Testing the rate isomorphy hypothesis using five statistical methods

Organisms are said to be in developmental rate isomorphy when the proportions of developmental stage durations are unaffected by temperature. Comprehensive stage-specific developmental data were generated on the cabbage beetle, Colaphellus bowringi Baly (Coleoptera: Chrysomelidae), at eight temperatures ranging from 16 degrees C to 30 degrees C (in 2 degrees C increments) and five analytical methods were used to test the rate isomorphy hypothesis, including: (i) direct comparison of lower developmental thresholds with standard errors based on the traditional linear equation describing developmental rate as the linear function of temperature; (ii) analysis of covariance to compare the lower developmental thresholds of different stages based on the Ikemoto-Takai linear equation; (iii) testing the significance of the slope item in the regression line of arcsin(root p) versus temperature, where p is the ratio of the developmental duration of a particular developmental stage to the entire pre-imaginal developmental duration for one insect or mite species; (iv) analysis of variance to test for significant differences between the ratios of developmental stage durations to that of pre-imaginal development; and (v) checking whether there is an element less than a given level of significance in the p-value matrix of rotating regression line. The results revealed no significant difference among the lower developmental thresholds or among the aforementioned ratios, and thus convincingly confirmed the rate isomorphy hypothesis.