Age-structured Population Model Research Articles

Coding Optimization for an Ecological non-linear Age-structured Fish Population Model with a Shepherd Recruitment Function

The study of the optimally density-regulated recruitment plays a crucial role in the overall management and determining of fishing efforts of marine fish populations. This paper will develop a Matlab code can determine what an optimal recruitment density regulation strategy would be for the un-fished population and what it changes to when fishing efforts are applied. This code can determine threshold values used to avoid fisheries from collapsing. The code will be applied to the Gulf of California Pacific sardine (Sardinops caeruleus) population. An age structured design with a Shepherd density regulating stock-recruitment function is used in this study. In this work, the parameter which is varied is captured in the Shepherd recruitment function and is associated with behavioral interventions such as selecting different drift routes and clumping on resources that will increase egg-larvae survival to the recruitment stage. A detailed background study of other models is explored, then a derivation of the Shepherd recruitment model is developed from the traditional discrete model. A special MATLAB code is then developed to illustrate the pair-wise invasive plots for the model structures. The code is for theoretical analysis of fish population models.

Stability analysis of an age structured population model with fractional time derivative

In this paper, we analyse the large time behaviour in a fractional nonlinear model of population daynamics with age dependent. We show the existence and uniqueness of the solution by using the method of seperation of variables, and we studied the Ulam-Hyers stability of the model.

A note on the compactness of the resolvent of the age-diffusion operator

The generator of the semigroup associated with linear age-structured population models including spatial diffusion is shown to have compact resolvent.

INVESTIGATION ON PREDICTING FAMILY PLANNING AND WOMEN’S AND CHILDREN’S HEALTH EFFECTS ON BANGLADESH BY CONDUCTING AGE STRUCTURE POPULATION MODEL

Bangladesh has a higher population density than most other nations in the world. This project aims to evaluate the effects of experimental family planning and maternal and child health. Bangladesh saw changes in the use of contraceptives, the continuation of contraception, fertility, and infant and child mortality between 2012 and 2022. The project's current goal is to guarantee improved family health. To satisfy the changing needs and priorities of families and to provide better health for all, this paper has proposed several novel initiatives, such as enhanced health and family planning services, and enhancing maternal and child health. The goal of this project is to improve the health of women and children through family planning using an age-structured population model. It also covers the graphical presentation of the data using programs like Matlab, Mathematica, Excel, and others.

Modeling and analysis of a multilayer solid tumour with cell physiological age and resource limitations

We study an avascular spherical solid tumour model with cell physiological age and resource constraints in vivo. We divide the tumour cells into three components: proliferating cells, quiescent cells and dead cells in necrotic core. We assume that the division rate of proliferating cells is nonlinear due to the nutritional and spatial constraints. The proportion of newborn tumour cells entering directly into quiescent state is considered, since this proportion can respond to the therapeutic effect of drug. We establish a nonlinear age-structured tumour cell population model. We investigate the existence and uniqueness of the model solution and explore the local and global stabilities of the tumour-free steady state. The existence and local stability of the tumour steady state are studied. Finally, some numerical simulations are performed to verify the theoretical results and to investigate the effects of different parameters on the model.

Pharmacodynamic Age Structured Population Model For Cell Trafficking

ObjectivesCell trafficking encompasses movement of the immune system cells (e.g., granulocytes, lymphocytes) between the blood and the extravascular tissues (e.g., lymph nodes). Corticosteroids are known to suppress cell trafficking. The age-structured cell population models introduce the transit time as a structure that allows one to quantify the distribution of times the immune cells spend in the blood and the extravascular tissues. The objective of this work is to develop an age-structured cell population model describing drug effects on cell trafficking and to implement the model in pharmacometric software to enable parameter estimation and simulations. MethodsWe adopted the well-known McKendrick age-structured population model to describe the age distributions in two cell populations: blood cells and cells in the extravascular space. The hazard of cell recirculation from the extravascular tissues was age dependent and described by the Weibull function with the shape ν and scale β parameters. The drug effect on cell trafficking was modeled as the product of the Emax function of the drug plasma concentration and the Weibull hazard. The model was implemented in NONMEM 7.5.1. The model was applied to the basophil data in 34 healthy subjects who received a single intramuscular or oral dose of 6 mg dexamethasone (DEX). A recently published pharmacokinetic model was applied to describe DEX plasma concentration. Typical values of parameter estimates were further used to simulate the DEX effect of the basophil mean transit time in the extravascular tissues. ResultsSimulations of basophil time courses for varying ν demonstrated that the rebound in the blood count data following drug administration is only possible for ν >1. The estimates of model parameters were ν = 3.02, β = 0.00863 1/h, and IC50 = 7.47 ng/mL. The calculated baseline mean transit times of basophils in the blood 7.2 h and extravascular tissues 104.9 h agree with the values reported in the literature. ConclusionsWe introduced an age-structured population model to describe cell trafficking between the blood and extravascular tissues. The model was adopted to account for the inhibitory drug effect on the cell recirculation. We showed that the age structure is essential to explain the rebound observed in the blood count response to a single dose drug administration. The model was validated using the basophil responses to DEX treatment in healthy subjects.

