Thermal constants of egg development in carabid beetles - variation resulting from using different estimation methods and among geographically distant European populations

Using equations based on the law of total effective temperatures, we estimated the thermal constants (LDT, the lower development threshold, and SET, the sum of effective temperatures) of egg development for 14 populations of 13 species of carabid beetles (eight belonging to the tribe Zabrini, one to Platynini and four to Pterostichini). We compared the estimates of the thermal constants obtained using three commonly used equations (D = SET / (T - LDT); 1 / D = a + b . T, where LDT = -a / b, and SET = 1 / b; and D . T = SET + D . LDT) and two data formats: data points for all the individuals and means for each temperature. We found that, for most species, estimates of both LDT and SET of egg development obtained using the three models were similar and that using means resulted in larger standard errors (SE) than using all data points. We provide evidence for inter-correlation among the thermal constants, showing that a decrease in the estimate of one constant is accompanied by an increase in the estimate of the other constant. For seven species for which sufficient data were available we investigated the geographical variation in their thermal constants. We found significant variation in both constants for three species, in only one in one species and in three species there was no significant variation among geographically distant populations at p < 0.05. For eight out of the nine autumn-breeding species studied, egg mortality significantly increased at high temperatures. For future studies, we recommend the use of the third method (D . T = SET + D . LDT) for estimating thermal constants for several reasons: (i) it is linear (i.e., simple to compute); (ii) the thermal constants are parameters of the equation, and therefore, their SEs are directly estimated; (iii) it allows the use of all data points (i.e., reduces the SE of the estimates of thermal constants); and (iv) the thermal requirements of different species or populations can be directly compared using ANCOVA.