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In this paper we investigate the population dynamics of a species with age structure in the case where the diffusion and death rates of the matured population are both age-dependent. We develop a new application of the age-structure technique in terms of an integral equation. For unbounded spatial domains, we study the existence of travelling waves, whilst in bounded domains, we investigate the existence of positive steady-state solutions and their stability. [ABSTRACT FROM PUBLISHER]

The article focuses on the demographic trends and transitions, which lead to population ageing in Malta. It states that the population in the republic is rapidly ageing because it has entered its second demographic transition. It mentions that the life expectancy in Malta is at 60 years of age. It notes that the introduction of family-friendly measure could create opportunities for transition in the lives of older people.

The paper explores how demographic change is confronting challenges in social, economic and welfare contexts in fran. Iran is currently confronted by great challenges as its demographic structure is changing. While life expectancy is increasing nationwide, citizens' ,or rather, seniors' expectations are changing too, in various ways. Other developing countries are experiencing similar problems. However, senior citizens need new policies, more welfare and medical assistance, lower poverty levels, independent lives and so on. The paper examines 452 families with ageing people in Tehran City - how they need assistance and care. The effects of demographic change would ultimately be on ageing people. [ABSTRACT FROM AUTHOR]

We consider a Leslie-type matrix approach to an SIR epidemic in discrete time. We give examples of the population of susceptibles, infectives, and removals for different birth rates and two different infection rates. Finally, when the infection rate depends on the number of infectives, we derive conditions for a steady state. [ABSTRACT FROM AUTHOR]

In this paper we deal with a nonlinear two-timescale discrete population model that couples age-structured demography with individual competition for resources. Individuals are divided into juvenile and adult classes, and demography is described by means of a density-dependent Leslie matrix. Adults compete to access resources; every time two adults meet, they choose either being aggressive (hawk) or non-aggressive (dove) to get the best pay-off. Individual encounters occur much more frequently than demographic events, what yields that the model takes the form of a two-timescale system. Approximate aggregation methods allow us to reduce the system while preserving at the same time crucial asymptotic information for the whole population. In this way, we are able to describe the total population size as function of individual aggressiveness level and environmental richness. Model analysis shows a general trend with species that look for richer environment having smaller proportions of hawk individuals with larger costs. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the entire solutions for a monostable age-structured population model in a 2D lattice strip, i.e., solutions defined in the whole space and for all time . In the quasi-monotone case, we first establish the existence and asymptotic behavior of solutions of the equation without () variable. Combining traveling wave fronts with different speeds and a solution without variable, the existence and qualitative features of entire solutions are then proved. In the non-quasi-monotone case, we introduce two auxiliary quasi-monotone equations and establish a comparison argument for the three systems. Some new entire solutions are then constructed by using the comparison argument, the traveling wave fronts and a solution without variable of the auxiliary equations. [Copyright &y& Elsevier]

How populations respond to climate change depends on the interplay between life history, resource availability, and the intensity of the change. Roe deer are income breeders, with high levels of allocation to reproduction, and are hence strongly constrained by the availability of high quality resources during spring. We investigated how recent climate change has influenced demographic processes in two populations of this widespread species. Spring began increasingly earlier over the study, allowing us to identify 2 periods with contrasting onset of spring. Both populations grew more slowly when spring was early. As expected for a long-lived and iteroparous species, adult survival had the greatest potential impact on population growth. Using perturbation analyses, we measured the relative contribution of the demographic parameters to observed variation in population growth, both within and between periods and populations. Within periods, the identity of the critical parameter depended on the variance in growth rate, but variation in recruitment was the main driver of observed demographic change between periods of contrasting spring earliness. Our results indicate that roe deer in forest habitats cannot currently cope with increasingly early springs. We hypothesise that they should shift their distribution to richer, more heterogeneous landscapes to offset energetic requirements during the critical rearing stage. [ABSTRACT FROM AUTHOR]

In this article we consider a juvenile-adult population model of amphibians in which juveniles are structured by age and adults are structured by size. We develop a second-order explicit high-resolution scheme to approximate the solution of the model. Convergence of the finite difference approximation to the unique weak solution with bounded total variation is proved. Numerical examples demonstrate the high-resolution property and the achievement of the designed accuracy for the scheme. The scheme is then applied to understand the dynamics of an urban amphibian population. [ABSTRACT FROM AUTHOR]

