Hal Caswell

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Verified

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• PhD
• Emeritus Research Scholar at Woods Hole Oceanographic Institution

Background. Interactions among kin have important consequences, including resource transfers, alloparenting, health care, and economic support. Some interactions require that the lives of the interacting relatives overlap. The overlap over a lifetime (lifetime kin overlap, LKO) depends on mortality (longer lives give more opportunity for overlap) a...

A heterogeneous population is a mixture of groups differing in vital rates. In such a population, some of the variance in demographic outcomes (e.g., longevity, lifetime reproduction) is due to heterogeneity and some is the result of stochastic demographic processes. Many studies have partitioned variance into its between-group and within-group com...

Online enhancements: supplemental PDF. abstract: In many species, individuals are embedded in a network of kin with whom they interact. Interactions between kin can affect survival and fertility rates and thus the life history of individuals. These interactions indirectly affect both the network of kin and the dynamics of the population. In this wa...

Environmental factors and individual attributes, and their interactions, impact survival, growth and reproduction of an individual throughout its life. In the clonal rotifer Brachionus, low food conditions delay reproduction and extend lifespan. This species also exhibits maternal effect senescence; the offspring of older mothers have lower surviva...

In many species, individuals are embedded in a network of kin with whom they interact. Interactions between kin can affect survival and fertility rates and thus the life history of individuals. These interactions indirectly affect both the network of kin and the dynamics of the population. In this way, a nonlinear feedback between the kin network a...

Over the past 150 years, life expectancy doubled and healthy life expectancy increased. Expectations reveal nothing about variability, so we present a stochastic analysis to investigate changes over time, age and gender of variation, among individuals, in healthy lifespan, for different levels of country income. To complement health-adjusted life e...

Every individual is connected to a network of kin-her/his family in the broad sense of that term-that develops and changes as that individual ages. Family networks a↵ect demographic , economic, and health-related aspects of life and society. Because of its importance, kinship dynamics deserves a formal theory that can link it to mortality, fertilit...

Human evolutionary demography is an emerging field blending natural science with social science. This edited volume provides a much-needed, interdisciplinary introduction to the field and highlights cutting-edge research for interested readers and researchers in demography, the evolutionary behavioural sciences, biology, and related disciplines. By...

A heterogeneous population is a mixture of groups differing in vital rates. In such a population, some of the variance in demographic outcomes (e.g., longevity, lifetime reproduction) is due to heterogeneity and some is the result of stochastic demographic processes. Many studies have partitioned variance into its between-group and within-group com...

Background The matrix model for kinship networks includes many demographic processes but is deterministic, projecting expected values of age-stage distributions of kin. It provides no information on (co)variances. Because kin populations are small, demographic stochasticity is expected to create appreciable inter-individual variation. Objectives T...

Background Although the family plays a pivotal role in older adults’ care, there is limited research on how evolving demographic trends affect older adults’ support networks and how the trends vary by race. To fill this gap, we examine the influence of shifting family demographics on future care needs for older adults with dementia, emphasizing the...

In many species, individuals are embedded in a network of kin with whom they interact. The interactions among kin may affect the survival and fertility rates, and thus the life history of individuals. These interactions indirectly influence both the network of kin and the dynamics of the population. In this way, non-linear feedback emerges between...

Demographers have long attempted to project future changes in the size and composition of populations, but have ignored what these processes will mean for the size, composition, and age distribution of family networks. Kinship structures matter because family solidarity—a crucial source of informal care for millions of people around the world—is co...

BACKGROUND: Individual lifespans differ. Some of those differences are due to heterogeneity, some to stochasticity. Some of the heterogeneity is due to socioeconomic, physiological, or environmental differences; some to unobserved latent factors. All of these are, from time to time, called inequality. OBJECTIVE: This paper aims to clarify the relat...

Demographers have long attempted to project future changes in the size and composition of populations, but have ignored what these processes will mean for the size, composition, and age distribution of family networks. Kinship structures matter because family solidarity--a crucial source of informal care for millions of people around the world--is...

Stage‐based demographic methods, such as matrix population models (MPMs), are powerful tools used to address a broad range of fundamental questions in ecology, evolutionary biology and conservation science. Accordingly, MPMs now exist for over 3000 species worldwide. These data are being digitised as an ongoing process and periodically released int...

Background: Kinship groups can have considerable importance (e.g., generational support, inheritance, and information for key life events). During demographic transitions, kinship networks are reshaped by changes in mortality and fertility rates. Objective: This paper analyzes consanguineous and female kin and explores the effect on the size and s...

