Use of the Gamma Distribution for Predicting Arrival Times of Invading Insect Populations

Abstract

Models that describe the distance traveled in a fixed time of a dispersing insect population are well-known. The gamma distribution is presented as a model for the inverse variable, namely the time required to travel a fixed distance. The use of the model is illustrated by fitting it to data on the consecutive northernmost captures of Apis mellifera swarms through Guatemala and Mexico. Point and interval estimates of predicted arrival time are obtained. The methodology is general and may be applied to other locations and species. The model also provides a tractable basis for the stochastic modeling of insect population density.