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).