This paper presents a bioeconomic analysis of a red deer population within a Norwegian institutional context. This population is managed by a well-defined manager, typically consisting of many landowners operating in a cooperative manner, with the goal of maximizing the present-value hunting related income while taking browsing and grazing damages into account. The red deer population is structured in five categories of animals (calves, female and male yearlings, adult females and adult males). It is shown that differences in the per-animal meat values and survival rates (‘biological discounted’ values) are instrumental in determining the optimal harvest composition. Fertility plays no direct role. It is argued that this is a general result working in stage-structured models with harvest values. In the numerical illustration it is shown that the optimal harvest pattern stays quite stable under various parameter changes. It is revealed which parameters and harvest restrictions that is most important. We also show that the current harvest pattern involves too much yearling harvest compared with the economically efficient level. [Copyright &y& Elsevier]

Climatic factors, especially temperature and precipitations, greatly affect the dynamics of the hare number and population. Climatic factors directly affect the physiological and reproductive processes of both individuals and entire populations, or indirectly, through the availability of food, competition with other species, predators and other. The age structure of the hare population at the end of the period of reproduction is an important indicator of the population growth that is used for planning the level of explotation of the hare population (hunting). The rational use of the hare's population is one of the most important protection procedures and it should be well monitored and controlled by the hunting professionals. We used the average monthly temperature and the sum of monthly precipitations in the hare reproductive period (March-September) during ten years (2000 - 2009), together with the percent of young in the hare population, on the territory of Bačka, for multiple regression (stepwise) analysis. Results of the regression analysis show an association between the percentage of young hares and the influence of climatic factors. The average temperature and sum of precipitation in June, are the strongest predictor of the percent of young in the hare's population in Bačka. According to the coefficient of determination (R²=0.50) climatic parameters account for 50% of variance in the percentage of young hares in Bačka. The regression correlation coefficient of all factors was R=0.70, which is on the border line between medium and high correlation. [ABSTRACT FROM AUTHOR]

We use two types of age-structured population models to study how the distribution of toxins among segments of the twigs of woody plants, by affecting the feeding behavior of snowshoe hares, might affect snowshoe hare population dynamics. In the first model a twig has N discrete toxin containing segments joined end to end. Depending on species these segments vary tremendously in length. Preferred browse species such as the deciduous shrub birch Betula glandulosa have a small number of long twig segments and defend only the youngest segments near the twig tip. Hares counter this defense by biting off a twig at an older segment, eating only the older segments and rejecting younger, more toxic attached segments. Twigs of less preferred foods, such as the juvenile developmental stages of the evergreen spruces Picea glauca and P. mariana, have an arrangement of toxin producing resin ducts along their twig's long axis that is best modeled using a large number of short segments. We also propose a continuous model as an alternative to the N-segment model in the case when N is large. For each model we determine completely the conditions for linear stability of the hare-extinct equilibrium. An important implication is that the most effective defense against hares is to defend twig segments of all diameters that a hare can eat, as does spruce. Numerical simulations of both models confirm and enhance our understanding of the dynamics of the interaction between woody plants and snowshoe hares. [ABSTRACT FROM AUTHOR]

Optimal management in a multi-cohort Beverton-Holt model with any number of age classes and imperfect selectivity is equivalent to finding the optimal fish lifespan by chosen fallow cycles. Optimal policy differs in two main ways from the optimal lifespan rule with perfect selectivity. First, weight gain is valued in terms of the whole population structure. Second, the cost of waiting is the interest rate adjusted for the increase in the pulse length. This point is especially relevant for assessing the role of selectivity. Imperfect selectivity reduces the optimal lifespan and the optimal pulse length. We illustrate our theoretical findings with a numerical example. Results obtained using global numerical methods select the optimal pulse length predicted by the optimal lifespan rule. [ABSTRACT FROM AUTHOR]

Biologists have criticized traditional biomass models in fishery economics for being oversimplified. Biological stock assessment models are more sophisticated with regard to biological content, but rarely account for economic objectives. This study includes a full age-structured population model for studying schooling fisheries and extends the delayed difference approach used in earlier studies. We take the total harvest as the choice variable, resulting in a simple analytical structure. The model produces optimal steady states that may be higher or lower compared to the delayed-difference formulation. The model is applied to the Baltic sprat fishery. Both ecological and harvesting cost data support specifying Baltic sprat as a schooling fishery. Given nonlinear harvesting costs, the optimal solution is a path toward a steady state with smooth annual harvest and population age structure. Sensitivity analysis shows that the optimal solution is highly dependent on the population level of the sprat's main predator Baltic cod. A linear cost function and an interest rate below 9 % imply pulse fishing instead of smooth continuous harvesting. Given nonlinear harvesting cost, the optimal steady state yield is rather insensitive to changes in the interest rate. However, under a high cod scenario, interest rates of 10 % or higher implies that no optimal steady state exists. [ABSTRACT FROM AUTHOR]

