We model the relationship of larval, pupal and adult animal numbers at time t+1 to the number of animals at time t using a system of three difference equations:

L_t = b A_t–1 exp(– c_el L_t–1 – c_ea A_t–1),

P_t = L_t–1 (1 – µ_l),

A_t = P_t–1 exp(– c_pa A_t–1) + A_t–1 (1 – µ_a).

In this model formulation, the first equation is for the number of feeding larvae (referred to as the L-stage), the second is for the number of large larvae, non-feeding larvae, pupae and callow adults (called the P-stage), and the third is for the number of sexually mature adults (A-stage animals). The unit of time is two weeks and is, approximately, the average amount of time spent in the feeding larval stage under our experimental conditions. The time unit is also approximately the average duration of the P-stage. The quantity b > 0 is the number of larval recruits per adult per unit of time in the absence of cannibalism. The fractions µ_l and µ_a are the larval and adult rates of mortality in one time unit. The exponential nonlinearities account for the cannibalism of eggs by both larvae and adults and the cannibalism of pupae by adults. The fractions exp(–c_el L_t–1) and exp(–c_ea A_t–1) are the probabilities that an egg is not eaten in the presence of L_t–1 larvae and A_t–1 adults in one time unit. The fraction exp(–c_pa A_t–1) is the survival probability of a pupa in the presence of A_t–1 adults in one time unit. Stochastic versions of this LPA model are used for parameter estimation model predictions.