1. 5101520 -0.10 0.10 Lag Partial ACF Fig. S4.1. Partial autocorrelation functions of the residuals from logistic regression models examining how Dendrolimus pini outbreak occurrence was influenced by temperature anomalies in the (a) current year, (b) previous year, and (c) previous decade. 5101520 -0.10 0.00 0.10 Lag Partial ACF 5101520 -0.10 0.00 0.10 Lag Partial ACF 0.00 (a) (b) (c) Appendix S4. Partial autocorrelation functions of the residuals from logistic regressions

2. 51015 -0.2 -0.1 0.0 0.1 0.2 Lag Partial ACF 51015 -0.2 -0.1 0.0 0.1 0.2 Lag Partial ACF 51015 -0.2 -0.1 0.0 0.1 0.2 Lag Partial ACF Fig. S4.2. Partial autocorrelation functions of the residuals from logistic regression models examining how Dendrolimus pini outbreak occurrence was influenced by precipitation anomalies in the (a) current year, (b) previous year, and (c) previous decade. (a) (b) (c)

3. 5101520 -0.10 0.00 0.10 Lag Partial ACF 5101520 -0.10 0.00 0.10 Lag Partial ACF 5101520 -0.10 0.00 0.10 Lag Partial ACF (a) (b) (c) Fig. S4.3. Partial autocorrelation functions of the residuals from logistic regression models examining how Diprion pini outbreak occurrence was influenced by temperature anomalies in the (a) current year, (b) previous year, and (c) previous decade.

4. 5101520 -0.10 0.00 0.10 Lag Partial ACF 5101520 -0.1 0.0 0.1 0.2 Lag Partial ACF 5101520 -0.2 -0.1 0.0 0.1 Lag Partial ACF Fig. S4.4. Partial autocorrelation functions of the residuals from logistic regression models examining how Diprion pini outbreak occurrence was influenced by precipitation anomalies in the (a) current year, (b) previous year, and (c) previous decade. (a) (b) (c)