Rethinking the basis of the population growth (original) (raw)

The paper goes back to the basis of population dynamics, especially the works of Malthus, and tries to model his pioneering vision again, this time taking into account such of his postulates as the necessity of food for survival, the reproduction of each individual and inequities of resource distribution. We construct a Conspecific Community Dynamics Model (CCDM), which is based on these well-known postulates of Malthus. Nevertheless, analysis of the model reveals quite interesting results. (1) The size of the community nontrivially depends on the level of equality between its members (for example, there is a given level of equality in which the size of the community becomes a maximum). (2) The size of the community is limited not only by the amount of resources, but the community's ability to utilize these resources. (3) A high level of equality leads to a dynamical instability, which, in turn, under certain conditions, may lead to extinction. Thereafter, we included in the model the fact that the level of equality in the community may be constantly changing under the influence of co-selection. This in turn leads to changes in average demographic characteristics and associated life-history traits. It is interesting that this model demonstrates a so-called demographic-economic paradox, which is traditionally considered to be the main empirical argument against the Malthus theory. In conclusion, we consider the anti-Malthus or pro-Condorcet model in which resources available to the community can grow at the same pace as the population. Despite the fact that such a community has always been unstable (has no equilibrium size or carrying capacity), it may nevertheless be limited and exist for a long time due to co-selection. Analysis of this model demonstrates a significant similarity in the results with the empirical model of demographic transition.

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Theories of populations in biological communities / F. B. Christiansen and T. M. Fenchel

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Cohort Dynamics Give Rise to Alternative Stable Community States

The American Naturalist, 2013

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Basics of Conspecific Community Dynamics approach

Preface This preface aims to make clear a look at population and population processes, which is not common in current biological literature, at least in context of population dynamics. Here, I will try to explain the essence of this research, using highly informal examples from everyday-life. Main goal of this chapter is to give a simple intuitive understanding of basic principles, rather than strict formal description. I also hope that this chapter will help readers who are not very familiar with this field to get some useful information and perhaps a sense of the hidden beauty of population dynamics. So, what is this thesis about? Essentially, it is about a special look at the population and about the special vision of population processes, which lies at the heart of any approach to population modeling. In order clearly illustrate this point, let me give a simple example. Let us look around; we can see different people around us (see picture 0.1). However, we can have a different ...

Population dynamics with and without selection

Physical Review E, 2001

A model describing population dynamics is presented. We study the effect of selection pressure and inbreeding on the time evolution of the population and the chances of survival. We find that the selection is in general beneficial, enabling survival of a population whose size is declining. Inbreeding reduces the survival chances since it leads to clustering of individuals. We have also found, in agreement with biological data, that there is a threshold value of the initial size of the population, as well as of the habitat, below which the population will almost certainly become extinct. We present analytical and computer simulation approaches.

Complexity and demographic stability in population models

Theoretical population biology, 2004

This article is concerned with relating the stability of a population, as defined by the rate of decay of fluctuations induced by demographic stochasticity, with its heterogeneity in age-specific birth and death rates. We invoke the theory of large deviations to establish a fluctuation theorem: The demographic stability of a population is positively correlated with evolutionary entropy, a measure of the variability in the age of reproducing individuals in the population. This theorem is exploited to predict certain correlations between ecological constraints and evolutionary trends in demographic stability, namely, (i) bounded growth constraints--a uni-directional increase in stability, (ii) unbounded growth constraints (large population size)--a uni-directional decrease in stability, (iii) unbounded growth constraints (small population size)--random, non-directional change in stability. These principles relating ecological constraints with trends in demographic stability are shown ...

Introduction to population dynamics and resource exploitation

ArXiv, 2021

The paper was suggested by a brief note of the second author about the application of the Hubbert’s curve to predict decay of resource exploitation. A further suggestion came from the interpretation of the Hubbert’s curve in terms of a specific Lotka-Volterra (LV) equation. The link with population dynamics was obvious as logistic function and LV equation were proposed within the demography science field. Mathematical population dynamics has a history of about two centuries. The first principle and model of population dynamics can be regarded the exponential law of T. R. Malthus. In the XIX century, the Malthusian demographic model was first refined to include mortality rate by B. Gompertz. In the early XIX century the model was further refined by P-F. Verhulst by introducing the standard logistic function. The previous models only concern the population of a single species. In the early XX century, the American demographer A.J. Lotka and the Italian mathematician V. Volterra propos...

Étude De Quelques Populations Structurées : Processus De Coalescence et Abondance D’Une Stratégie

2016

The emergence of cooperation in populations of selfish individuals is a fascinating topic that has inspired much theoretical work. An important model to study cooperation is the phenotypic model, where individuals are characterized by phenotypic properties that are visible to others. The phenotype of an individual can be represented for instance by a vector x = (x1, . . . , xn), where x1, . . . , xn are integers. The population can be well mixed in the sense that everyone is equally likely to interact with everyone else, but the behavioral strategies of the individuals can depend on their distance in the phenotype space. A cooperator can choose to help other individuals exhibiting the same phenotype and defects otherwise. Cooperation is said to be favored by selection if it is more abundant than defection in the stationary state. This means that the average frequency of cooperators in the stationary state strictly exceeds 1/2. Antal et al. [4] found conditions that ensure that coope...

[Development and testing of theories of population dynamics]. First annual report

1990

We proposed research on models of the dynamics of the interaction between Daphnia and its algal food supply, and of marine giant kelp populations. We planned to begin work on a model of the predatory backswimming bug, Notonecta. If time permitted we hoped to do further work on a model of red scale (an insect pest of citrus) and its biological control agent (the parasitoidAphytis), although we did not include this in the final planned research. In addition, we aimed to continue research into a central and controversial area, namely the effect of agvegation by predators on the stability of predator-prey interactions.

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