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A nonlinear optimal control problem in the Lotka–McKendrick population model is studied. It describes rational management of age-structured farmed populations in aquaculture and indoor farms. Employing generalized functions, we prove the impulse nature of optimal harvesting. Exact analytic solutions for sustainable harvesting strategies are obtained and used to analyze the optimal dynamics of harvesting age and rotation under technological innovations. [ABSTRACT FROM AUTHOR]

Abstract Understanding survival probabilities is critical for the sustainable harvest of wildlife and fisheries populations. Age‐ and stage class‐specific survival probabilities are needed to inform a suite of population models used to estimate abundance and track population trends. However, current techniques for estimating survival probabilities using age‐at‐harvest methods require restrictive assumptions or incorporate potentially unknown parameters within the model. Using a Bayesian approach, we developed a flexible age‐at‐harvest model that incorporates either age‐ or stage‐structured populations, while accounting for uncertainty in age structure, population growth rates and relative selectivity. Survival probabilities can vary by age or stage class, as well as by environmental covariates, and both population growth rates and selectivity for each age or stage class can be specified as fixed and known or these parameters can be specified as informative priors, allowing for the incorporation of expert opinion. We evaluated our model with simulations and empirical data from harvested bobcats Lynx rufus and American paddlefish Polyodon spathula. Models fit to simulated age‐at‐harvest data yielded unbiased estimates of survival probability when population growth rates and selectivity were centered on the data‐generating parameter. We obtained unbiased estimates of survival probability even with biased prior estimates of selectivity and random departures from the assumed stage distribution, although the latter increased uncertainty in those estimates. We found biased estimates of survival probability when the prior distribution for population growth rate was not centered on the data‐generating value. When fit to empirical harvest data, our proposed age‐at‐harvest model produced estimates of survival probability congruent to those reported in the literature within similar geographic regions. We demonstrate the utility of a novel age‐at‐harvest model that estimates survival probability and realistically account for uncertainty in model parameters, transcending the restrictive assumptions and auxiliary data requirements of other methods. Furthermore, we advise collecting information about population trends and age structure alongside age‐at‐harvest data to help reduce bias. Although our model cannot replace more rigorous methods, we believe our model will be transformative for wildlife and fisheries practitioners who collect age‐at‐harvest data to estimate age‐ or stage‐specific survival probabilities to help inform management decisions.

Understanding survival probabilities is critical for the sustainable harvest of wildlife and fisheries populations. Age‐ and stage class‐specific survival probabilities are needed to inform a suite of population models used to estimate abundance and track population trends. However, current techniques for estimating survival probabilities using age‐at‐harvest methods require restrictive assumptions or incorporate potentially unknown parameters within the model.Using a Bayesian approach, we developed a flexible age‐at‐harvest model that incorporates either age‐ or stage‐structured populations, while accounting for uncertainty in age structure, population growth rates and relative selectivity. Survival probabilities can vary by age or stage class, as well as by environmental covariates, and both population growth rates and selectivity for each age or stage class can be specified as fixed and known or these parameters can be specified as informative priors, allowing for the incorporation of expert opinion. We evaluated our model with simulations and empirical data from harvested bobcats Lynx rufus and American paddlefish Polyodon spathula.Models fit to simulated age‐at‐harvest data yielded unbiased estimates of survival probability when population growth rates and selectivity were centered on the data‐generating parameter. We obtained unbiased estimates of survival probability even with biased prior estimates of selectivity and random departures from the assumed stage distribution, although the latter increased uncertainty in those estimates. We found biased estimates of survival probability when the prior distribution for population growth rate was not centered on the data‐generating value. When fit to empirical harvest data, our proposed age‐at‐harvest model produced estimates of survival probability congruent to those reported in the literature within similar geographic regions.We demonstrate the utility of a novel age‐at‐harvest model that estimates survival probability and realistically account for uncertainty in model parameters, transcending the restrictive assumptions and auxiliary data requirements of other methods. Furthermore, we advise collecting information about population trends and age structure alongside age‐at‐harvest data to help reduce bias. Although our model cannot replace more rigorous methods, we believe our model will be transformative for wildlife and fisheries practitioners who collect age‐at‐harvest data to estimate age‐ or stage‐specific survival probabilities to help inform management decisions. [ABSTRACT FROM AUTHOR]