Background. The death of kin has psychological, physical, and economic effects on other members of a kinship network. Recently developed formal demographic models provide the deaths of kin, of any kind, at any age of a Focal individual. However, causes of death have yet to be accounted for. Objectives. Our objective is to extend the matrix kinship...

Stage-based demographic methods, such as matrix population models (MPMs), are powerful tools used to address a broad range of fundamental questions in ecology, evolutionary biology, and conservation science. Accordingly, MPMs now exist for over 3,000 species worldwide. These data are being digitised as an ongoing process and periodically released i...

In the last 150 years, in many populations life expectancy has more than doubled, the variation in length of life has decreased, and, as result, more individuals enjoy similarly longer lives (even though with important socio-demographic differences). When it comes to healthy longevity, today more and more people reach older ages in better health th...

The life histories of organisms are expressed as rates of development, reproduction, and survival. However, individuals may experience differential outcomes for the same set of rates. Such individual stochasticity generates variance around familiar mean measures of life history traits, such as life expectancy and the reproductive number R0. By writ...

The Covid-19 pandemic has not affected the population evenly. This must be acknowledged when it comes to understanding the Covid-19 death toll and answering the question of how many life years have been lost. We use level of geriatric care to account for variation in remaining life expectancy among individuals that died during 2020. Based on a link...

Background: Previous kinship models analyze female kin through female lines of descent, neglecting male kin and male lines of descent. Because males and females differ in mortality and fertility, including both sexes in kinship models is an important unsolved problem. Objective: The objectives are to develop a kinship model including female and mal...

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....

Most studies on unemployment have assessed its individual-level costs. However, beyond its effects on individuals, unemployment incurs costs for their immediate families and extended kin. Close kin provide the majority of social support for unemployed adults. Applying demographic and statistical techniques to official statistics and using COVID-19...

Kinship relations play a crucial role in structuring populations and shaping individual outcomes. Differences in kinship among individuals, cohorts, and subpopulations are one important aspect of these structures. Demography and related disciplines have proposed sophisticated approaches to study kinship in recent years. We argue that the developmen...

Many animals form long‐term monogamous pair bonds, and the disruption of a pair bond (through either divorce or widowhood) can have significant consequences for individual vital rates (survival, breeding, and breeding success probabilities) and life‐history outcomes (lifetime reproductive success [LRS], life expectancy). Here, we investigated the c...

The life histories of organisms are expressed as rates of development, reproduction, and survival. However, individuals may experience differential outcomes for the same set of rates. Such individual stochasticity generates variance around familiar mean measures of life history traits, such as life expectancy and the reproductive number R_0. By wri...

Background Previous kinship models analyze female kin through female lines of descent, neglecting male kin and male lines of descent. Because males and females differ in mortality and fertility, including both sexes in kinship models is an important unsolved problem. Objectives The objectives are to develop a kinship model including female and mal...

Variance among individuals in fitness components reflects both genuine heterogeneity between individuals and stochasticity in events experienced along the life cycle. Maternal age represents a form of heterogeneity that affects both the mean and the variance of lifetime reproductive output (LRO). Here, we quantify the relative contribution of mater...

An increasing number of empirical studies aim to quantify individual variation in demographic parameters because these patterns are key for evolutionary and ecological processes. Advanced approaches to estimate individual heterogeneity are now using a multivariate normal distribution with correlated individual random effects to account for the late...

Matrix population models (MPMs) are currently used in a range of fields, from basic research in ecology and evolutionary biology, to applied questions in conservation biology, management, and epidemiology. In MPMs individuals are classified into discrete stages, and the model projects the population over discrete time-steps. A rich analytical theor...

BACKGROUND Kinship models, from the pioneering work of Goodman, Keyfitz, and Pullum to the recent matrix-oriented approach of Caswell, have assumed time-invariant demographic rates, and computed the kinship structures implied by those rates. In reality, however, demographic rates vary with time and it is of interest to compute the consequences of s...

BACKGROUND Healthy longevity (HL) is an important measure of the prospects for quality of life in ageing societies. Incidence-based (cf. prevalence-based) models describe transitions among age classes and health stages. Despite the probabilistic nature of those transitions, analyses of healthy longevity have focused persistently on means (“health e...

Background. Healthy longevity (HL) is an important measure of the prospects for quality of life in ageing societies. Incidence-based (cf. prevalence-based) models describe transitions among age classes and health stages. Despite the probabilistic nature of those transitions, analyses of healthy longevity have focused persistently on means ("health...

