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The accurate measurement of poverty is essential for the development of effective poverty policy. Unfortunately, approaches that use poverty rates to assess the causes and consequences of poverty do not fully capture the components of change in the poverty population because changes in the conventional poverty rate can occur owing to processes of natural increase, migration, or transitions in and out of poverty. This article presents an accounting framework for changes in poverty within and between places. The framework, termed the poverty balancing equation, generates a series of summary statistics that can be used in place of the conventional poverty rate in future research. The approach is demonstrated using the 2014 panel of the Survey of Income and Program Participation to generate state-level estimates of the poverty components of change for three states in the American South between January and December of 2013. Results show that even when poverty rates remain constant, there is significant dynamism within poor and nonpoor populations. By applying this approach, either completely or in part, researchers can provide more specific and actionable evidence for poverty alleviation policy.

BackgroundTheWolbachiaincompatible insect technique (IIT) shows promise as a method for eliminating populations of invasive mosquitoes such asAedes aegypti(Linnaeus) (Diptera: Culicidae) and reducing the incidence of vector-borne diseases such as dengue, chikungunya and Zika. Successful implementation of this biological control strategy relies on high-fidelity separation of male from female insects in mass production systems for inundative release into landscapes. Processes for sex-separating mosquitoes are typically error-prone and laborious, and IIT programmes run the risk of releasingWolbachia-infected females and replacing wild mosquito populations.ResultsWe introduce a simple Markov population process model for studying mosquito populations subjected to aWolbachia-IIT programme which exhibit an unstable equilibrium threshold. The model is used to study, in silico, scenarios that are likely to yield a successful elimination result. Our results suggest that elimination is best achieved by releasing males at rates that adapt to the ever-decreasing wild population, thus reducing the risk of releasingWolbachia-infected females while reducing costs.ConclusionsWhile very high-fidelity sex separation is required to avoid establishment, release programmes tend to be robust to the release of a small number ofWolbachia-infected females. These findings will inform and enhance the next generation ofWolbachia-IIT population control strategies that are already showing great promise in field trials.

Amino acid substitution models are commonly used for phylogenetic inference, for ancestral sequence reconstruction, and for the inference of positive selection. All commonly used models explicitly assume that each site evolves independently, an assumption that is violated by both linkage and protein structural and functional constraints. We introduce two new models for amino acid substitution which incorporate linkage between sites, each based on the (population-genetic) Moran model. The first model is a generalized population process tracking arbitrarily many sites which undergo mutation, with individuals replaced according to their fitnesses. This model provides a reasonably complete framework for simulations but is numerically and analytically intractable. We also introduce a second model which includes several simplifying assumptions but for which some theoretical results can be derived. We analyze the simplified model to determine conditions where linkage is likely to have meaningful effects on sitewise substitution probabilities, as well as conditions under which the effects are likely to be negligible. These findings are an important step in the generation of tractable phylogenetic models that parameterize selective coefficients for amino acid substitution while accounting for linkage of sites leading to both hitchhiking and background selection.

International audience; Motivated by the study of a parasite infection in a cell line, we introduce a general class of Markov processes for the modelling of population dynamics.The population process evolves as a diffusion with positive jumps whose rate is a function of the population size. It also undergoes catastrophic events which kill a fraction of the population, at a rate depending on the population state. We study the long time behaviour of this class of processes.

The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time, a randomly selected portion of the population is eliminated. For this population process, we derive an asymptotic upper bound for the maximum value and prove the local large deviation principle., 22 pages

The setting considered in this paper concerns a discrete-time multivariate population process under Markov modulation. Our objective is to estimate the model parameters, based on periodic observations of the network population vector. These parameters relate to the arrival, routing and departure processes, but also to the (unobservable) Markovian background process. When opting for the classical likelihood-based approach, the evaluation of the likelihood is problematic. We show however, how an accurate saddlepoint approximation can be used. Numerical experiments illustrate our method and show that even under relatively complicated conditions the parameters are estimated relatively precisely.