Stationary status of discrete and continuous age-structured population models

From Leonhard Euler to Alfred Lotka and in recent years understanding the stationary process of the human population has been of central interest to scientists. Population reproductive measure NRR (net reproductive rate) has been widely associated with measuring the status of population stationarity and it is also included as one of the measures in the millennium development goals. This article argues how the partition theorem-based approach provides more up-to-date and timely measures to find the status of the population stationarity of a country better than the NRR-based approach. We question the timeliness of the value of NRR in deciding the stationary process of the country. We prove associated theorems on discrete and continuous age distributions and derive measurable functional properties. The partitioning metric captures the underlying age structure dynamic of populations at or near stationarity. As the population growth rates for an ever-increasing number of countries trend towards replacement levels and below, new demographic concepts and metrics are needed to better characterize this emerging global demography.

Using Decision Analysis to Determine the Feasibility of a Conservation Translocation

Conservation translocations, intentional movements of species to protect against extinction, have become widespread in recent decades and are projected to increase further as biodiversity loss continues worldwide. The literature abounds with analyses to inform translocations and assess whether they are successful, but the fundamental question of whether they should be initiated at all is rarely addressed formally. We used decision analysis to assess northern leopard frog reintroduction in northern Idaho, with success defined as a population that persists for at least 50 years. The Idaho Department of Fish and Game was the decision maker (i.e., the agency that will use this assessment to inform their decisions). Stakeholders from government, indigenous groups, academia, land management agencies, and conservation organizations also participated. We built an age-structured population model to predict how management alternatives would affect probability of success. In the model, we explicitly represented epistemic uncertainty around a success criterion (probability of persistence) characterized by aleatory uncertainty. For the leading alternative, the mean probability of persistence was 40%. The distribution of the modelling results was bimodal, with most parameter combinations resulting in either very low (<5%) or relatively high (>95%) probabilities of success. Along with other considerations, including cost, the Idaho Department of Fish and Game will use this assessment to inform a decision regarding reintroduction of northern leopard frogs. Conservation translocations may benefit greatly from more widespread use of decision analysis to counter the complexity and uncertainty inherent in these decisions. History: This paper has been accepted for the Decision Analysis Special Issue on Decision Analysis to Advance Environmental Sustainability. Funding: This work was supported by the Wilder Institute/Calgary Zoo, the U.S. Fish and Wildlife Service [Grant F18AS00095], the NSF Idaho EPSCoR Program and the National Science Foundation [Grant OIA-1757324], and the Hunt Family Foundation. Supplemental Material: The online appendix is available at https://doi.org/10.1287/deca.2023.0472 .

Numerical Analysis of Linearly Implicit Methods for Discontinuous Nonlinear Gurtin-MacCamy Model.

In this study, we study a nonlinear age-structured population models with discontinues mortality and fertility rates, motivated by the fact that different maturation period may cause the significant difference in rates. We develop a novel numerical method with two-layer boundary conditions, the linearly implicit -methods on a special mesh. With a uniform boundedness analysis of numerical solutions, the finite time convergence is proved piecewisely according to the fundamental approach for the smooth rates. For juvenile-adult models, the existence of numerical endemic equilibrium is determined by a numerical basic reproduction function, which converges to the exact one with accuracy of order 1. Moreover, it is shown that for juvenile-adult models, the global stability of the disease-free equilibrium and the local stability of the endemic equilibrium are approximately exhibited by the numerical processes. Finally, some numerical experiments on the Logistic models and tadpoles-frogs models illustrate the verification and the efficiency of our results.

Accounting for transgenerational effects of toxicant exposure in population models alters the predicted long-term population status.

