Demographic heterogeneity, cohort selection, and population growth

Verhulst-type equation and the universal pattern for global population growth

The global population [Formula: see text] (growth from 10,000 BCE to 2023) is discussed in frames of the Verhulst-type scaling, recalling the sustainable development concept. The analysis focuses on the per capita global population growth rate, for which the analytic counterpart is considered:[Formula: see text]. The focused insight reveals two near- linear domains for [Formula: see text] changes: from ~ 700 CE till ~1968 and from ~1968 till 2023. It can be considered a reference pattern for long-term global population changes. For models recalling the Verhulst-type scaling, such analysis indicates that a single pair of growth rate and system resource coefficients [Formula: see text] should describe the rise in the global population. However, the Verhulst relation with such effective parameters does not describe [Formula: see text] changes, which raises the question of whether it is adequate to describe global population changes. Notably is the new way of data preparation, based on their collections from various sources and numerical filtering to obtain a 'smooth' optimal set. The changes of [Formula: see text] were analyzed via the 'reversed protocol' analysis, in comparison to the standard pattern, namely: (i) first, the linearized, distortions-sensitive transformation of [Formula: see text] data is carried out; it indicates domains where the validated application of a given scaling equation is possible and yields optimal values of relevant parameters, (ii) the final fitting via the selected scaling equation is carried out for identified domains, and using obtained optimal values of parameters. The analysis reveals links between [Formula: see text] local 'disturbations' and some historical and prehistorical reference events, showing their global scale impacts.

Uncovering bighorn sheep life-history trajectories in multidimensional trait space

Individual heterogeneity shapes ecoevolutionary processes at multiple scales. Yet, the scarcity of long-term life-history data and limitations in classic statistical tools hinder our capacity to uncover and understand individual heterogeneity in wildlife populations. Here, we apply an underused multivariate statistical method to uncover four heterogenous life-history trajectories in wild female bighorn sheep (Ovis canadensis). Remarkably, these trajectories had remained unobserved in the population despite nearly five decades of monitoring. Our results indicate substantial among-trajectory heterogeneity in growth, senescence, life history trade-offs, fitness, and contributions to population growth. Some trajectories suggest the presence of life history trade-offs while others include silver spoon effects, leading to heterogenous life-history outputs. Then, we show that mother identity and year of birth are relatively good predictors of heterogeneity, indicating that individual trajectories could be largely set during early life. Critically, our results demonstrate that heterogeneity in life-history trajectories can be inconspicuous, yet substantial and structured across multiple traits within a population. Uncovering and understanding this heterogeneity in other wild populations will be key to advancing our knowledge of ecoevolutionary processes across populations and species.

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.

Food Preservation in the Industrial Revolution Epoch: Innovative High Pressure Processing (HPP, HPT) for the 21st-Century Sustainable Society

The paper presents the 'progressive review' for high pressure preservation/processing (HPP) (cold pasteurization) of foods and the next-generation high-pressure and high temperature (HPHT, HPT) food sterilization technologies. It recalls the basics of HPP and HPT, showing their key features and advantages. It does not repeat detailed results regarding HPP and HPT implementations for specific foods, available in numerous excellent review papers. This report focuses on HPP and HPT-related issues that remain challenging and can hinder further progress. For HPP implementations, the reliable modeling of microorganisms' number decay after different times of high pressure treatment or product storage is essential. This report indicates significant problems with model equations standard nonlinear fitting paradigm and introduces the distortion-sensitive routine enabling the ultimate validation. An innovative concept based on the barocaloric effect is proposed for the new generation of HPT technology. The required high temperature appears only for a strictly defined short time period controlled by the maximal pressure value. Results of the feasibility test using neopentyl glycol as the barocaloric medium are presented. Attention is also paid to feedback interactions between socioeconomic and technological issues in the ongoing Industrial Revolution epoch. It indicates economic constraints for HPP and HPT developments and emerging business possibilities. The discussion recalls the inherent feedback interactions between technological and socioeconomic innovations as the driving force for the Industrial Revolution epoch.

