COMADRE: a global data base of animal demography

Age × stage-classified demographic analysis: a comprehensive approach

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.

Sunning themselves in heaps, knots, and snarls: The extraordinary abundance and demography of island watersnakes

Snakes represent a sizable fraction of vertebrate biodiversity, but until recently, data on their demography have been sparse. Consequently, generalizations regarding patterns of variation are weak and the potential for population projections is limited. We address this information gap through an analysis of spatial and temporal variation in demography (population size, annual survival, and realized population growth) of the Lake Erie Watersnake, Nerodia sipedon insularum, and a review of snake survival more generally. Our study spans a period during which the Lake Erie Watersnake was listed as threatened under the U.S. Endangered Species Act, recovered, and was delisted. We collected capture-mark-recapture data at 14 study sites over 20 years, accruing 20,000 captures of 13,800 individually marked adults. Lake Erie Watersnakes achieve extraordinary abundance, averaging 520 adults per km of shoreline (ca. 260 adult per ha) at our study sites (range = 160-1,600 adults per km; ca. 80-800 adults per ha) and surpassing population recovery and postdelisting monitoring criteria. Annual survival averages 0.68 among adult females and 0.76 among adult males, varies among sites, and is positively correlated with body size among study sites. Temporal process variance in annual survival is low, averaging 0.0011 or less than 4% of total variance; thus, stochasticity in annual survival may be of minor significance to snake extinction risk. Estimates of realized population growth indicate that population size has been stable or increasing over the course of our study. More generally, snake annual survival overlaps broadly across continents, climate zones, families, subfamilies, reproductive modes, body size categories, maturation categories, and parity categories. Differences in survival in relation to size, parity, and maturation are in the directions predicted by life history theory but are of small magnitude with much variation around median values. Overall, annual survival appears to be quite plastic, varying with food availability, habitat quality, and other ecological variables.

Inferring transient dynamics of human populations from matrix non-normality

In our increasingly unstable and unpredictable world, population dynamics rarely settle uniformly to long-term behaviour. However, projecting period-by-period through the preceding fluctuations is more data-intensive and analytically involved than evaluating at equilibrium. To efficiently model populations and best inform policy, we require pragmatic suggestions as to when it is necessary to incorporate short-term transient dynamics and their effect on eventual projected population size. To estimate this need for matrix population modelling, we adopt a linear algebraic quantity known as non-normality. Matrix non-normality is distinct from normality in the Gaussian sense, and indicates the amplificatory potential of the population projection matrix given a particular population vector. In this paper, we compare and contrast three well-regarded metrics of non-normality, which were calculated for over 1000 age-structured human population projection matrices from 42 European countries in the period 1960 to 2014. Non-normality increased over time, mirroring the indices of transient dynamics that peaked around the millennium. By standardising the matrices to focus on transient dynamics and not changes in the asymptotic growth rate, we show that the damping ratio is an uninformative predictor of whether a population is prone to transient booms or busts in its size. These analyses suggest that population ecology approaches to inferring transient dynamics have too often relied on suboptimal analytical tools focussed on an initial population vector rather than the capacity of the life cycle to amplify or dampen transient fluctuations. Finally, we introduce the engineering technique of pseudospectra analysis to population ecology, which, like matrix non-normality, provides a more complete description of the transient fluctuations than the damping ratio. Pseudospectra analysis could further support non-normality assessment to enable a greater understanding of when we might expect transient phases to impact eventual population dynamics.

Delivering the promises of trait-based approaches to the needs of demographic approaches, and vice versa

Few facets of biology vary more than functional traits and life-history traits. To explore this vast variation, functional ecologists and population ecologists have developed independent approaches that identify the mechanisms behind and consequences of trait variation.Collaborative research between researchers using trait-based and demographic approaches remains scarce. We argue that this is a missed opportunity, as the strengths of both approaches could help boost the research agendas of functional ecology and population ecology.This special feature, which spans three journals of the British Ecological Society due to its interdisciplinary nature, showcases state-of-the-art research applying trait-based and demographic approaches to examine relationships between organismal function, life history strategies and population performance across multiple kingdoms. Examples include the exploration of how functional trait × environment interactions affect vital rates and thus explain population trends and species occurrence; the coordination of seed traits and dispersal ability with the pace of life in plants; the incorporation of functional traits in dynamic energy budget models; or the discovery of linkages between microbial functional traits and the fast-slow continuum.Despite their historical isolation, collaborative work between functional ecologists and population ecologists could unlock novel research pathways. We call for an integrative research agenda to evaluate which and when traits are functional, as well as their ability to describe and predict life history strategies and population dynamics. We highlight promising, complementary research avenues to overcome current limitations. These include a more explicit linkage of selection gradients in the context of functional trait-vital rate relationships, and the implementation of standardised protocols to track changes in traits and vital rates over time at the same location and individuals, thus allowing for the explicit incorporation of trade-offs in analyses of covariation of functional traits and life-history traits.

