Demographic heterogeneity impacts density-dependent population dynamics

Variety is the spice of life: nongenetic variation in life histories influences population growth and evolvability

Individual vital rates, such as mortality and birth rates, are key determinants of lifetime reproductive success, and variability in these rates shapes population dynamics. Previous studies have found that this vital rate heterogeneity can influence demographic properties, including population growth rates. However, the explicit effects of the variation within and the covariance between vital rates that can also vary throughout the lifespan on population growth remain unknown. Here, we explore the analytical consequences of nongenetic heterogeneity on long-term population growth rates and rates of evolution by modifying traditional age-structured population projection matrices to incorporate variation among individual vital rates. The model allows vital rates to be permanent throughout life ("fixed condition") or to change over the lifespan ("dynamic condition"). We reduce the complexity associated with adding individual heterogeneity to age-structured models through a novel application of matrix collapsing ("phenotypic collapsing"), showing how to collapse in a manner that preserves the asymptotic and transient dynamics of the original matrix. The main conclusion is that nongenetic individual heterogeneity can strongly impact the long-term growth rate and rates of evolution. The magnitude and sign of this impact depend heavily on how the heterogeneity covaries across the lifespan of an organism. Our results emphasize that nongenetic variation cannot simply be viewed as random noise, but rather that it has consistent, predictable effects on fitness and evolvability.

Individual Quality Drives Life History Variation in a Long-Lived Marine Predator

AbstractIndividual quality and environmental conditions may mask or interact with energetic trade-offs in life history evolution. Deconstructing these sources of variation is especially difficult in long-lived species that are rarely observed on timescales long enough to disentangle these effects. Here, we investigated relative support for variation in female quality and costs of reproduction as factors shaping differences in life history trajectories using a 32-year dataset of repeated reproductive measurements from 273 marked, known-age female gray seals (Halichoerus grypus). We defined individual reproductive investment using two traits, reproductive frequency (a female's probability of breeding) and provisioning performance (offspring weaning mass). Fitted hierarchical Bayesian models identified individual investment relative to conspecifics (over a female's entire life and in three age classes) and subsequently estimated how these investment metrics and the Atlantic Multidecadal Oscillation are associated with longevity. Individual differences (i.e., quality) contributed a large portion of the variance in reproductive traits. Females that consistently invest well in their offspring relative to other females survive longer. The best-supported model estimated survival as a function of age class-specific provisioning performance, where late-life performance was particularly variable and had the greatest impact on survival, possibly indicating individual variation in senescence. There was no evidence to support a trade-off in reproductive performance and survival at the individual level. Overall, these results suggest that in gray seals, individual quality is a stronger driver in life history variation than individual strategies resulting from energetic trade-offs.

Large offspring have enhanced lifetime reproductive success: Long-term carry-over effects of weaning size in gray seals (Halichoerus grypus)

An individual's size in early stages of life may be an important source of individual variation in lifetime reproductive performance, as size effects on ontogenetic development can have cascading physiological and behavioral consequences throughout life. Here, we explored how size-at-young influences subsequent reproductive performance in gray seals (Halichoerus grypus) using repeated encounter and reproductive data on a marked sample of 363 females that were measured for length after weaning, at ~4 weeks of age, and eventually recruited to the Sable Island breeding colony. Two reproductive traits were considered: provisioning performance (mass of weaned offspring), modeled using linear mixed effects models; and reproductive frequency (rate at which a female returns to breed), modeled using mixed effects multistate mark-recapture models. Mothers with the longest weaning lengths produced pups 8 kg heavier and were 20% more likely to breed in a given year than mothers with the shortest lengths. Correlation in body lengths between weaning and adult life stages, however, is weak: Longer pups do not grow to be longer than average adults. Thus, covariation between weaning length and future reproductive performance appears to be a carry-over effect, where the size advantages afforded in early juvenile stages may allow enhanced long-term performance in adulthood.