Demographic and evolutionary consequences of hunting of wild birds

Hunting has a long tradition in human evolutionary history and remains a common leisure activity or an important source of food. Herein, we first briefly review the literature on the demographic consequences of hunting and associated analytical methods. We then address the question of potential selective hunting and its possible genetic/evolutionary consequences. Birds have historically been popular models for demographic studies, and the huge amount of census and ringing data accumulated over the last century has paved the way for research about the demographic effects of harvesting. By contrast, the literature on the evolutionary consequences of harvesting is dominated by studies on mammals (especially ungulates) and fish. In these taxa, individuals selected for harvest often have particular traits such as large body size or extravagant secondary sexual characters (e.g. antlers, horns, etc.). Our review shows that targeting individuals according to such genetically heritable traits can exert strong selective pressures and alter the evolutionary trajectory of populations for these or correlated traits. Studies focusing on the evolutionary consequences of hunting in birds are extremely rare, likely because birds within populations appear much more similar, and do not display individual differences to the same extent as many mammals and fishes. Nevertheless, even without conscious choice by hunters, there remains the potential for selection through hunting in birds, for example by genetically inherited traits such as personality or pace-of-life. We emphasise that because so many bird species experience high hunting pressure, the possible selective effect of harvest in birds and its evolutionary consequences deserves far more attention, and that hunting may be one major driver of bird evolutionary trajectories that should be carefully considered in wildlife management schemes.

Juvenile survival increases with dispersal distance and varies across years: 15 years of evidence in a prairie perennial

Juvenile survival is critical to population persistence and evolutionary change. However, the survival of juvenile plants from emergence to reproductive maturity is rarely quantified. This is especially true for long-lived perennials with extended pre-reproductive periods. Furthermore, studies rarely have the replication necessary to account for variation among populations and cohorts. We estimated juvenile survival and its relationship to population size, density of conspecifics, distance to the maternal plant, age, year, and cohort for Echinacea angustifolia, a long-lived herbaceous perennial. In 14 remnant prairie populations over seven sampling years, 2007-2013, we identified 886 seedlings. We then monitored these individuals annually until 2021 (8-15 years). Overall, juvenile mortality was very high; for almost all cohorts fewer than 10% of seedlings survived to age 8 or to year 2021. Only two of the seedlings reached reproductive maturity within the study period. Juvenile survival increased with distance from the maternal plant and varied more among the study years than it did by age or cohort. Juvenile survival did not vary with population size or local density of conspecific neighbors. Our results suggest that low juvenile survival could contribute to projected population declines.

Population Dynamic Consequences of Context-Dependent Trade-Offs across Life Histories

AbstractTrade-offs are central to life history theory and play a role in driving life history diversity. They arise from a finite amount of resources that need to be allocated among different functions by an organism. Yet covariation of demographic rates among individuals frequently do not reflect allocation trade-offs because of variation in resource acquisition. The covariation of traits among individuals can thus vary with the environment and often increases in benign environments. Surprisingly, little is known about how such context-dependent expression of trade-offs among individuals affect population dynamics across species with different life histories. To study their influence on population stability, we develop an individual-based simulation where covariation in demographic rates varies with the environment. We use it to simulate population dynamics for various life histories across the slow-fast pace-of-life continuum. We found that the population dynamics of slower life histories are relatively more sensitive to changes in covariation, regardless of the trade-off considered. Additionally, we found that the impact on population stability depends on which trade-off is considered, with opposite effects of intraindividual and intergenerational trade-offs. Last, the expression of different trade-offs can feed back to influence generation time through selection acting on individual heterogeneity within cohorts, ultimately affecting population dynamics.

Global population: from Super-Malthus behavior to Doomsday criticality

The report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence: P t = P 0 e x p ± t / τ β , and SM-2 is the Malthus-type relation with the time-dependent growth rate r ( t ) or relaxation time τ ( t ) = 1 / r ( t ) : P t = P 0 e x p r t × t = P 0 e x p τ t / t . Population data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~ 3 billion): from the compressed exponential behavior ( β > 1 ) to the stretched exponential one ( β < 1 ). For SM-2 dependence, linear changes of τ T during the Industrial Revolutions period, since ~ 1700, led to the constrained critical behavior P t = P 0 e x p b ' t / T C - t , whereT C ≈ 2216 is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis.