The migration is energy-demanding and is expected to greatly affect the distribution of individuals over the species range and condition the choice of migratory routes. We investigated the wintering distributions and migratory flyways use of geographically contiguous populations of Lesser Black-backed Gulls (Larus fuscus) and difference in population winter age structure between migratory flyways. Recoveries of metal ringed pulli from Denmark, Sweden, and Finland were used. The results showed that contiguous populations can have distinct wintering distribution patterns and migratory flyways. More importantly, we found that depending on the place of origin, the population winter distribution may or may not show a latitudinal cline in the age structure. The population migrating via the eastern Atlantic flyway (western flyway) showed a winter age-related latitudinal cline, with adults staying at more northern latitudes than immatures. In contrast, no such pattern was found in the population migrating along the Mediterranean/Black sea flyway (eastern flyway). Interestingly, immatures within the eastern population showed a more dispersed pattern of migratory bearings. Overall, our results enhance the importance of the migration flyway in shaping the age structure of populations in the winter quarters and how it may influence the effect of other factors like sexual maturation. [ABSTRACT FROM AUTHOR]

Abstract: Understanding the processes generating fluctuations of natural populations lies at the very heart of academic ecology. It is also very important for applications such as fisheries management and pest control. We are interested in the effect of harvesting on population fluctuations and for that purpose we develop and analyze an age-structured model where recruitment is a stochastic process and the adult segment of the population is harvested. When a constant annual harvest is taken the coefficient of variation of the adult population increases for most parameter values due to the age truncation effect, i.e. an increased variability in a juvenescent population due to the removal of older individuals. However, if a constant proportion of the adults is harvested the age truncation effect is sometimes counteracted by a stabilizing dynamic effect of harvesting. Depending on parameter values mirroring different life histories, proportional harvest can either increase or decrease the relative fluctuations of an exploited population. When there is a demographic Allee effect the ratio of juveniles to adults may actually decrease with harvesting. We conclude that, depending on life history and harvest strategy, harvesting can either reinforce or dampen population fluctuations due to the relative importance of stabilizing dynamic effects and the age truncation effect. The strength of the latter is highly dependent on the fished population’s endogenous, age-structured dynamics. More specifically, we predict that populations with strong and positively autocorrelated dynamics will show stronger age truncation effect, a testable prediction that offers a simple rule-of-thumb assessment of a population’s vulnerability to exploitation. [Copyright &y& Elsevier]

In this article, we study a predator–prey interaction in a homogeneously complex habitat where predator takes a fixed time to develop from immature to its mature stage. The age-structure of the predator and its interaction with the prey is framed in a system of delay differential equations. The objective is to study the role of habitat complexity and the maturation delay of the predator on the overall dynamics of the model system. Different interesting dynamical behaviours can be obtained by regulating two key parameters, namely the degree of habitat complexity and the maturation delay. It is observed that the system becomes unstable from its stable condition when the maturation delay crosses some critical value. The periodic solutions bifurcated from the interior equilibrium is found to be supercritical and stable. Synchronization of population fluctuations is, however, possible by increasing the strength of habitat complexity. The predator population goes to extinction and the prey population reaches to its maximum, irrespective of the length of maturation delay, when the habitat complexity crosses some upper critical value. The qualitative dynamical behaviours of the model system are verified with the data of Paramecium aurelia (prey) and Didinium nasutum (predator) interaction. [ABSTRACT FROM PUBLISHER]

Abstract: The optimal treatment strategies with an age-structured model of HIV infection are investigated. The age-structured model allows for variations in the virion production rate and the death rate of infected T cells as a function of age, which is the length of time since infection. The optimal therapy protocol is derived by formulating and analyzing an optimal control problem and the existence of solutions to the optimal control problem is established. The optimal treatment strategy is obtained by solving the corresponding optimality system numerically. It is demonstrated by numerical simulations that the dynamic treatment strategy delays the time to reach the peak viral load and reduces the viral load. Moreover, we propose that optimal therapy protocols should be changed according to different viral production rates and death rates of infected T cells. [Copyright &y& Elsevier]

Many countries are facing a problem when the age-structure of the society is changing. The numbers of senior citizen are rising rapidly, and caretaking personnel numbers cannot match the problems and needs of these citizens. Using smart, ubiquitous technologies can offer ways in coping with the need of more nursing staff and the rising costs of taking care of senior citizens for the society. Helping senior citizens with a novel, easy to use interface that guides and helps, could improve their quality of living and make them participate more in daily activities. This paper presents a projection-based display system for elderly people with memory impairments and the proposed user interface for the system. The user's process recognition based on a sensor network is also described. Elderly people wearing the system can interact the projected user interface by tapping physical surfaces (such as walls, tables, or doors) using them as a natural, haptic feedback input surface. [ABSTRACT FROM AUTHOR]

