Statistical analyses
Before the statistical tests, we evaluated the assumptions of normality
and equality of variances using Kolmogorov–Smirnov and Levene tests. To
compare critical thermal limits and demographic variables among
experimental groups, we included thermal treatment as a factor with six
levels (C, V, CV, CC, VC and VV) that describe the thermal experience of
flies (direct experience through ontogeny, and indirect thermal
experience, through parental thermal exposition; see Figure 1). This
factor allowed us to compare phenotypic response between P and F1, and
also to perform comparisons across P and F1 groups. To compare critical
thermal limits among experimental groups, we employed linear mixed model
with trial as random effect (random intercept) and sex and treatment as
predictor variables. Also, to test the potential of trade-off between
fitness related traits ( \(R_{0}\) and \(T_{g}\))and CTmax the one tailed correlation analysis was
conducted.
Because the population density effected significantly \(R_{0}\) and\(T_{g}\) (Supplementary Table S1), we assessed the global response of\(R_{0}\) and \(T_{g}\) to temperature and density. We performed
a nonparametric regression analysis using a generalized additive model
(GAM) incorporating populational density (D), parental thermal
environment (T P), offspring thermal
environment (T F1), and thermal treatment
(treat ) as predictors. We performed GAM since it does not make
any a priori assumptions about the shape of relationships between
variables, which is key to our evaluation of the effects of population
density. Moreover, the main difference between GAMs and linear models is
that linear functions of the variables in GAM are replaced by unknown
smooth functions, giving additional flexibility to the modeling process
(Wood, 2017) .The complexity of the curve (the number of degrees of
freedom) and the smoothing terms were determined by penalized regression
splines and generalized cross-validation to avoid overfitting (Wood,
2017). Also, we allowed the shrinkage of the smoothers. This technique
allows for an extra penalty to be added in the model, and if the penalty
is high enough, it will shrink all smoothing coefficients to zero. Model
selection was done using the AIC criterion (ΔAICc < 2; Burnham
& Anderson (2002)). To perform pairwise comparisons between
experimental groups, we performed a posteriori Tukey test
following the linear mixed models or GAMs.
All analyses and visualizations were performed in the R statistical
environment (http://www.R-project.org/ ). The datasets generated
during the current study will be available in the DRYAD repository