Acute environmental stressors such as short-term exposure to pollutants can have lasting effects on organisms, potentially impacting future generations. Parental exposure to toxicants can result in changes to the epigenome (e.g., DNA methylation) that are passed down to subsequent, unexposed generations. However, it is difficult to gauge the cumulative population-scale impacts of epigenetic effects from laboratory experiments alone. Here, we developed a size- and age-structured delay-coordinate population model to evaluate the long-term consequences of epigenetic modifications on population sustainability. The model emulated changes in growth, mortality, and fecundity in the F0, F1, and F2 generations observed in experiments in which larval Menidia beryllina were exposed to environmentally relevant concentrations of bifenthrin (Bif), ethinylestradiol (EE2), levonorgestrel (LV), or trenbolone (TB) in the parent generation (F0) and reared in clean water up to the F2 generation. Our analysis suggests potentially dramatic population-level effects of repeated, chronic exposures of early-life stage fish that are not captured by models not accounting for those effects. Simulated exposures led to substantial declines in population abundance (LV and Bif) or near-extinction (EE2 and TB) with the exact trajectory and timeline of population decline dependent on the combination of F0, F1, and F2 effects produced by each compound. Even acute one-time exposures of each compound led to declines and recovery over multiple years due to lagged epigenetic effects. These results demonstrate the potential for environmentally relevant concentrations of commonly used compounds to impact the population dynamics and sustainability of an ecologically relevant species and model organism.

A delay induced nonlocal free boundary problem

We study the dynamics of a population with an age structure whose population range expands with time, where the adult population is assumed to satisfy a reaction–diffusion equation over a changing interval determined by a Stefan type free boundary condition, while the juvenile population satisfies a reaction–diffusion equation whose evolving domain is determined by the adult population. The interactions between the adult and juvenile populations involve a fixed time-delay, which renders the model nonlocal in nature. After establishing the well-posedness of the model, we obtain a rather complete description of its long-time dynamical behaviour, which is shown to follow a spreading–vanishing dichotomy. When spreading persists, we show that the population range expands with an asymptotic speed, which is uniquely determined by an associated nonlocal elliptic problem over the half line. We hope this work will inspire further research on age-structured population models with an evolving population range.

Numerical integration of an age-structured population model with infinite life span

The choice of age as a physiological parameter to structure a population and to describe its dynamics involves the election of the life-span. The analysis of an unbounded life-span age-structured population model is motivated because, not only new models continue to appear in this framework, but also it is required by the study of the asymptotic behaviour of its dynamics. The numerical integration of the corresponding model is usually performed in bounded domains through the truncation of the age life-span. Here, we propose a new numerical method that avoids the truncation of the unbounded age domain. It is completely analyzed and second order of convergence is established. We report some experiments to exhibit numerically the theoretical results and the behaviour of the problem in the simulation of the evolution of the Nicholson’s blowflies model.

Investigating the effect of pesticides on Daphnia population dynamics by inferring structure and parameters of a stochastic model

Identifying sublethal pesticide effects on aquatic organisms is a challenge for environmental risk assessment. Long-term population experiments can help assessing chronic toxicity. However, population experiments are subject to stochasticity (demographic, environmental, and genetic). Therefore, identifying sublethal chronic effects from “noisy” data can be difficult. Model-based analysis can support this process.We use stochastic, age-structured population models applied to data from long-term population experiments with Daphnia galeata in 1L aquaria with and without chronic pesticide treatments (diazinon and diuron) at sublethal concentrations. Posterior analysis following Bayesian inference of model parameters and states helped choosing an adequate description of life-history characteristics under the specific experimental conditions (a zero-inflated negative binomial distribution for reproduction and mortality without density dependence). For the insecticide treatments, the inferred marginal posterior parameter distributions indicated the need for a mortality rate that increases with time, indicating cumulative chronic toxic effects of diazinon on Daphnia populations. With this study, we demonstrate how stochastic models can be used to infer mechanisms from population data to help identifying sublethal pesticide effects.

Monitoring in a Discrete-Time Nonlinear Age-Structured Population Model with Changing Environment

This paper is a contribution to the modeling–methodological development of the application of mathematical systems theory in population biology. A discrete-time nonlinear Leslie-type model is considered, where both the reproduction and survival rates decrease as the total population size increases. In this context, the monitoring problem means that, from the observation of the size of certain age classes as a function of time, we want to recover (estimate) the whole state process (i.e., the time-dependent size of the rest of the classes). First, for the linearization approach, conditions for the existence and asymptotic stability of a positive equilibrium are obtained, then the discrete-time observer design method is applied to estimate an unknown state trajectory near the equilibrium, where we could observe a single age class. It is also shown how the observer design can be used to detect an unknown change in the environment that affects the population dynamics. The environmental change is supposed to be generated by additional dynamics (exosystem). Now, the Leslie-type model is extended with this exosystem, and the observer design is applied to this extended system. In this way, an estimation can be obtained for different (constant or periodic) environmental changes as well.

An age-structured population model with delayed and space-limited recruitment

A new age-structured model for a closed population with space-limited recruitment is proposed. The problem incorporates a time delay in the settlement process representing, for a marine population of invertebrates, the pelagic larval phase previous to the sessile stage. The model possesses a nontrivial steady state which is investigated. For a deeper analysis of the stability of this equilibrium, depending on the delay, an appropriate numerical method is proposed. The nontrivial equilibrium of the numerical scheme, based on the representation of the solution along the characteristics lines, is also analyzed. For a test model associated with the dynamics of a population of barnacles, numerical experiments describing the asymptotic behavior of the solutions varying the delay are provided. In this case, the delay behaves as a destabilizing parameter of the dynamics of the model.

