Estimating the functional form for the density dependence from life history data

Two contrasting approaches to the analysis of population dynamics are currently popular: demographic approaches where the associations between demographic rates and statistics summarizing the population dynamics are identified; and time series approaches where the associations between population dynamics, population density, and environmental covariates are investigated. In this paper, we develop an approach to combine these methods and apply it to detailed data from Soay sheep (Ovis aries). We examine how density dependence and climate contribute to fluctuations in population size via age- and sex-specific demographic rates, and how fluctuations in demographic structure influence population dynamics. Density dependence contributes most, followed by climatic variation, age structure fluctuations and interactions between density and climate. We then simplify the density-dependent, stochastic, age-structured demographic model and derive a new phenomenological time series which captures the dynamics better than previously selected functions. The simple method we develop has potential to provide substantial insight into the relative contributions of population and individual-level processes to the dynamics of populations in stochastic environments.     

Using Modeling to Improve Monitoring of Structured Populations: Are We Collecting the Right Data?

Abstract:  Population monitoring is central to most demographic studies and conservation efforts, but it may not always be directed at the most appropriate life stage. We used stochastic simulation modeling to evaluate the effectiveness of a monitoring program for a well-studied population of Eastern Imperial Eagles ( Aquila heliaca ) in Kazakhstan. Specifically, we asked whether the most appropriate data were being collected to understand system state and population dynamics. Our models were parameterized with data collected over the course of 25 years of study of this population. We used the models to conduct simulation experiments to evaluate relationships between monitored or potentially monitored parameters and the demographic variables of interest—population size ( N ) and population growth (λ). Static analyses showed that traditional territory-based monitoring was a poor indicator of eagle population size and growth and that monitoring survivorship would provide more information about these parameters. Nevertheless, these same traditionally monitored territory-based parameters had greater power to detect long-term changes in population size than did survivorship or population structure. Regardless of the taxa considered, threats can have immediate impacts on population size and growth or longer-term impacts on population dynamics. Prudently designed monitoring programs for any species will detect the demographic effects of both types of threats.     

Demographic heterogeneity, cohort selection, and population growth

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 lambda 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 lambda, but the increase occurs even for negative parent-offspring correlations. The effect of heterogeneity in reproductive rate on lambda 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 lambda have important implications for population dynamics, population viability analysis, and evolution.     

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.     

Nonlinear relationships between vital rates and state variables in demographic models

To accurately estimate population dynamics and viability, structured population models account for among-individual differences in demographic parameters that are related to individual state. In the widely used matrix models, such differences are incorporated in terms of discrete state categories, whereas integral projection models (IPMs) use continuous state variables to avoid artificial classes. In IPMs, and sometimes also in matrix models, parameterization is based on regressions that do not always model nonlinear relationships between demographic parameters and state variables. We stress the importance of testing for nonlinearity and propose using restricted cubic splines in order to allow for a wide variety of relationships in regressions and demographic models. For the plant Borderea pyrenaica, we found that vital rate relationships with size and age were nonlinear and that the parameterization method had large effects on predicted population growth rates, X (linear IPM, 0.95; nonlinear IPMs, 1.00; matrix model, 0.96). Our results suggest that restricted cubic spline models are more reliable than linear or polynomial models. Because even weak nonlinearity in relationships between vital rates and state variables can have large effects on model predictions, we suggest that restricted cubic regression splines should be considered for parameterizing models of population dynamics whenever linearity cannot be assumed.     

