A model of age-dependent population dynamics providing simple criteria for growth or extinction.

The Gurtin-MacCamy model for age-dependent population dynamics is reduced to a single ordinary differential equation. (This is done by assuming a specific form of the mortality function, and by assuming fertility to be age-dependent only.) The model is then applied to a population of greater horseshoe bats.     

A dynamic population model for tsetse (Diptera: Glossinidae) area-wide integrated pest management

A spatial model of tsetse (Glossina palpalis ssp. and G. pallidipes) life cycle was created in FORTRAN, and four control measures [aerial spraying of non-residual insecticides, traps and targets, insecticide-treated livestock (ITL) and the sterile insect technique] were programmed into the model to assess how much of each of various combinations of these control tactics would be necessary to eradicate the population. The model included density-independent and -dependent mortality rates, temperature-dependent mortality, an age-dependent mortality, two mechanisms of dispersal and a component of aggregation. Sensitivity analyses assessed the importance of various life history features and indicated that female fertility and factors affecting survivorship had the greatest impact on the equilibrium of the female population. The female equilibrium was likewise reduced when dispersal and aggregation were acting together. Sensitivity analyses showed that basic female survivorship, age-dependent and temperature-dependent survivorship of adults, teneral-specific survivorship, daily female fertility, and mean temperature had the greatest effect on the four applied control measures. Time to eradication was reduced by initial knockdown of the population and due to the synergism of certain combinations of methods [e.g., traps-targets and sterile insect technique (SIT); ITL and SIT]. Competitive ability of the sterile males was an important parameter when sterile to wild male overflooding ratios were small. An aggregated wild population reduced the efficiency of the SIT, but increased it with increased dispersal. The model can be used interactively to facilitate decision making during the planning and implementation of operational area-wide integrated pest management programs against tsetse.     

Viable controls in age-dependent population dynamics

The classical age-dependent population model is considered, where the mortality depends on total population and the fertility is age dependent. Conditions are determined under which such a system may be steered to a specific population level and held there.     

Separable models in age-dependent population dynamics

A class of population models is considered in which the parameters such as fecundity, mortality and interaction coefficients are assumed to be age-dependent. Conditions for the existence, stability and global attractivity of steady-state and periodic solutions are derived. The dependence of these solutions on the maturation periods is analyzed. These results are applied to specific single and multiple population models. It is shown that periodic solutions cannot occur in a general class of single population age-dependent models. Conditions are derived that determine whether increasing the maturation period has a stabilizing effect. In specific cases, it is shown that any number of switches in stability can occur as the maturation period is increased. An example is given of predator-prey model where each one of these stability switches corresponds to a stable steady state losing its stability via a Hopf bifurcation to a periodic solution and regaining its stability upon further increase of the maturation period.     

Age-specific demography in Plantago: uncovering age-dependent mortality in a natural population

Accurate measures of age-dependent mortality are critical to life-history analysis and measures of fitness, yet these measures are difficult to obtain in natural populations. Age-dependent mortality patterns can be obscured not only by seasonal variation in environmental conditions and reproduction but also by changes in the heterogeneity among individuals in the population over time due to selection. This study of Plantago lanceolata uses longitudinal data from a field study with a large number of individuals to develop a model to estimate the shape of the baseline hazard function that represents the age-dependent risk of mortality. The model developed here uses both constant (genetics, spatial location) and time-varying (temperature, rainfall, reproduction, size) covariates not only to estimate the underlying mortality pattern but also to demonstrate that the risk of mortality associated with fitness components can change with time/age. Moreover, this analysis suggests that increasing size after reproductive maturity may allow this plant species to escape from demographic senescence.     

Age-structured optimal control in population economics

This paper brings both intertemporal and age-dependent features to a theory of population policy at the macro-level. A Lotka-type renewal model of population dynamics is combined with a Solow/Ramsey economy. We consider a social planner who maximizes an aggregate intertemporal utility function which depends on per capita consumption. As control policies we consider migration and saving rate (both age-dependent). By using a new maximum principle for age-structured control systems we derive meaningful results for the optimal migration and saving rate in an aging population. The model used in the numerical calculations is calibrated for Austria.     