Population and evolutionary dynamics in spatially structured seasonally varying environments

Increasingly imperative objectives in ecology are to understand and forecast population dynamic and evolutionary responses to seasonal environmental variation and change. Such population and evolutionary dynamics result from immediate and lagged responses of all key life‐history traits, and resulting demographic rates that affect population growth rate, to seasonal environmental conditions and population density. However, existing population dynamic and eco‐evolutionary theory and models have not yet fully encompassed within‐individual and among‐individual variation, covariation, structure and heterogeneity, and ongoing evolution, in a critical life‐history trait that allows individuals to respond to seasonal environmental conditions: seasonal migration. Meanwhile, empirical studies aided by new animal‐tracking technologies are increasingly demonstrating substantial within‐population variation in the occurrence and form of migration versus year‐round residence, generating diverse forms of ‘partial migration’ spanning diverse species, habitats and spatial scales. Such partially migratory systems form a continuum between the extreme scenarios of full migration and full year‐round residence, and are commonplace in nature.

Here, we first review basic scenarios of partial migration and associated models designed to identify conditions that facilitate the maintenance of migratory polymorphism. We highlight that such models have been fundamental to the development of partial migration theory, but are spatially and demographically simplistic compared to the rich bodies of population dynamic theory and models that consider spatially structured populations with dispersal but no migration, or consider populations experiencing strong seasonality and full obligate migration. Second, to provide an overarching conceptual framework for spatio‐temporal population dynamics, we define a ‘partially migratory meta‐population’ system as a spatially structured set of locations that can be occupied by different sets of resident and migrant individuals in different seasons, and where locations that can support reproduction can also be linked by dispersal. We outline key forms of within‐individual and among‐individual variation and structure in migration that could arise within such systems and interact with variation in individual survival, reproduction and dispersal to create complex population dynamics and evolutionary responses across locations, seasons, years and generations. Third, we review approaches by which population dynamic and eco‐evolutionary models could be developed to test hypotheses regarding the dynamics and persistence of partially migratory meta‐populations given diverse forms of seasonal environmental variation and change, and to forecast system‐specific dynamics. To demonstrate one such approach, we use an evolutionary individual‐based model to illustrate that multiple forms of partial migration can readily co‐exist in a simple spatially structured landscape. Finally, we summarise recent empirical studies that demonstrate key components of demographic structure in partial migration, and demonstrate diverse associations with reproduction and survival. We thereby identify key theoretical and empirical knowledge gaps that remain, and consider multiple complementary approaches by which these gaps can be filled in order to elucidate population dynamic and eco‐evolutionary responses to spatio‐temporal seasonal environmental variation and change.

Time-lagged effects of weather on plant demography: drought and Astragalus scaphoides

Temperature and precipitation determine the conditions where plant species can occur. Despite their significance, to date, surprisingly few demographic field studies have considered the effects of abiotic drivers. This is problematic because anticipating the effect of global climate change on plant population viability requires understanding how weather variables affect population dynamics. One possible reason for omitting the effect of weather variables in demographic studies is the difficulty in detecting tight associations between vital rates and environmental drivers. In this paper, we applied Functional Linear Models (FLMs) to long-term demographic data of the perennial wildflower, Astragalus scaphoides, and explored sensitivity of the results to reduced amounts of data. We compared models of the effect of average temperature, total precipitation, or an integrated measure of drought intensity (standardized precipitation evapotranspiration index, SPEI), on plant vital rates. We found that transitions to flowering and recruitment in year t were highest if winter/spring of year t was wet (positive effect of SPEI). Counterintuitively, if the preceding spring of year t - 1 was wet, flowering probabilities were decreased (negative effect of SPEI). Survival of vegetative plants from t - 1 to t was also negatively affected by wet weather in the spring of year t - 1 and, for large plants, even wet weather in the spring of t - 2 had a negative effect. We assessed the integrated effect of all vital rates on life history performance by fitting FLMs to the asymptotic growth rate, log(λt). Log(λt) was highest if dry conditions in year t - 1 were followed by wet conditions in the year t. Overall, the positive effects of wet years exceeded their negative effects, suggesting that increasing frequency of drought conditions would reduce population viability of A. scaphoides. The drought signal weakened when reducing the number of monitoring years. Substituting space for time did not recover the weather signal, probably because the weather variables varied little between sites. We detected the SPEI signal when the analysis included data from two sites monitored over 20 yr (2 × 20 observations), but not when analyzing data from four sites monitored over 10 yr (4 × 10 observations).

