These correlations prevented the simultaneous use of these variables in the same model ( Graham, 2003). We used stem density as an explanatory variable in linear

models, rather than stand age, mean tree height or diameter, as stem density is easier to estimate and to control through forest management (e.g. by thinning). We first assessed the effect of stem density on the mean number of nests per hectare (PPM population density) using a GLM with a Poisson error distribution accounting for overdispersion [“dispmod” R package (Scrucca, 2012); see also Breslow (1984)]. GLM with binomial error were used to assess the effect of stem density on the percentage of infested trees (Williams, 1982). The same dataset was used to test the effects of tree attributes (height, diameter and location AZD2281 molecular weight within stands) on the probability of a tree being attacked by PPM, but with trees as replicates. The individual trees could not be considered to be independent, due to the sampling design (trees nested within plots, nested within stands) and therefore mixed-effect models were used, with stands and plots treated as nested random factors. Tree diameter was positively and strongly correlated with tree height (n = 3334, r = 0.905, P < 0.0001),

precluding the inclusion of these two variables together in the same model ( Graham, 2003). Tree height is harder to measure reliably (particularly LY2109761 price as trees grow taller) and tree diameter was measured on all trees. We therefore preferred to

use tree diameter in our analyses. Although tree diameter and stand density were not independent (because of regular thinning as trees grow larger), both variables are likely to control tree infestation by the PPM, and it is important to tease apart these two potential effects. We therefore built first a binomial (GLMM) to analyze the presence/absence of PPM nests on individual trees, using the following fixed effects: stand density + tree diameter + plot location + tree diameter × plot location. The interior plots (IP1, IP2 and IP3) were pooled together so that plot location was treated as a two-level factor, contrasting edge plots vs. interior plots. This first model was then simplified by sequentially removing explanatory variables, staring by the two-ways interaction. This set of models was compared using information NADPH-cytochrome-c2 reductase theory. The set of best-fitting models was selected based on Akaike’s information criterion, corrected for small sample sizes (AICc, Burnham and Anderson, 2002) using the selMod function from the “pgirmess” package ( Giraudoux, 2013). Among the best fitting models, the minimum adequate model (MAM), i.e. most parsimonious model, was that with the lowest number of estimable parameters (K) within 2 AICc units of the model with the lowest AICc. Differences in AICc scores (Δi) of >2 are usually interpreted as indicating strong support for the MAM compared to poorer models ( Burnham and Anderson, 2002).