Tsetse: the limits to population growth.

Growth rates of tsetse populations were estimated by calculating the dominant eigenvalues of appropriate Leslie matrices. The individual effects of four variables (pre-adult and adult survival probability, interlarval period and pupal duration), have been investigated by varying each one over a wide range of values, while the other three are held constant. R, the log of the growth rate, was found to vary approximately linearly with adult and pre-adult death rate; a 1% change in the adult death rate causes approximately a 10-fold change in R. R varies linearly with the log of fecundity and of the pupal duration. An increase in the pupal duration results in a decrease in the growth rate for populations which have a positive growth rate, but an increase for populations which have a negative growth rate. For a population at equilibrium, a change in the pupal duration has no effect. Small changes in fecundity have less effect on the growth rate than small changes in the death rate; this fact is advanced as an important contributor to the generally very cautious nature of female tsetse, and their aversion to man, particularly as a potential host. A simple linear model is described which relates R to all four variables and their first order interactions. The model is used to produce a set of graphs which encapsulate the relationship between the growth rate and the vital parameters over a wide range of values. It is also used to draw the loci on one side of which tsetse populations grow, and on the other of which they decline. Population resilience is discussed in relation to the problem of tsetse eradication; it is concluded that if one can impose and sustain an added mortality of 4% per day on any female tsetse population then it must go extinct, regardless of the strength of the density dependent processes; and it seems likely that in most field conditions only an added 2-3% is required. It is pointed out that ground and aerial spraying techniques produce much higher daily mortalities than this, but they may often not be sustained for sufficiently long to achieve eradication. When odour-baited targets are used the increased death rate is much smaller, but it can be sustained as required; recent work in Zimbabwe shows that there is a good correspondence between the calculated imposed death rate and the observed rate of decline of tsetse populations.