Electronic Supplementary Material

Appendix 1. Phase 1 methods

Model set– We considered sets of six models each for the five infiltration variables (sorptivity under ponding and tension, steady-state infiltration under ponding and tension, macropore ratio), ranging from 4 to 10 parameters. Rather than attempting to model the complex interrelations among the various infiltration variables, we constructed separate model sets for each infiltration variable. The most complex was the global model (Figure A1). The simplest was the independence model, which specified zero correlation among the variables in the model. The “Stipa→crust” removed model form, posits that due to our sampling strategy of collecting a wide gradient of crust cover both in and out of the presence of Stipa, these two variables will be uncorrelated and the path removed from the model. The “Stipa→rabbit” removed model form applies the same reasoning to rabbit disturbance. The “rabbit→infiltration” removed model form posits that rabbit disturbance has no direct effect upon infiltration, and that its effects are mediated via the rabbit impact upon crust cover. Finally, we considered an “all three removed” model which excluded all three of these pathways simultaneously.

Results: AIC values for the model sets are presented in Table A1.The Akaike Information Criterion (AIC) value itself has no upper bound, thus the value has no absolute interpretation; rather it is useful in evaluating the differences among models in a set. The ∆AIC is simply the difference between a given model’s AIC value, and that of the lowest value in the set. As a rule of thumb it is generally accepted that a clear best model will be identified when the next best model has an ∆AIC value greater than about 2 (Burnham and Anderson 2002).

Table A1. A Summary of Akaike’s Information Criterion (AIC) Values for the Six Models Explored Within Each of the Five Response Variables Considered in This Study.

Response / Model form / No. of parameters / AIC / ΔAIC
Steady–state infiltration under ponding / 1. Global / 10 / 20.00 / 5.53
2.Stipa to crust removed / 9 / 18.00 / 3.55
3. Stipa to rabbit removed / 9 / 18.35 / 3.91
4. Rabbit to infiltration removed / 9 / 18.10 / 3.61
5. All three removed / 7 / 14.45 / 0
6. Independence / 4 / 25.18 / 10.74
Sorptivity under ponding / 1. Global / 10 / 20.00 / 5.42
2.Stipa to crust removed / 9 / 18.00 / 3.42
3.Stipa to rabbit removed / 9 / 18.35 / 3.77
4. Rabbit to infiltration removed / 9 / 18.23 / 3.65
5. All three removed / 7 / 14.58 / 0
6. Independence / 4 / 30.71 / 16.13
Steady–state infiltration under tension / 1. Global / 10 / 20.00 / 5.63
2. Stipa to crust removed / 9 / 18.00 / 3.63
3. Stipa to rabbit removed / 9 / 18.35 / 3.98
4. Rabbit to infiltration removed / 9 / 18.02 / 3.65
5. All three removed / 7 / 14.37 / 0
6. Independence / 4 / 67.30 / 52.93
Sorptivity under ponding / 1. Global / 10 / 20.00 / 4.56
2. Stipa to crust removed / 9 / 18.00 / 2.56
3. Stipa to rabbit removed / 9 / 18.35 / 2.91
4. Rabbit to infiltration removed / 9 / 18.09 / 3.65
5. All three removed / 7 / 15.44 / 0
6. Independence / 4 / 70.39 / 54.95
Macropore ratio / 1. Global / 10 / 20.00 / 4.57
2. Stipa to crust removed / 9 / 18.00 / 2.57
3. Stipa to rabbit removed / 9 / 18.35 / 2.92
4. Rabbit to infiltration removed / 9 / 18.08 / 3.65
5. All three removed / 7 / 15.43 / 0
6. Independence / 4 / 63.22 / 47.78

The best model of each set (bold text) was selected based upon the lowest AIC value and an AIC value at least 2 units lower than the next model (reflected by ∆AIC).

Figure A1.A priori model forms used in phase one of data analysis. Dashed boxes represent conceptual variables, and solid boxes represent measured variables which pertain to these concepts. Arrows represent hypothesized causal influences. For each of the five measured variables pertaining to infiltration, six model forms were considered. All model forms can be generated from this global model, by removal of paths corresponding to the model form number used in Table A1.