The existence and uniqueness of solutions of the boundary value problem for the recently introduced McKendrick-Von Foerster equation with continuous stochastic noise is proven. Motivated by the applications in mathematical biology, the boundary conditions are assumed to depend on the aggregated age variables, which makes the problem both non-local and nonlinear. The techniques used in the paper are based on a special transformation method converting the stochastic McKendrick-Von Foerster equation into a pair of finite dimensional systems of stochastic functional differential equations. [ABSTRACT FROM AUTHOR]

Background: The long-term impact of sexual transmission on the hepatitis B virus (HBV) infection in China remains unclear. This study aims to estimate the independent influence of sexual transmission on HBV infection.Methods: Based on the natural history of HBV infection and three national serosurvey data of hepatitis B in China, we developed an age- and sex-specific discrete model to describe the transmission dynamics of HBV. The initial conditions of the model were determined according to the age- and sex-specific national serosurvey data in 1992. Based on the national survey data of hepatitis B in 1992 and 2006, by using the Markov Chain Monte Carlo (MCMC) method, we estimated the age- and sex-specific seroclearance rates of hepatitis B surface antigen (HBsAg) and the horizontal transmission rates as well as their 95% confidence intervals (CI). Then we used the age- and sex-specific national serosurvey data of hepatitis B in 2014 to test the accuracy of our model-based estimation. Finally, we evaluated the independent impact of sexual transmission on HBV infection and discussed the long-term effect of promotion of condom use in China.Results: We estimated that the annual rates of HBsAg seroclearance for males and females aged 1-59 years were respectively 1.04% (95% CI, 0.49-1.59%) and 1.92% (95% CI, 1.11-2.73%). Due to sexual transmission, in 2014, the total number of chronic HBV infections in people aged 0-100 years increased 292,581, of which males increased 189,200 and females increased 103,381. In 2006, the acute HBV infections due to sexual transmission accounted for 24.76% (male: 31.33%, female: 17.94%) and in 2014, which accounted for 34.59% (male: 42.93%, female: 25.73%). However, if the condom usage rate was increased by 10% annually starting in 2019, then compared with current practice, the total number of acute HBV infections from 2019 to 2035 would be reduced by 16.68% (male: 21.49%, female: 11.93%). The HBsAg prevalence in people aged 1-59 years in 2035 would be reduced to 2.01% (male: 2.40%, female: 1.58%).Conclusions: Sexual transmission has become the predominant route of acute HBV infection in China, especially for men. The promotion of condom use plays a significant role in reducing the cases of acute HBV infection. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we study a size-structured population model with infinite states-at-birth and distributed delay in birth process. We are interested in the asymptotic behavior of the considered system and, particularly, in the effect of time lag on the long-term dynamics. To this end, we formally linearize the system around a steady state and study the linearized system using -semigroup framework and spectral analysis methods. In this manner, we achieve some results on linearized stability, instability, and asynchronous exponential growth for the system under some conditions. The obtained results are also illustrated by some examples and simulations. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study an age-structured model which has strong biological background about mosquito plasticity. Firstly, we prove the existence of solutions and the comparison principle for a generalized system. Then, we prove the existence of the optimal control for the best harvesting. Finally, we establish necessary optimality conditions. [ABSTRACT FROM AUTHOR]

We study a nonlinear age‐structured model of locust population dynamics with variable time of egg incubation that describes the phase shifting and behavior of desert locust, Schistocerca gregaria. The model is based on the 2‐compartment system of transport equations with nonlinear density‐dependent fertility rates with time delay in boundary conditions. It describes the dynamics of the density of 2 phases of locust's population—solitarious and gregarious. Such system is studied both theoretically and numerically. The analysis of asymptotical stability of the trivial and nontrivial equilibria of the autonomous system allows to understand the conditions and the particularities of bidirectional phase shifts between solitarious and gregarious S gregaria. We found that the parameter of maturation age was very important in the 2‐phase dynamics. We extrapolate that a rapid change in environmental conditions that may trigger the maturation process of dormant solitarious population may also decrease, overall, the maturation age and hence destabilize the solitarious subpopulation from a near zero population size towards much larger populations and hence initiate quickly good conditions for gregarization. We also observed that the most realistic population dynamics of locusts was when the attraction point of a stable solitarious population size was above the gregarization threshold. This means that solitarious populations may last through time only near a zero size, but as soon as environmental conditions become favorable to population increase, the gregarization may happen. This outlines the intrinsic character of outbreaking dynamics that a species such as desert locust displays. [ABSTRACT FROM AUTHOR]

