Table 3 Relative variable importance estimated with a random forest model and a hierarchical Bayesian model

Environmental predictor variable	Random forest model	Bayesian model
	Importance Values	Probability of variable inclusion	Direction of effect (slope±1 s.d.)	Degree
Flow regime Disturbance index	0.002	0.85	Negative (–0.015±0.010)	1.5
Mean accumulated soil water surplus for summer	0.001	0.39	Negative (–0.001±0.004)	0.6
Stream and valley percentage extant woodland cover	0.001	0.34	Negative (–0.001±0.003)	0.5
Fish condition index	0.001	0.34	Positive (0.001±0.004)	0.5
Annual mean net primary productivity	0.001	0.42	Negative (–0.002±0.006)	0.7
Coefficient of variation of annual totals of accumulated soil water surplus	0.001	0.39	Positive (0.001±0.005)	0.6
Annual mean accumulated soil water surplus	0.002	0.56	Negative (–0.006±0.009)	1.0
Barrier free flow path length	0.001	0.38	Negative (–0.001±0.004)	0.6
Average spring temperature	0.001	0.38	Negative (–0.002±0.006)	0.6
Stream and valley percentage extant forest cover	0.001	0.40	Negative (–0.002±0.004)	0.6
Fish nativeness score	0.001	0.40	Negative (–0.003±0.006)	0.7

Importance values for the random forest model are proportional to the reduction in root-mean-square errors when a given predictor variable is included in the model; higher values indicate a more important variable. Importance values for the Bayesian model are posterior probabilities of inclusion for each environmental predictor variable. For the Bayesian model, we also present the model averaged parameter estimates for the slope and degree. The prior probability of variable inclusion was 0.5, and hence values >0.75 correspond with odds ratios >3. The slope of a given effect indicates the direction of a variable’s effect, and the degree is the number of knots included in the spline term for a given variable, indicating the nonlinearity of a variable’s effect (0 is no effect, 1 is a linear effect, 2 is a quadratic effect and 3 is a cubic effect).

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