In this paper, a numerical model is developed for analyzing the role of species life history and age structure for the optimal management of a commercial resident species that is exposed to an invasive species. It is shown that reproduction and mortality characteristics of both species ands age structure of the invader at the time of invasion are important for the costs of invasions when the invader and resident species compete for scarce resources. Commercially harvested species with low juvenile survival and high reproduction are found to be economically more robust against invasions. Species with these life-history traits are also the most damaging as invaders. Properties of the harvesting cost function and the discount rate are shown to be of importance for the development of the invader population over time. Hence, it is possible to identify specific combinations of life-history characteristics and economic conditions under which invasions cause particularly large economic damage. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this paper is to complement the literature concerned with the captive cohort method for estimating age structure including (1) graphic techniques to visualize and thus better understand the underlying life table identity in which the age structure of a stationary population equals the time-to-death distribution of the individuals within it; (2) re-derive the basic model for estimating age structure in non-stationary population in demographic rather than statistical notation; and (3) describe a simplified method for estimating changes in the mean age of a wild population. [Copyright &y& Elsevier]

In this paper we study the effects that woody plant chemical defenses may have on interactions between boreal hares that in winter feed almost entirely on twigs. We focus particularly on the fact that toxin concentration often varies with the age of twig segments. The model incorporates the fact that the woody internodes of the youngest segments of the twigs of the deciduous angiosperm species that these hares prefer to eat are more defended by toxins than the woody internodes of the older segments that subtend and support the younger segments. Thus, the per capita daily intake of the biomass of the older segments of twigs by hares is much higher than their intake of the biomass of the younger segments of twigs. This age-dependent toxicity of twig segments is modeled using age-structured model equations which are reduced to a system of delay differential equations involving multiple delays in the woody plant-hare dynamics. A novel aspect of the modeling was that it had to account for mortality of non-consumed younger twig segment biomass when older twig biomass was bitten off and consumed. Basic mathematical properties of the model are established together with upper and lower bounds on the solutions. Necessary and sufficient conditions are found for the linear stability of the equilibrium in which the hare is extinct, and sufficient conditions are found for the global stability of this equilibrium. Numerical simulations confirmed the analytical results and demonstrated the existence of limit cycles over ranges of parameters reasonable for hares browsing on woody vegetation in boreal ecosystems. This showed that age dependence in plant chemical defenses has the capacity to cause hare-plant population cycles, a new result. [ABSTRACT FROM AUTHOR]

Ecology Letters (2012) 15: 658-665 Abstract Fluctuations of fish populations abundances are shaped by the interplay between population dynamics and the stochastic forcing of the environment. Age-structured populations behave as a filter of the environment. This filter is characterised by the species-specific life cycle and life-history traits. An increased mortality of mature individuals alters these characteristics and may therefore induce changes in the variability of populations. The response of a generic age-structured model was analysed to investigate the expected changes in the fluctuations of fish populations in response to decreased adult survival. These expectations were then tested on an extensive dataset. In accordance with theory, the analyses revealed that decreased adult survival and mean age of spawners were linked to an increase in the relative importance of short-term fluctuations. It suggests that intensive exploitation can lead to a change in the variability of fish populations, an issue of central interest from both conservation and management perspectives. [ABSTRACT FROM AUTHOR]

Abstract: In the demand for a decision support tool to guide farmers wanting to control Salmonella Dublin (S. Dublin) in Danish dairy herds, we developed an age-structured stochastic, mechanistic and dynamic simulation model of S. Dublin in dairy herds, which incorporated six age groups (neonatal, preweaned calves, weaned calves, growing heifers, breeding heifers and cows) and five infection states (susceptible, acutely infected, carrier, super shedder and resistant). The model simulated population and infection dynamics over a period of 10 years in weekly time steps as: 1) population sizes of each of the six age-groups; 2) S. Dublin incidence and number of animals in each infection state; and 3) S. Dublin related morbidity and mortality in the acutely infected animals. The effects of introducing one infectious heifer on the risk of spread of S. Dublin within the herd and on the duration of infection were estimated through 1000 simulation iterations for 48 scenarios. The scenarios covered all combinations of three herd sizes (70, 200 and 400 cows), four hygiene levels indicating infectious contact parameters, and four herd susceptibility levels indicating different susceptibility parameters for the individual animals in each of the six age groups in the herd. The hygiene level was highly influential on the probability that the infection spread within the herd, duration of infection and epidemic size. The herd susceptibility level was also influential, but not likely to provide sufficient prevention and control of infection on its own. Herd size did not affect the probability of infection spread upon exposure, but the larger the herd the more important were management and housing practices that improve hygiene and reduce susceptibility to shorten durations of infection in the herd and to increase the probability of extinction. In general, disease and mortality patterns followed epidemic waves in the herds. However, an interesting pattern was seen for acute infections and abortions in adult cattle after the first 2 years of infection in herds with poor hygiene and high susceptibility. Repeated infections in young stock lead to a high proportion of resistant adult cattle, which lead to a dampening effect on acute infections in adults and associated abortions. Sensitivity analyses of 24 alternative scenarios showed that a super shedder state was not essential to mimic the infection dynamics and persistence patterns known from field studies, but a persistent carrier state was required in the model to mimic real life S. Dublin infections. [Copyright &y& Elsevier]

