Reproductive value and analyses of population dynamics of age-structured populations

2021 ◽  
pp. 285-298
Author(s):  
Bernt-Erik Sæther ◽  
Steinar Engen
Keyword(s):  
Growth Rate ◽  
Population Dynamics ◽  
Age Structure ◽  
Good Description ◽  
Age Distribution ◽  
Reproductive Rate ◽  
Environmental Stochasticity ◽  
Reproductive Value ◽  
Long Run ◽  
Age Structured

Many populations of especially long-lived species show large temporal variation in age structure, which can complicate estimating of important population parameters. This occurs because it can be difficult to disentangle whether variation in numbers is due to fluctuations in the environment or caused by changes in the age distribution. This chapter shows that fluctuations in the total reproductive value of the population, that is, the sum of all individual reproductive values, often provide a good description of the population dynamics but still is not confounded by fluctuations in age structure. Because the change in the total reproductive rate is exactly equal to the growth rate of the population, this quantity enables decomposition of the long-run growth rate into stochastic components caused by age-specific variation in demographic and environmental stochasticity. The chapter illustrates the practical application of this approach in stochastic demography by analyses of the dynamics of several populations of birds and mammals. It puts a strong focus on these methods being particularly useful in viability analyses of small populations of vulnerable or endangered species.

scholarly journals The demographic dividend is more than an education dividend

2020 ◽  
Vol 117 (42) ◽  
pp. 25982-25984
Author(s):  
Rainer Kotschy ◽  
Patricio Suarez Urtaza ◽  
Uwe Sunde
Keyword(s):  
Human Capital ◽  
Age Structure ◽  
Age Distribution ◽  
Age Groups ◽  
Demographic Dividend ◽  
Positive Growth ◽  
Working Age ◽  
Age Structured ◽  
Positive Effect ◽  
Effect Of Age

The demographic dividend has long been viewed as an important factor for economic development and provided a rationale for policies aiming at a more balanced age structure through birth control and family planning. Assessing the relative importance of age structure and increases in human capital, recent work has argued that the demographic dividend is related to education and has suggested a dominance of improving education over age structure. Here we reconsider the empirical relevance of shifts in the age distribution for development for a panel of 159 countries over the period 1950 to 2015. Based on a flexible model of age-structured human capital endowments, the results document important interactions between age structure and human capital endowments, suggesting that arguments of clear dominance of education over age structure are unwarranted and lead to potentially misleading policy conclusions. An increase in the working-age population share has a strong and significant positive effect on growth, even conditional on human capital, in line with the conventional notion of a demographic dividend. An increase in human capital only has positive growth effects if combined with a suitable age structure. An increasing share of the most productive age groups has an additional positive effect on economic performance. Finally, the results show considerable heterogeneity in the effect of age structure and human capital for different levels of development. Successful policies for sustainable development should take this heterogeneity into account to avoid detrimental implications of a unidimensional focus on human capital without accounting for demography.

scholarly journals Breeding transients in capture–recapture modeling and their consequences for local population dynamics

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Daniel Oro ◽  
Daniel F. Doak
Keyword(s):  
Growth Rate ◽  
Population Dynamics ◽  
Population Growth ◽  
Population Growth Rate ◽  
Local Population ◽  
Environmental Stochasticity ◽  
Adult Survival ◽  
Local Survival ◽  
First Reproduction ◽  
Capture Recapture

Abstract Standard procedures for capture–mark–recapture modelling (CMR) for the study of animal demography include running goodness-of-fit tests on a general starting model. A frequent reason for poor model fit is heterogeneity in local survival among individuals captured for the first time and those already captured or seen on previous occasions. This deviation is technically termed a transience effect. In specific cases, simple, uni-state CMR modeling showing transients may allow researchers to assess the role of these transients on population dynamics. Transient individuals nearly always have a lower local survival probability, which may appear for a number of reasons. In most cases, transients arise due to permanent dispersal, higher mortality, or a combination of both. In the case of higher mortality, transients may be symptomatic of a cost of first reproduction. A few studies working at large spatial scales actually show that transients more often correspond to survival costs of first reproduction rather than to permanent dispersal, bolstering the interpretation of transience as a measure of costs of reproduction, since initial detections are often associated with first breeding attempts. Regardless of their cause, the loss of transients from a local population should lower population growth rate. We review almost 1000 papers using CMR modeling and find that almost 40% of studies fitting the searching criteria (N = 115) detected transients. Nevertheless, few researchers have considered the ecological or evolutionary meaning of the transient phenomenon. Only three studies from the reviewed papers considered transients to be a cost of first reproduction. We also analyze a long-term individual monitoring dataset (1988–2012) on a long-lived bird to quantify transients, and we use a life table response experiment (LTRE) to measure the consequences of transients at a population level. As expected, population growth rate decreased when the environment became harsher while the proportion of transients increased. LTRE analysis showed that population growth can be substantially affected by changes in traits that are variable under environmental stochasticity and deterministic perturbations, such as recruitment, fecundity of experienced individuals, and transient probabilities. This occurred even though sensitivities and elasticities of these parameters were much lower than those for adult survival. The proportion of transients also increased with the strength of density-dependence. These results have implications for ecological and evolutionary studies and may stimulate other researchers to explore the ecological processes behind the occurrence of transients in capture–recapture studies. In population models, the inclusion of a specific state for transients may help to make more reliable predictions for endangered and harvested species.

