Appendix 1 Sensitivity Analysis for Pasture Module in Landclim

Appendix 1 – Sensitivity analysis for pasture module in LandClim.

Appendix 2 – Landscape maps for Pré aux Veaux and Jura Vaudois.

Appendix 3 – Relationships between slope and vegetation and global utilization by livestock.

Appendix 1. Sensitivity analysis for the pasture module in LandClim.

Methods

The outcome of the new pasture module in LandClim is determined by three important input parameters; maximum grass biomass (B), number of livestock in the pasture (animals) and grazing duration (days). Parameters were varied within ranges informed by published data when available (Table S1).

For the sensitivity analysis, a Latin Hypercube sampling design was used to create 200 parameter combinations. A Latin hypercube sampling design is an example of a forced stratified random design, and the results are robust even with small sample sizes (Saltelli et al., 2008). To generate the combination of input parameters, we used the ‘lhs’ package in R version 3.3.1 (http://cran.r-project.org/) with the “maximinLHS” function to maximize the minimum dis- tance between input values, and to make sure the entire parameter space is sampled. We used the Pré aux Veaux pasture landscape (described in the manuscript) and ran the model for 1000 simulation years. Climate, landscape and soil data remained the same as described in the manuscript.

Table A1. Parameters tested in the sensitivity analysis for the new pasture module in Land- Clim. The standard value was used as input for the simulations in the manuscript for the Pré aux Veaux pasture, and the range tested was for the input parameters in the Latin hypercube sampling design. The number of animals and grazing duration, the range was from 0 to twice the current value.

Paramete Description Standard Range tested Reference r value B Maximum grass biomass (t ha-1) 4 2 – 6 Thrippleton et al. (2016)

Animals # of adult cows in the pasture 78 0 – 150 0 – 2 x observation Grazing Number of days cattle were 124 0 – 250 0 – 2 x observation duration grazed in the pasture

Output measures

The sensitivity analyses were based on three different measurements that were calculated from the model output.

Open – this is a dichotomous variable that indicates if the pasture has any trees (0) or if the entire pasture is open with no trees at all (1). The simulations which had no trees were exclud- ed from the remaining calculations.

Global utilization (GU) – global utilization is stocking density (GSD) divided by carrying ca- pacity (GCC). Equations and additional information about GU, GSD and GCC are described in the manuscript. GU values are calculated at the pasture level.

Tree cover – mean tree cover in the pasture, based on tree cover for each grid cell. The sensitivity of model output to input values was quantified based on regression and correlation analyses. The dichotomous measure (Open) was analyzed with a logistic regression. The other two measurements (GU and Tree cover) were analyzed using the correlation coefficient (CC), the standardized regression coefficient (SRC), and the partial correlation coefficient (PCC) on the rank-transformed data. All three input parameters were included in the analyses, and thus the adjusted R2 value is reported.

Results

All three parameters were significant for determining if the pasture was completely open or if trees remained (Table S2). Increasing the number of animals and the grazing duration in- creased the probability of a completely open pasture, with animal number having a slightly higher impact that grazing days. Maximum biomass grass biomass had a negative relationship with the probability of an open pasture, i.e., lower grass biomass was more likely to have an open pasture.

Table A2. Results of the logistic regression for the new pasture module in LandClim. The re- sponse variable tested, Open, was a dichotomous variable for it the pasture was 100% open without any trees (1) or if trees were present (0).

Parameter Logistic Regression Open B (maximum grass biomass) p < 0.001 odds = 0.079 Animals p < 0.001 odds = 1.14 Grazing duration p < 0.001 odds = 1.09

Global utilization and tree cover were strongly correlated (r = -0.94), and both indicators were strongly influenced by the number of animals and the grazing duration (Fig. S1). Both input parameters are used to calculate a global stocking density (i.e., the same GSD can be achieved through either a greater number of animals or a longer grazing period). Maximum grass biomass had a smaller impact on global utilization and arguably very little impact on tree cover.

2 Figure A1. Results from the sensitivity analysis for the new pasture module in LandClim, (a) global utilization of the pasture, and (b) mean tree cover. SRC –standardized regression coefficient, LCC – linear correlation coefficient, PCC – partial correlation coefficient.

References Saltelli A, Chan K, Scott EM (2008) Sensitivity Analysis. Wiley & Sons, Ltd., Chichester.

Thrippleton T, Bugmann H, Kramer-Priewasser K, Snell RS (2016) Herbaceous understory - an overlooked player in forest landscape dynamics? Ecosystems.

3 Appendix 2. Landscape and environmental maps for Pré aux Veaux and Jura Vaudois regions.

Figure A2. Topographic and geologic maps for Pré aux Veaux pasture. Note that the percentage of rocky outcrops in the Pré aux Veaux is only used as input for the WoodPaM model.

4 Figure A3. Topographic maps for the Jura Vaudois region.

5 Appendix 3. Relationships between slope and tree cover, forage production and global utilization for the Jura Vaudois.

Figure A4. Relationship between slope and (a) mean tree cover in each grid cell (%), (b) the proportion of each 1 ha pasture covered in trees, (c) mean grass biomass in each pasture (t/ha), and (d) mean global utilization rate for each pasture. Due to the scale of (d), 8 points are not shown which have GU values >2. LandClim simulations are for the Jura Vaudois region and are the mean of 10 landscape replicates.