produce offspring of different mean phenotype, the inheritance function can have a large influence on both the mean and variance of the trait at different ages and thus on the population growth rate. We provide new tools to understand how phenotypic variation influences population dynamics and discuss in which life histories we expect this influence to be large. For instance, in our short-lived life history, individual variability has larger effect than in our long-lived life history. We conclude by indicating future directions of analysis.
Project description:Variance in life history outcomes among individuals is a requirement for natural selection, and a determinant of the ecological dynamics of populations. Heterogeneity among individuals will cause such variance, but so will the inherently stochastic nature of their demography. The relative contributions of these variance components - stochasticity and heterogeneity - to life history outcomes are presented here in a general, demographic calculation. A general formulation of sensitivity analysis is provided for the relationship between the variance components and the demographic rates within the life cycle. We illustrate these novel methods with two examples; the variance in longevity within and between frailty groups in a laboratory population of fruit flies, and the variance in lifetime reproductive output within and between initial environment states in a perennial herb in a stochastic fire environment. In fruit flies, an increase in mortality would increase the variance due to stochasticity and reduce that due to heterogeneity. In the plant example, increasing mortality reduces, and increasing fertility increases both variance components. Sensitivity analyses such as these can provide a powerful tool in identifying patterns among life history stages and heterogeneity groups and their contributions to variance in life history outcomes.
Project description:Most mammalian populations suffer from natural or human-induced disturbances; populations are no longer at the equilibrium (i.e., at stable [st]age distribution) and exhibit transient dynamics. From a literature survey, we studied patterns of transient dynamics for mammalian species spanning a large range of life-history tactics and population growth rates. For each population, we built an age-structured matrix and calculated six metrics of transient dynamics. After controlling for possible confounding effects of the phylogenetic relatedness among species using a phylogenetic principal component analysis and phylogenetic generalized least squares models, we found that short-term demographic responses of mammalian populations to disturbance are shaped by generation time and growth rate. Species with a slow pace of life (i.e., species with a late maturity, a low fecundity, and a long life span) displayed decreases in population size after a disturbance, whereas fast-living species increased in population size. The magnitude of short-term variation in population size increased with asymptotic population growth, being buffered in slow-growing species (i.e., species with a low population growth rate) but large in fast-growing species. By demonstrating direct links between transient dynamics, life history (generation time), and ecology (demographic regime), our comparative analysis of transient dynamics clearly improves our understanding of population dynamics in variable environments and has clear implications for future studies of the interplay between evolutionary and ecological dynamics. As most populations in the wild are not at equilibrium, we recommend that analyses of transient dynamics be performed when studying population dynamics in variable environments.
Project description:A number of demographic factors, many of which related to human-driven encroachments, are predicted to decrease the effective population size (N(e)) relative to the census population size (N), but these have been little investigated. Yet, it is necessary to know which factors most strongly impact N(e), and how to mitigate these effects through sound management actions. In this study, we use parentage analysis of a stream-living brown trout (Salmo trutta) population to quantify the effect of between-individual variance in reproductive success on the effective number of breeders (N(b)) relative to the census number of breeders (N(i)). Comprehensive estimates of the N(b)/N ratio were reduced to 0.16-0.28, almost entirely due to larger than binomial variance in family size. We used computer simulations, based on empirical estimates of age-specific survival and fecundity rates, to assess the effect of repeat spawning (iteroparity) on N(e) and found that the variance in lifetime reproductive success was substantially higher for repeat spawners. Random family-specific survival, on the other hand, acts to buffer these effects. We discuss the implications of these findings for the management of small populations, where maintaining high and stable levels of N(e) is crucial to extenuate inbreeding and protect genetic variability.
