Population Dynamics fills the gap between the classical supply-side population theory of Malthus and the modern demand-side theory of economic demography. In doing so, author Cyrus Chu investigates specifically the dynamic macro implications of various static micro family economic decisions. Holding the characteristic composition of the macro population to always be an aggregate result of some corresponding individual micro decision, Chu extends his research on the fertility-related decisions of families to an analysis of other economic determinations. (...) Within this framework, Chu studies the income distribution, attitude composition, job structure, and aggregate savings and pensions of the population. While in some cases a micro-macro connection is easily established under regular behavioral assumptions, in several chapters Chu enlists the mathematical tool of branching processes to determine the connection. Offering a wealth of detail, this book provides a balanced discussion of background motivation, theoretical characterization, and empirical evidence in an effort to bring about a renewal in the economic approach to population dynamics. This welcome addition to the research and theory of economic demography will interest professional economists as well as professors and graduate students of economics. (shrink)

The balance between births and deaths in an age-structured population is strongly influenced by the spatial distribution of sub-populations. Our aim was to describe the demographic process of a fish population in an hierarchical dendritic river network, by taking into account the possible movements of individuals. We tried also to quantify the effect of river network changes (damming or channelling) on the global fish population dynamics. The Salmo trutta life pattern was taken as an example for.We (...) proposed a model which includes the demographic and the migration processes, considering migration fast compared to demography. The population was divided into three age-classes and subdivided into fifteen spatial patches, thus having 45 state variables. Both processes were described by means of constant transfer coefficients, so we were dealing with a linear system of difference equations. The discrete case of the variable aggregation method allowed the study of the system through the dominant elements of a much simpler linear system with only three global variables: the total number of individuals in each age-class. (shrink)

Nowadays, around half of the global population lives in urban areas. This rate is expected to increase up to two-thirds by the year 2050. Most studies analyze urban dynamics in wide geographic ranges, focusing mainly on cities. According to them, the global population is spatially distributed in two extremes: large urban agglomerations and rural deserts. However, this remark is excessively general and imprecise. For this reason, it remains essential to analyze these dynamics at other spatial scales. (...) A close-up look in thinly populated regions shows how urban dynamics are also noticeable. In this paper, we analyze spatiotemporal patterns of population distribution in a predominantly rural area by applying a local-scale approach. These patterns are represented by using spatial networks with nodes representing the human settlements and links showing hierarchies between nodes. This case study is conducted in a small municipality located in northwestern Spain. It is a predominantly rural area with a very particular spatial pattern of population distribution. (shrink)

The most fascinating aspect of human language is grammar. Grammar is a computational system that mediates a mapping between linguistic form and meaning. Grammar is the machinery that gives rise to the unlimited expressibility of human language.

Busseola fusca is a maize and sorghum pest that can cause significant damage to both crops. Given that maize is one of the main cereals grown in the worldwide, this pest is a major challenge for maize production and therefore for the economies of several countries . In this paper , based on the life cycle of B. fusca, we propose a mathematical model to study the population dynamics of this insect pest . A sensitivity analysis using the (...) eFast method was performed to show the most important parameters of the model. We present the theoretical analysis of the model. More precisely, we derive a threshold parameter 0 , called basic offspring number and show that the trivial equilibrium is globally asymptotically stable whenever 0≤1 , while if 0>1 , the non trivial equilibrium is globally asymptotically stable. The theoretical results are supported by numerical simulations. (shrink)

A model is proposed for the population dynamics of an annual plant (Sesbania vesicaria) with a seed bank (i.e. in which a proportion of seeds remain dormant for at least one year). A simple linear matrix model is deduced from the life cycle graph. The dominant eigenvalue of the projection matrix is estimated from demographic parameters derived from field studies. The estimated values for population growth rate () indicates that the study population should be experiencing a (...) rapid exponential increase, but this was not the case in our population.The addition of density dependent effects on seedling survivorship and adult fecundity, effects for which field studies provide evidence, considerably improves our model. Depending on the demographic parameters, the model leads to stable equilibrium, oscillations, or chaos. Study of the behaviour of this model in the parameter space shows that the existence of a seed bank allows higher among-year variation of adult fecundity, without leaving the region of demographic stability. Field data obtained over 3 years confirm this prediction. (shrink)