Female reproductive skew exacerbates the extinction risk from poaching in the eastern black rhino

Variation in individual demographic rates can have large consequences for populations. Female reproductive skew is an example of structured demographic heterogeneity where females have intrinsic qualities that make them more or less likely to breed. The consequences of reproductive skew for population dynamics are poorly understood in non-cooperatively breeding mammals, especially when coupled with other drivers such as poaching. We address this knowledge gap with population viability analyses using an age-specific, female-only, individual-based, stochastic population model built with long-term data for three Kenyan populations of the Critically Endangered eastern black rhino (Diceros bicornis michaeli). There was substantial reproductive skew, with a high proportion of females not breeding or doing so at very low rates. This had a large impact on the projected population growth rate for the smaller population on Ol Jogi. Moreover, including female reproductive skew exacerbates the effects of poaching, increasing the probability of extinction by approximately 70% under a simulated poaching pressure of 5% offtake per year. Tackling the effects of reproductive skew depends on whether it is mediated by habitat or social factors, with potential strategies including habitat and biological management respectively. Investigating and tackling reproductive skew in other species requires long-term, individual-level data collection.

Distinguishing within- from between-individual effects: How to use the within-individual centring method for quadratic patterns

Any average pattern observed at the population level (cross-sectional analysis) may confound two different types of processes: some processes that occur among individuals and others that occur within individuals. Separating within- from among-individual processes is critical for our understanding of ecological and evolutionary dynamics. The within-individual centring method allows distinguishing within- from among-individual processes and this method has been widely used in ecology to investigate both linear and quadratic patterns. Here we show that two alternative equations could be used for the investigation of quadratic within-individual patterns. We explain the different assumptions and constraints of both equations. Reviewing the literature, we found that mainly one of these two equations has been used in studies investigating quadratic patterns. Yet this equation might not be the most appropriate in all circumstances leading to bias and imprecision. We show that these two alternative equations make different assumptions about the shape of the within-individual pattern. One equation assumes that the within-individual effect is related to an absolute process whereas the other assumes the effect arises from an individual relative process. The choice of using one equation instead of the other should depend upon the biological process investigated. Using simulations, we showed that a mismatch between the assumptions made by the equation used to analyse the data and the biological process investigated might led to flawed inference affecting output of model selection and accuracy of estimates. We stress that the equation used should be chosen carefully. We provide step by step guidelines for choosing an equation when studying quadratic pattern with the within-individual centring approach. We encourage the use of the within-individual centring method, promoting its relevant application for nonlinear relationships.

Demystifying individual heterogeneity

Among-individual variation in vital rates, such as mortality and birth rates, exists in nearly all populations. Recent studies suggest that this individual heterogeneity produces substantial life-history and fitness differences among individuals, which in turn scale up to influence population dynamics. However, our ability to understand the consequences of individual heterogeneity is limited by inconsistencies across conceptual frameworks in the field. Studies of individual heterogeneity remain filled with contradicting and ambiguous terminology that introduces risks of misunderstandings, conflicting models and unreliable conclusions. Here, we synthesise the existing literature into a single and comparatively straightforward framework with explicit terminology and definitions. This work introduces a distinction between potential vital rates and realised vital rates to develop a coherent framework that maps directly onto mathematical models of individual heterogeneity. We suggest the terms "fixed condition" and "dynamic condition" be used to distinguish potential vital rates that are permanent from those that can change throughout an individual's life. To illustrate, we connect the framework to quantitative genetics models and to common classes of statistical models used to infer individual heterogeneity. We also develop a population projection matrix model that provides an example of how our definitions are translated into precise quantitative terms.

Variation in the vital rates of an Antarctic marine predator: the role of individual heterogeneity