Age-structured model reveals prolonged immigration is key for colony establishment in Gentoo Penguins

AbstractUnderstanding the mechanisms of site colonization and range expansion is crucial to understanding population dynamics, particularly for colonial seabirds that may struggle to shift their breeding ranges under climate change. We provide an alternative and simple approach to estimating the number of migrating individuals among colonies when original mark–recapture datasets are not available for use in more integrated and established methods. Here we fit an age-structured population model with published vital rates and breeding success rates to simple point counts of abundance using rejection-based approximate Bayesian computation (ABC) to estimate the contribution of immigration to four recently colonized Gentoo Penguin (Pygoscelis papua) breeding sites on the Western Antarctic Peninsula. We found that sustained immigration over several years was required to generate the rapid population growth observed, with some sites even showing evidence of an accelerating immigration rate following initial colonization. We demonstrate that our method is capable of estimating the contribution of immigration to population growth in a species where mark–recapture datasets are unavailable. By leveraging census data that are relatively easy to obtain, our approach provides a new method for understanding how range expansions occur in species such as Antarctic penguins whose habitat is undergoing changing climate conditions.

Global dynamics of an age-structured model for HIV viral dynamics with latently infected T cells

This study focuses on an age-structured population model which describes the in host dynamics of HIV/AIDS. This model also considers the proportion of latently infected CD4+ T cells by HIV. After the formulation of the model, we derive steady-state solutions of the model. By constructing an appropriate Lyapunov function, we check the stability of infection-free steady-state. We show that if reproduction number R0 is less than 1, then the infection-free equilibrium is stable. We also study the role of anti-retroviral therapy to slow down the process of HIV in the human body. We consider our model with anti-retroviral therapy and again check the global stability of the infection-free steady state for better comparison. We also solve our model numerically to study the primary spread of HIV virus.

Effects of climate variability on the demography of wild geladas.

Nonhuman primates are an essential part of tropical biodiversity and play key roles in many ecosystem functions, processes, and services. However, the impact of climate variability on nonhuman primates, whether anthropogenic or otherwise, remains poorly understood. In this study, we utilized age‐structured matrix population models to assess the population viability and demographic variability of a population of geladas (Theropithecus gelada) in the Simien Mountains, Ethiopia with the aim of revealing any underlying climatic influences. Using data from 2008 to 2019 we calculated annual, time‐averaged, and stochastic population growth rates (λ) and investigated relationships between vital rate variability and monthly cumulative rainfall and mean temperature. Our results showed that under the prevailing environmental conditions, the population will increase (λ s = 1.021). Significant effects from rainfall and/or temperature variability were widely detected across vital rates; only the first year of infant survival and the individual years of juvenile survival were definitively unaffected. Generally, the higher temperature in the hot‐dry season led to lower survival and higher fecundity, while higher rainfall in the hot‐dry season led to increased survival and fecundity. Overall, these results provide evidence of greater effects of climate variability across a wider range of vital rates than those found in previous primate demography studies. This highlights that although primates have often shown substantial resilience to the direct effects of climate change, their vulnerability may vary with habitat type and across populations.

Random attractors for a stochastic age-structured population model

In this paper, we are concerned about the existence of a random attractor for a stochastic nonlocal delayed reaction–diffusion equation (SNDRDE) under a Dirichlet boundary condition. This equation models the spatial–temporal evolution of the mature individuals for a two-stage species whose juvenile and adults both diffuse under random perturbations. By adopting the random dynamical system theory together with the stochastic inequality technique, we first give a uniform estimate of the solution and then prove the asymptotic compactness of the random dynamic system generated by the SNDRDE and, subsequently, obtain the existence of a random attractor.

Propagation dynamics for an age-structured population model in time-space periodic habitat

How do environmental heterogeneity influence propagation dynamics of the age-structured invasive species? We investigate this problem by considering a yearly generation invasive species in time-space periodic habitat. Starting from an age-structured population growth law, we formulate a reaction-diffusion model with time-space periodic dispersal, mortality and recruitment. Thanks to the fundamental solution for linear part of the model, we reduce to study the dynamics of a time-space periodic semiflow which is defined by the solution map. By the recent developed dynamical theory in Fang et al. (J Funct Anal 272:4222-4262, 2017), we obtained the spreading speed and its coincidence with the minimal wave speed of time-space periodic traveling waves, as well as the variational characterization of spreading speed in terms of a principal eigenvalue problem. Such results are also proved back to the reaction-diffusion model.