Modeling Distributions of Insect Development Time: a Literature Review and Application of the Weibull Function

TLDR: A stochastic approach for modeling insect development based on a single, temperature-independent distribution of normalized development times, which can be used in population models to distribute cohort development through time under variable temperature conditions.

Abstract: We describe a stochastic approach for modeling insect development based on a single, temperature-independent distribution of normalized development times. We review other stochastic approaches, as well as problems encountered in modeling distributions of development time. A computer program, assembled from the Statistical Analysis System library, constructs cumulative probability distributions from frequency data on insect development times. These data are obtained from constant temperature experiments. The computer program normalizes the times of these distributions on their median time, identifies a single empirical distribution representative of all normalized distributions, and fits a cumulative Weibull function to this standard curve. The program determines the starting values of the three Weibull parameters and computes least-square estimates of these parameters using Marquardt techniques. This normalized probability function was tested against 23 data sets with good results, and can be used in population models to distribute cohort development through time under variable temperature conditions.