Demographic Side Effects of Selective Hunting in Ungulates and Carnivores

Abstract:  Selective harvesting regimes are often implemented because age and sex classes contribute differently to population dynamics and hunters show preferences associated with body size and trophy value. We reviewed the literature on how such cropping regimes affect the demography of the remaining population (here termed demographic side effects ). First, we examined the implications of removing a large proportion of a specific age or sex class. Such harvesting strategies often bias the population sex ratio toward females and reduce the mean age of males, which may consequently delay birth dates, reduce birth synchrony, delay body mass development, and alter offspring sex ratios. Second, we reviewed the side effects associated with the selective removal of relatively few specific individuals, often large trophy males. Such selective harvesting can destabilize social structures and the dominance hierarchy and may cause loss of social knowledge, sexually selected infanticide, habitat changes among reproductive females, and changes in offspring sex ratio. A common feature of many of the reported mechanisms is that they ultimately depress recruitment and in some extreme cases even cause total reproductive collapse. These effects could act additively and destabilize the dynamics of populations, thus having a stronger effect on population growth rate than first anticipated. Although more experimental than observational studies reported demographic side effects, we argue that this may reflect the quite subtle mechanisms involved, which are unlikely to be detected in observational studies without rigorous monitoring regimes. We call for more detailed studies of hunted populations with marked individuals that address how the expression of these effects varies across mating systems, habitats, and with population density. Theoretical models investigating how strongly these effects influence population growth rates are also required.     

Ability of Matrix Models to Explain the Past and Predict the Future of Plant Populations

Uncertainty associated with ecological forecasts has long been recognized, but forecast accuracy is rarely quantified. We evaluated how well data on 82 populations of 20 species of plants spanning 3 continents explained and predicted plant population dynamics. We parameterized stage‐based matrix models with demographic data from individually marked plants and determined how well these models forecast population sizes observed at least 5 years into the future. Simple demographic models forecasted population dynamics poorly; only 40% of observed population sizes fell within our forecasts’ 95% confidence limits. However, these models explained population dynamics during the years in which data were collected; observed changes in population size during the data‐collection period were strongly positively correlated with population growth rate. Thus, these models are at least a sound way to quantify population status. Poor forecasts were not associated with the number of individual plants or years of data. We tested whether vital rates were density dependent and found both positive and negative density dependence. However, density dependence was not associated with forecast error. Forecast error was significantly associated with environmental differences between the data collection and forecast periods. To forecast population fates, more detailed models, such as those that project how environments are likely to change and how these changes will affect population dynamics, may be needed. Such detailed models are not always feasible. Thus, it may be wiser to make risk‐averse decisions than to expect precise forecasts from models. Habilidad de los Modelos Matriciales para Explicar el Pasado y Predecir el Futuro de las Poblaciones de Plantas     

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.     

Seed dispersal by pulp consumers, not "legitimate" seed dispersers, increases Guettarda viburnoides population growth

We examined the effect of seed dispersal by Purplish Jays (Cyanocorax cyanomelas; pulp consumers) and the Chestnut-eared Ara?ari (Pteroglossus castanotis; "legitimate" seed dispersers) on population growth of the small tree Guettarda viburnoides (Rubiaceae) in northeastern Bolivian savannas. Because each bird species differs with respect to feeding and post-feeding behavior, we hypothesized that seed dispersal by each species will contribute differently to the rate of increase of G. viburnoides, but that seed dispersal by either species will increase population growth when compared to a scenario with no seed dispersal. To examine the effects of individual dispersers on the future population size of G. viburnoides, we projected population growth rate using demographic models for G. viburnoides that explicitly incorporate data on quantitative and qualitative aspects of seed dispersal by each frugivore species. Our model suggests that seed dispersal by C. cyanomelas leads to positive population growth of G. viburnoides, whereas seed dispersal by P. castanotis has a detrimental effect on the population growth of this species. To our knowledge, this is the first study to report negative effects of a "legitimate" seed disperser on the population dynamics of the plant it consumes. Our results stress the importance of incorporating frugivore effects into population projection matrices, to allow a comprehensive analysis of the effectiveness of different dispersers for plant population dynamics.     

Aging and demographic plasticity in response to experimental age structures in honeybees (<Emphasis Type="Italic">Apis mellifera</Emphasis> L)

