A Novel Rate Model of Temperature-Dependent Development for Arthropods

Abstract

Two novel and simple mathematical models of arthropod temperature-dependent development are proposed. These models are easy to use and have 3 (equation 1) and 4 (equation 2) ecologically meaningful parameters, respectively. Each parameter can be estimated using nonlinear regression. These models were used to compare developmental rates at constant temperatures for our own experiments on Lobesia botrana (Dennis & Schiffermuller) and for data from 6 insect species described (a total of 13 stages). In all cases, we obtained an accurate nonlinear description of the rate of development against temperature given by the adjusted R² (Kvalseth, 1985). The adjusted R² calculated extended from 0.86 to 0.99 and were identical for our equations 1 and 2. In all cases, equation 2 provided the lowest residual sums of squares. The models gave upper T_L and lower T₀ temperature threshold estimations, and the estimations obtained were better by using equation 1 rather equation 2. Confidence intervals for each parameter were given and a comparison between estimated and observed temperature thresholds were presented.