Age-structured Population Dynamics Model Research Articles

Modeling Population Growth under Climate Stressors Using Age-Structured Matrix Models.

Climate resilience, a focus of many recent studies, has been examined from ecological, physiological, and evolutionary perspectives. However, sampling biases toward adults, males, and certain species have made establishing the link between environmental change and population-level change problematic. Here, we used data from four laboratory studies, in which we administered pre- and postnatal stressors, such as suboptimal incubation temperature, heat stress, and food restriction, to zebra finches. We then quantified hatching success, posthatch survival, and reproductive success, to parameterize age-structured population dynamics models with the goal of estimating the effect of the stressors on relative population growth rates. Using the same model structure, we tested the hypothesis that early life stages influence population growth rate more than later life stages. Our models suggested that stressful events during embryonic development, such as suboptimal incubation temperatures and reduced gas exchange for the embryos, have a greater total impact on population growth than posthatch stressors, such as heat stress and food restriction. However, among life history traits, differences in hatching success and sex ratio of offspring in response to stressors changed population growth rates more than differences in any other demographic rate estimates. These results suggest that when predicting population resilience against climate change, it is critical to account for effects of climate change on all life stages, including early stages of life, and to incorporate individuals' physiology and stress tolerance that likely influence future stress responses, reproduction, and survival.

An Inverse Problem for an Age-Structured Population Dynamics Model with Migration Flows

An Inverse Problem for an Age-Structured Population Dynamics Model with Migration Flows

Global asymptotic stability for Gurtin-MacCamy’s population dynamics model

In this paper, we investigate the global asymptotic stability of an age-structured population dynamics model with a Ricker’s type of birth function. This model is a hyperbolic partial differential equation with a nonlinear and nonlocal boundary condition. We prove a uniform persistence result for the semiflow generated by this model. We obtain the existence of global attractors and we prove the global asymptotic stability of the positive equilibrium by using a suitable Lyapunov functional. Furthermore, we prove that our global asymptotic stability result is sharp, in the sense that Hopf bifurcation may occur as close as we want from the region global stability in the space of parameter.

Factors influencing size-structured models’ ability to estimate natural mortality

Natural mortality (M) is crucially important for stock assessment since it strongly influences estimates of spawning stock biomass, MSY and fishing mortality. Variation in M can occur between sexes, maturity stages and temporally. Estimates of M are confounded with those of catchability, recruitment, and growth. Previous studies, which focused on age-structured population dynamics models, suggest that it would be better to estimate M rather than pre-specify it. Size-structured population dynamics models, used for species that are hard to age such as crabs, have unique characteristics such as a size-transition matrix and the possibility of a terminal molt, which could impact the ability to estimate M. Therefore, this study explores the ability of size-structured stock assessment models to estimate M for several scenarios. These scenarios include whether the operating model and estimation method have a terminal molt, whether M is constant, time-varying, or sex- and maturity stage-specific, the quality/sample size of the biomass index and the size-composition data and whether growth is estimated simultaneously with M. The results show that size-structured models can estimate time-varying, sex- and maturity stage-specific M when the estimation method mirrors the operating model. Surprisingly, terminal molt does not affect the ability to estimate M. However, estimating growth simultaneously with M has a negative impact on the ability to estimate M but a positive effect on the quality of the estimates of spawning stock biomass.

Unveiling the recovery dynamics of walleye after the invisible collapse

Walleye (Sander vitreus) populations in Alberta, Canada, collapsed by the mid-1990s and were a case study in the paper Canada’s Recreational Fisheries: The Invisible Collapse? Here we fit age-structured population dynamics models to data from a landscape-scale monitoring program to assess walleye population status and reconstruct recruitment dynamics following the invisible collapse. Assessments indicated that populations featured low Fmsyvalues of approximately 0.2–0.3 under conservative assumptions for the stock–recruitment relationship but that many populations were lightly exploited during 2000–2018. Recruitment reconstructions showed that recovery from collapse in 33/55 lakes was driven in part by large positive recruitment anomalies that occurred during 1998–2002. Additionally, 15/55 lakes demonstrated cyclic recruitment dynamics. The documented recruitment anomalies and cyclic fluctuations could be due to environmental effect(s) or cannibalism, and experimentation is likely necessary to resolve this uncertainty. These findings contribute new information on the recovery dynamics of walleye following the invisible collapse and demonstrate the effectiveness of coupling traditional fisheries science models with broad-scale monitoring data to improve understanding of population dynamics and sustainability across landscapes.

