After reading this article you will learn about the modelling of populations and their interaction in a community.
The effects of different types of interaction amongst the community’s component populations may be modelled in terms of their consequences for population growth and dynamics.
The models used to describe the dynamics of such population fall in effect into two distinct ‘families’ based on differential equations (modelling populations with continuous growth) or difference equations (used to model populations with more discrete pattern of growth and non-overlapping generations).
In an unlimited environment, population growth will follow a simple geometric progression as the full natural rate of increase of population is expressed; if one generation have x population which doubles i.e. 2x in the next generation and so on. The growth of such a population can be simply expressed as
dN/dt = rntN ….(1)
where dN/dt, denotes the rate of change of numbers over time, equal the products of the natural rate of increase, rnt, and population size at any instant, N. Such growth clearly cannot be maintained indefinitely; as resources become limiting intraspecific competition has a dampening or depressive effect on such free growth.
We may incorporate a second element into our equation to represent this dampening effect of intraspecific competition, as
dN/dt = rmN(1 – N/K) ….(2)
when N is again instantaneous population size, rm is intrinsic rate of increase and K is a measure of total population size that the environment can support at balance; the carrying capacity of the environment. In this simple equations one can extend further to accommodate interaction with more than one competing species.
Subsequently a logistic model of population growth were first suggested by Lotka (1925) and Voltera (1926). In this type of model, equation for unrestricted population growth may be expressed as
Nt+1 = λNt
where Nt or Nt+1 represent the numbers of organisms in the population at Ume t and t+1 respectively and λt the finite rate of increase, is the number of times the population multiplies itself each generation.