Influence of growth and survival costs of reproduction on Atlantic cod, Gadus morhua, population growth rate

1999 ◽  
Vol 56 (9) ◽  
pp. 1612-1623 ◽  
Author(s):  
Jeffrey A Hutchings
Keyword(s):  
Growth Rate ◽  
Population Growth ◽  
Gadus Morhua ◽  
Atlantic Cod ◽  
Environmental Stochasticity ◽  
Individual Growth ◽  
Growth And Survival ◽  
Individual Growth Rate ◽  
Age Structured ◽  
Reproductive Rates

A stochastic, age-structured life history model was used to examine how age at maturity (theta), pre- (Zimm) and postreproductive (Zmat) mortality, and postreproductive growth rate can affect maximum reproductive rates of fish at low population size. Simulations suggest that annual (r) and per-generation (R0) metrics of population growth for Newfoundland's northern Grand Bank Atlantic cod, Gadus morhua, are primarily influenced by changes to mortality prior to and following reproduction. At observed weights at age and Zmat = 0.2, r ranged between 0.135 and 0.164 for cod maturing at between 4 and 7 years. Incremental increases in either Zimm or Zmat of 0.1 were associated with 0.03-0.05 reductions in r. To effect similar reductions, individual growth rate would have to decline by approximately one half. At observed weights at age, increases in Zmat from 0.20 to 0.45 increased the probability of negative per-generation growth from 3 to 26% for cod maturing at 4 years and from 6 to 46% for cod maturing at 7 years. Thus, even in the absence of fishing mortality, little or no population growth by Atlantic cod may not be unexpected in the presence of environmental stochasticity, particularly when accompanied by increases in mortality and declining individual growth.

scholarly journals Decomposing variation in population growth into contributions from environment and phenotypes in an age-structured population

2011 ◽  
Vol 279 (1727) ◽  
pp. 394-401 ◽  
Author(s):  
Fanie Pelletier ◽  
Kelly Moyes ◽  
Tim H. Clutton-Brock ◽  
Tim Coulson
Keyword(s):  
Population Dynamics ◽  
Population Growth ◽  
Age Structure ◽  
Life History Traits ◽  
Population Fluctuations ◽  
Relative Importance ◽  
Ecological Interactions ◽  
Structured Population ◽  
Individual Covariates ◽  
Age Structured

Evaluating the relative importance of ecological drivers responsible for natural population fluctuations in size is challenging. Longitudinal studies where most individuals are monitored from birth to death and where environmental conditions are known provide a valuable resource to characterize complex ecological interactions. We used a recently developed approach to decompose the observed fluctuation in population growth of the red deer population on the Isle of Rum into contributions from climate, density and their interaction and to quantify their relative importance. We also quantified the contribution of individual covariates, including phenotypic and life-history traits, to population growth. Fluctuations in composition in age and sex classes ((st)age structure) of the population contributed substantially to the population dynamics. Density, climate, birth weight and reproductive status contributed less and approximately equally to the population growth. Our results support the contention that fluctuations in the population's (st)age structure have important consequences for population dynamics and underline the importance of including information on population composition to understand the effect of human-driven changes on population performance of long-lived species.

Population age structure and growth in four syntopic amphibian species inhabiting a large river floodplain

2003 ◽  
Vol 81 (6) ◽  
pp. 1096-1106 ◽  
Author(s):  
Dan Cogalniceanu ◽  
Claude Miaud
Keyword(s):  
Growth Rate ◽  
Life History ◽  
Age Structure ◽  
Environmental Conditions ◽  
Age Distribution ◽  
Large River ◽  
Danube River ◽  
Population Age Structure ◽  
River Floodplain ◽  
River Floodplains