Population dynamic models combine density dependence and environmental effects. Ignoring sampling uncertainty might lead to biased estimation of the strength of density dependence. This is typically addressed using state‐space model approaches, which integrate sampling error and population process estimates. Such models seldom include an explicit link between the sampling procedures and the true abundance, which is common in capture–recapture settings. However, many of the models proposed to estimate abundance in the presence of capture heterogeneity lead to incomplete likelihood functions and cannot be straightforwardly included in state‐space models. We assessed the importance of estimating sampling error explicitly by taking an intermediate approach between ignoring uncertainty in abundance estimates and fully specified state‐space models for density‐dependence estimation based on autoregressive processes. First, we estimated individual capture probabilities based on a heterogeneity model for a closed population, using a conditional multinomial likelihood, followed by a Horvitz–Thompson estimate for abundance. Second, we estimated coefficients of autoregressive models for the log abundance. Inference was performed using the methodology of integrated nested Laplace approximation (INLA). We performed an extensive simulation study to compare our approach with estimates disregarding capture history information, and using R‐package VGAM, for different parameter specifications. The methods were then applied to a real data set of gray‐sided voles Myodes rufocanus from Northern Norway. We found that density‐dependence estimation was improved when explicitly modeling sampling error in scenarios with low process variances, in which differences in coverage reached up to 8% in estimating the coefficients of the autoregressive processes. In this case, the bias also increased assuming a Poisson distribution in the observational model. For high process variances, the differences between methods were small and it appeared less important to model heterogeneity., We assessed the importance of including capture history information in the estimation of density dependence from capture–recapture data. We performed an extensive simulation study, evaluating the performance of different methods in the estimation of different population processes. We found that disregarding sampling error can bias the density‐dependence estimates in low variance autoregressive population models.

The Wolbachia Incompatible Insect Technique (IIT) shows promise as a method for eliminating invasive mosquitoes such as Aedes aegypti (Linnaeus)(Diptera: Culicidae) and reducing the incidence of vector-borne diseases such as dengue, chikungunya and Zika. Successful implementation of this biological control strategy relies on high-fidelity separation of male from female insects in mass production systems for inundative release into landscapes. Processes for sex-separating mosquitoes are typically error prone, laborious and IIT programs run the risk of releasing Wolbachia infected females and replacing wild mosquito populations. We introduce a simple Markov Population Process (MPP) model for studying mosquito populations subjected to a Wolbachia-IIT program which exhibit an unstable equilibrium threshold. The model is used to study, in silico, scenarios that are likely to yield a successful elimination result. Our results suggest that elimination is best achieved by releasing males at rates that adapt to the ever-decreasing wild population, thus reducing the risk of releasing Wolbachia-infected females while reducing costs. While very high-fidelity sex-separation is required to avoid establishment, release programs tend to be robust to the release of a small number of Wolbachia-infected females. These findings will inform and enhance the next generation of Wolbachia-IIT control strategies that are already showing great promise in field trials.

For a generalized continuous-state branching process with non-vanishing diffusion part, finite expectation and a directed (“left-to-right”) interaction, we construct the height process of its forest of genealogical trees. The connection between this height process and the population size process is given by an extension of the second Ray–Knight theorem. This paper generalizes earlier work of the two last authors which was restricted to the case of continuous branching mechanisms. Our approach is different from that of Berestycki et al. (Probab Theory Relat Fields 172:725–788, 2018). There the diffusion part of the population process was allowed to vanish, but the class of interactions was more restricted.

We derive and analyze the time-dependent probability density function for the number of individuals in a population at a given time in a general logistic population model with harvesting effort using the Fokker–Planck equation. The time-dependent probability density function (obtained as the unique principal solution of the Fokker–Planck equation corresponding to certain initial value and boundary conditions) is used to describe how the distribution of the population process changes with time. We assume the environment is randomly varying and the population is subject to a continuous spectrum of disturbances, with fluctuations in the intrinsic growth rate and the harvesting effort. The randomness is expressed as independent white noise processes. The effect of changes in the intrinsic growth rate, harvesting effort, and noise intensities on the distribution is investigated. In addition, conditions for the existence of optimal harvesting policy are obtained using properties of the time-dependent probability density function. The results obtained in this work are validated using population and published parameters.

The article discusses the necessity to refer to the notion of demographic process selectivity in the Demography course at the bachelor’s degree program, examples of selectivity manifestation of various demographic processes are given.