We formulate a model describing the dynamics for the spatial propagation of an SIS epidemic within a population, with age structure, living in an environment divided into two sites. An analysis of the model is given. We prove the existence of a unique disease free equilibrium (DFE) and its (local and global) stability. Further, we assume that fast infection processes and fast migration processes take place in the above-mentioned model; i.e. such processes last only a few days (less than a week). In opposition to such processes, demographic processes such as birth, death and maturation last quite a lot of years. Such a gap between the time scales gives rise to a multiple time scales model, in particular a singularly perturbed model. Through a singular perturbation analysis, based on Tikhonov theorem, we prove that for certain classes of initial conditions the nonlinear perturbed model can be approximated with very good accuracy by lower-dimensional linear models. [ABSTRACT FROM AUTHOR]

We describe an unbiased length-based, age-structured mark-recapture (LAMR) model for estimating length-based abundance and recruitment of fish populations. Many mark-recapture studies employ capture gear that is size-selective, leading to a larger and faster growing marked sub-population with a different capture probability than the unmarked sub-population, resulting in a basic violation of assumptions for many mark-recapture models. Persistent differences in marked and unmarked individuals are estimated in our model using growth-type group accounting. Simulation-evaluation results indicate that the model produces largely unbiased estimates of recruitment and abundance across a range of sampling scenarios and population life-history types, and is robust to growth parameter misspecification. However, in older, slow growing populations, the model is prone to ‘smearing’ of recruitment estimates across early year-classes. The LAMR model is applied to data from multiple wild populations of rainbow trout to estimate recruitment and abundance. Overall, results indicate that the LAMR model addresses shortcomings associated with using size-selective gear in mark-recapture studies to produce reliable estimates of recruitment and size-based abundance. [ABSTRACT FROM AUTHOR]

In this paper we consider class-structured populations in discrete time in the limit of weak selection and with the inverse of the intensity of selection as unit of time. The aim is to establish a continuous model that approximates the discrete model. More precisely, we study frequency-dependent growth in an infinite haploid population structured into a finite number of classes such that individuals in each class contribute to a given subset of classes from one time step to the next. These contributions take the form of generalized fecundity parameters with perturbations of order 1 / N that depends on the class frequencies of each type and the type frequencies. Moreover, they satisfy some mild conditions that ensure mixing in the long run. The dynamics in the limit as N→∞ with N time steps as unit of time is considered first in the case of a single type, and second in the case of multiple types. The main result is that the type frequencies as N→∞ obey the replicator equation with instantaneous growth rates for the different types that depend only on instantaneous equilibrium class frequencies and reproductive values. An application to evolutionary game theory complemented by simulation results is presented. [ABSTRACT FROM AUTHOR]

In this paper, we present a new method for the prediction and uncertainty quantification of data-driven multivariate systems. Traditionally, either mechanistic or non-mechanistic modeling methodologies have been used for prediction; however, it is uncommon for the two to be incorporated together. We compare the forecast accuracy of mechanistic modeling, using Bayesian inference, a non-mechanistic modeling approach based on state space reconstruction, and a novel hybrid methodology composed of the two for an age-structured population data set. The data come from cannibalistic flour beetles, in which it is observed that the adults preying on the eggs and pupae result in non-equilibrium population dynamics. Uncertainty quantification methods for the hybrid models are outlined and illustrated for these data. We perform an analysis of the results from Bayesian inference for the mechanistic model and hybrid models to suggest reasons why hybrid modeling methodology may enable more accurate forecasts of multivariate systems than traditional approaches. [ABSTRACT FROM AUTHOR]

