Instar Determination of Blaptica dubia (Blattodea: Blaberidae) using Gaussian Mixture Models

Abstract

Instar determination is fundamental to both basic entomological research and its application. The cockroach, Blaptica dubia Serville (Blattodea: Blaberidae), is a popular pet and an excellent feeder insect for many reptiles and amphibians. A new method using Caussian mixture models to determine the number of instars in this species is developed. Application ofthe method is illustrated by analysis of data collected on B. dubia. The analysis indicates that there are seven instars in B. dubia and that the growth ratio follows the Brooks-Dyar rule. The growth ratio of pronotal length, pronotal width, and head width are 1.26,1.24, and 1.19, respectively. Because B. dubia shares a similar growth pattern with other paurometabolous insects, this method may be applicable to other species as well.

Determining the number of instars in potato tuber moth Phthorimaea operculella (Zeller) using density‐based DBSCAN clustering

“…Overlapping size‐frequency distributions occurred between head capsule length and mandible width of second to third larval instars; however, these instars were distinguished by the three clustering algorithms, indicating that these algorithms can be used to determine instars of insects. The Gaussian mixture model (centroid‐based clustering) and the k ‐means clustering method (distribution‐based clustering) have been successfully used to determine instars of insects in previous studies (Wu et al, ; Yang et al, ). However, the DBSCAN clustering algorithm has yet to be used to determine instars of insects.…”

“…The BIC for parameterized Gaussian mixture models was fitted using the EM algorithm initialized by model‐based hierarchical clustering. Detailed information regarding these procedures has been described in previous studies (Scrucca, Michael, Murphy, & Raftery, ; Wu et al, ).…”

“…When the Crosby index is more than 10%, it indicates that the given character cannot be used to determine the number of instars. The equation can also be written as:where e b is the growth‐ratio constant, and a is the theoretical size resulting from 0 instars (Wu et al, ). The Crosby ratio is equal to the difference between consecutive growth ratios (Crosby, ), which is equivalent to the following linear regression equation:…”

“…Potato tuber moth morphological characteristics were also analysed using Gaussian mixture models, and the results of this analysis were compared with those obtained from the DBSCAN clustering method. ing these procedures has been described in previous studies (Scrucca, Michael, Murphy, & Raftery, 2016;Wu et al, 2013).…”

“…However, occasionally, as was the case for Simulium quinquestriatum , the overlapping size‐frequency distributions prevent instar grouping and analyses (Baba, ). To account for these problems, some cluster analyses such as Gaussian mixture models (GMM; Wu, Appel, & Hu, ), the linear discriminant method (LDA; Hunt & Chapman, ), the K‐means clustering algorithm (Yang et al, ), univariate kernel density estimation (Chen & Seybold, ), the adaptive kernel smoothing method (Cen et al, ) and the adaptive bivariate kernel smoothing method (Cen et al, ) have been proposed.…”