In this study, gaussian mixture models with constrained parameter spaces are applied to the instar determination of insect species. Finite mixture models are often utilized to classify instars without knowing the instar number. Generally, parsimonious models with fewer free parameters would allow a more efficient estimation if underlying assumptions are valid. This work derives parsimonious gaussian mixture models using a parameter constraint motivated by Dyar's rule. Dyar's rule explains the growth pattern of larvae and nymphs of insects by assuming a constant ratio of head capsule width for every adjacent two development stages. Accordingly, every mean value of log-transformed data in each instar stage is considered a linear function. Two Dyar constants are an intercept and the slope of an instar stage, respectively, in the function. This idea allows estimating two free parameters instead of mean parameters in all instar stages in inferring the instar distribution. Along with this, the homogeneity of variance for every instar can be considered. As a result, four model hypotheses are proposed for each assumption of instar counts depending on whether or not these two parameter constraints are applied. After estimating models, the proposed method uses the ICL criterion to choose the optimal instar inference of models. Then, parametric bootstrap LR tests are applied to decide the most efficient model for parameter constraints given an instar counts inference. The proposed method represents that it can find the correct model settings during the simulation study, where various cases regarding mean parameters and the overlap between two groups are underlain. The result for Meimuna mongolica data shows that all observations are well divided into five instar stages. Parametric bootstrap LR tests also indicate the discrepancy of Dyar's rule in their datasets by selecting a model that does not assume Dyar's rule.