Honeybee colonies are highly integrated functional units characterized by a pronounced division of labor. Division of labor among workers is mainly age-based, with younger individuals focusing on in-hive tasks and older workers performing the more hazardous foraging activities. Thus, experimental disruption of the age composition of the worker hive population is expected to have profound consequences for colony function. Adaptive demography theory predicts that the natural hive age composition represents a colony-level adaptation and thus results in optimal hive performance. Alternatively, the hive age composition may be an epiphenomenon, resulting from individual life history optimization. We addressed these predictions by comparing individual worker longevity and brood production in hives that were composed of a single-age cohort, two distinct age cohorts, and hives that had a continuous, natural age distribution. Four experimental replicates showed that colonies with a natural age composition did not consistently have a higher life expectancy and/or brood production than the single-cohort or double-cohort hives. Instead, a complex interplay of age structure, environmental conditions, colony size, brood production, and individual mortality emerged. A general tradeoff between worker life expectancy and colony productivity was apparent, and the transition from in-hive tasks to foraging was the most significant predictor of worker lifespan irrespective of the colony age structure. We conclude that the natural age structure of honeybee hives is not a colony-level adaptation. Furthermore, our results show that honeybees exhibit pronounced demographic plasticity in addition to behavioral plasticity to react to demographic disturbances of their societies.     

Seasonal density dependence, timing of mortality, and sustainable harvesting

Birth-pulse populations are often characterized with discrete-time models, that use a single function to relate the post-breeding population size to the post-breeding size of the previous year. Recently, models of seasonal density dependence have been constructed that emphasize interactions during shorter time periods also. Here, we study two very simple forms of density-dependent mortality, that lead to Ricker and Beverton-Holt type population dynamics when viewed over the whole year. We explore the consequences of harvest timing to equilibrium population sizes under such density dependence. Whether or not individual mortality compensates for the harvested quota, the timing of harvesting has a strong impact on the sustainability of a harvesting quota. Further, we show that careless discretization of a continuous mortality scheme may seriously underestimate the reduction in population size caused by hunting and overestimate the sustainable yield. We also introduce the concept of the demographic value of an individual, which reflects the expected contribution to population size over time in the presence of density dependence. Finally, we discuss the possibility of calculating demographic values as means of optimizing harvest strategies. Here, a Pareto optimal harvest strategy will minimize the loss of demographic value from the population for a given yield.     

Transient population dynamics in periodic matrix models: methodology and effects of cyclic permutations

Many biological populations are subject to periodically changing environments such as years with or without fire, or rotation of crop types. The dynamics and management options for such populations are frequently investigated using periodic matrix models. However the analysis is usually limited to long-term results (asymptotic population growth rate and its sensitivity to perturbations of vital rates). In non-periodic matrix models it has been shown that long-term results may be misleading as populations are rarely in their stable structure. We therefore develop methods to analyze transient dynamics of periodic matrix models. In particular, we show how to calculate the effects of perturbations on population size within and at the end of environmental cycles. Using a model of a weed population subject to a crop rotation, we show that different cyclic permutations produce different patterns of sensitivity of population size and different population sizes. By examining how the starting environment interacts with the initial conditions, we explain how different patterns arise. Such understanding is critical to developing effective management and monitoring strategies for populations subject to periodically recurring environments.     

Photographic mark-recapture analysis of local dynamics within an open population of dolphins

Identifying demographic changes is important for understanding population dynamics. However, this requires long-term studies of definable populations of distinct individuals, which can be particularly challenging when studying mobile cetaceans in the marine environment. We collected photo-identification data from 19 years (1992-2010) to assess the dynamics of a population of bottlenose dolphins (Tursiops truncatus) restricted to the shallow (<7 m) waters of Little Bahama Bank, northern Bahamas. This population was known to range beyond our study area, so we adopted a Bayesian mixture modeling approach to mark-recapture to identify clusters of individuals that used the area to different extents, and we specifically estimated trends in survival, recruitment, and abundance of a "resident" population with high probabilities of identification. There was a high probability (p= 0.97) of a long-term decrease in the size of this resident population from a maximum of 47 dolphins (95% highest posterior density intervals, HPDI = 29-61) in 1996 to a minimum of just 24 dolphins (95% HPDI = 14-37) in 2009, a decline of 49% (95% HPDI = approximately 5% to approximately 75%). This was driven by low per capita recruitment (average approximately 0.02) that could not compensate for relatively low apparent survival rates (average approximately 0.94). Notably, there was a significant increase in apparent mortality (approximately 5 apparent mortalities vs. approximately 2 on average) in 1999 when two intense hurricanes passed over the study area, with a high probability (p = 0.83) of a drop below the average survival probability (approximately 0.91 in 1999; approximately 0.94, on average). As such, our mark-recapture approach enabled us to make useful inference about local dynamics within an open population of bottlenose dolphins; this should be applicable to other studies challenged by sampling highly mobile individuals with heterogeneous space use.     

