41 Seed Choice for Fitting Gaussian Mixture Models of Instar Characteristics in Lepidopterans

Oregon Convention Center 

Estimation of a lepidopteran's instar prior to pupation has applications in applied research. We modeled successive larval instars for the study species Hyphantria cunea based on head capsule width data using Gaussian mixture models (GMMs) fit by Estimation-Maximization (EM). To generate starting values under the assumption of n instars, we calculated n head capsule widths consistent with Brooks-Dyar spacing with the smallest value positioned at a small quantile q1 of the observed head capsule widths and the largest value positioned at a large quantile qn of the observed widths. We used the means of the n resulting clusters as starting values for the means of the Gaussian distributions, the variances of the head capsule widths in each cluster as starting values for the variances of the Gaussian distributions, and the proportions in each cluster as starting values for the mixing proportions of the Gaussian distributions. We used Brooks-Dyar spacing to select the number of instars. We found that this form of seed, in contrast to other methods of generating seeds, produces reliable, rapid convergence of the EM algorithm to biologically reasonable models.

Brooks-Dyar’s rule

Gaussian mixture model

instar

EM seed 

Section on Statistics and the Environment