Individual‐based Models in Population Ecology

Abstract

The individual‐based approach is a concept of population ecology that rests on the premise that population properties should be derived from properties of individuals. It was developed due to conceptual advances in evolutionary biology in the second half of the twentieth century and as a consequence of access to computers. The advances in biology have allowed the rejection of the notion of adaptations of units of natural selection other than individuals whereas the computers made possible the simulations of very complex phenomena in many fields of science, engineering and economy. Investigations of individual variation have shown its origin and its impact on population dynamics. Computer simulations of particular ecological systems, especially those of economic and conservation importance, have proven to be very useful and able to discover relations that cannot be found out by analytical inquiries. It seems that in the future the individual‐based approach will be fully integrated into theoretical and applied ecology.

Key Concepts:

  • Individual plants and animals differ not only in their sex and age but also in other phenotypic features.

  • Individual differences affect resource partitioning by individuals within the population, explain the mechanisms of scramble or contest competition and consequently the conditions for population stability and persistence.

  • Absolutely equal resource partitioning by population members makes population stability and persistence impossible.

  • By itself, individual variation in resource partitioning is not sufficient for population persistence and its ability to survive sudden drop in the availability of resources; some degree of resource monopolisation is required.

  • The best examples of situation in which we can observe monopolisation of resources are populations of plants competing for light and birds or other animals defending individual territories.

  • The important ecological phenomenon – despotic distribution which forces some individuals to move into worse habitat where their fitness is lower is possible only with some degree of monopolisation of available resources.

  • Another ecological phenomenon – the existence of the source and sink system, which is important in population dynamics, can be maintained due to resource monopolisation by some population members.

  • Individual variability and individual properties, as well as spatial population structure are difficult to describe by general models with analytical solutions but computer simulations make their description much easier and the exploration of their consequences much more effective.

  • Computer simulation of ecological phenomena uses methods and concepts developed in other fields of science and technology, like agent‐based models or complex adaptive systems.

  • Agent‐based models are used not only for the study of population dynamics but also to explain collective animal behaviour and other population or community‐level phenomena.

Keywords: scramble and contest competition; within population variability; population dynamics; resource monopolisation; free and despotic distribution; population source and sink; agent‐based model; complex adaptive system

Figure 1.

The mechanism of ideal scramble and ideal contest competition. Left and middle diagrams present individual resource intake y by the population of N individuals supplied with V units of resources, as a function of individual rank x, which may or may not be the rank in social hierarchy. This model considers nonoverlapping generations, and generation time equal to time unit. An individual may take the maximum amount a of the resource and for survival to reproduction time it requires at least m units of resources. The number of progeny an individual leaves in the next generation is given by the positive value of the expression h(ym), where h is the number of progeny produced from one unit of resources. In the case of ideal scramble competition all individuals take identical amounts of resources. The upper left diagram shows the situation when V/m>N>V/a, whereas the upper middle diagram when N>V/m which implies that all individuals die without leaving progeny, because their resource intake y<m. The right diagrams show population size Nt+1 at generation t+1, as the function of population size Nt in the earlier generation. The hatched lines represent Nt+1=Nt and are drawn to show how the mutual position of these lines and Nt+1(Nt) lines determines system stability. It is done by moving in every step the value of Nt+1 from vertical to horizontal axes. As shown elsewhere (Lomnicki, ) this model allows local stability if m<1/h. Since 1/h is the cost of producing single progeny, which for all plants and animals is lower than the cost of survival to the reproduction time, local stability at the ideal scramble competition is impossible. The condition for the persistence is a little less rigid when m(1−m/a)<1/h, but it seems equally impossible to meet. Concluding, the ideal scramble competition with ideally equal resource partitioning is impossible in the real world. Lower left and middle diagrams present individual resource intakes in the case of ideal contest competition. V/a individuals get maximum amount y=a, whereas all others (N−V/a) get nothing (y=0). As shown in the lower right diagram, this model is locally stable and persistent for any set of parameters but such ideal monopolisation of resources by some members of the population is a rare phenomenon.

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Further Reading

DeAngelis DL and Gross LJ (eds) (1992) Individual‐based Models and Approaches to Ecology. New York: Chapman and Hall.

Sutherland WJ (1996) From Individual Behaviour to Population Ecology. Oxford: Oxford University Press.

Uchmanski J, Aikman D, Wyszomirski T and Grimm V (eds) (1999) Individual‐based modelling in ecology. Ecological Modelling 115: 109–290.

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Lomnicki, Adam(Oct 2011) Individual‐based Models in Population Ecology. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0003312.pub2]