The Basic Model

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

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:

page 224

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:

To calculate the impact of reproductive inhibition it is necessary to further expand expression (2) (after Knipling & McGuire 1972) as follows:

where

• 
• MN = normal males
• MS = sterile males
• FN = normal females
• FS = sterile females
• P = progeny.