The Intrinsic Rate of Natural Increase of an Insect Population

The intrinsic rate of increase is a basic parameter which an ecologist may wish to establish for an insect population. We define it as the rate of increase per head under specified physical conditions, in an unlimited environment where the effects of increasing density do not need to be considered. The growth of such a population is by definition exponential. Many authors, including Malthus and Darwin, have been concerned with this and related concepts, but there has been no general agreement in recent times on definitions. Chapman (I93i) referred to it as 'biotic potential', and although he does state in one place that biotic potential should in some way combine fecundity rate, sex ratio and survival rate, he never precisely defined this expression. Stanley (I 946) discussed a somewhat similar concept which he called the 'environmental index'. This gives a measure of the relative suitability of different environments, but it does not give the actual rate of increase of the insect under these different conditions. An index for the possible rate of increase under different physical conditions would at the same time provide a measure of the relative suitability of different environments. Birch (I 945c) attempted to provide this in an index comnbining the total number of eggs laid, the survival rate of immature stages, the rate of development and the sex ratio. This was done when the author was unaware of the relevance of cognate studies in human demography. A sounder approach to insect populations based on demographic procedures is now suggested in this paper. The development of this branch of population mathematics is principally due to A. J. Lotka. From the point of view of the biologist, convenient summaries of his fundamental contributions to this subject will be found in Lotka (I925, Chapter 9; I939 and I945). A numerical example of the application of Lotka's methods in the case of a human population will be found in Dublin & Lotka (I925). The parameter which Lotka has developed for human populations, and which he has variously called the 'true' or 'inherent' or 'intrinsic' rate of natural increase, has obvious application to populations of animals besides the human species. The first determination of the intrinsic rate of increase of an animal other than man was made by Leslie & Ranson (I940). They calculated the 'true rate of natural increase' of the vole, Microtus agrestis, from agespecific rates of fecundity and mortality determined under laboratory conditions. With the use of matrices Leslie has extended these methods and, as an example, calculated the true rate of natural increase of the brown rat, Rattus norvegicus (Leslie, 1945). The author is much indebted to Mr Leslie for having drawn his attention to the possible application of actuarial procedures to insect populations. He has been completely dependent upon him for the methods of calculation used in this paper. Before proceeding to discuss the reasons for the particular terminology adopted in this paper, it is necessary first to consider the true nature of the parameter with which we are concerned.