Holobionts, consisting of a host and diverse microbial symbionts, function as distinct biological entities anatomically, metabolically, immunologically, and developmentally. Symbionts can be transmitted from parent to offspring by a variety of vertical and horizontal methods. Holobionts can be considered levels of selection in evolution because they are well-defined interactors, replicators/reproducers, and manifestors of adaptation. An initial mathematical model is presented to help understand how holobionts evolve. The model offered combines the processes of horizontal symbiont transfer, within-host symbiont proliferation, vertical symbiont (...) transmission, and holobiont selection. The model offers equations for the population dynamics and evolution of holobionts whose hologenomes differ in gene copy number, not in allelic or loci identity. The model may readily be extended to include variation among holobionts in the gene identities of both symbionts and host. (shrink)

The purpose of this work is reviewing some reduction results to deal with systems of nonautonomous ordinary differential equations with two time scales. They could be included among the so-called approximate aggregation methods. The existence of different time scales in a system, together with some long-term features, are used to build up a simpler system governed by a lesser number of state variables. The asymptotic behavior of the latter system is then used to describe the asymptotic behaviour of the former (...) one. The reduction results are stated in two particular but important cases: periodic systems and asymptotically autonomous systems. The reduction results are illustrated with the help of simple spatial SIS epidemic models including either periodic or asymptotically autonomous terms. (shrink)

The ArgumentThe development of modern mathematical biology took place in the 1920s in three main directions: population dynamics, population genetics, and mathematical theory of epidemics. This paper focuses on the first trend which is considered the most significant. Modern mathematical theory of population dynamics is characterized by three aspects (the first two being in a somewhat critical relationship): the emergence of the mathematical modeling approach, the attempt at establishing it in a reductionist-mechanist conceptual framework, and (...) the revival of Darwinism. The first section is devoted to the analysis of the concept of mathematical model and the second one presents an example of a mathematical model (Van der Pol's model of heartbeat) which is a good prototype of that concept. In section 3 the main trends of mathematization of biology and the cultural and scientific contexts in which they found their development are discussed. Sections 4 and 5 are devoted to the contributions of V. Volterra and A. J. Lotka, to the analysis of the differences of their scientific conceptions, and to a discussion of a case study: the priority dispute concerning the discovery of the Volterra-Lotka equations. The historical analysis developed in this paper is also intended to detect the roots of some recent trends of mathematization of biology. (shrink)

Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand (...) how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production. We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations. (shrink)

The problem of stability in population dynamics concerns many domains of application in demography, biology, mechanics and mathematics. The problem is highly generic and independent of the population considered (human, animals, molecules,…). We give in this paper some examples of population dynamics concerning nucleic acids interacting through direct nucleic binding with small or cyclic RNAs acting on mRNAs or tRNAs as translation factors or through protein complexes expressed by genes and linked to DNA as transcription (...) factors. The networks made of these interactions between nucleic acids (considered respectively as edges and nodes of their interaction graph) are complex, but exhibit simple emergent asymptotic behaviours, when time tends to infinity, called attractors. We show that the quantity called attractor entropy plays a crucial role in the study of the stability and robustness of such genetic networks. (shrink)