Variation in life-history traits such as lifespan and lifetime reproductive output is thought to arise, in part, due to among-individual differences in the underlying probabilities of survival and reproduction. However, the stochastic nature of demographic processes can also generate considerable variation in fitness-related traits among otherwise-identical individuals. An improved understanding of life-history evolution and population dynamics therefore depends on evaluating the relative role of each of these processes. Here, we used a 33-yr data set with reproductive histories for 1,274 female Weddell seals from Erebus Bay, Antarctica, to assess the strength of evidence for among-individual heterogeneity in the probabilities of survival and reproduction, while accounting for multiple other sources of variation in vital rates. Our analysis used recent advances in Bayesian model selection techniques and diagnostics to directly compare model fit and predictive power between models that included individual effects on survival and reproduction to those that did not. We found strong evidence for costs of reproduction to both survival and future reproduction, with breeders having rates of survival and subsequent reproduction that were 3% and 6% lower than rates for non-breeders. We detected age-related changes in the rates of survival and reproduction, but the patterns differed for the two rates. Survival rates steadily declined from 0.92 at age 7 to 0.56 at the maximal age of 31 yr. In contrast, reproductive rates increased from 0.68 at age 7 to 0.79 at age 16 and then steadily declined to 0.37 for the oldest females. Models that included individual effects explained more variation in observed life histories and had better estimated predictive power than those that did not, indicating their importance in understanding sources of variation among individuals in life-history traits. We found that among-individual heterogeneity in survival was small relative to that for reproduction. Our study, which found patterns of variation in vital rates that are consistent with a series of predictions from life-history theory, is the first to provide a thorough assessment of variation in important vital rates for a long-lived, high-latitude marine mammal while taking full advantage of recent developments in model evaluation.

Optimizing lifetime reproductive output: Intermittent breeding as a tactic for females in a long-lived, multiparous mammal

In iteroparous species, intermittent breeding is an important life-history tactic that can greatly affect animal population growth and viability. Despite its importance, few studies have quantified the consequences of breeding pauses on lifetime reproductive output, principally because calculating lifetime reproductive output requires knowledge of each individual's entire reproductive history. This information is extremely difficult to obtain in wild populations. We applied novel statistical approaches that account for uncertainty in state assessment and individual heterogeneity to an 18-year capture-recapture dataset of 6,631 female southern elephant seals from Macquarie Island. We estimated survival and breeding probabilities, and investigated the consequences of intermittent breeding on lifetime reproductive output. We found consistent differences in females' demographic performance between two heterogeneity classes. In particular, breeding imbued a high cost on survival in the females from the heterogeneity class 2, assumed to be females of lower quality. Individual quality also appeared to play a major role in a female's decision to skip reproduction with females of poorer quality more likely to skip breeding events than females of higher quality. Skipping some breeding events allowed females from both heterogeneity classes to increase lifetime reproductive output over females that bred annually. However, females of lower quality produced less offspring over their lifetime. Intermittent breeding seems to be used by female southern elephant seals as a tactic to offset reproductive costs on survival and enhance lifetime reproductive output but remains unavoidable and driven by individual-specific constraints in some other females.

Individual heterogeneity determines sex differences in mortality in a monogamous bird with reversed sexual dimorphism

Sex differences in mortality are pervasive in vertebrates, and usually result in shorter life spans in the larger sex, although the underlying mechanisms are still unclear. On the other hand, differences in frailty among individuals (i.e. individual heterogeneity), can play a major role in shaping demographic trajectories in wild populations. The link between these two processes has seldom been explored. We used Bayesian survival trajectory analysis to study age-specific mortality trajectories in the Eurasian sparrowhawk (Accipiter nisus), a monogamous raptor with reversed sexual size dimorphism. We tested the effect of individual heterogeneity on age-specific mortality, and the extent by which this heterogeneity was determined by average reproductive output and wing length as measures of an individual's frailty. We found that sex differences in age-specific mortality were primarily driven by the differences in individual heterogeneity between the two sexes. Females were more heterogeneous than males in their level of frailty. Thus, a larger number of females with low frailty are able to survive to older ages than males, with life expectancy for the least frail adult females reaching up to 4·23 years, while for the least frail adult males it was of 2·68 years. We found that 50% of this heterogeneity was determined by average reproductive output and wing length in both sexes. For both, individuals with high average reproductive output had also higher chances to survive. However, the effect of wing length was different between the two sexes. While larger females had higher survival, larger males had lower chances to survive. Our results contribute a novel perspective to the ongoing debate about the mechanisms that drive sex differences in vital rates in vertebrates. Although we found that variables that relate to the cost of reproduction and sexual dimorphism are at least partially involved in determining these sex differences, it is through their effect on the level of frailty that they affect age patterns of mortality. Therefore, our results raise the possibility that observed differences in age-specific demographic rates may in fact be driven by differences in individual heterogeneity.