Pelophylax esculentus is a vertebrate animal with hemiclonal heredity, attracting the interest of many reproductive and evolutionary biologists. It is a hybrid between P. ridibundus and P. lessonae. These three taxa form the so-called Pelophylax esculentus complex with a population structure usually comprising a hybrid taxa and one parental species. Data on population types at the southernmost distribution area of their sympatry are rare. Here we sampled five sites in inland Croatia in order to analyse the population structure, sex ratio and age structure. The individual genotypes of 93 randomly collected water frogs were verified with allozyme markers for three species-specific polymorphic loci. In order to estimate population age structure, the annual growth rate (skeletochronology) and growth index profiles were also investigated. The growth index profiles were analysed by an estimation of number of lines of arrested growth visible in the cross-section of femur bones. Our results revealed the presence of the R-E-L population with a dominance of P. esculentus. Pelophylax ridibundus was the least abundant taxon but with a relatively high age estimate of eight years on average. Its annual growth rate did not differ from the remaining two species. Gene introgression of mostly ridibundus alleles was also observed in hybrids. Most profiles of gonads in hybrids showed presence of both parental genomes with dominance of ridibundus alleles. The study area represents one of the southernmost distributions of the hybrid taxon in Europe, making it attractive to study gene flow and impact of P. esculentus on P. ridibundus, a typical water frog representative of the Balkan Peninsula. [ABSTRACT FROM AUTHOR]

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction–diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction–diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth. [ABSTRACT FROM AUTHOR]

A new age-structured epidemic model with imperfect vaccination and relapse is proposed. The total population of our model is partitioned into five subclasses: susceptible class S , vaccinated class V , exposed class E , infectious class I and removed class R . Age-structures are equipped with in exposed and recovered classes. Furthermore, imperfect vaccination is also introduced in our model. The basic reproduction number R 0 is defined and proved as a threshold parameter of the model. Asymptotic smoothness of solutions and uniform persistence of the system are showed via reformulating the system as a system of Volterra integral equation. Furthermore, by constructing proper Volterra-type Lyapunov functional we get when R 0 < 1 , the disease-free equilibrium is globally asymptotically stable. When R 0 > 1 , the endemic equilibrium is globally stable. Our results show that to increase the efficiency of vaccination and reduce influence of relapse are vital essential for controlling epidemic. [ABSTRACT FROM AUTHOR]

Climatic change is expected to affect individual life histories and population dynamics, potentially increasing vulnerability to extinction. The importance of genetic diversity has been highlighted for adaptation and population persistence. However, whether responses of life-history traits to a given environmental condition depend on the genetic characteristics of a population remains elusive. Here we tested this hypothesis in the lizard Zootoca vivipara by simultaneously manipulating habitat humidity, a major climatic predictor of Zootoca’s distribution, and adult male color morph frequency, a trait with genome-wide linkage. Interactive effects of humidity and morph frequency had immediate effects on growth and body condition of juveniles and yearlings, as well as on adult survival, and delayed effects on offspring size. In yearlings, higher humidity led to larger female body size and lower humidity led to higher male compared to female survival. In juveniles and yearlings, some treatment effects were compensated over time. The results show that individual responses to environmental conditions depend on the population’s color morph frequency, age class, and sex and that these affect intra– and inter–age class competition. Moreover, humidity affected the competitive environment rather than imposing trait-based selection on specific color morphs. This indicates that species’ responses to changing environments (e.g., to climate change) are highly complex and difficult to accurately reconstruct and predict without information on the genetic characteristics and demographic structure of populations. [ABSTRACT FROM AUTHOR]

In this study, Haar wavelet method is implemented for solving the nonlinear age-structured population model which is the nonclassic type of partial differential equation associated with boundary integral equation. This paper develops the flexibility of Haar wavelet method for reduction of the partial differential equation with nonlocal boundary conditions to an algebraic system. In fact, the simple structure of piecewise orthogonal Haar basis functions which leads to sparse matrices causes the convergence and computational efficiency. Some illustrative results show the reliability and accuracy of the presented method. [ABSTRACT FROM AUTHOR]

We present bounded dynamic (but observer-free) output feedback laws that achieve global stabilization of equilibrium profiles of the partial differential equation (PDE) model of a simplified, agestructured chemostat model. The chemostat PDE state is positive-valued, which means that our global stabilization is established in the positive orthant of a particular function space-a rather non-standard situation, for which we develop non-standard tools. Our feedback laws do not employ any of the (distributed) parametric knowledge of the model. Moreover, we provide a family of highly unconventional Control Lyapunov Functionals (CLFs) for the age-structured chemostat PDE model. Two kinds of feedback stabilizers are provided: stabilizers with continuously adjusted input and sampled-data stabilizers. The results are based on the transformation of the first-order hyperbolic partial differential equation to an ordinary differential equation (one-dimensional) and an integral delay equation (infinitedimensional). Novel stability results for integral delay equations are also provided; the results are of independent interest and allow the explicit construction of the CLF for the age-structured chemostat model. [ABSTRACT FROM AUTHOR]