In this paper, we present a deterministic time discrete mathematical model based on multiregional periodic matrices to describe the dynamics of Sardina pilchardus in the Central Atlantic area of the Moroccan coast. This model deals with two stages (immature and mature) and three spatial zones where sardines are supposed to migrate from one zone to another. The population dynamics is described by an autonomous recurrence equation N ( t + 1) = A . N ( t ), (...) where A is a positive matrix whose entries are estimated using data collected during biannual acoustic surveys carried out from 2001 to 2003 onboard the Norwegian research vessel “Dr Fridtjof Nansen”. The dominant eigenvalue λ of A that gives the long-term growth rate of fish population is smaller than one. This agrees with the stock decrease observed in the data collected. We show that λ is highly sensitive to the recruitment rate and much less sensitive to the reproduction rate. These results can clearly be used to define an efficient scenario in order to fight for instance against a stock decrease. (shrink)

The effect of nutrition on fertility and its contribution thereby to population dynamics are assessed in three social groups (elite, tradesmen and subsistence) in a marginal, pre-industrial population in northern England. This community was particularly susceptible to fluctuations in the price of grains, which formed their basic foodstuff. The subsistence class, who formed the largest part of the population, had low levels of fertility and small family sizes, but women from all social groups had a characteristic (...) and marked subfecundity in the early part of their reproductive lives. The health and nutrition of the mother during pregnancy was the most important factor in determining fertility and neonatal mortality. Inadequate nutrition had many subtle effects on reproduction which interacted to produce a complex web of events. A population boom occurred during the second half of the 18th century; fertility did not change but there was a marked improvement in infant mortality and it is suggested that the steadily improving nutritional standards of the population, particularly during crucial periods in pregnancy (i.e. the last trimester), probably made the biggest contribution to the improvement in infant mortality and so was probably the major factor in triggering the boom. (shrink)

Biologists have long known that animal population dynamics are regulated by a combination of bottom-up and top-down forces. Yet, economists have argued that human population dynamics can also be influenced by intraspecific cooperation. Despite awareness of the role of interspecific cooperation in influencing resource availability and animal population dynamics, the role of intraspecific cooperation under different environmental conditions has rarely been considered. Here we examine the role of what we call “lateral forces” that act (...) within populations and interact with external top-down and bottom-up forces in influencing population dynamics using an individual-based model linking environmental quality, intraspecific cooperation, and population size. We find that the proportion of cooperators is higher when the environment is poor and population sizes are greatest under intermediate resources levels due to the contrasting effects of resource availability on behavior and population size. We also show that social populations are more resilient to environmental change than non-social ones because the benefits of intraspecific cooperation can outweigh the effects of constrained resource availability. Our study elucidates the complex relationship between environmental harshness, cooperation, and population dynamics, which is important for understanding the ecological consequences of cooperation. (shrink)

Many predator species feed on prey that fluctuates in abundance from year to year. Birds of prey can face large fluctuations in food abundance i.e. small mammals, especially voles. These annual changes in prey abundance strongly affect the reproductive success and mortality of the individual predators and thus can be expected to influence their population dynamics and persistence. The barn owl, for example, shows large fluctuations in breeding success that correlate with the dynamics in voles, their main (...) prey species. Analysis of the impact of fluctuations in vole abundance with a simple predator prey model parameterized with literature data indicates population persistence is especially affected by years with low vole abundance. In these years the population can decline to low owl numbers such that the ensuing peak vole years cannot be exploited. This result is independent of the length and regularity of vole fluctuations. The relevance of this result for conservation of the barn owl and other birds of prey that show a numerical response to fluctuating prey species is discussed. (shrink)

Many predator species feed on prey that fluctuates in abundance from year to year. Birds of prey can face large fluctuations in food abundance i.e. small mammals, especially voles. These annual changes in prey abundance strongly affect the reproductive success and mortality of the individual predators and thus can be expected to influence their population dynamics and persistence. The barn owl, for example, shows large fluctuations in breeding success that correlate with the dynamics in voles, their main (...) prey species. Analysis of the impact of fluctuations in vole abundance (their amplitude, peaks and lows, cycle length and regularity) with a simple predator prey model parameterized with literature data indicates population persistence is especially affected by years with low vole abundance. In these years the population can decline to low owl numbers such that the ensuing peak vole years cannot be exploited. This result is independent of the length and regularity of vole fluctuations. The relevance of this result for conservation of the barn owl and other birds of prey that show a numerical response to fluctuating prey species is discussed. (shrink)