A model for analyzing insect stage-frequency data when mortality varies with time

A model is developed for the analysis of insect stage-frequency data which may be applied to populations with age-dependent mortality. The analysis of stage-frequency data is divided into two steps. In the first step, the number of different mortality rates and their values are estimated. The second step provides estimates of developmental rates and variances for each developmental stage and in addition provides estimates of the number of recruits to each stage. The model may be used both in analysis and prediction of insect stage frequencies. Hence, in addition to estimating developmental and mortality rates from stage-frequency data, it may also be used as a simulation model for an insect population. The model is applied to two populations of Hemileuca oliviaeCockerell , a lepidopterous pest of New Mexico grasslands. The model identifies, in the two populations, different mortality rates that are related to plant productivity.     

Optimal age-dependent sustainable harvesting of natural resource populations: Sustainability value

We studied the optimal age-dependent harvesting of a natural resource population that achieves a maximum income under the constraint of sustainability, i.e. the reproductive adults numbers must exceed a given minimum. The resource species is assumed to be semelparous (a single reproduction over a life). The economic value and natural mortality coefficient can vary with age. The optimal age-dependent harvesting under the sustainability constraint is obtained using Pontryagin’s maximum principle. The constraint of resource sustainability can be treated as an additional term measured in the same units as economic income. Specifically, three terms: (1) current harvesting value, (2) future harvesting value, and (3) sustainability value, are calculated for each age, and the resources should be harvested at the maximum rate when their current harvesting value is greater than the sum of future harvesting value and sustainability value, and should not be harvested otherwise. Numerical analyses of several cases demonstrated that the optimal harvesting schedule depends critically on the natural mortality coefficient and the functional form of the economic value of the resource.     

Dynamics of maturing populations and their asymptotic behaviour

Summary It is well known that the partial differential equation of the traditional model describing the dynamics of an age-dependent population is of the first order hyperbolic type. An equation of that type cannot simultaneously accommodate a renewal type birth boundary condition and a death boundary condition by old age (accumulation of aging injury) and thus lacks biological realism (mortality by old age). In this paper a governing equation of a parabolic type is derived to represent the expected size of a stochastically maturing population. Using techniques well known for the solution of parabolic partial differential and Volterra integral equations, the asymptotic behaviour of such a maturing population is discussed. Due to a non-local boundary condition, the boundary value problem encountered appears to be new.     

Stochastic dynamic population model for northern corn rootworm (Coleoptera: Chrysomelidae).

A stochastic dynamic population model for the complete life cycle of northern corn rootworm, Diabrotica barberi Smith & Lawrence, is described. Adult population dynamics from emergence to oviposition are based on a published single-season model for which temperature-dependent development and age-dependent advancement determine adult population dynamics and oviposition. Randomly generated daily temperatures make this model component stochastic. Stochastic hatch is 50+/-8%. A stochastic nonlinear density-dependent larval survival model is estimated using field data from artificial infestation experiments. A regional model of corn phenology is estimated to incorporate the effect of dispersal on adult mortality. Random daily weather is generated using parameters for Brookings, SD. Model performance is evaluated with deterministic simulations, which show that the population converges to zero unless adult mortality is reduced by the availability of corn pollen from the regional model of corn phenology. Stochastic model performance is evaluated with stochastic daily weather, egg hatch, and larval survival in various combinations. Sensitivity analysis is conducted to evaluate model responsiveness to each parameter. Model results are generally consistent with published data.     

The effect of differential survivorship on the stability of reproductive queueing

Queues, in which individuals inherit resources in a predictable, temporally stable order, are widespread in animal social groups. We develop an analytic model to explore the effect of differential survivorship on the stability of a reproductive queue. We show that unless fighting for dominance is potentially fatal, future direct benefits are not alone sufficient to stabilize a queue of non-relatives under constant (age-independent) mortality rates, regardless of whether a dominant becomes an isolate or remains a dominant on the death of the first subordinate. In the absence of fatal fighting, stabilization of such a queue by future direct benefits alone requires either the dominant or the subordinate to have age-dependent mortality rates. Even when the queue is stabilized by present direct reproduction, however, the shape of the lifespan distribution can make a significant difference to the size of the required incentive. In contrast to non-relatives, queues of relatives can be stable without age-dependent mortality, so long as relatedness exceeds a critical value; however, age-dependent mortality can lower this critical value.     

