Phylogenetic Generalized Linear Models
To test the effect of traits on the responses and population trend, the
responses on each other, as well as the effect of responses on
population trends, we applied Phylogenetic Generalized Least Squares
(PGLS; Freckleton et al. 2002; also called Phylogenetic
Generalized Linear Models; Symonds & Blomberg 2014) through thepgls function as implemented in the caper R-package (Orme
2018). The PGLS method is an extension to generalized least squares
where the phylogenetic relationships of species are incorporated into
the modeling framework via estimation of covariance in multispecies
data. Related species cannot be considered independent from each other
in neither their life history traits (Freckleton et al. 2002;
Ives & Zhu 2006) nor in their responses to environmental change (Davieset al. 2013; Fei et al. 2017). Thus, any model residuals
of closely related species would often be more similar than by chance,
which requires modification to the estimated slopes and intercepts of
the models (Revell 2010; Symonds & Blomberg 2014). To allow controlling
for phylogenetic dependence, we constructed a phylogenetic tree for the
289 species based on the hypothesis derived by Pöyry et al. (2017) for
Nordic Macrolepidoptera (available in the associated data:
(https://github.com/MariaHallfors/LepidopteraShift). We measured
the phylogenetic signal in our data which confirmed that controlling for
phylogenetic relatedness in subsequent analyses was needed to account
for phylogenetic non-independence of the species. For more details and
description of multicollinearity checks and scaling of variables, see
Text S4.