Linking diet switching to reproductive performance across populations of two critically endangered mammalian herbivores

Optimal foraging theory predicts that animals maximise energy intake by consuming the most valuable foods available. When resources are limited, they may include lower-quality fallback foods in their diets. As seasonal herbivore diet switching is understudied, we evaluate its extent and effects across three Kenyan reserves each for Critically Endangered eastern black rhino (Diceros bicornis michaeli) and Grevy's zebra (Equus grevyi), and its associations with habitat quality, microbiome variation, and reproductive performance. Black rhino diet breadth increases with vegetation productivity (NDVI), whereas zebra diet breadth peaks at intermediate NDVI. Black rhino diets associated with higher vegetation productivity have less acacia (Fabaceae: Vachellia and Senegalia spp.) and more grass suggesting that acacia are fallback foods, upending conventional assumptions. Larger dietary shifts are associated with longer calving intervals. Grevy's zebra diets in high rainfall areas are consistently grass-dominated, whereas in arid areas they primarily consume legumes during low vegetation productivity periods. Whilst microbiome composition between individuals is affected by the environment, and diet composition in black rhino, seasonal dietary shifts do not drive commensurate microbiome shifts. Documenting diet shifts across ecological gradients can increase the effectiveness of conservation by informing habitat suitability models and improving understanding of responses to resource limitation.

Risk for Esophageal Cancer Based on Lifestyle Factors-Smoking, Alcohol Consumption, and Body Mass Index: Insight from a South Korean Population Study in a Low-Incidence Area

Esophageal cancer constitutes a global public health challenge. However, South Korean population-specific information on the association of lifestyle (smoking, alcohol consumption, and obesity status) with esophageal cancer risk is sparse. This nested case-control study analyzed the Korean national health screening cohort data (2002-2019) of 1114 patients with esophageal cancer and 4456 controls (1:4 propensity-score matched for sex, age, income, and residential region). Conditional and unconditional logistic regression analyses, after adjustment for multiple covariates, determined the effects of lifestyle factors on esophageal cancer risk. Smoking and alcohol consumption increased the esophageal cancer risk (adjusted odds ratio [95% confidence interval]: 1.37 [1.15-1.63] and 1.89 [1.60-2.23], respectively). Overweight (body mass index [BMI] ≥ 23 to <25 kg/m2), obese I (BMI ≥ 25 to <30 kg/m2), or obese II (BMI ≥ 30 kg/m2) categories had reduced odds of esophageal cancer (0.76 [0.62-0.92], 0.59 [0.48-0.72], and 0.47 [0.26-0.85], respectively). In the subgroup analyses, the association of incident esophageal cancer with smoking and alcohol consumption persisted, particularly in men or those aged ≥55 years, whereas higher BMI scores remained consistently associated with a reduced esophageal cancer likelihood across all age groups, in both sexes, and alcohol users or current smokers. Underweight current smokers exhibited a higher propensity for esophageal cancer. In conclusion, smoking and alcohol drinking may potentially increase the risk, whereas weight maintenance, with BMI ≥ 23 kg/m2, may potentially decrease the risk, for esophageal cancer in the South Korean population. Lifestyle modification in the specific subgroups may be a potential strategy for preventing esophageal cancer.

Alzheimer's Disease and Different Types of Cancer Likelihood: Unveiling Disparities and Potential Protective Effects in a Korean Cohort Study

The link between Alzheimer's disease and cancer risk is a concern in public health. However, research has yielded limited and sometimes contrasting results, suggesting the need for more validation. We analyzed a large cohort to examine the long-term association between Alzheimer's disease (AD) and the risk of developing cancer. In total, 24,664 AD patients and 98,656 control participants were selected from the National Health Insurance Cohort database of Korea, spanning from 2002 to 2019. Propensity score matching and overlap-weighted adjustment techniques were used to balance the standardized differences between the AD and control groups. The Cox proportional hazards model was applied to calculate hazard ratios (HRs) with 95% confidence intervals (CIs) for various cancers, considering relevant covariates. Results indicated that patients with AD had a significantly lower likelihood of overall malignancy (HR 0.63; 95% CI, 0.59-0.68) and each of the 10 site-specific cancers compared to the control group. Among these, pancreatic cancer (HR, 0.50) exhibited the strongest inverse association, followed by hepatic (HR, 0.60), gastric (HR, 0.63), kidney (HR, 0.63), lung (HR, 0.64), thyroid (HR, 0.65), colorectal (HR, 0.67), gallbladder and biliary duct (HR, 0.73), hematologic malignancy (HR, 0.73), and bladder cancers (HR, 0.76). This protective effect against certain organ-specific cancers persisted over the 16-year follow-up period, except for in kidney cancer and hematologic malignancies. The protective effect against specific cancer types (gastric, colorectal, lung, hepatic, and pancreatic) was more prominent in individuals aged 60 years and older, regardless of their sex. However, there were some variations in the specific types of cancer observed between males and females. In summary, Korean patients with AD had a lower risk of cancer, especially in individuals 60 years and older, during the 16-year follow-up period.