Modelling the influence of demographic parameters on group structure in social species with dispersal asymmetry and group fission

Female philopatry characterizes many mammal populations subdivided into social groups. Fission of these social groups is a relatively discrete event in the life of groups or of individuals, leading to the distribution of females among several newly formed groups. Fission is an important event because it can be a way for females to disperse. Group fissions have rarely been observed and their modalities generally remain poorly known, the best-documented species being primates. Most group fissions occur along lines of maternal relatedness, but the death of a matriarch may disrupt the cohesion within a matriline, inducing separation of sisters, accompanied by their descendants, when a group splits. Our model shows that the numbers and sizes of matrilines within groups depend on the precise demographic parameters and age structure of a population and not only on its rate of increase. For comparable population-growth periods, high survival rates of adult females induce an increase in the sizes of matrilines, whereas high survival rates of immature individuals induce an increase in the numbers of matrilines. Following fission, groups of a given size included, in the first case, only a few large matrilines, whereas in the second case, they consisted mainly of many small matrilines. The present study constitutes a preliminary stage, before modelling consequences of demographic structure of groups or populations on their genetic structure.     

Ability of Wildlife Overpasses to Provide Connectivity and Prevent Genetic Isolation

Abstract:  We reviewed research on wildlife overpasses in the context of their genetic effectiveness to provide connectivity between population patches that have been isolated by road construction. The potential ecological consequences of such habitat fragmentation include reduction of gene flow between subpopulations and hence an increase in genetic differentiation and a decrease in genetic diversity. Among the solutions to provide connectivity between patches isolated by roads, wildlife overpasses are one of the most expensive alternatives. Despite the high costs associated with their construction, most of the studies assessing their use by wildlife remain observational, reporting evidence for passage use but few data on the number of individual crossings. Moreover, the use itself of wildlife overpasses does not appear sufficient to assess their effectiveness from a genetic viewpoint because a minimum number of individuals is required to assure gene flow between population patches and because the spatiotemporal dimension of individual movements and demographic parameters of subpopulations must be considered. So far, there is no evidence that wildlife overpasses do or do not efficiently address genetic issues. This lack of data is probably due to the fact that few mitigation efforts have implemented monitoring programs that incorporate sufficient experimental designs into pre- and postconstruction evaluation. To assess the genetic effectiveness of wildlife overpasses, long-term monitoring programs, including fieldwork and genetic analyses, are needed.     

Size-mediated non-trophic interactions and stochastic predation drive assembly and dynamics in a seabird community

Theoretical and empirical evidence suggests that body size is a major life-history trait impacting on the structure and functioning of complex food webs. However, long-term analyses of size-dependent interactions within simpler network modules, for instance, competitive guilds, are scant. Here, we model the assembly dynamics of the largest breeding seabird community in the Mediterranean basin during the last 30 years. This unique data set allowed us to test, through a "natural experiment," whether body size drove the assembly and dynamics of an ecological guild growing from very low numbers after habitat protection. Although environmental stochasticity accounted for most of community variability, the population variance explained by interspecific interactions, albeit small, decreased sharply with increasing body size. Since we found a demographic gradient along a body size continuum, in which population density and stability increase with increasing body size, the numerical effects of interspecific interactions were proportionally higher on smaller species than on larger ones. Moreover, we found that the per capita interaction coefficients were larger the higher the size ratio among competing species, but only for the set of interactions in which the species exerting the effect was greater. This provides empirical evidence for long-term asymmetric interspecific competition, which ultimately prompted the local extinction of two small species during the study period. During the assembly process stochastic predation by generalist carnivores further triggered community reorganizations and global decays in population synchrony, which disrupted the pattern of interspecific interactions. These results suggest that the major patterns detected in complex food webs can hold as well for simpler sub-modules of these networks involving non-trophic interactions, and highlight the shifting ecological processes impacting on assembling vs. asymptotic communities.     