Estimation by capture-recapture of recruitment and dispersal over several sites

Dispersal in animal populations is intimately linked with accession to reproduction, i.e. recruitment, and population regulation. Dispersal processes are thus a key component of population dynamics to the same extent as reproduction or mortality processes. Despite the growing interest in spatial aspects of population dynamics, the methodology for estimating dispersal, in particular in relation with recruitment, is limited. In many animal populations, in particular vertebrates, the impossibility of following individuals over space and time in an exhaustive way leads to the need to frame the estimation of dispersal in the context of capture-recapture methodology. We present here a class of age-dependent multistate capture-recapture models for the simultaneous estimation of natal dispersal, breeding dispersal, and age-dependent recruitment. These models are suitable for populations in which individuals are marked at birth and then recaptured over several sites. Under simple constraints, they can be used in populations where non-breeders are not observed, as is often the case with colonial waterbirds monitored on their breeding grounds. Biological questions can be addressed by comparing models differing in structure, according to the generalized linear model philosophy broadly used in capture-recapture methodology. We illustrate the potential of this approach by an analysis of recruitment and dispersal in the roseate tern Sterna dougallii .     

Mortality modeling of early detection programs

Summary .   Consider a group of subjects who are offered an opportunity to receive a sequence of periodic special examinations for the purpose of diagnosing a chronic disease earlier relative to usual care. The mortality for the early detection group is to be compared with a group receiving usual care. Benefit is reflected in a potential reduction in mortality. This article develops a general probability model that can be used to predict cumulative mortality for each of these groups. The elements of the model assume (i) a four-state progressive disease model in which a subject may be in a disease-free state (or a disease state that cannot be detected), preclinical disease state (capable of being diagnosed by a special exam), clinical state (diagnosis by usual care), and a death state; (ii) age-dependent transitions into the states; (iii) age-dependent examination sensitivity; (iv) age-dependent sojourn time in each state; and (v) the distribution of disease stages on diagnosis conditional on modality of detection. The model may be used to (i) compare mortality rates for different screening schedules; (ii) explore potential benefit of subpopulations; and (iii) compare relative reductions in disease-specific mortality due to advances and dissemination of both treatment and early detection screening programs.     

Estimation of population size and survival of sheep blowfly,Lucilia cuprina,in the field from serial recoveries of marked flies affected by weather dispersal and age-dependent trappability

A model is presented for analysis of mark-recapture data of mobile insects which, unlike the Lincoln Index, does not require marked individuals to remain within the sampling area or to mix uniformly with the wild population. The model assumes a single or multiple releases of marked insects from the centre of the sampling area and that captured individuals are not returned to the population. Dispersal rates of marked insects are estimable from serial recaptures and, for catches that are either unaffected by or have been corrected for weather effects, the model also provides estimates of mortality and age-dependent trappability. Application of the model is illustrated using mark-recapture data for adults of the Australian sheep blowfly Lucilia cuprina.     

年龄相关的种群系统的最优生育率控制

讨论了一类与年龄相关的时变种群系统最优生育率控制的非线性问题,利用Ba- nach空间的Saks-Masur引理,证明了系统最优生育率控制的存在唯一性,并得到了控制为最优的必要条件和最优性组．所得结果可为种群系统控制问题的实际研究提供必要的数学理论基础．     

Optimal reproductive strategies in age-structured populations of zooplankton

SUMMARY. We describe a model of zooplankton population dynamics that accounts for differences in mortality and physiology among animals of different ages or sizes. The model follows changes in numbers of individuals and changes in individual and egg biomass through time and it expresses mortality and net assimilation as functions of animal size.
We investigated the effect of egg size, age at first reproduction, and size at first reproduction on the per capita growth rates of populations growing under different conditions. In the absence of predation or when exposed to vertebrate predators that prefer large prey, populations achieve maximum growth rates when animals hatch from small eggs and reach maturity quickly at small sizes. Populations exposed to invertebrate predators that concentrate on small animals may increase r in two different ways. One way is for animals to increase juvenile survivorship by hatching from large eggs and by shortening the juvenile period. An alternative strategy is for animals to hatch from small eggs and to postpone maturity until they grow beyond the range of sizes available to their predators. Certain life history strategies maximize r if animals continue to grow after they reach maturity. By growing larger, non-primiparous females are able to hatch larger clutches and thereby increase the overall rate of population growth.
The model analysis shows how to assess age-dependent mortality rates from field data. The net rate of population increase and the age distribution of eggs together provide specific, quantitative information about mortality.     