Chronic Periodontitis and the Potential Likelihood of Gastric Cancer: A Nested Case-Control Study in the Korean Population Utilizing a National Health Sample Cohort

There is limited information regarding the potential association between chronic periodontitis (CP) and gastric cancer, especially in the Korean population. This study aimed to explore this relationship. This nested case-control study analyzed data from 10,174 patients with gastric cancer and 40,696 controls from the Korean National Health Insurance Service-National Sample Cohort using propensity score matching. Standardized differences were used to compare baseline characteristics between study groups. Logistic regression analyses adjusted for confounders were conducted to assess the association between history of CP and gastric cancer occurrence. CP histories and comprehensive subgroup analyses in the 1- and 2-year periods preceding the index date were evaluated. Individuals with a history of CP within the 1-year and 2-year periods showed an increased likelihood of developing gastric cancer. Subgroup analyses consistently supported these findings in male participants aged <65 years and individuals with various income levels or living in residential areas. However, no significant associations were observed among participants aged ≥65 years. In conclusion, CP may be a potential risk factor for gastric cancer development in the Korean population. Regular screening for gastric cancer may be necessary for high-risk individuals, specifically men aged <65 years with a history of CP.

When the going gets tough, the tough get going: Effect of extreme climate on an Antarctic seabird's life history

Individuals differ in many ways. Most produce few offspring; a handful produce many. Some die early; others live to old age. It is tempting to attribute these differences in outcomes to differences in individual traits, and thus in the demographic rates experienced. However, there is more to individual variation than meets the eye of the biologist. Even among individuals sharing identical traits, life history outcomes (life expectancy and lifetime reproduction) will vary due to individual stochasticity, that is to chance. Quantifying the contributions of heterogeneity and chance is essential to understand natural variability. Interindividual differences vary across environmental conditions, hence heterogeneity and stochasticity depend on environmental conditions. We show that favourable conditions increase the contributions of individual stochasticity, and reduce the contributions of heterogeneity, to variance in demographic outcomes in a seabird population. The opposite is true under poor conditions. This result has important consequence for understanding the ecology and evolution of life history strategies.

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.

Spatial familial networks to infer demographic structure of wild populations

In social species, reproductive success and rates of dispersal vary among individuals resulting in spatially structured populations. Network analyses of familial relationships may provide insights on how these parameters influence population-level demographic patterns. These methods, however, have rarely been applied to genetically derived pedigree data from wild populations.Here, we use parent-offspring relationships to construct familial networks from polygamous boreal woodland caribou (Rangifer tarandus caribou) in Saskatchewan, Canada, to inform recovery efforts. We collected samples from 933 individuals at 15 variable microsatellite loci along with caribou-specific primers for sex identification. Using network measures, we assess the contribution of individual caribou to the population with several centrality measures and then determine which measures are best suited to inform on the population demographic structure. We investigate the centrality of individuals from eighteen different local areas, along with the entire population.We found substantial differences in centrality of individuals in different local areas, that in turn contributed differently to the full network, highlighting the importance of analyzing networks at different scales. The full network revealed that boreal caribou in Saskatchewan form a complex, interconnected familial network, as the removal of edges with high betweenness did not result in distinct subgroups. Alpha, betweenness, and eccentricity centrality were the most informative measures to characterize the population demographic structure and for spatially identifying areas of highest fitness levels and family cohesion across the range. We found varied levels of dispersal, fitness, and cohesion in family groups. Synthesis and applications: Our results demonstrate the value of different network measures in assessing genetically derived familial networks. The spatial application of the familial networks identified individuals presenting different fitness levels, short- and long-distance dispersing ability across the range in support of population monitoring and recovery efforts.