Some studies show that latency and relapse, especially the age-dependent latency and relapse, may affect the transmission dynamics of tuberculosis model. Meanwhile, the immigration of infected individuals induces the loss of disease-free steady state and hence no basic reproduction number. In our work, a class of age-structured tuberculosis model with immigration is proposed, where the new individuals can immigrate into the susceptible, latent, infectious and removed compartments. We show that the endemic steady state is unique and globally asymptotically stable by using the Lyapunov functional. Numerical simulations are given to support our theoretical results. [ABSTRACT FROM AUTHOR]

The dynamics from nonlinear discrete age-structured population models is under consideration. Focus is on bifurcations, as well as nonstationary and chaotic dynamics. We also explore different mechanisms which may lead to periodic phenomena. Some new results are also presented, in particular from models where both fecundity and survival terms contain nonlinear elements. [ABSTRACT FROM AUTHOR]

A variety of data types can be included in contemporary integrated stock assessments to simultaneously provide information on all estimated parameters. Conflicts between data, which are often a symptom of model misspecification and evident as model misfit, can affect the estimates of important parameters and derived quantities. Unfortunately, there are few standard diagnostic tools available for integrated stock assessment models that can provide the analyst with all the information needed to determine if there is substantial model misspecification. In this study, we use simulation methods to evaluate the ability of commonly-used and recently-proposed diagnostic tests to detect model misspecification in the observation model process (i.e., the incorrect form for survey selectivity), systems dynamics (i.e., incorrect assumed values for steepness of the stock-recruitment relationship and natural mortality), and incorrect data weighting. The diagnostic tests evaluated here were: i) residuals analysis (SDNR and runs test); ii) retrospective analysis; iii) the R 0 likelihood component profile; iv) the age-structured production model (ASPM); and v) catch-curve analysis (CCA). The efficacy of the diagnostic tests depended on whether the misspecification was in the observation or systems dynamics model. Residual analyses were easily the best detector of misspecification of the observation model while the ASPM test was the only good diagnostic for detecting misspecification of system dynamics model. Retrospective analysis and the R 0 likelihood component profile infrequently detected misspecified models, and CCA had a high probability of rejecting correctly-specified models. Finally, applying multiple carefully selected diagnostics can increase the power to detect misspecification without substantially increasing the probability of falsely concluding there is misspecification when the model is correctly specified. [ABSTRACT FROM AUTHOR]

Population growth is governed by many external and internal factors. In order to study their effects on population dynamics, we develop an age-structured time-dependent population model with logistic-type nonlinearity. We prove existence of a unique nonnegative bounded solution. Our main concern is to study asymptotic behavior of a solution in the general case, and especially for a periodic environment. We use the method of lower and upper solutions known in the theory of integral equations to formulate lower and upper boundaries of population density. In the periodic case, we discover a connection between the period of oscillation and its effect on population growth. [ABSTRACT FROM AUTHOR]

We are interested in the long time behaviour of the positive solutions of the Cauchy problem involving the integro-di erential equation ∂tu(t,x) =∫Ωm(x,y)(u(t,y)-u(t,x))dy+(a(x)-∫Ωk(x,y)u(t,y)dy)u(t,x), supplemented by the initial condition u(0,.)= u0 in Ω. Such a problem is used in population dynamics models to capture the evolution of a clonal population structured with respect to a phenotypic trait. In this context, the function u represents the density of individuals characterized by the trait, the domain of trait values is a bounded subset of ℝN, the kernels k and m respectively account for the competition between individuals and the mutations occurring in every generation, and the function a represents a growth rate. When the competition is independent of the trait, we construct a positive stationary solution which belongs to the space of Radon measures on Ω . Moreover, in the case where this measure is regular and bounded, we prove its uniqueness and show that, for any non-negative initial datum in L1(Ω)∩L∞(Ω), the solution of the Cauchy problem converges to this limit measure in L2(Ω). We also exhibit an example for which the measure is singular and non-unique, and investigate numerically the long time behaviour of the solution in such a situation. The numerical simulations seem to reveal a dependence of the limit measure with respect to the initial datum. [ABSTRACT FROM AUTHOR]