Project description:This paper presents a comprehensive theory for the demographic analysis of populations in which individuals are classified by both age and stage. The earliest demographic models were age classified. Ecologists adopted methods developed by human demographers and used life tables to quantify survivorship and fertility of cohorts and the growth rates and structures of populations. Later, motivated by studies of plants and insects, matrix population models structured by size or stage were developed. The theory of these models has been extended to cover all the aspects of age-classified demography and more. It is a natural development to consider populations classified by both age and stage. A steady trickle of results has appeared since the 1960s, analyzing one or another aspect of age × stage-classified populations, in both ecology and human demography. Here, we use the vec-permutation formulation of multistate matrix population models to incorporate age- and stage-specific vital rates into demographic analysis. We present cohort results for the life table functions (survivorship, mortality, and fertility), the dynamics of intra-cohort selection, the statistics of longevity, the joint distribution of age and stage at death, and the statistics of life disparity. Combining transitions and fertility yields a complete set of population dynamic results, including population growth rates and structures, net reproductive rate, the statistics of lifetime reproduction, and measures of generation time. We present a complete analysis of a hypothetical model species, inspired by poecilogonous marine invertebrates that produce two kinds of larval offspring. Given the joint effects of age and stage, many familiar demographic results become multidimensional, so calculations of marginal and mixture distributions are an important tool. From an age-classified point of view, stage structure is a form of unobserved heterogeneity. From a stage-classified point of view, age structure is unobserved heterogeneity. In an age × stage-classified model, variance in demographic outcomes can be partitioned into contributions from both sources. Because these models are formulated as matrices, they are amenable to a complete sensitivity analysis. As more detailed and longer longitudinal studies are developed, age × stage-classified demography will become more common and more important.
Project description:The high extinction risk of small populations is commonly explained by reductions in fecundity and breeder survival associated with demographic and environmental stochasticity. However, ecological theory suggests that population extinctions may also arise from reductions in the number of floaters able to replace the lost breeders. This can be particularly plausible under harsh fragmentation scenarios, where species must survive as small populations subjected to severe effects of stochasticity. Using a woodpecker study in fragmented habitats (2004-2016), we provide here empirical support for the largely neglected hypothesis that floaters buffer population extirpation risks. After controlling for population size, patch size and the intrinsic quality of habitat, populations in patches with floaters had a lower extinction probability than populations in patches without floaters (0.013 versus 0.131). Floaters, which often replace the lost breeders, were less likely to occur in small and low-quality patches, showing that population extirpations may arise from unnoticed reductions in floater numbers in poor-quality habitats. We argue that adequate pools of the typically overlooked floaters may buffer extirpation risks by reducing the detrimental impacts of demographic and environmental stochasticity. However, unravelling the influence of floaters in buffering stochastic effects and promoting population stability require additional studies in an ample array of species and stochastic scenarios.
Project description:Modernization has increased longevity and decreased fertility in many human populations, but it is not well understood how or to what extent these demographic transitions have altered patterns of natural selection. I integrate individual-based multivariate phenotypic selection approaches with evolutionary demographic methods to demonstrate how a demographic transition in 19th century female populations of Utah altered relationships between fitness and age-specific survival and fertility. Coincident with this demographic transition, natural selection for fitness, as measured by the opportunity for selection, increased by 13% to 20% over 65 years. Proportional contributions of age-specific survival to total selection (the complement to age-specific fertility) diminished from approximately one third to one seventh following a marked increase in infant survival. Despite dramatic reductions in age-specific fertility variance at all ages, the absolute magnitude of selection for fitness explained by age-specific fertility increased by approximately 45%. I show that increases in the adaptive potential of fertility traits followed directly from decreased population growth rates. These results suggest that this demographic transition has increased the adaptive potential of the Utah population, intensified selection for reproductive traits, and de-emphasized selection for survival-related traits.
Project description:How climate change influences the dynamics of plant populations is not well understood, as few plant studies have measured responses of vital rates to climatic variables and modeled the impact on population growth. The present study used 25 y of demographic data to analyze how survival, growth, and fecundity respond to date of spring snowmelt for a subalpine plant. Fecundity was estimated by seed production (over 15 y) and also divided into flower number, fruit set, seeds per fruit, and escape from seed predation. Despite no apparent effects on flower number, plants produced more seeds in years with later snowmelt. Survival and probability of flowering were reduced by early snowmelt in the previous year. Based on demographic models, earlier snowmelt with warming is expected to lead to negative population growth, driven especially by changes in seedling establishment and seed production. These results provide a rare example of how climate change is expected to influence the dynamics of a plant population. They furthermore illustrate the potential for strong population impacts even in the absence of more commonly reported visual signs, such as earlier blooming or reduced floral display in early melting years.