River floodplains are disturbance-dominated landscapes where floods are major regulators of both aquatic and nearby terrestrial communities. Amphibians are common inhabitants of floodplains and their life cycle depends on both aquatic and terrestrial habitats. We focused on how different syntopic species of amphibians reacted to the environmental conditions of a large river floodplain. We examined life-history traits such as population age structure and growth in small- and large-bodied species of anurans and urodeles in the lower Danube River floodplain in Romania. Two newt species, Triturus vulgaris (small-bodied) and Triturus dobrogicus (large-bodied), and two anuran taxa, Bombina bombina (small-bodied) and the Rana esculenta complex (large-bodied), were included in the study. The ages of individuals estimated by skeletochronology varied from 3 to 5–6 years for T. vulgaris and from 2–3 to 4–5 years for T. dobrogicus. In the anurans, ages varied from 2 to 5 years in B. bombina and from 4 to 10 years in the R. esculenta complex. The numbers of breeding opportunities (i.e., the number of years the adults reproduce) are similar in both newt species (3), while growth rates and age at maturity differ between the large- and small-bodied species. In anurans, the number of breeding opportunities for the smallest species, B. bombina (4), is associated with a high growth rate and earlier maturation. In the larger R. esculenta complex, the higher number of breeding opportunities (7) is associated with a low growth rate and delayed maturation. The study of age distribution and associated parameters provides useful information on population life history. We discuss how age structure and growth of amphibian populations in large river floodplains can be used as indicators of environmental conditions.

scholarly journals Age structure is critical to the population dynamics and survival of honeybee colonies

2016 ◽  
Vol 3 (11) ◽  
pp. 160444 ◽  
Author(s):  
M. I. Betti ◽  
L. M. Wahl ◽  
M. Zamir
Keyword(s):  
Population Dynamics ◽  
Age Structure ◽  
Division Of Labour ◽  
Natural Consequence ◽  
Substantial Impact ◽  
Severity Of Disease ◽  
Bee Colony ◽  
Honeybee Colony ◽  
Age Structured ◽  
Over Time

Age structure is an important feature of the division of labour within honeybee colonies, but its effects on colony dynamics have rarely been explored. We present a model of a honeybee colony that incorporates this key feature, and use this model to explore the effects of both winter and disease on the fate of the colony. The model offers a novel explanation for the frequently observed phenomenon of ‘spring dwindle’, which emerges as a natural consequence of the age-structured dynamics. Furthermore, the results indicate that a model taking age structure into account markedly affects the predicted timing and severity of disease within a bee colony. The timing of the onset of disease with respect to the changing seasons may also have a substantial impact on the fate of a honeybee colony. Finally, simulations predict that an infection may persist in a honeybee colony over several years, with effects that compound over time. Thus, the ultimate collapse of the colony may be the result of events several years past.

scholarly journals Mathematical Model of Three Age-Structured Transmission Dynamics of Chikungunya Virus

2016 ◽  
Vol 2016 ◽  
pp. 1-31 ◽  
Author(s):  
Folashade B. Agusto ◽  
Shamise Easley ◽  
Kenneth Freeman ◽  
Madison Thomas
Keyword(s):  
Age Structure ◽  
Stable Disease ◽  
Chikungunya Virus ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Age Distribution ◽  
Transmission Dynamics ◽  
Globally Asymptotically Stable ◽  
Age Structured ◽  
Disease Free

We developed a new age-structured deterministic model for the transmission dynamics of chikungunya virus. The model is analyzed to gain insights into the qualitative features of its associated equilibria. Some of the theoretical and epidemiological findings indicate that the stable disease-free equilibrium is globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, the model undergoes, in the presence of disease induced mortality, the phenomenon of backward bifurcation, where the stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number is less than unity. Further analysis of the model indicates that the qualitative dynamics of the model are not altered by the inclusion of age structure. This is further emphasized by the sensitivity analysis results, which shows that the dominant parameters of the model are not altered by the inclusion of age structure. However, the numerical simulations show the flaw of the exclusion of age in the transmission dynamics of chikungunya with regard to control implementations. The exclusion of age structure fails to show the age distribution needed for an effective age based control strategy, leading to a one size fits all blanket control for the entire population.

scholarly journals Towards a replicator dynamics model of age structured populations

2021 ◽  
Vol 82 (5) ◽  
Author(s):  
K. Argasinski ◽  
M. Broom
Keyword(s):  
Sex Ratio ◽  
Age Structure ◽  
Replicator Dynamics ◽  
Structured Populations ◽  
Reproductive Value ◽  
Leslie Matrix ◽  
Age Classes ◽  
Structured Population Model ◽  
Age Class ◽  
Age Structured