Routine public health surveillance of notifiable infectious diseases gives rise to weekly counts of reported cases-possibly stratified by region and/or age group. We investigate how an age-structured social contact matrix can be incorporated into a spatio-temporal endemic-epidemic model for infectious disease counts. To illustrate the approach, we analyze the spread of norovirus gastroenteritis over six age groups within the 12 districts of Berlin, 2011-2015, using contact data from the POLYMOD study. The proposed age-structured model outperforms alternative scenarios with homogeneous or no mixing between age groups. An extended contact model suggests a power transformation of the survey-based contact matrix toward more within-group transmission. [ABSTRACT FROM AUTHOR]

The global dynamics of an SVEIR epidemic model with age-dependent waning immunity, latency and relapse are studied. Sharp threshold properties for global asymptotic stability of both disease-free equilibrium and endemic equilibrium are given. The asymptotic smoothness, uniform persistence and the existence of interior global attractor of the semi-flow generated by a family of solutions of the system are also addressed. Furthermore, some related strategies for controlling the spread of diseases are discussed. [ABSTRACT FROM AUTHOR]

The paper considers the ecological variability of the round goby, Neogobius melanostomus (Pall.), in different environments. The dietary spectrum and morphological variability of round goby populations were studied in two water bodies with different environmental conditions. The sizes and body weights of specimens were the largest in Obytichna Bay and the smallest in Kakhovka Reservoir. Differences in the morphological indices of gobies from freshwater and marine bodies of water were determined using discriminant analysis. At the study sites the round goby chiefly fed on benthic organisms that varied in species composition and energy equivalent. A significant portion of the diet comprised bivalves such as Abra ovata, Cerastoderma glaucum, and Parvicardium exiguum, which have the highest energy capacity. The average energy equivalent indices of prey items were higher in Obytichna Bay and the lowest in Kakhovka Reservoir. [ABSTRACT FROM AUTHOR]

Discrete time models are used in Ecology for describing the dynamics of an age-structured population. They can be introduced from a deterministic or from a stochastic viewpoint. We analyze a stochastic model for the case in which the dynamics of the population is described by means of a projection matrix. In this statistical model, fertility rates and survival rates are unknown parameters which are estimated by using a Bayesian approach and also data cloning, which is a simulation-based method especially useful with complex hierarchical models. Both methodologies are applied to real data from the population of Steller sea lions located in the Alaska coast since 1978–2004. The estimates obtained from these methods show a good behavior when they are compared to the nonmissing actual values. [ABSTRACT FROM PUBLISHER]

Cyclic processes, in particular the cell cycle, are of great importance in cell biology. Continued improvement in cell population analysis methods like fluorescence microscopy, flow cytometry, CyTOF or single-cell omics made mathematical methods based on ergodic principles a powerful tool in studying these processes. In this paper, we establish the relationship between cell cycle analysis with ergodic principles and age structured population models. To this end, we describe the progression of a single cell through the cell cycle by a stochastic differential equation on a one dimensional manifold in the high dimensional dataspace of cell cycle markers. Given the assumption that the cell population is in a steady state, we derive transformation rules which transform the number density on the manifold to the steady state number density of age structured population models. Our theory facilitates the study of cell cycle dependent processes including local molecular events, cell death and cell division from high dimensional “snapshot” data. Ergodic analysis can in general be applied to every process that exhibits a steady state distribution. By combining ergodic analysis with age structured population models we furthermore provide the theoretic basis for extensions of ergodic principles to distribution that deviate from their steady state. [ABSTRACT FROM AUTHOR]

How ecological context shapes mutualistic relationships remains poorly understood. We combined long-term tree census data with ant censuses in a permanent 25-ha Amazonian forest dynamics plot to evaluate the effect of the mutualistic ant Myrmelachista schumanni (Formicinae) on the growth and survival of the common Amazonian tree Duroia hirsuta (Rubiaceae), considering its interactions with tree growth, population structure, and habitat. We found that the mutualist ant more than doubled tree relative growth rates and increased odds of survival. However, host tree size and density of conspecific neighbors modified the effect of the ant. Smaller trees hosting the mutualist ant consistently grew faster when surrounded by higher densities of conspecifics, suggesting that the benefit to the tree outweighs any negative effects of high conspecific densities. Moreover, our findings suggest that the benefit afforded by the ant diminishes with plant age and also depends on the density of conspecific neighbors. We provide the first long-term large-scale evidence of how mutualism affects the population biology of an Amazonian tree species. [ABSTRACT FROM AUTHOR]