Following its introduction over 30 years ago, the Markov cohort state-transition model has been used extensively to model population trajectories over time in health decision modeling and cost-effectiveness analysis studies. We recently showed that a cohort model represents the average of a continuous-time stochastic process on a multidimensional integer lattice governed by a master equation, which represents the time-evolution of the probability function of an integer-valued random vector. By leveraging this theoretical connection, this study introduces an alternative modeling method using a stochastic differential equation (SDE) approach, which captures not only the mean behavior but also the variance of the population process. We show the derivation of an SDE model from first principles, describe an algorithm to construct an SDE and solve the SDE via simulation for use in practice, and demonstrate the two applications of an SDE in detail. The first example demonstrates that the population trajectories, and their mean and variance, from the SDE and other commonly used methods in decision modeling match. The second example shows that users can readily apply the SDE method in their existing works without the need for additional inputs beyond those required for constructing a conventional cohort model. In addition, the second example demonstrates that the SDE model is superior to a microsimulation model in terms of computational speed. In summary, an SDE model provides an alternative modeling framework which includes information on variance, can accommodate for time-varying parameters, and is computationally less expensive than a microsimulation for a typical cohort modeling problem.

Effective conservation and management of animal populations requires knowledge of abundance and trends. For many species, these quantities are estimated using systematic visual surveys. Additional individual-level data are available for some species. Integrated population modeling (IPM) offers a mechanism for leveraging these data sets into a single estimation framework. IPMs that incorporate both population- and individual-level data have previously been developed for birds, but have rarely been applied to cetaceans. Here, we explore how IPMs can be used to improve the assessment of cetacean populations. We combined three types of data that are typically available for cetaceans of conservation concern: population-level visual survey data, individual-level capture-recapture data, and data on anthropogenic mortality. We used this IPM to estimate the population dynamics of the Cook Inlet population of beluga whales (CIBW; Delphinapterus leucas) as a case study. Our state-space IPM included a population process model and three observational submodels: (1) a group detection model to describe group size estimates from aerial survey data; (2) a capture-recapture model to describe individual photographic capture-recapture data; and (3) a Poisson regression model to describe historical hunting data. The IPM produces biologically plausible estimates of population trajectories consistent with all three data sets. The estimated population growth rate since 2000 is less than expected for a recovering population. The estimated juvenile/adult survival rate is also low compared to other cetacean populations, indicating that low survival may be impeding recovery. This work demonstrates the value of integrating various data sources to assess cetacean populations and serves as an example of how multiple, imperfect data sets can be combined to improve our understanding of a population of interest. The model framework is applicable to other cetacean populations and to other taxa for which similar data types are available.

Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a stochastic model for the evolution of a discrete population structured by a trait taking finitely many values, with density-dependent competition. Traits are vertically inherited unless a mutation occurs, and can also be horizontally transferred by unilateral conjugation with frequency dependent rate. Our goal is to analyze the trade-off between natural evolution to higher birth rates on one side, and transfer which drives the population towards lower birth rates on the other side. Simulations show that evolutionary outcomes include evolutionary suicide or cyclic re-emergence of small populations with well-adapted traits. We focus on a parameter scaling where individual mutations are rare but the global mutation rate tends to infinity. This implies that negligible sub-populations may have a strong contribution to evolution. Our main result quantifies the asymptotic dynamics of subpopulation sizes on a logarithmic scale. We characterize the possible evolutionary outcomes with explicit criteria on the model parameters. An important ingredient for the proofs lies in comparisons of the stochastic population process with linear or logistic birth-death processes with immigration. For the latter processes, we derive several results of independent interest.

Survival is an important population process in fisheries stock assessment models and is typically treated as deterministic. Recently developed state-space assessment models can estimate stochastic deviations in survival, which represent variability in some ambiguous combination of natural mortality (M), fishing mortality (F), and migration. These survival deviations are generally treated as independent by age and year, despite our understanding that many population processes can be autocorrelated and that not accounting for autocorrelation can result in notable bias. We address these concerns, as well as the strong retrospective pattern found in the last assessment of Southern New England yellowtail flounder (Limanda ferruginea), by incorporating two-dimensional (2D, age and year) first-order autocorrelation in survival and M. We found that deviations were autocorrelated among both years (0.53 ± 0.09, 0.63 ± 0.16) and ages (0.33 ± 0.12, 0.40 ± 0.16) when estimated for survival or M, respectively. Models with 2D autocorrelation on survival or M fit the data better and had reduced retrospective pattern than models without autocorrelation. The best fit model included 2D autocorrelated deviations in survival as well as independent deviations in M and altered estimates of spawning stock biomass by 18 % and F by 21 % in model years. In short-term projections with F = 0, including 2D autocorrelation in survival or M reduced spawning stock biomass by 48 %. We conclude that incorporating 2D autocorrelated variation in survival or M could improve the assessment of Southern New England yellowtail flounder in terms of model fit and consistency of biomass projections.