Radopholus Similis or burrowing nematode, is one of the most damaging and widespread nematodes attacking bananas, causing toppling or blackhead disease. A mathematical model for the population dynamics of R. Similis is considered, with the aim of investigating the impact of climatic factors on the growth of R. Similis. In this paper, based on the life cycle of R. Similis, we first propose a mathematical model to study and control the population dynamics of this banana pest. (...) We show also how control terms based on biological and chemical controls can be integrated to reduce the population of R. Similis within banana-plantain roots. Sensitivity analysis was performed to show the most important parameters of the model. We present the theoretical analysis of the model. More precisely, we derive a threshold parameter N0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{N}}_0$$\end{document}, called the basic offspring number and show that the trivial equilibrium is globally asymptotically stable whenever N0≤1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{N}}_0\le 1$$\end{document}, while when N0>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{N}}_0> 1$$\end{document}, the non trivial equilibrium is globally asymptotically stable. After, we extend the proposed model by taking account climatic factors that influence the growth of this pest. Biological and chemical controls are now introduced through impulsive equations. Threshold and equilibria are obtained and global stabilities have been studied. The theoretical results are supported by numerical simulations. Numerical results of model with biological and chemical controls reveal that biological methods are more effective than chemical methods. We also found that the month February is the best time to apply these controls. (shrink)

The aim of this work is to present aggregation methods of hierarchically organized systems allowing one to replace the initial micro-system by a macro-system described by a few global variables. We also study the relations between the fast micro-dynamics and the slow macro-dynamics which can produce global properties. Emergence corresponds to a bottom-up coupling that is the result effected by a micro-level at a macro-level. As an example, we present prey-predator models with different time scales in an heterogeneous (...) environment. A fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to growth and interactions between the populations. Preys must go on spatial patches where resources are located and where predators can attack them. The efficiency of the predators to catch preys is patch dependent. Perturbation methods allow us to aggregate the initial system of differential equations for the patch sub-populations into a macro-system of two differential equations governing the total population densities. We study the case of density independent and density dependent migrations. In the latter case, we show that different functional responses can emerge in the macro prey-predator model as a result of the coupling between the slow and fast systems. (shrink)

In this paper, we present a deterministic time discrete mathematical model based on multiregional periodic matrices to describe the dynamics of Sardina pilchardus in the Central Atlantic area of the Moroccan coast. This model deals with two stages (immature and mature) and three spatial zones where sardines are supposed to migrate from one zone to another. The population dynamics is described by an autonomous recurrence equation N(t + 1) = A.N(t), where A is a positive matrix whose (...) entries are estimated using data collected during biannual acoustic surveys carried out from 2001 to 2003 onboard the Norwegian research vessel “Dr Fridtjof Nansen”. The dominant eigenvalue λ of A that gives the long-term growth rate of fish population is smaller than one. This agrees with the stock decrease observed in the data collected. We show that λ is highly sensitive to the recruitment rate and much less sensitive to the reproduction rate. These results can clearly be used to define an efficient scenario in order to fight for instance against a stock decrease. (shrink)