An optimal harvesting problem is analyzed in the Lotka-McKendrick model of age-structured populations. Depending on the imposed constraints, this problem possesses bang-bang or impulse regimes, which have meaningful interpretations and relevant policy implications. A steady state analysis of the model produces closed-form solutions for the optimal sustainable harvesting in a new and an existing population. [ABSTRACT FROM AUTHOR]

. Previous mathematical modeling of the population dynamics of Georges Bank Atlantic cod fishery employed discrete-time models without age-structure. To make use of a much wider variety of data on fisheries and fish stocks than was possible with an unstructured model, we introduce a juvenile-adult age-structured production exploited fishery model with a very general recruitment function. We use the age-structured model to study the interaction between fish exploitation levels and recruitment dynamics. As case studies, we use our model results and historical fish population data from Georges Bank to investigate the impact of recent harvesting levels on the sustainability of cod fishery. We show that a constant harvesting policy with the same harvesting rate of 2007 would lead to the recovery and sustainability of Georges Bank cod fishery. [ABSTRACT FROM AUTHOR]

It has long been recognized that age-structure data contain useful information for assessing the status and dynamics of wildlife populations. For example, age-specific survival rates can be estimated with just a single sample from the age distribution of a stable, stationary population. For a population that is not stable, age-specific survival rates can be estimated using techniques such as inverse methods that combine time series of age-structure data with other demographic data. However, estimation of survival rates using these methods typically requires numerical optimization, a relatively long time series of data, and smoothing or other constraints to provide useful estimates. We developed general models for possibly unstable populations that combine time series of age-structure data with other demographic data to provide explicit maximum likelihood estimators of age-specific survival rates with as few as two years of data. As an example, we applied these methods to estimate survival rates for female bison (Bison bison) in Yellowstone National Park, USA. This approach provides a simple tool for monitoring survival rates based on age-structure data. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a numerical method for solving the nonlinear age-structured population models is presented which is based on Bernstein polynomials approximation. Operational matrices of integration, differentiation, dual and product are introduced and are utilized to reduce the age-structured population problem to the solution of algebraic equations. The method in general is easy to implement, and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique. [Copyright &y& Elsevier]

Abstract: Age plays an important role in the transmission of some infectious diseases. A discrete SEIT model with age-structure is formulated and studied. The basic reproduction number, , of the model is defined. It is proved that is a threshold to determine the disease extinction or persistence. The disease-free equilibrium is globally stable (unstable) if (if ). There exists an endemic equilibrium, and the system is uniformly persistent if . The numerical simulation demonstrates that the endemic equilibrium may be globally asymptotically stable. The model is applied to describe tuberculosis (TB) transmission in China. The total number of the population, the incidence rate, the prevalent rate and its age structure match the statistical data well. [Copyright &y& Elsevier]

A new model for the mosquito life-cycle is introduced. The model is separated into age classes (egg, larva, pupa, adult). The temperature dependency is modelled via boundary functions which include increasing and decreasing functions as necessary. The model and a numerical discretization are given and numerical results are provided to establish the validity of the model. The long-term objective is to use this model for the basis of a mosquito-borne epidemic model. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The recent rapid growth of the woodpigeon population in the British Isles is a cause for concern for environmental managers. It is unclear what has driven their increase in abundance. Using a mathematical model, we explored two possible mechanisms, reduced intraspecific competition for food and increased reproductive success. We developed an age-structured hybrid model consisting of a system of ordinary differential equations that describes density-dependent mortality and a discrete component, which represents the birth-pulse. We investigated equilibrium population dynamics using our model. The two hypotheses predict contrasting population age profiles at equilibrium. We adapted the model to examine the impacts of control measures. We showed that an annual shooting season that follows the period of density-dependent mortality is the most effective control strategy because it simultaneously removes adult and juvenile woodpigeons. The model is a first step towards understanding the processes that influence the dynamics of woodpigeon populations. [Copyright &y& Elsevier]