Trading off retained daily catch for longer seasons to maximize angler benefits in recreational fisheries management

Abstract Recreational fishing benefits associated with angling opportunity, such as fishing season duration and certainty of season duration, may outweigh trip-based benefits, such as retained catch, in measures of angler utility. We developed an age-structured population dynamics model to predict how these three beneficial attributes are affected by four recreational management parameters: minimum size limit; bag limit; inter-season quota transfer limits; and in-season adjustment of season duration. We incorporated results of stated-preference angler surveys to produce a bioeconomic model for two case studies: Atlantic Florida red snapper, and central Oregon Pacific halibut. In maximizing long-term total utility, a strong trade-off between season length and retained daily catch was observed in both fisheries, arising from increased minimum size limits which lengthened fishing seasons but reduced daily retained catch. The optimal management policy across the combination of beneficial attributes was sensitive to assumptions of the curvature of utility functions, i.e. to the degree to which anglers value those attributes with diminishing marginal returns, but generally involved satisfying the strong stated preferences for increased angling opportunity.

Null Controllability of a Four Stage and Age-Structured Population Dynamics Model

This paper is devoted to study the null controllability properties of a population dynamics model with age structuring and nonlocal boundary conditions. More precisely, we consider a four-stage model with a second derivative with respect to the age variable. The null controllability is related to the extinction of eggs, larvae, and female population. Thus, we estimate a time T to bring eggs, larvae, and female subpopulation density to zero. Our method combines fixed point theorem and Carleman estimate. We end this work with numerical illustrations.

The impact of alternative age-length sampling schemes on the performance of stock assessment methods

Stock assessments based on fitting age-structured population dynamics models using the integrated approach usually require data on the length-/age-structure of fishery removals and age-length data to estimate key population parameters such as growth rates, recruitment, natural mortality rates and selectivity. The errors in the estimates of these population parameters directly impact the ability to estimate biomass and hence recommended catch limits based on harvest control rules. The performance of a stock assessment method therefore depends in part on the quality of these “composition” data. Simulation is used to evaluate the effect of a range of effective sample sizes for the length-composition and conditional age-at-length data on the errors in estimating spawning biomass, depletion, recruitment, selected population model parameters, and key model outputs, including catch limit recommendations. Multiple operating models, including those that result in the estimation method being mis-specified, are considered, and the simulations account for the effects of life history, catch history and current stock status. As expected, the errors in estimates of management-related quantities are less for greater effective sample sizes, but effective sample size is seldom the major determinant of the magnitude of estimation errors. The effect of sample size on relative errors is neither linear nor exponential, and spatially-unbalanced sampling is more detrimental than infrequent collection of composition data but with larger sample sizes. The quantitative results are likely case-specific, as they depend on several aspects of the operating model; the framework of this paper can be applied to specific fisheries, in combination with an algorithm that links effective to actual sample sizes.

Stability Analysis of Delayed Age-Structured Resource-Consumer Model of Population Dynamics With Saturated Intake Rate

This article studies nonlinear n-resource-consumer autonomous system with age-structured consumer population. The model of consumer population dynamics is described by a delayed transport equation, and the dynamics of resource patches are described by ODE with saturated intake rate. The delay models the digestion period of generalist consumer and is included in the calorie intake rate, which impacts the consumer’s fertility and mortality. Saturated intake rate models the inhibition effect from the behavioral change of the resource patches when they react to the consumer population growing or from the crowding effect of the consumer. The conditions for the existence of trivial, semi-trivial, and non-trivial equilibria and their local asymptotic stability were obtained. The local asymptotic stability/instability of non-trivial equilibrium of a system with depleted patches is defined by new derived criteria, which relate the demographic characteristics of consumers with their search rate, growth rate of resource in patches, and behavioral change of the food resource when consumer population grows. The digestion period of a generalist consumer does not cause local asymptotical instabilities of consumer population at the semi-trivial and nontrivial equilibria. These theoretical results may be used in the study of metapopulation dynamics, desert locust populations dynamics, prey-predator interactions in fisheries, etc. The paper uses numerical experiments to confirm and illustrate all dynamical regimes of the n-resource-consumer population.

An economic and disease transmission model of human papillomavirus and oropharyngeal cancer in Texas

In 2017, 46,157 and 3,127 new oropharyngeal cancer (OPC) cases were reported in the U.S. and Texas, respectively. About 70% of OPC were attributed to human papillomavirus (HPV). However, only 51% of U.S. and 43.5% of Texas adolescents have completed the HPV vaccine series. Therefore, modeling the demographic dynamics and transmission of HPV and OPC progression is needed for accurate estimation of the economic and epidemiological impacts of HPV vaccine in a geographic area. An age-structured population dynamic model was developed for the U.S. state of Texas. With Texas-specific model parameters calibrated, this model described the dynamics of HPV-associated OPC in Texas. Parameters for the Year 2010 were used as the initial values, and the prediction for Year 2012 was compared with the real age-specific incidence rates in 23 age groups for model validation. The validated model was applied to predict 100-year age-adjusted incidence rates. The public health benefits of HPV vaccine uptake were evaluated by computer simulation. Compared with current vaccination program, increasing vaccine uptake rates by 50% would decrease the cumulative cases by 4403, within 100 years. The incremental cost-effectiveness ratio of this strategy was $94,518 per quality-adjusted life year (QALY) gained. Increasing the vaccine uptake rate by 50% can: (i) reduce the incidence rates of OPC among both males and females; (ii) improve the quality-adjusted life years for both males and females; (iii) be cost-effective and has the potential to provide tremendous public health benefits in Texas.

