2.2 Computations and statistical analysis
The variables of average life span (survival), age-specific survival (lx) and age-specific fecundity (mx) were estimated for each species and temperature assay (x was defined as the age interval in days, lx as the proportion of surviving individuals at the beginning of the age interval and mx as the number of offspring produced per female alive from the start until the end of any age interval (Poole, 1974). The intrinsic rate of population increase (r ) was also estimated from these data using Lotka’s equation (Lotka, 1907):
r=∑e-rx *lx mx = 1
Kaplan-Meier survival curves were calculated to compare survival across species and across temperatures. Differences between survival functions were analyzed pairwise using a log-rank test. To further estimate the effect on lifespan and fecundity by species, temperature, and their interaction, we used generalized linear models (GLMs). We selected the best-fitting model based on the AIC criteria (Zuur, Leno, Walker, Saveliev, & Smith, 2009). To compare fecundity among the species and temperature treatments we used the non-parametric Kruskal–Wallis one-way analysis of variance. For pairwise comparisons the pairwise Wilcox test was used with a Bonferroni correction for the p-values. Non parametric tests were used for comparisons, as all of the assumptions to perform Analysis of Variance (ANOVA; normal distribution of the data, normal distribution of the residuals, and homoscedasticity) were violated. To compare the intrinsic rate of increase (r ), the 95% confidence interval was estimated via bootstrapping with 199 iterations (Weithoff & Wacker, 2007) using an R script (personal communication Dr. Wacker). All statistical analyses were performed using R 3.4.1 (R Core Team).