This paper presents a novel analysis for the solution of nonlinear age-structured problem which is of extreme importance in biological sciences. The presented model is very useful but quite complicated. Modified variational iteration method (MVIM) coupled with auxiliary parameter is used to cope with the complexity of the model which subsequently shows better results as compared to some existing results available in literature. Furthermore, an appropriate way is used for the identification of auxiliary parameter by means of residual function. Numerical examples are presented for the analysis of the proposed algorithm. Graphical results along with the discussions re-confirm the efficiency of proposed algorithm. The work proposes a new algorithm where He's polynomials and an auxiliary parameter are merged with correction functional. The suggested scheme is implemented on nonlinear age-structured population models. Graphs are plotted for the residual function that reflects the accuracy and convergence of the presented algorithm. [ABSTRACT FROM AUTHOR]

Structured population models, particularly size- or age-structured, have a long history of informing conservation and natural resource management. While size is often easier to measure than age and is the focus of many management strategies, age-structure can have important effects on population dynamics that are not captured in size-only models. However, relatively few studies have included the simultaneous effects of both age- and size-structure. To better understand how population structure, particularly that of age and size, impacts restoration and management decisions, we developed and compared a size-structured integral projection model (IPM) and an age- and size-structured IPM, using a population of Crassostrea gigas oysters in the northeastern Pacific Ocean. We analyzed sensitivity of model results across values of local retention that give populations decreasing in size to populations increasing in size. We found that age- and size-structured models yielded the best fit to the demographic data and provided more reliable results about long-term demography. Elasticity analysis showed that population growth rate was most sensitive to changes in the survival of both large (>175 mm shell length) and small (<75 mm shell length) oysters, indicating that a maximum size limit, in addition to a minimum size limit, could be an effective strategy for maintaining a sustainable population. In contrast, the purely size-structured model did not detect the importance of large individuals. Finally, patterns in stable age and stable size distributions differed between populations decreasing in size due to limited local retention and populations increasing in size due to high local retention. These patterns can be used to determine population status and restoration success. The methodology described here provides general insight into the necessity of including both age- and size-structure into modeling frameworks when using population models to inform restoration and management decisions. [ABSTRACT FROM AUTHOR]

Age and growth are key biological aspects for the age-structured assessment of exploited fish populations. Confirming the consistency of fish age interpretation by validation/corroboration studies is essential for providing accurate age estimates to the stock assessment process. The Atlantic Iberian stock of four-spot-megrim ( Lepidorhombus boscii ), an important exploited demersal fish, is annually assessed by age-structured models in ICES, and specimens are routinely aged by IEO expert readers for this purpose. A total of 11,741 otoliths of this stock were aged from 23 annual groundfish surveys carried out in Cantabrian Sea and Galician waters (ICES Div. VIIIc, IXa) and following internationally standardized protocols. Annual age-length-keys were built using the respective age estimates and applied to the length distribution of each survey, thus obtaining a matrix of abundance indices by age and year. Similar mean lengths are obtained for each age group along most of the time-series. The von Bertalanffy growth parameters for the time-series are estimated (L ∞ : 49.0; k: 0.13; t 0 : −1.13) and the results are compared with previous studies. The annual growth pattern estimated for L. boscii is here corroborated by tracking cohort abundance indices in the surveys. The current otolith age estimation criterion used and the resulting age estimates obtained by the age readers can be considered valid. Strong and weak cohorts are well tracked along most of their age classes, and the correlations between age abundance indices are statistically significant up to the age 6, which represent around 95% of the total number of this species caught in the surveys. The findings here presented on the age of L. boscii and its corroboration can help to reduce the uncertainty in the estimation of its demographic structure and hence, ultimately, it will be important for a better understanding of its relevance in the functioning of the benthic community of the shelf. [ABSTRACT FROM AUTHOR]

