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1. Instar determination of the Dubia cockroach (Blaptica dubia): a maximum likelihood approach Hao Wu, Arthur G. Appel and Xing Ping Hu Department of Entomology and Plant Pathology Auburn University May 21, 2012
2. The Dubia Cockroach (B. dubia, Blaberidae) Diets: Omnivoures Reproduction: • Ovoviviparity Sociality: • Subsocial Relation to Human: • Pet, Pet Diet (only cockroach without odor)
3. Instar determination • Basic research and application  Growth, evolution  Life table analysis • Brooks‐Dyar rule (Brooks 1886, Dyar 1890, Hutchinson 1984) • Objective: Find a general way to determine instars of B. duia
4. Methods Data collection • 1925 cockroaches were measured • Measure the three variables: head width, pronotum length and width of the Dubia cockroach rearing in the lab (30℃, 12:12 (L:D) and supplied with water and dry dog Chow) Statistical analysis Overview
5. Methods Statistical analysis • Assumption: The measurement of sclerotized characters in each instar is Gaussian (normal) distribution
6. Methods Statistical analysis • Gaussian Mixture model (GMM) (Johnson & Wichern 2007) Mixture of two Gaussian
7. Gaussian Mixture model (GMM) Three variables: head Width, Pronotum Length and Pronotum Width. The multivariate case More than two groups
8. Likelihood Inference is based on maximum likelihood (Johnson & Wichern 2007) GMM
9. Likelihood We do not know the group the data belong to. i.e. We do not know which instar the insect is, when we take the measurements  • Hierarchical clustering, EM algorithms and Bayesian Information Criterion (BIC) • Software : R package mclust (Fraley & Adrian 2012)
10. Results Table 1. The 95% simultaneous ‐intervals of the three characters (mm) in each instar Instar 1 Instar 2 Instar 3 Instar 4 Instar 5 Instar 6 Instar 7 N 137 152 148 234 356 324 178 Length [2.37,2.45] [2.91,3.03] [3.77,3.87] [4.84,4.98] [6.11,6.23] [7.46,7.63] [9.30,9.47] Width [4.14,4.22] [5.13,5.30] [6.40,6.54] [7.89,8.13] [9.86,10.04] [12.15,12.41] [15.04,15.30] Head [1.78,1.80] [2.06,2.11] [2.47,2.51] [2.94,3.00] [3.53,3.58] [4.21,4.28] [5.00,5.07]
11. Result assessment Table 2. The mean of the three characters(mm) in each instar and growth ratio Characters Instar 1 Instar 2 Instar 3 Instar 4 Instar 5 Instar 6 Instar 7 Ratio Length 2.41 2.97 3.82 4.91 6.17 7.54 9.39 1.26 Width 4.18 5.21 6.47 8.01 9.95 12.28 15.17 1.24 Head 1.79 2.08 2.49 2.97 3.55 4.24 5.04 1.19 Brooks‐Dyar rule
12. Summary • This approach can be used to determinate instars of the Dubia cockroaches. 1. The growth rates follow Brooks‐Dyar rule. 2. There are 7 instars in the Dubia cockroaches Blaptica dubia. 3. The ratio of growth in pronotum length, pronotum width and head width are 1.26, 1.24, 1.19 respectively. • This approach should be applicable to other insects, since the Dubia cockroaches comply with the same growth model with other insects
13. Acknowledgement • Dr. Arthur Appel • Dr. Xing Ping Hu • Dr. Peng Zeng • Marla Eva • Charles Stephen • Zachary Devries • Znar Barwary • Yao Xu