Some directions in ecological theory

The role of theory within ecology has changed dramatically in recent decades. Once primarily a source of qualitative conceptual framing, ecological theories and models are now often used to develop quantitative explanations of empirical patterns and to project future dynamics of specific ecological systems. In this essay, I recount my own experience of this transformation, in which accelerating computing power and the widespread incorporation of stochastic processes into ecological theory combined to create some novel integration of mathematical and statistical models. This stronger integration drives theory towards incorporating more biological realism, and I explore ways in which we can grapple with that realism to generate new general theoretical insights. This enhanced realism, in turn, may lead to frameworks for projecting ecological responses to anthropogenic change, which is, arguably, the central challenge for 21st-century ecology. In an era of big data and synthesis, ecologists are increasingly seeking to infer causality from observational data; but conventional biometry provides few tools for this project. This is a realm where theorists can and should play an important role, and I close by pointing towards some analytical and philosophical approaches developed in our sister discipline of economics that address this very problem. While I make no grand prognostications about the likely discoveries of ecological theory over the coming century, you will find in this essay a scattering of more or less far-fetched ideas that I, at least, think are interesting and (possibly) fruitful directions for our field.

Combined Influences of Model Choice, Data Quality, and Data Quantity When Estimating Population Trends

Estimating and projecting population trends using population viability analysis (PVA) are central to identifying species at risk of extinction and for informing conservation management strategies. Models for PVA generally fall within two categories, scalar (count-based) or matrix (demographic). Model structure, process error, measurement error, and time series length all have known impacts in population risk assessments, but their combined impact has not been thoroughly investigated. We tested the ability of scalar and matrix PVA models to predict percent decline over a ten-year interval, selected to coincide with the IUCN Red List criterion A.3, using data simulated for a hypothetical, short-lived organism with a simple life-history and for a threatened snail, Tasmaphena lamproides. PVA performance was assessed across different time series lengths, population growth rates, and levels of process and measurement error. We found that the magnitude of effects of measurement error, process error, and time series length, and interactions between these, depended on context. We found that high process and measurement error reduced the reliability of both models in predicted percent decline. Both sources of error contributed strongly to biased predictions, with process error tending to contribute to the spread of predictions more than measurement error. Increasing time series length improved precision and reduced bias of predicted population trends, but gains substantially diminished for time series lengths greater than 10-15 years. The simple parameterization scheme we employed contributed strongly to bias in matrix model predictions when both process and measurement error were high, causing scalar models to exhibit similar or greater precision and lower bias than matrix models. Our study provides evidence that, for short-lived species with structured but simple life histories, short time series and simple models can be sufficient for reasonably reliable conservation decision-making, and may be preferable for population projections when unbiased estimates of vital rates cannot be obtained.

Consequences of dispersal heterogeneity for population spread and persistence

Dispersal heterogeneity is increasingly being observed in ecological populations and has long been suspected as an explanation for observations of non-Gaussian dispersal. Recent empirical and theoretical studies have begun to confirm this. Using an integro-difference model, we allow an individual's diffusivity to be drawn from a trait distribution and derive a general relationship between the dispersal kernel's moments and those of the underlying heterogeneous trait distribution. We show that dispersal heterogeneity causes dispersal kernels to appear leptokurtic, increases the population's spread rate, and lowers the critical reproductive rate required for persistence in the face of advection. Wavespeed has been shown previously to be determined largely by the form of the dispersal kernel tail. We qualify this by showing that when reproduction is low, the precise shape of the tail is less important than the first few dispersal moments such as variance and kurtosis. If the reproductive rate is large, a dispersal kernel's asymptotic tail has a greater influence over wavespeed, implying that estimating the prevalence of traits which correlate with long-range dispersal is critical. The presence of multiple dispersal behaviors has previously been characterized in terms of long-range versus short-range dispersal, and it has been found that rare long-range dispersal essentially determines wavespeed. We discuss this finding and place it within a general context of dispersal heterogeneity showing that the dispersal behavior with the highest average dispersal distance does not always determine wavespeed.

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.