一类具年龄结构的线性周期种群动力系统的最优控制

研究一类具有年龄结构的线性周期种群线性动力系统的最优控制问题,即讨论了具有周期的生死率和周期变化的控制项的模型．利用Mazur's定理,证明了最优控制问题最优解的存在性,同时由法锥概念的特征刻画,我们还得到了最优控制问题最优解存在的必要条件．     

Diet, sex, and death in field crickets

Senescence is shaped by age-dependent trade-offs between fitness components. Because males and females invest different resources in reproduction, the trade-offs behind age-dependent reproductive effort should be resolved differently in the sexes. In this study, we assess the effects of diet (high carbohydrate and low protein vs. equal carbohydrate and protein) and mating (once mated vs. virgin) on lifespan and age-dependent mortality in male and female field crickets (Teleogryllus commodus), and on male calling effort. Females always had higher actuarial ageing rates than males, and we found a clear lifespan cost of mating in females. Mated males, however, lived longer than virgin males, possibly because virgins call more than mated males. The fastest age-dependent increases in mortality were among mated males on the high-carbohydrate diet. Males on a high-carbohydrate diet showed a faster increase in calling effort earlier in life, and a more pronounced pattern of senescence once they reached this peak than did males on a diet with equal amounts of protein and carbohydrates. Our results provide evidence that the cost of mating in this cricket species is both diet and sex-dependent, and that the underlying causes of sex differences in life-history traits such as lifespan and senescence can be complex.     

The role of heat shock protein 70 in mediating age-dependent mortality in sepsis

Sepsis is primarily a disease of the aged, with increased incidence and mortality occurring in aged hosts. Heat shock protein (HSP) 70 plays an important role in both healthy aging and the stress response to injury. The purpose of this study was to determine the role of HSP70 in mediating mortality and the host inflammatory response in aged septic hosts. Sepsis was induced in both young (6- to 12-wk-old) and aged (16- to 17-mo-old) HSP70(-/-) and wild-type (WT) mice to determine whether HSP70 modulated outcome in an age-dependent fashion. Young HSP70(-/-) and WT mice subjected to cecal ligation and puncture, Pseudomonas aeruginosa pneumonia, or Streptococcus pneumoniae pneumonia had no differences in mortality, suggesting HSP70 does not mediate survival in young septic hosts. In contrast, mortality was higher in aged HSP70(-/-) mice than aged WT mice subjected to cecal ligation and puncture (p = 0.01), suggesting HSP70 mediates mortality in sepsis in an age-dependent fashion. Compared with WT mice, aged septic HSP70(-/-) mice had increased gut epithelial apoptosis and pulmonary inflammation. In addition, HSP70(-/-) mice had increased systemic levels of TNF-α, IL-6, IL-10, and IL-1β compared with WT mice. These data demonstrate that HSP70 is a key determinant of mortality in aged, but not young hosts in sepsis. HSP70 may play a protective role in an age-dependent response to sepsis by preventing excessive gut apoptosis and both pulmonary and systemic inflammation.     

Disease regulation of age-structured host populations

A lethal, contagious disease can generate a density-dependent regulation of its host, provided the hosts' contact rate grows with population size. The condition for disease-induced population control is that the expected number of offspring of an infected newborn be less than one. In vertebrates that acquired immunity if they survive infection, the disease changes the age structure of its host population. The steady-state age structure of a disease-regulated host with age-dependent fecundity is computed. Local stability analysis indicates that the equilibrium age structure is always stable. However, when the usual exponentially distributed duration of the disease is replaced by a constant duration, the population can exhibit oscillations with a long period.