Studying populations, be it a microbe colony or mankind, is important for understanding how complex systems evolve and exist. Such knowledge also often provides insights into evolution, history and different aspects of human life. By and large, populations’ prosperity and decline is about transformation of certain resources into quantity and other characteristics of populations through growth, replication, expansion and acquisition of resources. We introduce a general model of population change, applicable to different types of populations, which interconnects numerous factors (...) influencing population dynamics, such as nutrient influx and nutrient consumption, reproduction period, reproduction rate, etc. It is also possible to take into account specific growth features of individual organisms. We considered two recently discovered distinct growth scenarios: first, when organisms do not change their grown mass regardless of nutrients availability, and the second when organisms can reduce their grown mass by several times in a nutritionally poor environment. We found that nutrient supply and reproduction period are two major factors influencing the shape of population growth curves. There is also a difference in population dynamics between these two groups. Organisms belonging to the second group are significantly more adaptive to reduction of nutrients and far more resistant to extinction. Also, such organisms have substantially more frequent and lesser in amplitude fluctuations of population quantity for the same periodic nutrient supply (compared to the first group). Proposed model allows adequately describing virtually any possible growth scenario, including complex ones with periodic and irregular nutrient supply and other changing parameters, which present approaches cannot do. (shrink)

In the interwar years the Gran Paradiso ibex population followed two subsequent, contrasting trends: a steady rise once the national park was established in 1922, followed by a precipitous fall after the Fascist regime took direct control of conservation in 1934, which almost led to the colony’s extinction. This paper addresses the issue of how models taken from population ecology may inform historical narratives. The data for the interwar years were analyzed using a statistical model based on climate (...) and population density, which has proved reliable for most of the post-World War II period. The article highlights the pivotal role of anthropic variables in determining the inter-war trends and how these are best analyzed using historical scholarship. (shrink)

Matrix models are widely used in biology to predict the temporal evolution of stage-structured populations. One issue related to matrix models that is often disregarded is the sampling variability. As the sample used to estimate the vital rates of the models are of finite size, a sampling error is attached to parameter estimation, which has in turn repercussions on all the predictions of the model. In this study, we address the question of building confidence bounds around the predictions of matrix (...) models due to sampling variability. We focus on a density-dependent Usher model, the maximum likelihood estimator of parameters, and the predicted stationary stage vector. The asymptotic distribution of the stationary stage vector is specified, assuming that the parameters of the model remain in a set of the parameter space where the model admits one unique equilibrium point. Tests for density-dependence are also incidentally provided. The model is applied to a tropical rain forest in French Guiana. (shrink)

A survey of three types of cell population models is presented in this paper. The main issue in all the surveyed words is whether or not there exists astable type distribution (s.t.d.). In the last few years, many efforts were directed towards describing the most general models which still exhibits.t.d. Progress made in the case ofsize density models are discussed. A slightly extended version of atime continous daughter cell model, studied in Arino et al. (1991), is presented. Recently, some (...) authors have undertaken the task of comparing models of various origins and types. Such works are alluded to in a discussion. (shrink)

The dynamics of neural populations capture the laws of the mindThis paper focuses on the level of neural networks. Examining the case of recurrent neural networks, the paper argues that the dynamics of neural populations form a privileged level of explanation in cognitive science. According to Schöner, this level is privileged, because it enables cognitive scientists to discover the laws governing organisms’ cognition and behaviour.

A systematic, rigorous, comprehensive, and unified overview of evolutionary game theory.

In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes, lemmings, and seal carcasses. The positivity and asymptotically uniform boundedness of the solutions of the system have been derived. Analytically, we have studied the criteria for the feasibility and stability of different equilibrium points. In addition, we have (...) derived sufficient conditions for the existence of local bifurcations of codimension 1. It is also observed that there is some time lag between the time of perceiving predator signals through vocal cues and the reduction of prey’s birth rate. So, we have analyzed the dynamical behaviour of the delayed predator-prey-subsidy model. Numerical computations have been performed using MATLAB to validate all the analytical findings. Numerically, it has been observed that the predator, prey, and subsidy can always exist at a nonzero subsidy input rate. But, at a high subsidy input rate, the prey population cannot persist and the predator population has a huge growth due to the availability of food sources. (shrink)