Background Kinship models generally assume time-invariant demographic rates, and compute the kinship structures implied by those rates. It is important to compute the consequences of time variation in demographic rates for kinship stuctures. Objectives Our goal is to develop a matrix model for the dynamics of kinship networks subject to arbitrary...

Significance Maternal effect senescence, the decline in offspring quality with increasing maternal age, is common in animals despite its negative impact on fitness. To understand how maternal effect senescence might evolve, we built matrix population models to calculate selection gradients on survival and fertility as functions of maternal age. We...

Background Recent kinship models focus on the age structures of kin as a function of the age of the focal individual. However, variables in addition to age have important impacts. Generalizing age-specific models to multistate models including other variables is an important and hitherto unsolved problem. Objectives Our aim is to develop a multist...

Variance in life history outcomes among individuals is a requirement for natural selection, and a determinant of the ecological dynamics of populations. Heterogeneity among individuals will cause such variance, but so will the inherently stochastic nature of their demography. The relative contributions of these variance components - stochasticity a...

The study of eco-evolutionary dynamics is based on the idea that ecological and evolutionary processes may operate on the same, or very similar, time scales, and that interactions of ecological and evolutionary processes may have important consequences. Here we develop a model that combines Mendelian population genetics with nonlinear demography to...

Maternal effect senescence---a decline in offspring fitness with maternal age---has been demonstrated in a range of taxa, including humans. Despite decades of phenotypic studies, it remains unclear how maternal effect senescence impacts population structure or evolutionary fitness. To understand the impact of maternal effect senescence on populatio...

The Paris Agreement is a multinational initiative to combat climate change by keeping a global temperature increase in this century to 2°C above preindustrial levels while pursuing efforts to limit the increase to 1.5°C. Until recently, ensembles of coupled climate simulations producing temporal dynamics of climate en route to stable global mean te...

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....

The outcome of natural selection depends on the demographic processes of birth, death, and development. Here, we derive conditions for protected polymorphism in a population characterized by age- or stage-dependent demography with two sexes. We do so using a novel two-sex matrix population model including basic Mendelian genetics (one locus, two al...

This open access book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear an...

This book relies on this set of mathematical techniques. This chapter introduces the basics, which will be used throughout the text. For more information, I recommend four sources in particular. The most complete treatment, but not the easiest starting point, is the book by Magnus and Neudecker (1988).

Demography is a science that connects individual processes and events to the development of cohorts and then to the dynamics of populations.

The first step in developing any kind of structured population model is choosing one or more variables in terms of which to describe the population structure. The job of these i-state variables is to encapsulate all the information about the past experience of an individual that is relevant to its future behavior (Metz and Diekmann 1986; Caswell 20...

Demography is the study of the population consequences of the fates of individuals. As an individual organism develops through its life cycle it may increase in size, change its morphology, develop new physiological functions, exhibit new behaviors, or move to new locations.

Nonlinearities in demographic models arise due to density dependence, frequency dependence (in 2-sex models), feedback through the environment or the economy, recruitment subsidy due to immigration, and from the scaling inherent in calculations of proportional population structure.

Short-term, transient population dynamics can differ in important ways from long-term asymptotic dynamics. Just as perturbation analysis (sensitivity and elasticity) of the asymptotic growth rate reveals the effects of the vital rates on long-term growth (Chap. 3), the perturbation analysis of transient dynamics can reveal the determinants of short...

When Markov chains are used as mathematical models of natural or social phenomena, the transition intensities or probabilities are usually defined in terms of parameters that are relevant to the scientific question at hand. Sensitivity analysis of such models is important because it quantifies the dependence of the model behavior on the parameters.

As we have seen repeatedly, Markov chains are often used as mathematical models of demographic (as well as other natural) phenomena, with transition probabilities defined in terms of parameters that are of interest in the scientific question at hand. Sensitivity analysis is an important way to quantify the effects of changes in these parameters on...

Periodic matrix models are often used to study cyclical temporal variation (seasonal or interannual), sometimes as a (perhaps crude) approximation to stochastic models. However, formally periodic models also appear when multiple processes (e.g., demography and dispersal) operate within a single projection interval. The models take the form of perio...

A similarly basic outcome of population, at the individual or cohort level, is longevity: the length of individual life. The most commonly encountered description of longevity is its expectation, the life expectancy.

The essence of stable population theory is the fact that a population subject to time invariant vital rates will (with a few exceptions not of interest here) converge to a stable structure and grow exponentially at a constant rate (the population growth rate, or intrinsic rate of increase).

The basic unit of comparative demography is a study that reports the value of some demographic outcome in two populations that differ in a set of vital rates. One challenge of such studies is to account for the difference in outcomes by decomposing that difference into contributions from differences in each of the parameters. It frequently happens...