On the existence of solution of a four-stage and age-structured population dynamics model

We consider a linear system coming from a population dynamics model with age structuring and nonlocal boundary conditions. Our population dynamics model is a four-stage model with a second derivative with respect to the age variable. Using Banach fixed point theorem, we show the existence and unicity of a non negative solution and illustrations of numerical simulations are given.

SPop: Age-structured discrete-time population dynamics model in C, Python, and R.

This article describes the sPop packages implementing the deterministic and stochastic versions of an age-structured discrete-time population dynamics model. The packages enable mechanistic modelling of a population by monitoring the age and development stage of each individual. Survival and development are included as the main effectors and they progress at a user-defined pace: follow a fixed rate, delay for a given time, or progress at an age-dependent manner. The model is implemented in C, Python, and R with a uniform design to ease usage and facilitate adoption. Early versions of the model were previously employed for investigating climate-driven population dynamics of the tiger mosquito and the chikungunya disease spread by this vector. The sPop packages presented in this article enable the use of the model in a range of applications extending from vector-borne diseases towards any age-structured population including plant and animal populations, microbial dynamics, host-pathogen interactions, infectious diseases, and other time-dependent epidemiological processes.

Evaluating the effectiveness of management measures on skates in a changing world

Global declines in elasmobranchs have been observed. Conservation measures such as area closures and fisheries prohibitions have been put in place to support the recovery of vulnerable species. However, the effectiveness of such measures is rarely evaluated in the context of other factors that may affect population abundance. This study investigates the effectiveness of management measures using 1) General additive mixed model derivative changes, taking into account environmental factors that may affect population stochasticity and 2) an age-structured density dependent population dynamic model. The Raja undulata (undulate ray) 2009 targeted fisheries prohibition was used as a case study. Potential beneficial responses on sympatric species Raja clavata (thornback ray) were modelled.A significant increase in abundance was observed in both IUCN red list species during the ban. Surface seawater temperature had a marginal effect on the abundance of both species. The prohibition was in place for an insufficient length of time for long lasting effects to be detected on skate length. The population dynamic model indicated that the increase in abundance was only possible when combining the fisheries ban with increased juvenile discard survival. Our results indicate that species conservation measures may not only have positive effects on the species in question, but also on species with a niche overlap. Nonetheless, due to ongoing fishing for other species, the full potential of fisheries prohibitions may not be realised. For real benefits to be assessed, evaluation of bans should take place once a steady state is observed.

Integrated multi-timescale modeling untangles anthropogenic, environmental, and biological effects on catchability

Catchability plays a central role in fisheries stock assessment. Since catchability often varies with time depending on population density, environmental factors, and anthropogenic effects, assuming constant catchability in population models can lead to biased abundance estimates. Here we present a novel way to simultaneously estimate time-varying catchability and abundance by integrating a short-term (month-based) removal method and a long-term (year-based) age-structured population dynamics model. We applied this approach to commercial fishery data for a Japanese pufferfish (Takifugu rubripes) population and found that the models with time-varying catchability greatly outperformed the models with constant catchability in terms of predictive ability and model consistency. The temporal variation in catchability was parsimoniously predicted by fishing effort and population size, indicating the existence of effort- and density-dependent catchability. Our approach, integrating population dynamics at different timescales, will help avoid inadvertent overexploitation and contribute to sustainable harvesting by enhancing the estimation accuracy of time-varying catchability and abundance.

Asynchronous H∞ Control for Positive Discrete-time Markovian Jump Systems

This paper deals with the asynchronous H??? control for discrete-time positive Markovian jump systems (PMJSs). In previous results about PMJSs, asynchronous behaviors are always overlooked and the designed controller is based on the synchronization between the system modes and controller modes. Sufficient conditions for stochastic stability are proposed by the use of Lyapunov-Krasovskii functional. The asynchronous controller is designed to ensure the closed-loop system stochastically stable with a prescribed H??? performance index. All the conditions are given in linear matrix inequality framework. Finally, a pest???s age-structured population dynamic model is illustrated to show the validity of the present design.