Simple signals indicate which period of the annual cycle drives declines in seasonal populations

For declining wild populations, a critical aspect of effective conservation is understanding when and where the causes of decline occur. The primary drivers of decline in migratory and seasonal populations can often be attributed to a specific period of the year. However, generic, broadly applicable indicators of these season-specific drivers of population decline remain elusive. We used a multi-generation experiment to investigate whether habitat loss in either the breeding or non-breeding period generated distinct signatures of population decline. When breeding habitat was reduced, population size remained relatively stable for several generations, before declining precipitously. When non-breeding habitat was reduced, between-season variation in population counts increased relative to control populations, and non-breeding population size declined steadily. Changes in seasonal vital rates and other indicators were predicted by the season in which habitat loss treatment occurred. Per capita reproductive output increased when non-breeding habitat was reduced and decreased with breeding habitat reduction, whereas per capita non-breeding survival showed the opposite trends. Our results reveal how simple signals inherent in counts and demographics of declining populations can indicate which period of the annual cycle is driving declines.

Beyond the proportional frailty model: Bayesian estimation of individual heterogeneity on mortality parameters

Today, we know that demographic rates can be greatly influenced by differences among individuals in their capacity to survive and reproduce. These intrinsic differences, commonly known as individual heterogeneity, can rarely be measured and are thus treated as latent variables when modeling mortality. Finite mixture models and mixed effects models have been proposed as alternative approaches for inference on individual heterogeneity in mortality. However, in general models assume that individual heterogeneity influences mortality proportionally, which limits the possibility to test hypotheses on the effect of individual heterogeneity on other aspects of mortality such as ageing rates. Here, we propose a Bayesian model that builds upon the mixture models previously developed, but that facilitates making inferences on the effect of individual heterogeneity on mortality parameters other than the baseline mortality. As an illustration, we apply this framework to the Gompertz-Makeham mortality model, commonly used in human and wildlife studies, by assuming that the Gompertz rate parameter is affected by individual heterogeneity. We provide results of a simulation study where we show that the model appropriately retrieves the parameters used for simulation, even for low variances in the heterogeneous parameter. We then apply the model to a dataset on captive chimpanzees and on a cohort life table of 1751 Swedish men, and show how model selection against a null model (i.e., without heterogeneity) can be carried out.

Introducing risk inequality metrics in tuberculosis policy development

Global stakeholders including the World Health Organization rely on predictive models for developing strategies and setting targets for tuberculosis care and control programs. Failure to account for variation in individual risk leads to substantial biases that impair data interpretation and policy decisions. Anticipated impediments to estimating heterogeneity for each parameter are discouraging despite considerable technical progress in recent years. Here we identify acquisition of infection as the single process where heterogeneity most fundamentally impacts model outputs, due to selection imposed by dynamic forces of infection. We introduce concrete metrics of risk inequality, demonstrate their utility in mathematical models, and pack the information into a risk inequality coefficient (RIC) which can be calculated and reported by national tuberculosis programs for use in policy development and modeling.

Failure to account for heterogeneity in TB risk can mislead model-based evaluation of proposed interventions. Here, the authors introduce a metric to estimate the distribution of risk in populations from routinely collected data and find that variation in infection acquisition is the most impactful.

Measurement error of state variables creates substantial bias in results of demographic population models

Integral projection and matrix population models are commonly used in ecological and conservation studies to assess the health and extinction risk of populations. These models use one (or more) measurable state variable(s), such as size or age, to predict individual performance, which, ideally, is the sole determinant of an individual's expected fate. However, even if ecologists successfully identify and measure the observable state variable(s) that best predicts individual fate, we are rarely, if ever, able to perfectly measure state for many species, especially those with size structure, where total plant biomass or starch stores, for example, may be the best predictors of fate. Here, we used a series of simulations to test how this imperfect quantification of actual state ("measurement error") leads to inaccurate prediction of state-dependent fates and influences the predictions of structured population models. We simulated 10 yr of best practice field data collection using known vital rate functions and incorporated measurement error of different magnitudes and types (completely random, temporal, and individual based) for two size-structured life histories. We found that even for conservative error rates, most types of measurement error increased the median predicted population growth rate by 1-2% growth per year. However, the magnitude of this error differed substantially with life history strategy and error type, with some scenarios resulting in >8% median overestimation of population growth rate. This effect arises largely from the well-known econometrics problem of "regression dilution" (overestimation of the intercept and underestimation of the slope of a regression when the predictor variable is measured with error), which in our simulations typically results in overly optimistic predictions of small or young individuals' vital rates. Our results suggest that the problem of measurement error for state variables, present in many demographic studies but virtually unacknowledged in the ecological literature, may lead to substantial misestimation of population behavior, resulting in erroneous inferences about not only growth, but also extinction risk and other aspects of population dynamics.