Macroeconomic dynamics and the at-risk-of-poverty population in Slovakia This paper deals with analysis and presentation of the core findings under the EU SILC 2009 project. Particularly we are oriented on study of the socially vulnerable groups of population identified according their income situation. As a sorting criterion for this purpose we use the standard methodology set by OECD and Eurostat. It means the 60% of the national median equivalized disposable income is applied for this criterion as the (...) poverty threshold. The national income variable is firstly calculated as a total income for each surveyed household and dived by the equivalized size of household. By this procedure the households of various structures are transformed onto generally accepted scale. The special attention of our study is oriented on the cluster of population living on income below the poverty threshold. For this population we calculate so called social deficit. Through this value we show the volume of financial means needed to upgrade the living standard of the population living bellow poverty threshold at least to the poverty threshold level.Special section of the paper is devoted to study of relation among the core macroeconomic indicators and level and size of the at-risk-of-poverty population during the period of last economic development, including both economic growth and economic recession. According our tentative findings we did not find the significant impact of economic growth on the status of socially vulnerable population. This finding however should be studied in broader context, with longer time series of relevant data and with broader set of explanatory variables. (shrink)

We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective cooperation pressures. To this end we generalise existing path-integral approaches to replicator systems with random asymmetric couplings. This technique allows one to formulate an effective dynamical theory, which is exact in the thermodynamic limit and which can be solved for persistent order parameters in a fixed-point (...) regime regardless of the symmetry of the interactions. The onset of instability can be determined self-consistently. We calculate quantities such as the diversity of the respective populations and their fitnesses in the stationary state, and compare results with data from a numerical integration of the replicator equations. -/- . (shrink)

This communication presents a very simple model for the global growth of the human population. It is shown that the solution of the simple equation.

This paper investigates a stochastic two-patch predator-prey model with ratio-dependent functional responses. First, the existence of a unique global positive solution is proved via the stochastic comparison theorem. Then, two different methods are used to discuss the long-time properties of the solutions pathwise. Next, sufficient conditions for extinction and persistence in mean are obtained. Moreover, stochastic persistence of the model is discussed. Furthermore, sufficient conditions for the existence of an ergodic stationary distribution are derived by a suitable Lyapunov function. Next, (...) we apply the main results in some special models. Finally, some numerical simulations are introduced to support the main results obtained. The results in this paper generalize and improve the previous related results. (shrink)

We wish here to consider the theory of a population or system made up of individuals whose number and size change with time. As usual, the description of these changes will be referred to as the kinetics, whereas the description of the special circumstances under which unchanging conditions subsist will be called the statics of the population. A third category, the conditions for a steady state, i.e., when the variables inside the system do not change, but linked variables (...) outside do, will be described by what we shall call the rheostatics of the system. All three, statics, rheostatics, and kinetics are subdivisions of the general dynamics of the system. (shrink)

As part of a survey of the biological history of Alpine populations, the lineages of all the families of the Vallouise valley (a French of the Hautes Alpes) have been reconstructed over several centuries. The genealogies have been included in a computerized population record, known as 20th centuries)Canadian programme Analypop. Most of the professions of the family heads were included in the files. In this study, various profession groups were identified and their descents determined over successive generations. In this (...) mountain area, where over 92% of marriages took place among relatives during the 19th century, the profession groups modulated their descents according to chosen strategies, sometimes with considerable differences among groups but with a remarkable consistency of behaviour. Moreover, there was weak interpenetration in the descents of each profession at both the 2nd and 3rd generations. (shrink)

Conservation Biologists have found that demographic stochasticity causes the mean time to extinction to increase exponentially with population size. This has proved helpful in analyses determining extinction times and characterizing the pathway to extinction. The aim of this investigation is to explore the possible interactions between environmental/demographic noises and the scaling effect of the mean population size with its variance, which is expected to follow Taylor’s power law relationship. We showed that the combined effects of environmental/demographic noises and (...) the scaling of population size variability interact with the population dynamics and affect the mean time to extinction. (shrink)