Finite‐time asynchronous control for positive discrete‐time Markovian jump systems

Finite-time asynchronous control problem is discussed for positive Markovian jump systems in this study. The non-synchronous behaviours generated between the system modes and controller modes are fully considered. To ensure the closed-loop system positivity and finite-time boundedness with a guaranteed $H_\infty $H ∞ performance level, a sufficient condition on the existence of an asynchronous controller is first established by applying Lyapunov-Krasovskii functional approach and recursive matrix inequality methods. Then, with the aid of matrix conversions, the specific form of controller gain matrices can be constructed by solving linear matrix inequality (LMI) conditions. A numerical example is presented and application is illustrated to validate the proposed results by employing a pest's age-structured population dynamic model.

SPop: Age-structured discrete-time population dynamics model in C, Python, and R.

This article describes the sPop packages implementing the deterministic and stochastic versions of an age-structured discrete-time population dynamics model. The packages enable mechanistic modelling of a population by monitoring the age and development stage of each individual. Survival and development are included as the main effectors and they progress at a user-defined pace: follow a fixed-rate, delay for a given time, or progress at an age-dependent manner. The model is implemented in C, Python, and R with a uniform design to ease usage and facilitate adoption. Early versions of the model were previously employed for investigating climate-driven population dynamics of the tiger mosquito and the chikungunya disease spread by this vector. The sPop packages presented in this article enable the use of the model in a range of applications extending from vector-borne diseases towards any age-structured population including plant and animal populations, microbial dynamics, host-pathogen interactions, infectious diseases, and other time-dependent epidemiological processes.

SPop: Age-structured discrete-time population dynamics model in C, Python, and R

This article describes the sPop packages implementing the deterministic and stochastic versions of an age-structured discrete-time population dynamics model. The packages enable mechanistic modelling of a population by monitoring the age and development stage of each individual. Survival and development are included as the main effectors and they progress at a user-defined pace: follow a fixed rate, delay for a given time, or progress at an age-dependent manner. The model is implemented in C, Python, and R with a uniform design to ease usage and facilitate adoption. Early versions of the model were previously employed for investigating climate-driven population dynamics of the tiger mosquito and the chikungunya disease spread by this vector. The sPop packages presented in this article enable the use of the model in a range of applications extending from vector-borne diseases towards any age-structured population including plant and animal populations, microbial dynamics, host-pathogen interactions, infectious diseases, and other time-dependent epidemiological processes.

SPop: Age-structured discrete-time population dynamics model in C, Python, and R.

This article describes the sPop packages implementing the deterministic and stochastic versions of an age-structured discrete-time population dynamics model. The packages enable mechanistic modelling of a population by monitoring the age and development stage of each individual. Survival and development are included as the main effectors and they progress at a user-defined pace: follow a fixed-rate, delay for a given time, or progress at an age-dependent manner. The model is implemented in C, Python, and R with a uniform design to ease usage and facilitate adoption. Early versions of the model were previously employed for investigating climate-driven population dynamics of the tiger mosquito and the chikungunya disease spread by this vector. The sPop packages presented in this article enable the use of the model in a range of applications extending from vector-borne diseases towards any age-structured population including plant and animal populations, microbial dynamics, host-pathogen interactions, infectious diseases, and other time-delayed epidemiological processes.

Simulated bat populations erode when exposed to climate change projections for western North America.

Recent research has demonstrated that temperature and precipitation conditions correlate with successful reproduction in some insectivorous bat species that live in arid and semiarid regions, and that hot and dry conditions correlate with reduced lactation and reproductive output by females of some species. However, the potential long-term impacts of climate-induced reproductive declines on bat populations in western North America are not well understood. We combined results from long-term field monitoring and experiments in our study area with information on vital rates to develop stochastic age-structured population dynamics models and analyzed how simulated fringed myotis (Myotis thysanodes) populations changed under projected future climate conditions in our study area near Boulder, Colorado (Boulder Models) and throughout western North America (General Models). Each simulation consisted of an initial population of 2,000 females and an approximately stable age distribution at the beginning of the simulation. We allowed each population to be influenced by the mean annual temperature and annual precipitation for our study area and a generalized range-wide model projected through year 2086, for each of four carbon emission scenarios (representative concentration pathways RCP2.6, RCP4.5, RCP6.0, RCP8.5). Each population simulation was repeated 10,000 times. Of the 8 Boulder Model simulations, 1 increased (+29.10%), 3 stayed approximately stable (+2.45%, +0.05%, -0.03%), and 4 simulations decreased substantially (-44.10%, -44.70%, -44.95%, -78.85%). All General Model simulations for western North America decreased by >90% (-93.75%, -96.70%, -96.70%, -98.75%). These results suggest that a changing climate in western North America has the potential to quickly erode some forest bat populations including species of conservation concern, such as fringed myotis.