We study the impact of age-structure and temporal environmental variability on the persistence of populations. We use a linear age-structured model with time-dependent vital rates. It is the same as the one presented by Chipot in (Arch. Ration. Mech. Anal. 82(1):13-25, 1983), but the assumptions on the vital rates are slightly different. Our main interest is in describing the large-time behavior of a population provided that we know its initial distribution and transient vital rates. Using upper and lower solutions for the characteristic equation, we define time-dependent upper and lower boundaries for a solution in a constant environment. Moreover, we estimate solutions for the general time-dependent case and also for a special case when the environment is changing periodically. [ABSTRACT FROM AUTHOR]

Growth – the way that fish get bigger as they get older – is one component of the population models used in fisheries stock assessments. I review current practice related to this component in age-structured models, discussing how growth is specified, its functions in the stock assessment model, and how growth-related data are used. I then discuss some associated problems and suggest that (a) we should be cautious about assuming that all fishery selectivities are size-based, and that an age–size sample is always random at size; (b) the jury is still out on the question of whether growth variation by phenotype is a useful model feature; (c) when growth is time-varying, conditional age-at-size data might better used outside the model (as an age–size key); and (d) that it is often difficult to extract much growth information from size composition data. I conclude by presenting a strategy for addressing the structural, procedural, and statistical decisions that must be made in finding the growth model best suited to our data. [ABSTRACT FROM AUTHOR]

Length-frequency data and derived catch at age matrices are used in north Atlantic albacore ( Thunnus alalunga ) stock assessment conducted within the International Commission for the Conservation of Atlantic Tunas (ICCAT). Growth is assumed to follow the von Bertalanffy model with the assumption that growth parameters are constant over time and the same for all fish. However, individual growth variability is an important factor not considered and affecting the input into the modelling of the population. This study describes a Bayesian hierarchical model applied to model the individual variability in the parameters asymptotic length ( L ∞ ) and growth rate ( K ) of the von Bertalanffy growth model for North Atlantic albacore. The method assumes that the L ∞ and K values for each individual fish are drawn from a random distribution centered on the population mean values, with estimated variances. Multiple observations of spine diameter at age for individual fish were obtained by direct reading of spine sections collected in 2011 and 2012. A suite of back calculation methods were then applied to the measurements of annuli diameters in the aged individuals observed to back-calculate lengths at each age. The von Bertalanffy model was fitted to the measured and back-calculated lengths. Models with and without individual growth variability were compared using the deviance information criterion (DIC) to find the best model. Normal and log-normal error distribution models were used to analyse the data. Additionally, subsamples of the data were used to evaluate whether an unbalanced age-distribution in the data affects estimates of growth parameters. It was found that North Atlantic albacore asymptotic length ( L ∞ ) varies significantly between individual fish but not individual rate growth ( K ), for all back-calculation methods. Furthermore, negatively correlated relationships between von Bertalanffy growth parameters of asymptotic mean ( L ∞ ) and growth rate (K) were estimated for North Atlantic albacore with the array of models explored. The overall estimated values of K and population mean L ∞ parameters were similar to values estimates in previous north Atlantic albacore growth studies. [ABSTRACT FROM AUTHOR]

Analysts conducting stock assessments using integrated, age-structured models must discretize length data into a limited number of bins (data bins). Furthermore, some modeling frameworks also allow users to specify a distinct structure for how lengths of fish are represented in the model (model bins). The effect of choices regarding the number and width of these bins on model output is unclear, and these choices are made inconsistently in assessments across regions and species. Here, we used the stock synthesis modeling framework, and the ss3sim stock assessment simulation package, to explore the effects of choices about length discretization on stock assessment performance for three fish life-history types and four data cases. We found that, with all other aspects of a model fixed, increasing the model bin width tended to increase estimates of spawning biomass, but this effect depended on the shape of length-based processes (e.g., growth, maturity, and selectivity). Thus, we suggest analysts using model bins wider than 1 cm explore the effect of this decision on derived management quantities. In the context of estimation, there generally was a predictable tradeoff between estimation accuracy and model run time, with finer model and data bins always improving estimation accuracy and model convergence, but increasing run time. In some cases, wider data bins reduced run time (by up to 50%) with little sacrifice in model estimation performance, particularly those using conditional age-at-length data. This study identifies key aspects to consider when binning length, and provides pertinent information for stock assessment best practice guidelines. [ABSTRACT FROM AUTHOR]