The Intrinsic Rate of Natural Increase of an Insect Population

Abstract

The parameter known as the intrinsic rate of natural increase, which was developed for demographic analyses by A. J. Lotka, is introduced as a useful concept for the study of insect populations. It is suggested that for the sake of uniformity of terminology in population biology and for precision of definition, that the term `intrinsic rate of natural increase' might be considered more appropriate than an alternative term `biotic-potential' which is more frequently used in relation to insect populations. The intrinsic rate of natural increase is defined as the exponent `r' in the exponential equation for population increase in an unlimited environment. The rate of increase of such a population is given by dN/dt=rN. The parameter r refers to the rate of increase of a population with a certain fixed age distribution known as the stable age distribution. Both the intrinsic rate of natural increase and the stable age distribution may be calculated from the age-specific survival rates (life table) and age-specific fecundity rates. The methods of calculation are exemplified with data for the rice weevil, Calandra oryzae (L.), and some adapted from the flour beetle, Tribolium confusum Duval. It is shown in this example that the intrinsic rate of natural increase is determined to a much greater extent by the rate of oviposition in the first 2 weeks of adult life than by the total number of eggs laid in the entire life time. The oviposition rates in the first 2 weeks account for 85% of the value of r whereas only 27% of the total number of eggs are laid in that time. With each successive week in the life of the adult, eggs laid make a lessened contribution to the value of r. The methods of calculation of r provide a means of determining the extent to which the various components--the life table, the fecundity table and the length of the pre-reproductive stages--enter into the value of r. It is suggested that analyses of this sort may provide a clue to the life patterns characteristic of different species. The importance of the age distribution of populations which initiate seasonal increase in the autumn and spring is discussed. These age distributions depend on the nature of the overwintering or over-summering stage. It is suggested that this particular stage, whether it be adult, larva, pupa or egg, has been selected by virtue not only of its resistance to the unfavourable season, but also in relation to its merits in initiating rapid establishment of a population in the succeeding season. It is shown how the value of r for Calandra oryzae varies with temperature. Four other parameters are also defined: the net reproduction rate, the mean length of a generation, the infinitesimal birth-rate and the infinitesimal death-rate. The methods of calculation of these parameters are also exemplified with data for C. oryzae.