Occupancy time in sets of states for demographic models

As an individual moves through its life cycle, it passes through a series of states (age classes, size classes, reproductive states, spatial locations, health statuses, etc.) before its eventual death. The occupancy time in a state is the time spent in that state over the individual's life. Depending on the life cycle description, the occupancy times describe different demographic variables, for example, lifetime breeding success, lifetime habitat utilisation, or healthy longevity. Models based on absorbing Markov chains provide a powerful framework for the analysis of occupancy times. Current theory, however, can completely analyse only the occupancy of single states, although the occupancy time in a set of states is often desired. For example, a range of sizes in a size-classified model, an age class in an age×stage model, and a group of locations in a spatial stage model are all sets of states. We present a new mathematical approach to absorbing Markov chains that extends the analysis of life histories by providing a comprehensive theory for the occupancy of arbitrary sets of states, and for other demographic variables related to these sets (e.g., reaching time, return time). We apply this approach to a matrix population model of the Southern Fulmar (Fulmarus glacialoides). The analysis of this model provides interesting insight into the lifetime number of breeding attempts of this species. Our new approach to absorbing Markov chains, and its implementation in matrix oriented software, makes the analysis of occupancy times more accessible to population ecologists, and directly applicable to any matrix population models.

Aging across the tree of life: The importance of a comparative perspective for the use of animal models in aging

Use of model organisms in aging research is problematic because our ability to extrapolate across the tree of life is not clear. On one hand, there are conserved pathways that regulate lifespan in organisms including yeast, nematodes, fruit flies, and mice. On the other, many intermediate taxa across the tree of life appear not to age at all, and there is substantial variation in aging mechanisms and patterns, sometimes even between closely related species. There are good evolutionary and mechanistic reasons to expect this complexity, but it means that model organisms must be used with caution and that results must always be interpreted through a broader comparative framework. Additionally, it is essential to include research on non-traditional and unusual species, and to integrate mechanistic and demographic research. There will be no simple answers regarding the biology of aging, and research approaches should reflect this. This article is part of a Special Issue entitled: Animal models of aging - edited by Houtkooper Riekelt.

The genealogical decomposition of a matrix population model with applications to the aggregation of stages

Matrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors. This decomposition of the projection matrix separates properties associated with lineages from those associated with individuals. It also clarifies the relationships between many quantities commonly used to describe such models, including the relationship between eigenvalue sensitivities and elasticities. We illustrate the utility of such a decomposition by introducing a new method for aggregating classes in a matrix population model to produce a simpler model with a smaller number of classes. Unlike the standard method, our method has the advantage of preserving reproductive values and elasticities. It also has conceptually satisfying properties such as commuting with changes of units.

Lifetime reproductive output: individual stochasticity, variance, and sensitivity analysis

Lifetime reproductive output (LRO) determines per-generation growth rates, establishes criteria for population growth or decline, and is an important component of fitness. Empirical measurements of LRO reveal high variance among individuals. This variance may result from genuine heterogeneity in individual properties, or from individual stochasticity, the outcome of probabilistic demographic events during the life cycle. To evaluate the extent of individual stochasticity requires the calculation of the statistics of LRO from a demographic model. Mean LRO is routinely calculated (as the net reproductive rate), but the calculation of variances has only recently received attention. Here, we present a complete, exact, analytical, closed-form solution for all the moments of LRO, for age- and stage-classified populations. Previous studies have relied on simulation, iterative solutions, or closed-form analytical solutions that capture only part of the sources of variance. We also present the sensitivity and elasticity of all of the statistics of LRO to parameters defining survival, stage transitions, and (st)age-specific fertility. Selection can operate on variance in LRO only if the variance results from genetic heterogeneity. The potential opportunity for selection is quantified by Crow’s index \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {I}$\end{document}I, the ratio of the variance to the square of the mean. But variance due to individual stochasticity is only an apparent opportunity for selection. In a comparison of a range of age-classified models for human populations, we find that proportional increases in mortality have very small effects on the mean and variance of LRO, but large positive effects on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {I}$\end{document}I. Proportional increases in fertility increase both the mean and variance of LRO, but reduce \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {I}$\end{document}I. For a size-classified tree population, the elasticity of both mean and variance of LRO to stage-specific mortality are negative; the elasticities to stage-specific fertility are positive.

Towards Process-based Range Modeling of Many Species

Understanding and forecasting species' geographic distributions in the face of global change is a central priority in biodiversity science. The existing view is that one must choose between correlative models for many species versus process-based models for few species. We suggest that opportunities exist to produce process-based range models for many species, by using hierarchical and inverse modeling to borrow strength across species, fill data gaps, fuse diverse data sets, and model across biological and spatial scales. We review the statistical ecology and population and range modeling literature, illustrating these modeling strategies in action. A variety of large, coordinated ecological datasets that can feed into these modeling solutions already exist, and we highlight organisms that seem ripe for the challenge.