We present a formulation of branching and aging processes that allows age distributions along lineages to be studied within populations, and provides a new interpretation of classical results in the theory of aging. We establish a variational principle for the stable age distribution along lineages. Using this optimal lineage principle, we show that the response of a population's growth rate to age-specific changes in mortality and fecundity-a key quantity that was first calculated by Hamilton-is given directly by the age distribution along lineages. We apply our method also to the Bellman-Harris process, in which both mother and progeny are rejuvenated at each reproduction event, and show that this process can be mapped to the classic aging process such that age statistics in the population and along lineages are identical. Our approach provides both a theoretical framework for understanding the statistics of aging in a population, and a new method of analytical calculations for populations with age structure. We discuss generalizations for populations with multiple phenotypes, and more complex aging processes. We also provide a first experimental test of our theory applied to bacterial populations growing in a microfluidics device. [ABSTRACT FROM AUTHOR]

Abstract: A superprocess limit for an interacting birth–death particle system modeling a population with trait and physical age-structures is established. Traits of newborn offspring are inherited from the parents except when mutations occur, while ages are set to zero. Because of interactions between individuals, standard approaches based on the Laplace transform do not hold. We use a martingale problem approach and a separation of the slow (trait) and fast (age) scales. While the trait marginals converge in a pathwise sense to a superprocess, the age distributions, on another time scale, average to equilibria that depend on traits. The convergence of the whole process depending on trait and age, only holds for finite-dimensional time-marginals. We apply our results to the study of examples illustrating different cases of trade-off between competition and senescence. [Copyright &y& Elsevier]

Abstract: Some systems of parabolic equations with nonlocal initial conditions are studied. The systems arise when considering steady-state solutions to diffusive age-structured cooperative or competing species. Local and global bifurcation techniques are employed to derive a detailed description of the structure of positive coexistence solutions. [Copyright &y& Elsevier]

Duality in the optimal harvesting for a nonlinear age-spatial structured population dynamic model is studied in the framework of optimal control problem. In this paper the duality theory that displays the conjugacy of the primal problem is established and an application is given. Duality theory plays an important role in both optimization theory and methodology and the results may be applied to a realistic biological system on the point of optimal harvesting. [ABSTRACT FROM AUTHOR]

Age-structured population dynamics models play an important role in fisheries assessments. Such models have traditionally been estimated using crude likelihood approximations or more recently using Bayesian techniques. We contribute to this literature with three main messages. Firstly, we demonstrate how to estimate such models efficiently by simulated maximum likelihood using Laplace importance samplers for the likelihood function. Secondly, we demonstrate how simulated maximum likelihood estimates may be validated using different importance samplers known to approach the exact likelihood function in different regions of the parameter space. Thirdly, we show that our method works in practice by Monte Carlo simulations using parameter values as estimated from data on the Northeast Arctic cod () stock. The simulations suggest that we are able to recover the unknown true maximum likelihood estimates using moderate importance sample sizes and show that we are able to adequately recover the true parameter values. [ABSTRACT FROM AUTHOR]

We analyze weak fluctuating selection on a quantitative character in an age-structured population not subject to density regulation. We assume that early in the first year of life before selection, during a critical state of development, environments exert a plastic effect on the phenotype, which remains constant throughout the life of an individual. Age-specific selection on the character affects survival and fecundity, which have intermediate optima subject to temporal environmental fluctuations with directional selection in some age classes as special cases. Weighting individuals by their reproductive value, as suggested by Fisher, we show that the expected response per year in the weighted mean character has the same form as for models with no age structure. Environmental stochasticity generates stochastic fluctuations in the weighted mean character following a first-order autoregressive model with a temporally autocorrelated noise term and stationary variance depending on the amount of phenotypic plasticity. The parameters of the process are simple weighted averages of parameters used to describe age-specific survival and fecundity. The 'age-specific selective weights' are related to the stable distribution of reproductive values among age classes. This allows partitioning of the change in the weighted mean character into age-specific components. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the traveling waves in a single species population model which is derived by considering the nonlocal dispersal and age-structure. If the birth function is monotone, then the existence of traveling wavefront is reduced to the existence of a pair of super and subsolutions without the requirement of smoothness. It is proved that the traveling wavefront is strictly increasing and unique up to a translation. The asymptotic behavior of traveling wavefronts is also obtained. If the birth function is not monotone, the existence of traveling wave solution is affirmed by introducing two auxiliary nonlocal dispersal equations with quasi-monotonicity. [Copyright &y& Elsevier]

