Drought sensitivity assessment
To determine if the climate sensitivity of ∆13C varied
between the trees that died early versus late in the outbreak, we used
both a hypothesis testing and model comparison approach. For both, we
conducted linear mixed-effects modeling with repeated-measures that also
accounted for the nested design of early- and late-dying trees per site.
The repeated measurement was raw ∆13C with a first
order autoregressive residual covariance structure to account for
temporal autocorrelation. For the hypothesis testing approach, we tested
∆13C responses with an interaction between the most
influential climate variable (see below) and timing of death (early or
late) where the presence or absence of a significant interaction would
determine the importance of drought-sensitivity during the progression
of beetle outbreaks. For the model comparison approach, we examined
three competing models using Akaike information criterion (AIC) and
likelihood ratio tests (Burnham and Anderson 2002). The first model
assumed no difference in the climate sensitivity of early- vs late-dying
trees, the second included an intercept effect of timing of death (early
vs late) in addition to climate, and the third, included an interaction
between timing of death and climate. Regression analyses were conducted
using the “nlme” and “visreg” packages in R (R Core Team 2016;
Breheny and Burchett 2017; Pinheiro et al. 2017). Before
assessing the influence of host drought stress in driving beetle
outbreaks, we first identified which metrics and months best captured
drought stress at our sites by calculating correlations between monthly
and seasonally resolved climate variables calculated from Climate WNA
(Wang et al. 2016) and tree-ring variables (Appendix S1; Table S2).
Variables of interest included climatic moisture deficit (CMD) defined
as precipitation minus reference evapotranspiration for June, July, and
August (after the Hargreaves method, Yates and Strzepek 1994),
temperature, water year precipitation (previous October to current
September), and the Palmer Drought Severity Index (PDSI, Palmer 1965;
Guttman and Quayle 1996).