Population growth in snow geese: a modeling approach integrating demographic and survey information

There are few analytic tools available to formally integrate information coming from population surveys and demographic studies. The Kalman filter is a procedure that facilitates such integration. Based on a state-space model, we can obtain a likelihood function for the survey data using a Kalman filter, which we may then combine with a likelihood for the demographic data. In this paper, we used this combined approach to analyze the population dynamics of a hunted species, the Greater Snow Goose (Chen caerulescens atlantica), and to examine the extent to which it can improve previous demographic population models. The state equation of the state-space model was a matrix population model with fecundity and regression parameters relating adult survival and harvest rate estimated in a previous capture-recapture study. The observation equation combined the output from this model with estimates from an annual spring photographic survey of the population. The maximum likelihood estimates of the regression parameters from the combined analysis differed little from the values of the original capture-recapture analysis, though their precision improved. The model output was found to be insensitive to a wide range of coefficient of variation (CV) in fecundity parameters. We found a close match between the surveyed and smoothed population size estimates generated by the Kalman filter over an 18-year period, and the estimated CV of the survey (0.078-0.150) was quite compatible with its assumed value (approximately 0.10). When we used the updated parameter values to predict future population size, the model underestimated the surveyed population size by 18% over a three-year period. However, this could be explained by a concurrent change in the survey method. We conclude that the Kalman filter is a promising approach to forecast population change because it incorporates survey information in a formal way compared with ad hoc approaches that either neglect this information or require some parameter or model tuning.     

Demographic Forecasting in Koala Conservation

Abstract: The koala currently needs conservation intervention. There is clear evidence of decline in many populations, but the existence of other stable or expanding populations offers the possibility of a variety of creative solutions to their conservation problems. The 1998 National Koala Conservation Strategy emphasizes the need to obtain demographic information and to use this information to assess management options for koalas. We need accurate diagnoses of the status of koala populations and forecasts of their demographic future with and without particular management actions. In a qualitative fashion, this process has been undertaken many times on a local and national scale. Quantitative demographic forecasting tools are increasingly available, and koala management could benefit from their application both at the scale of individual populations and more broadly. There is already a considerable body of suitable data on the dispersal, effects of normal and catastrophic environmental variation on reproduction and survival, and on the effects of habitat change. Demographic forecasting, however, is hampered because the full suite of information is rarely available from a single population. In two Queensland populations, retrospective population viability analyses provided forecasts that were in agreement with observed population trends. Work is needed to determine whether data from one population can be applied to other populations. Models can then be developed to make projections at a multipopulation level on the basis of local population dynamics and dispersal. Certain koala populations, because of their long history of study, offer the opportunity to test demographic models retrospectively. These tests will not only aid in fine-tuning the models for koala biology and data but will also assist with the more general process of validating the models.     

Uncertainty analysis of transient population dynamics

Two types of demographic analyses, perturbation analysis and uncertainty analysis, can be conducted to gain insights about matrix population models and guide population management. Perturbation analysis studies how the perturbation of demographic parameters (survival, growth, and reproduction parameters) may affect the population projection, while uncertainty analysis evaluates how much uncertainty there is in population dynamic predictions and where the uncertainty comes from. Previously, both perturbation analysis and uncertainty analysis were conducted on the long-term population growth rate. However, the population may not reach its equilibrium state, especially when there is management by harvesting or hunting. Recently, there has been an increased interest in short-term transient dynamics, which can differ from asymptotic long-term dynamics. There are currently techniques to conduct perturbation analyses of short-term transient dynamics, but no techniques have been proposed for uncertainty analysis of such dynamics. In this study, we introduced an uncertainty analysis technique, the general Fourier Amplitude Sensitivity Test (FAST), to study uncertainties in transient population dynamics. The general FAST is able to identify the amount of uncertainty in transient dynamics and contributions by different demographic parameters. We applied the general FAST to a mountain goat (Oreamnos americanus) matrix population model to give a clear illustration of how uncertainty analysis can be conducted for transient dynamics arising from matrix population models.