This paper examines the possible ecological and economic effects of sea lice from salmon farms on wild salmon populations and fisheries. A bioeconomic model is developed incorporating an age-structured population dynamics model of wild pink and chum salmon with mortality caused by farm-derived sea lice. Our model incorporates capture fisheries under two management policy scenarios. Results suggest that the ecological and economic effects are minor when the sea lice induced mortality rate is below 20%, while they can be severe if the mortality is greater than 30%. Sea lice have greater ecological and economic impacts on pink salmon than on chum salmon. The impact of farm lice epizootics on wild salmon is greater under a fixed exploitation rate than under a target escapement policy. As a result, a precautionary principle should be adopted, and appropriate management schemes and policy strategies should be developed to minimize these effects. [Copyright &y& Elsevier]

Abstract: The purpose of the present study was to investigate the prevalence of types of child maltreatment and co-occurring risks in an entire county population of children in public education and to examine the unique relations of the child maltreatment types and timing on children''s early academic success while accounting for the children''s multiple-risk context. A cohort of 11,835 second grade students who were born in the county and attended the public school district served as participants. Information on first reported experiences of substantiated physical abuse, neglect, unsubstantiated child maltreatment reports, health, maternal, and social risks, and academic and behavioral outcomes was obtained and linked through a county-wide integrated data system. Results indicated that after controlling for demographics and the set of other risks, substantiated child neglect and unsubstantiated reports were associated with poorer outcomes than physical abuse. Also, first substantiated child maltreatment and unsubstantiated reports prior to kindergarten were related to a more comprehensive set of poor outcomes than post-kindergarten first reports. The differential patterns that emerged for the association between age of first reported maltreatment by type and educational outcomes were discussed with implications for future research and policy. [Copyright &y& Elsevier]

1. Spatially defined restrictions on fishing activity are considered to be important for biodiversity conservation in marine ecosystems. However, it is uncertain whether such restrictions also benefit wider populations of exploited fish species, in terms of a reduced risk of overexploitation. Since fishing leads to contraction of the age structure, one potential benefit of protection is recovery of the highly fecund older age classes, potentially leading to higher recruitment levels. This investigation explores the benefits of protecting older fish and how spatial management can be used to adjust the age structure and improve the sustainability of the catch (productivity). 2. We use a non-spatial equilibrium model accounting for biomass growth, mortality and recruitment to describe the relationship between mean age of the population and productivity for the South African deepwater hake Merluccius paradoxus trawl fishery. Our results indicate that management measures capable of increasing the mean age at which fish are caught may be of benefit. Furthermore, although the contribution of older fish to recruitment is important, the biomass growth of individuals before they are caught is responsible for the most significant productivity benefit of an older population age structure. 3. Older M. paradoxus are found in deeper water, so that distinct age classes can be defined spatially using empirical data. We describe a non-equilibirum model to examine spatial management alternatives for adjusting the age structure by targetting these different age classes. We investigate the benefits of protecting either older or younger fish, with results suggesting that it is more important to limit fishing on the younger (shallow) sections of the population if productivity benefits are to be realized. 4. Synthesis and applications. We conclude that the age structure of a population can be modified through spatially managed targeting of different age classes, and that, contrary to previous assumptions for M. paradoxus, protecting older fish has a negative consequence for the age structure of the resource. Instead, younger sections of the population should be protected through limitations on fishing in shallower waters, if older age classes are to recover. [ABSTRACT FROM AUTHOR]

The world is currently in the midst of the greatest demographic upheaval in human history. Dramatic reductions in mortality, followed (but with a lag) by equally marked reductions in fertility, resulted in a doubling of world population between 1960 and 2000. A further increase of 2 to 4.5 billion is projected for the current half-century, with the increase concentrated in the world's least developed countries. Despite alarmist predictions, historical increases in population have not been economically catastrophic. Moreover, changes in population age structure have opened the door to increased prosperity. Demographic changes have had and will continue to have profound repercussions for human well-being and progress, with some possibilities for mediating those repercussions through policy intervention. [ABSTRACT FROM AUTHOR]

The effects of the following modes of density-dependent control of population growth: density-dependent birth rate, adult survival rate, juvenile survival rate are compared based on the mathematical model of population dynamics. It is shown that the most efficient mechanisms limiting population size are decreasing with the growth of the adult population birth rate and/or the decreasing survival rate of the offspring with the increase in their number. However, these same mechanisms are responsible for oscillations of the population size and its chaotic change. The density-dependence of the adult survival rate is not efficient in constraining the population growth, but it can substantially limit the magnitude of oscillations of the population size. [Copyright &y& Elsevier]