AbstractWe present a new modelling framework combining replicator dynamics, the standard model of frequency dependent selection, with an age-structured population model. The new framework allows for the modelling of populations consisting of competing strategies carried by individuals who change across their life cycle. Firstly the discretization of the McKendrick von Foerster model is derived. We show that the Euler–Lotka equation is satisfied when the new model reaches a steady state (i.e. stable frequencies between the age classes). This discretization consists of unit age classes where the timescale is chosen so that only a fraction of individuals play a single game round. This implies a linear dynamics and individuals not killed during the round are moved to the next age class; linearity means that the system is equivalent to a large Bernadelli–Lewis–Leslie matrix. Then we use the methodology of multipopulation games to derive two, mutually equivalent systems of equations. The first contains equations describing the evolution of the strategy frequencies in the whole population, completed by subsystems of equations describing the evolution of the age structure for each strategy. The second contains equations describing the changes of the general population’s age structure, completed with subsystems of equations describing the selection of the strategies within each age class. We then present the obtained system of replicator dynamics in the form of the mixed ODE-PDE system which is independent of the chosen timescale, and much simpler. The obtained results are illustrated by the example of the sex ratio model which shows that when different mortalities of the sexes are assumed, the sex ratio of 0.5 is obtained but that Fisher’s mechanism, driven by the reproductive value of the different sexes, is not in equilibrium.

scholarly journals Age-structured Jolly-Seber model expands inference and improves parameter estimation from capture-recapture data

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0252748
Author(s):  
Nathan J. Hostetter ◽  
Nicholas J. Lunn ◽  
Evan S. Richardson ◽  
Eric V. Regehr ◽  
Sarah J. Converse
Keyword(s):  
Population Dynamics ◽  
Population Growth ◽  
Age Structure ◽  
Growth Rates ◽  
Lifetime Reproductive Success ◽  
Polar Bears ◽  
Population Growth Rates ◽  
Age Dependent ◽  
Capture Recapture ◽  
Age Structured

Understanding the influence of individual attributes on demographic processes is a key objective of wildlife population studies. Capture-recapture and age data are commonly collected to investigate hypotheses about survival, reproduction, and viability. We present a novel age-structured Jolly-Seber model that incorporates age and capture-recapture data to provide comprehensive information on population dynamics, including abundance, age-dependent survival, recruitment, age structure, and population growth rates. We applied our model to a multi-year capture-recapture study of polar bears (Ursus maritimus) in western Hudson Bay, Canada (2012–2018), where management and conservation require a detailed understanding of how polar bears respond to climate change and other factors. In simulation studies, the age-structured Jolly-Seber model improved precision of survival, recruitment, and annual abundance estimates relative to standard Jolly-Seber models that omit age information. Furthermore, incorporating age information improved precision of population growth rates, increased power to detect trends in abundance, and allowed direct estimation of age-dependent survival and changes in annual age structure. Our case study provided detailed evidence for senescence in polar bear survival. Median survival estimates were lower (<0.95) for individuals aged <5 years, remained high (>0.95) for individuals aged 7–22 years, and subsequently declined to near zero for individuals >30 years. We also detected cascading effects of large recruitment classes on population age structure, which created major shifts in age structure when these classes entered the population and then again when they reached prime breeding ages (10–15 years old). Overall, age-structured Jolly-Seber models provide a flexible means to investigate ecological and evolutionary processes that shape populations (e.g., via senescence, life expectancy, and lifetime reproductive success) while improving our ability to investigate population dynamics and forecast population changes from capture-recapture data.

scholarly journals Age-structure and transient dynamics in epidemiological systems

2019 ◽  
Vol 16 (156) ◽  
pp. 20190151 ◽  
Author(s):  
F. M. G. Magpantay ◽  
A. A. King ◽  
P. Rohani
Keyword(s):  
Age Structure ◽  
Transition Period ◽  
Homogeneous Model ◽  
Age Distribution ◽  
Secular Trends ◽  
Transient Dynamics ◽  
Effective Vaccine ◽  
Infection Prevalence ◽  
Transmission Rates ◽  
Age Structured

Mathematical models of childhood diseases date back to the early twentieth century. In several cases, models that make the simplifying assumption of homogeneous time-dependent transmission rates give good agreement with data in the absence of secular trends in population demography or transmission. The prime example is afforded by the dynamics of measles in industrialized countries in the pre-vaccine era. Accurate description of the transient dynamics following the introduction of routine vaccination has proved more challenging, however. This is true even in the case of measles which has a well-understood natural history and an effective vaccine that confers long-lasting protection against infection. Here, to shed light on the causes of this problem, we demonstrate that, while the dynamics of homogeneous and age-structured models can be qualitatively similar in the absence of vaccination, they diverge subsequent to vaccine roll-out. In particular, we show that immunization induces changes in transmission rates, which in turn reshapes the age distribution of infection prevalence, which effectively modulates the amplitude of seasonality in such systems. To examine this phenomenon empirically, we fit transmission models to measles notification data from London that span the introduction of the vaccine. We find that a simple age-structured model provides a much better fit to the data than does a homogeneous model, especially in the transition period from the pre-vaccine to the vaccine era. Thus, we propose that age structure and heterogeneities in contact rates are critical features needed to accurately capture transient dynamics in the presence of secular trends.

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