Linear Birth-Immigration-Death Models

Abstract

Consider now modeling the single population of sizeX (t)with linear birth and death rates:

$$ {\lambda _X} = {a_1}Xand\mu x = {a_1}X. $$

(5.1)

The immigration rate is again assumed to beI.This is called the LBID model. Clearly this model with linear (density-independent) growth rates could hold in the case of a_l> a₂only for periods of initial population growth. The model will be illustrated for such initial population growth for both the African bee and the muskrat examples in Chapter 2.