Demographic processes and ecological interactions are central to understanding evolution and vice versa. We present a novel framework that combines basic Mendelian genetics with the powerful demographic approach of matrix population models. The ecological components of the model may be stage classified or age classified, linear or nonlinear, time i...

Climate change is affecting species’ distributions and abundances worldwide. Baseline population estimates, against which future observations may be compared, are necessary if we are to detect ecological change. Arctic sea ice ecosystems are changing rapidly and we lack baseline population estimates for many ice‐associated species. Provided we can...

Objectives Two processes generate total variance in age at death: heterogeneity (between-group variance) and individual stochasticity (within-group variance). Limited research has evaluated how these two components have changed over time. We quantify the degree to which area-level deprivation contributed to total variance in age at death in Scotlan...

Background Mortality inequalities demonstrate a double burden: the most deprived socioeconomic groups experience the lowest average age of death and the highest variation in age at death. Two processes generate variation in age at death: individual stochasticity (within-group variance) and heterogeneity (between-group inequality). No known research...

Recent studies unravelled the effect of climate changes on populations through their impact on functional traits and demographic rates in terrestrial and freshwater ecosystems, but such understanding in marine ecosystems remains incomplete. Here, we evaluate the impact of the combined effects of climate and functional traits on population dynamics...

Background: Increases in human longevity have made it critical to distinguish healthy longevity from longevity without regard to health. Current methods focus on expectations of healthy longevity, and are often limited to binary health outcomes (e.g., disabled vs. not disabled). We present a new matrix formulation for the statistics of healthy lon...

History matters when individual prior conditions contain important information about the fate of individuals. We present a general framework for demographic models which incorporates the effects of history on population dynamics. The framework incorporates prior condition into the i-state variable and includes an algorithm for constructing the popu...

Models of sexually-reproducing populations that consider only a single sex cannot capture the effects of sex-specific demographic differences and mate availability. We present a new framework for two-sex demographic models that implements and extends the birth-matrix mating-rule approach of Pollak. The model is a continuous-time matrix model that e...

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...

The demographic consequences of stochasticity in processes such as survival and reproduction are modulated by the heterogeneity within the population. Therefore, to study effects of stochasticity on population growth and extinction risk, it is critical to use structured population models in which the most important sources of heterogeneity (e.g. ag...

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...

1 Abstract Wildlife populations are often affected by natural or artificial disasters that reduce their vital rates leading to drastic fluctuations in population dynamics. We use a stage‐structured matrix model to study the recovery process of a population given an environmental disturbance. We focus on the time it takes the population to recover t...

We discovered an error in Eq. (12) (p. 1621).

As population-level patterns of interest in forests emerge from individual vital rates, modelling forest dynamics requires making the link between the scales at which data are collected (individual stems) and the scales at which questions are asked (e.g. populations and communities). Structured population models (e.g. integral projection models (IP...

Figures S1 and S2. S1 shows the distribution of the time required to return to the set target set Bb for an individual initially in the state successful breeder, under each environmental conditions. S2 shows the distribution of the time required to reach the set Bb for an individual initially in the state non breeder, under each environmental condi...

This file contains the MATLAB codes to carry out the calculations presented in this paper for any transition matrix and any target set. This file contains also the transition matrices used in the Example.

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 tim...

Demographic population models are derived from descriptions of how individuals move through their life cycles. In this sense all demographic models are based on information about individuals. Individuals are described in terms of their i-states (sensu Metz and Diekmann), which provide the information necessary to specify the response of an individu...

Individuals are heterogeneous in many ways. Some of these differences are incorporated as individual states (e.g. age, size, breeding status) in population models. However, substantial amounts of heterogeneity may remain unaccounted for, due to unmeasurable genetic, maternal or environmental factors. Such unobserved heterogeneity (UH) affects the b...

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 stochastici...

Mathematical models are essential for combining data from multiple sources to quantify population endpoints. This is especially true for species, such as marine mammals, for which data on vital rates are difficult to obtain. Since the effects of an environmental disaster are not fixed, we develop time-varying (nonautonomous) matrix population mod-...

Leprosy (or Hansen’s disease) remains an important public health challenge globally, with an estimated 5.5 million total number of cases and 200,000–300,000 new cases reported annually. The nine-banded armadillo (Dasypus novemcinctus) is the only known natural non-human vertebrate host of Mycobacterium leprae, the causative agent of leprosy, in the...

MATLAB scripts to calculate and decompose the variance in longevity for the matrix formulation of the gamma-Gompertz?Makeham model.