Proceedings of the First Symposium on Marsupials in New Zealand

The Basic Model

The Basic Model

A population's pattern of growth is typically sigmoid, and may be represented by the following: Equation describing a population's growth.

where

  • N = the number in the population
  • t = time
  • e = the base of the natural logarithm
  • r = the exponential rate of increase.

The rate of increase (e r) is a function of reproduction and survival, and it is necessary to separate these functions when modelling reproductive inhibition of part of a population. Thus Knipling & McGuire (1972) expanded expression (1) as follows: Equation describing a population's growth.

where

  • R = the size of the adult breeding population
  • e S = adult survival rate from t-1 to t
  • e I = the rate of recruitment to the adult population (in terms of animals recruited per adult female) and describes both birth and death rates of juveniles.

The exponents S and I are linear functions of the number in the population, so that: Equations describing survival rate within a population.

To calculate the impact of reproductive inhibition it is necessary to further expand expression (2) (after Knipling & McGuire 1972) as follows: Equation describing a population's growth when modelling reproductive inhibition.

where

  • Equation describing number of progeny over time.
  • MN = normal males
  • MS = sterile males
  • FN = normal females
  • FS = sterile females
  • P = progeny.