Major modifications to river systems and their associated floodplains throughout the world have detrimental consequences for biodiversity. A reduction in the frequency of large-scale flooding events is one change that could have significant negative effects. In the Murray-Darling Basin of Australia many species of waterbirds breed in large colonies on inland floodplain systems when appropriate flooding occurs. Across the Murray-Darling Basin populations of many of these species are now at very low levels and breeding events occur much more infrequently than they did historically. I used an age-structured population model of a generic egret to assess how frequently breeding must occur to maintain populations. Using simulation I explored how sensitive results were to demographic parameter values. The results indicated that: (1) most egrets must breed every one to two years for populations to persist; and (2) the results are sensitive to adult survival, suggesting that management may also need to consider habitat availability between breeding events to ensure high adult survival. The results highlight a need to determine over what spatial scale egret populations function so that a sufficient frequency of breeding events is provided at the appropriate scale. Results were less sensitive to juvenile survival, but juvenile survival rates that average between 25 and 35% per year are probably required for persistence. Hence it is important that future research also determines whether the recent practice of managing breeding events only until fledging is achieved does not have a detrimental effect on juvenile survival. Maintaining a high frequency of flooding events that lead to successful breeding will be necessary for any species with similar life-histories. [ABSTRACT FROM AUTHOR]

The lionfish, Pterois volitans (Linnaeus) and Pterois miles (Bennett), invasion of the Western Atlantic Ocean, Caribbean Sea and Gulf of Mexico has the potential to alter aquatic communities and represents a legitimate ecological concern. Several local removal programs have been initiated to control this invasion, but it is not known whether removal efforts can substantially reduce lionfish numbers to ameliorate these concerns. We used an age-structured population model to evaluate the potential efficacy of lionfish removal programs and identified critical data gaps for future studies. We used high and low estimates for uncertain parameters including: length at 50% vulnerability to harvest (Lvul), instantaneous natural mortality (M), and the Goodyear compensation ratio (CR). The model predicted an annual exploitation rate between 35 and 65% would be required to cause recruitment overfishing on lionfish populations for our baseline parameter estimates for M and CR (0.5 and 15). Lionfish quickly recovered from high removal rates, reaching 90% of unfished biomass six years after a 50-year simulated removal program. Quantifying lionfish natural mortality and the size-selective vulnerability to harvest are the most important knowledge gaps for future research. We suggest complete eradication of lionfish through fishing is unlikely, and substantial reduction of adult abundance will require a long-term commitment and may be feasible only in small, localized areas where annual exploitation can be intense over multiple consecutive years. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we analyze two new second-order characteristic schemes in time and age for an age-structured population model with nonlinear diffusion and reaction. By using the characteristic difference to approximate the transport term and the average along the characteristics to treat the nonlinear spatial diffusion and reaction terms, an implicit second-order characteristic scheme is proposed. To compute the nonlinear approximation system, an explicit second-order characteristic scheme in time and age is further proposed by using the extrapolation technique. The global existence and uniqueness of the solution of the nonlinear approximation scheme are established by using the theory of variation methods, Schauder’s fixed point theorem, and the technique of prior estimates. The optimal error estimates of second order in time and age are strictly proved for both the implicit and the explicit characteristic schemes. Numerical examples are given to illustrate the performance of the methods. [Copyright &y& Elsevier]

Abstract: Seasonal variation in temperature is known to drive annual patterns of tick activity and can influence the dynamics of tick-borne diseases. An age-structured model of the dynamics of Ixodes ricinus populations was developed to explore how changes in average temperature and different levels of temperature variability affect seasonal patterns of tick activity and the transmission of tick-borne diseases. The model produced seasonal patterns of tick emergence that are consistent with those observed throughout Great Britain. Varying average temperature across a continuous spectrum produced a systematic pattern in the times of peak emergence of questing ticks which depends on cumulative temperature over the year. Examination of the effects of between-year stochastic temperature variation on this pattern indicated that peak emergence times are more strongly affected by temperature stochasticity at certain levels of average temperature. Finally the model was extended to give a simple representation of the dynamics of a tick-borne disease. A threshold level of annual cumulative temperature was identified at which disease persistence is sensitive to stochastic temperature variation. In conclusion, the effect of changing patterns of temperature variation on the dynamics of I. ricinus ticks and the diseases they transmit may depend on the cumulative temperature over the year and will therefore vary across different locations. The results also indicate that diapause mechanisms have an important influence on seasonal patterns of tick activity and require further study. [Copyright &y& Elsevier]