Table 2.

Comparison of the climate-expectation Gamma (log-linked) GLMs for the prediction of shift responses (n = 270) ranked in terms of AICc values (for information on the model coefficients, see Table S2).

Model	M1 (Full model)	M2	M3	M4	Mclimate
Climate velocity	+	+	+	+	+
Directional Agreement (DA)	+	+	+	+
Shift Location (SL)	+	+	+	+
Biological Identity (BI)	+	+	+	+
DA × SL		+	+	+
DA × BI		+		+
BI × SL		+	+
DA × BI × SL	+
AICc	6446.1	6898.8	7072	7306.1	9928.9
∆AICc	−	452.72	625.96	860.02	3482.8
Weight	1	<0.001	<0.001	<0.001	<0.001
D-squared	0.66	0.636	0.629	0.614	0.404

Models fit the fourth-root transformed observed shifts (km/decade) weighted by the number of observed years per observation on the fourth-root transformed climate velocity estimate (km/year) and the three-way interaction among biological identity, shift location, and directional agreement between thermal gradients and current flows. Selection was based on the Akaike Information Criterion corrected for finite sample sizes (AICc). The D-squared statistic denotes the proportion of total variance explained by the model and has an analogous interpretation to that of the coefficient of determination used in linear regression models. The results are presented for the first 4 ranked models and the climate-expectation model (i.e., using only climate velocity as a predictor).