Variance in animal longevity: contributions of heterogeneity and stochasticity

Variance in longevity among individuals may arise as an effect of heterogeneity (differences in mortality rates experienced at the same age or stage) or as an effect of individual stochasticity (the outcome of random demographic events during the life cycle). Decomposing the variance into components due to heterogeneity and stochasticity is crucial for evolutionary analyses.In this study, we analyze longevity from ten studies of invertebrates in the laboratory, and use the results to partition the variance in longevity into its components. To do so, we fit finite mixtures of Weibull survival functions to each data set by maximum likelihood, using the EM algorithm. We used the Bayesian Information Criterion to select the most well supported model. The results of the mixture analysis were used to construct an age × stage-classified matrix model, with heterogeneity groups as stages, from which we calculated the variance in longevity and its components. Almost all data sets revealed evidence of some degree of heterogeneity. The median contribution of unobserved heterogeneity to the total variance was 35%, with the remaining 65% due to stochasticity. The differences among groups in mean longevity were typically on the order of 30% of the overall life expectancy. There was considerable variation among data sets in both the magnitude of heterogeneity and the proportion of variance due to heterogeneity, but no clear patterns were apparent in relation to sex, taxon, or environmental conditions.

Food availability affects adult survival trajectories depending on early developmental conditions

Food availability modulates survival in interaction with (for example) competition, disease and predators, but to what extent food availability in natural populations affects survival independent of these factors is not well known. We tested the effect of food availability on lifespan and actuarial senescence in a large population of captive zebra finches by increasing the effort required to obtain food, reflecting natural contrasts in food availability. Food availability may not affect all individuals equally and we therefore created heterogeneity in phenotypic quality by raising birds with different numbers of siblings. Low food availability had no effect on lifespan for individuals from benign developmental conditions (raised in small broods), but shortened lifespan for individuals from harsh developmental conditions. The lifespan difference arose through higher baseline mortality rate of individuals from harsh developmental conditions, despite a decrease in the rate of actuarial senescence. We found no evidence for sex-specific environmental sensitivity, but females lived shorter than males due to increased actuarial senescence. Thus, low food availability by itself shortens lifespan, but only in individuals from harsh developmental conditions. Our food availability manipulation resembles dietary restriction as applied to invertebrates, where it extends lifespan in model organisms and we discuss possible reasons for the contrasting results.

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.

From early life to senescence: individual heterogeneity in a long-lived seabird

Although population studies have long assumed that all individuals of a given sex and age are identical, ignoring among‐individual differences may strongly bias our perception of eco‐evolutionary processes. Individual heterogeneity, often referred to as individual quality, has received increasing research attention in the last decades. However, there are still substantial gaps in our current knowledge. For example, there is little information on how individual heterogeneity influences various life‐history traits simultaneously, and studies describing individual heterogeneity in wild populations are generally not able to jointly identify possible sources of this variation. Here, based on a mark–recapture data set of 9,685 known‐aged Wandering Albatrosses (Diomedea exulans), we investigated the existence of individual quality over the entire life cycle of this species, from early life to senescence. Using finite mixture models, we investigated the expression of individual heterogeneity in various demographic traits, and examined the origin of these among‐individual differences by considering the natal environmental conditions. We found that some individuals consistently outperformed others during most of their life. In old age, however, the senescence rate was stronger in males that showed high demographic performance at younger ages. Variation in individual quality seemed strongly affected by extrinsic factors experienced during the ontogenetic period. We found that individuals born in years with high population density tended to have lower performances during their lifespan, suggesting delayed density dependence effects through individual quality. Our study showed that among‐individual differences could be important in structuring individual life history trajectories, with substantial consequences at higher ecological levels such as population dynamics.