A Markov population decision chain concerns the control of a population of individuals in different states by assigning an action to each individual in the system in each period. This article solves the problem of finding policies that maximize expected system utility over a finite horizon in Markov population decision chains with finite state-action space under the following assumptions: (1) The utility function exhibits constant risk posture, (2) the progeny vectors of distinct individuals are independent, and (3) the progeny vectors of individuals in a state who take the same action are identically distributed. The main result is that it is possible to solve the problem with the original state-action space without augmenting it to include information about the population in each state or any other aspect of the system history. In particular, there exists an optimal policy that assigns the same action to all individuals in a given state and period, independently of the population in that period and such a policy can be computed efficiently. The optimal utility operators that find the maximum of a finite collection of polynomials (rather than affine functions) yield an optimal solution with effort linear in the number of periods.© 2016 Wiley Periodicals, Inc. Naval Research Logistics, 2016

The paper solves the problem of modeling an outbreak of the species, which begins with the achievement of a specific nontrivial state of a dynamic system. Population process is divided into a sequence of substantially different stages. The model simulates the effect of spontaneous transition from weak fluctuations through accelerated reproductive activity to exceeded ecological capacity of the environment followed by the phase of rapid spontaneous decay. To describe the transition between final stages of the outbreak, the method of controlled functional realization of metamorphoses of trajectory behavior are used. Differential equations are combined with predicative constructions in software environment. The original computational unit is based on discrete-continuous time and allows us to apply the scenario approach to the consideration of environmental situations. The significance of the results is justified by the analysis of the data about outbreaks of small insect pests that eat on a limited number of suitable plants and, under certain conditions, can get out of control of parasitic wasps.

Economic mobilization of the wireless communication system causes the broadcast explosion error to occur in a multi-layered fading state in many ways, and band loss is difficult. It is necessary to investigate error series that can provide insights into error patterns or 5 G wireless data transfer behavior. This market share concept is that the 5th Generation (5 G) cellular systems Internet of Things use will be a powerful inspiration in the future. Device-to-Device (D2D) communication is an essential method of evolving and gaining significant benefits and supports for Markov chain integration. It is possible to effectively increase the 5 G network internet requirements for research matters for economic accuracy forecasting. To overcome the issue, proposed the method Economic Probability Agglomeration Based Markov Model (EPAMM). The radio error model 5 G wireless communication helps provide a complete understanding of the population process, allowing less complicated predictions and shorter simulation time to control and evaluate error strategies. The error sequences generated from the 5 G wireless simulation and the Markov model show that can fully model the error behavior of the 5 G simulation using the Markov model.

We define and study an open stochastic SIR (Susceptible -- Infected -- Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same time scale. Population transition intensities are assumed to be density-dependent with a constant component, the amplitude of which determines the overall scale of the population process. Standard branching approximation results for the epidemic process are first given, along with a numerical computation method for the probability of a major epidemic outbreak. This procedure is illustrated using real data on trade-related cattle movements from a densely populated livestock farming region in western France (Finist\`ere) and epidemiological parameters corresponding to an infectious epizootic disease. Then we exhibit an exponential lower bound for the extinction time and the total size of the epidemic in the stable endemic case as a scaling parameter goes to infinity using results inspired by the Freidlin-Wentzell theory of large deviations from a dynamical system., Comment: 31 pages

Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the levels are distributed on $[0,\lambda ]$, whereas in the infinite intensity limit $\lambda\rightarrow\infty$, at each time $t$, the joint distribution of types and levels is conditionally Poisson, with mean measure $\Xi (t)\times \ell$ where $\ell$ denotes Lebesgue measure and $\Xi (t)$ is a measure-valued population process. The time-evolution of the levels captures the genealogies of the particles in the population. Key forces of ecology and genetics can be captured within this common framework. Models covered incorporate both individual and event based births and deaths, one-for-one replacement, immigration, independent `thinning' and independent or exchangeable spatial motion and mutation of individuals. Since birth and death probabilities can depend on type, they also include natural selection. The primary goal of the paper is to present particle-with-level or lookdown constructions for each of these elements of a population model. Then the elements can be combined to specify the desired model. In particular, a non-trivial extension of the spatial $\Lambda$-Fleming-Viot process is constructed.

