Explaining variation in the magnitude and sign of *I*. Untransformed population-level *I* as a function of (*A*) the degrees of separation between *R* and *T*, and (*B*) log_{10}(*B*_{T}^{+}). Colored symbols highlight all of the CART leaves whose mean was within the top 5% strongest *I*. Strong negative *I* included one degree, “simple” (one path) effects of *R* on basal *T* where *R* is *T'*s only consumer (dark red) or one of two consumers (orange), or “diffuse” (multiple possible paths) effects of high biomass *R* on high biomass *T* where the weighted sum of path signs <0 (yellow). Strong positive *I* included simple and diffuse effects of high biomass *R* on high biomass *T* where the weighted sum of path signs ≥0 (purple, blue, and green). (*C* and *D*) The same data as *B* but with log_{10}|*I*| on the *y* axis. Color codes in *C* are the same as in *A* and *B*. Colors in *D* indicate upper (light red) and lower (blue) 50% quantiles of *B*_{R}. Multiple linear regression: log_{10}|*I*| = −1.34 + 0.71 log_{10}(*B*_{T}^{+}) + 0.22 log_{10}(*B*_{R}), R^{2} = 0.65 and 0.63 in the training and test data, respectively. *B*_{T}^{+} is the biomass of *T* with *R* present, and *B*_{R} is the biomass of *R*.

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