The 'Evo-Demo' Implications of Condition-Dependent Mortality

Animals in the wild die from a variety of different mortality sources, including predation, disease, and starvation. Different mortality sources selectively remove individuals with different body condition in different ways, and this variation in the condition dependence of mortality has evolutionary and demographic implications. Subsequent population dynamics are influenced by the strength of condition-dependent mortality during specific periods, with population growth impacted in different ways in short- versus long-lived species. The evolution of lifespan is strongly influenced by condition-dependent mortality, with strikingly different outcomes expected in senescence rates when the relationship between condition and mortality is altered. A coupling of field and laboratory studies is now required to further reveal the evolutionary implications of condition-dependent mortality.

Consecutive cohort effects driven by density-dependence and climate influence early-life survival in a long-lived bird

Conditions during early life, including maternal cohort effects, can influence the future fitness of individuals. This may be particularly true for long-distance migrating birds, because, apart from conditions experienced by cohorts during rearing, conditions during early life in regions far from breeding grounds may also influence their population dynamics. Very little is known about the fitness consequences of those conditions experienced by juveniles after independence, especially in wild populations and for long-lived birds. We used multi-event capture-recapture-recovery models and a unique 26-year dataset for the Audouin's gull (Larus audouinii) to assess for the first time whether survival was influenced by early conditions, both during the rearing period (i.e. a maternal cohort effect potentially affected by density dependence) and the first winter (i.e. a cohort effect driven by climate when birds disperse to wintering grounds). Our results show that juvenile survival was highly sensitive to early-life conditions and that survival decreased with stronger density dependence and harsh climate. The two consecutive cohort effects were of similar magnitude and they may represent a selection filter. Thus, early-life conditions had a strong impact on survival, and neglecting this complexity may hinder our understanding on how populations of long-lived animals fluctuate and respond to perturbations.

Successful by Chance? The Power of Mixed Models and Neutral Simulations for the Detection of Individual Fixed Heterogeneity in Fitness Components

Heterogeneity in fitness components consists of fixed heterogeneity due to latent differences fixed throughout life (e.g., genetic variation) and dynamic heterogeneity generated by stochastic variation. Their relative magnitude is crucial for evolutionary processes, as only the former may allow for adaptation. However, the importance of fixed heterogeneity in small populations has recently been questioned. Using neutral simulations (NS), several studies failed to detect fixed heterogeneity, thus challenging previous results from mixed models (MM). To understand the causes of this discrepancy, we estimate the statistical power and false positive rate of both methods and apply them to empirical data from a wild rodent population. While MM show high false-positive rates if confounding factors are not accounted for, they have high statistical power to detect real fixed heterogeneity. In contrast, NS are also subject to high false-positive rates but always have low power. Indeed, MM analyses of the rodent population data show significant fixed heterogeneity in reproductive success, whereas NS analyses do not. We suggest that fixed heterogeneity may be more common than is suggested by NS and that NS are useful only if more powerful methods are not applicable and if they are complemented by a power analysis.

Inter-class competition in stage-structured populations: effects of adult density on life-history traits of adult and juvenile common lizards

Ecological and evolutionary processes in natural populations are largely influenced by the population's stage-structure. Commonly, different classes have different competitive abilities, e.g., due to differences in body size, suggesting that inter-class competition may be important and largely asymmetric. However, experimental evidence states that inter-class competition, which is important, is rare and restricted to marine fish. Here, we manipulated the adult density in six semi-natural populations of the European common lizard, Zootoca vivipara, while holding juvenile density constant. Adult density affected juveniles, but not adults, in line with inter-class competition. High adult density led to lower juvenile survival and growth before hibernation. In contrast, juvenile survival after hibernation was higher in populations with high adult density, pointing to relaxed inter-class competition. As a result, annual survival was not affected by adult density, showing that differences in pre- and post-hibernation survival balanced each other out. The intensity of inter-class competition affected reproduction, performance, and body size in juveniles. Path analyses unravelled direct treatment effects on early growth (pre-hibernation) and no direct treatment effects on the parameters measured after hibernation. This points to allometry of treatment-induced differences in early growth, and it suggests that inter-class competition mainly affects the early growth of the competitively inferior class and thereby their future performance and reproduction. These results are in contrast with previous findings and, together with results in marine fish, suggest that the strength and direction of density dependence may depend on the degree of inter-class competition, and thus on the availability of resources used by the competing classes.

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.

Des différences, pourquoi? Transmission, maintenance and effects of phenotypic variance

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.