The Moran model with recombination is considered, which describes the evolution of the genetic composition of a population under recombination and resampling. There are $n$ sites (or loci), a finite number of letters (or alleles) at every site, and we do not make any scaling assumptions. In particular, we do not assume a diffusion limit. We consider the following marginal ancestral recombination process. Let $S = \{1,...,n\}$ and $\mathcal A=\{A_1, ..., A_m\}$ be a partition of $S$. We concentrate on the joint probability of the letters at the sites in $A_1$ in individual $1$, $...$, and at the sites in $A_m$ in individual $m$, where the individuals are sampled from the current population without replacement. Following the ancestry of these sites backwards in time yields a process on the set of partitions of $S$, which, in the diffusion limit, turns into a marginalised version of the $n$-locus ancestral recombination graph. With the help of an inclusion-exclusion principle, we show that the type distribution corresponding to a given partition may be represented in a systematic way, with the help of so-called recombinators and sampling functions. The same is true of correlation functions (known as linkage disequilibria in genetics) of all orders. We prove that the partitioning process (backward in time) is dual to the Moran population process (forward in time), where the sampling function plays the role of the duality function. This sheds new light on the work of Bobrowski, Wojdyla, and Kimmel (2010). The result also leads to a closed system of ordinary differential equations for the expectations of the sampling functions, which can be translated into expected type distributions and expected linkage disequilibria., 29 pages, 6 figures

This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in parallel. The links that connect the queues have the special feature that they are unreliable, in the sense that their status alternates between ‘up’ and ‘down’. If a link between two nodes is down, with a fixed probability each of the clients attempting to use that link is lost; otherwise the client remains at the origin node and reattempts using the link (and jumps to the destination node when it finds the link restored). For these networks we present the following results: (a) a system of coupled partial differential equations that describes the joint probability generating function corresponding to the queues’ time-dependent behavior (and a system of ordinary differential equations for its stationary counterpart), (b) an algorithm to evaluate the (time-dependent and stationary) moments, and procedures to compute user-perceived performance measures which facilitate the quantification of the impact of the links’ outages, (c) a diffusion limit for the joint queue length process. We include explicit results for a series relevant special cases, such as tandem networks and symmetric fully connected networks.

Conservation and management decision making in natural resources is challenging due to numerous uncertainties and unknowns, especially relating to understanding system dynamics. Adaptive resource management (ARM) is a formal process to making logical and transparent recurrent decisions when there are uncertainties about system dynamics. Despite wide recognition and calls for implementing adaptive natural resource management, applications remain limited. More common is a reactive approach to decision making, which ignores future system dynamics. This contrasts with ARM, which anticipates future dynamics of ecological process and management actions using a model-based framework. Practitioners may be reluctant to adopt ARM because of the dearth of comparative evaluations between ARM and more common approaches to making decisions. We compared the probability of meeting management objectives when managing a population under both types of decision frameworks, specifically in relation to typical uncertainties and unknowns. We use a population of Sandhill Cranes as our case study. We evaluate each decision process under varying levels of monitoring and ecological uncertainty, where the true underlying population dynamics followed a stochastic age-structured population model with environmentally driven vital rate density dependence. We found that the ARM framework outperformed the currently employed reactive decision framework to manage Sandhill Cranes in meeting the population objective across an array of scenarios. This was even the case when the candidate set of population models contained only naive representations of the true population process. Under the reactive decision framework, we found little improvement in meeting the population objective even if monitoring uncertainty was eliminated. In contrast, if the population was monitored without error within the ARM framework, the population objective was always maintained, regardless of the population models considered. Contrary to expectation, we found that age-specific optimal harvest decisions are not always necessary to meet a population objective when population dynamics are age structured. Population managers can decrease risks and gain transparency and flexibility in management by adopting an ARM framework. If population monitoring data has high sampling variation and/or limited empirical knowledge is available for constructing mechanistic population models, ARM model sets should consider a range of mechanistic, descriptive, and predictive model types.

For Markov chain in stochastic process model, bilateral birth and death process is a typical Markov chain. To endow the track structure of birth and death with clear probability direct meaning and make in-depth research on the quantity, it is extremely significant to research the probability property of minimal process. This article has mainly discussed the probability property of minimal process corresponding to bilateral birth and death matrix.

Recent progress has been made on spatial mathematical models of population processes. We review a few of these: the spatial Galton–Watson model, modern versions that add migration and immigration and thereby may avoid the increasing concentration of population into an ever smaller space (clusterization), models involving a random environment, and two versions of the Bolker–Pakala model, in which mortality (or birth rate) is affected by competition.