Electronic Appendix A
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ELECTRONIC APPENDIX A
Figure A.1. Mean temperature (bars) and precipitation (line) for the growing season (May-August) at Hol 2003-2007. Normal value (1961-1990) is given as a reference. Table A.1. Number of plots (= replicates) per species in each of the sheep density treatments (high, low, no sheep).
Species No Low High Alchemilla alpina 8 9 9 Bistorta vivipara 9 9 9 Hieracium alpinum 9 9 8 Leontodon autumnalis 9 5 6 Omalotheca norvegica 10 9 7 Omalotheca supina 7 8 9 Potentilla erecta 6 4 3 Pyrola minor 7 5 8 Ranunculus acris 6 9 9 Rumex acetosa 9 10 9 Saussurea alpina 4 8 4 Sibbaldia procumbens 8 9 9 Solidago virgaurea 8 4 7 Trientalis europaea 9 9 9 Viola palustris 5 6 4 Table A.2. Fixed effects of linear mixed effects models relating year, sheep density to (a) grazing frequency (arcsin-transformed), (b) flowering frequency (arcsin-transformed), c) plant height (ln- transformed) and d) plant density at the herb community level. Parameter estimates for random effects (plot nested in enclosure) are not shown. The intercept refers to the no sheep treatment in
2003. Significant effects are shown in bold.
a) Grazing frequency
Fixed effects Coefficient df t P-value
157 (Intercept) 0.017±0.019 2 0.883 0.3773
157 Y2004 -0.017±0.024 2 -0.690 0.4904
157 Y2005 0.003±0.024 2 0.140 0.8890
157 Y2006 -0.011±0.024 2 -0.444 0.6575
157 Y2007 -0.005±0.024 2 -0.184 0.8541
Low 0.092±0.027 6 3.393 0.0146
High 0.219±0.027 6 7.980 0.0002
157 Y2004:Low vs No sheep -0.046±0.035 2 -1.341 0.1800
157 Y2005:Low vs No sheep -0.036±0.035 2 -1.048 0.2949
157 Y2006:Low vs No sheep -0.034±0.035 2 -0.969 0.3328
157 Y2007:Low vs No sheep -0.006±0.035 2 -0.161 0.8720
Y2004:High vs No sheep -0.088±0.035 157 -2.507 0.0123 2
157 Y2005:High vs No sheep -0.070±0.035 2 -1.999 0.0458
157 Y2006:High vs No sheep -0.054±0.035 2 -1.553 0.1205
157 Y2007:High vs No sheep -0.036±0.035 2 -1.034 0.3014
b) Flowering frequency
Fixed effects Coefficient df t P-value
157 (Intercept) -0.048±0.031 2 -1.534 0.1252
157 Y2004 -0.017±0.039 2 -0.447 0.6551
157 Y2005 0.046±0.039 2 1.197 0.2316
157 Y2006 0.053±0.039 2 1.369 0.1712
157 Y2007 -0.112±0.039 2 -2.909 0.0037
Low -0.136±0.044 6 -3.056 0.0223
High -0.132±0.045 6 -2.915 0.0268
157 Y2004:Low vs No sheep 0.093±0.055 2 1.679 0.0933
157 Y2005:Low vs No sheep 0.051±0.055 2 0.923 0.3560
157 Y2006:Low vs No sheep 0.061±0.055 2 1.105 0.2692
157 Y2007:Low vs No sheep 0.098±0.055 2 1.770 0.0770
157 Y2004:High vs No sheep 0.045±0.056 2 0.805 0.4209
157 Y2005:High vs No sheep -0.030±0.056 2 -0.531 0.5958
157 Y2006:High vs No sheep -0.027±0.056 2 -0.482 0.6296
Y2007:High vs No sheep 0.072±0.056 157 1.290 0.1972 2
b) Plant height
Fixed effects Coefficient df t P-value
157 (Intercept) 2.074±0.092 2 22.493 0.0000
157 Y2004 -0.148±0.058 2 -2.572 0.0102
157 Y2005 -0.012±0.058 2 -0.215 0.8297
157 Y2006 0.003±0.058 2 0.048 0.9617
157 Y2007 -0.024±0.058 2 -0.419 0.6749
Low -0.051±0.128 6 -0.398 0.7049
High -0.250±0.131 6 -1.910 0.1047 157 Y2004:Low vs No sheep 0.039±0.082 2 0.472 0.6364
157 Y2005:Low vs No sheep -0.027±0.082 2 -0.326 0.7444
157 Y2006:Low vs No sheep -0.034±0.082 2 -0.408 0.6836
157 Y2007:Low vs No sheep -0.030±0.082 2 -0.359 0.7198
157 Y2004:High vs No sheep 0.044±0.083 2 0.532 0.5948
157 Y2005:High vs No sheep -0.054±0.083 2 -0.654 0.5132
157 Y2006:High vs No sheep -0.077±0.083 2 -0.926 0.3547
157 Y2007:High vs No sheep -0.087±0.083 2 -1.042 0.2975 d) Plant density
Fixed effects Coefficient df t P-value
157 (Intercept) -0.575±0.154 2 -3.727 0.0002
157 Y2004 0.376±0.134 2 2.802 0.0051
157 Y2005 0.183±0.134 2 1.364 0.1729
157 Y2006 0.149±0.134 2 1.107 0.2684
157 Y2007 -0.009±0.134 2 -0.068 0.9461
Low 0.141±0.215 6 0.662 0.5327
High 0.114±0.220 6 0.520 0.6214
157 Y2004:Low vs No sheep -0.297±0.191 2 -1.550 0.1214
157 Y2005:Low vs No sheep -0.090±0.192 2 -0.468 0.6400
157 Y2006:Low vs No sheep -0.014±0.192 2 -0.074 0.9410
157 Y2007:Low vs No sheep -0.237±0.192 2 -1.236 0.2168
157 Y2004:High vs No sheep -0.295±0.193 2 -1.527 0.1268
157 Y2005:High vs No sheep -0.004±0.193 2 -0.022 0.9821
157 Y2006:High vs No sheep 0.040±0.193 2 0.205 0.8377
157 Y2007:High vs No sheep -0.345±0.193 2 -1.786 0.0744 Table A.3. Summary of LME models in the term of t-values for each parameter for all herb species included in the experiment with significant responses to the grazing treatment. Grazing = grazing frequency, Height = plant height, Flowering = flowering frequency, Density = plant density. For simplicity, the values in bold indicate a significant difference (p < 0.05) from the intercept (enclosures with no sheep in 2003). Bistorta vivipara
Fixed effects Grazing Height Flowering Density
df t t t t
Y2004 98 -0.60 -1.16 -0.79 0.32
Y2005 98 0.54 -0.44 2.34 1.28
Y2006 98 -0.23 -0.43 0.52 0.56
Y2007 98 0.19 1.73 -1.39 -0.30
Low 6 3.48 0.66 -0.81 -0.70
High 6 1.95 -0.61 -1.24 -0.45
Y2004:Low vs No sheep 98 -2.08 1.32 3.94 -0.08
Y2005:Low vs No sheep 98 -1.47 0.56 1.23 -1.20
Y2006:Low vs No sheep 98 -1.90 0.59 3.34 0.43
Y2007:Low vs No sheep 98 -0.99 -1.47 0.64 0.98
Y2004:High vs No sheep 98 0.34 0.45 1.44 2.02
Y2005:High vs No sheep 98 -0.59 -1.17 -0.45 0.98
Y2006:High vs No sheep 98 -0.71 -0.84 0.16 2.64
Y2007:High vs No sheep 98 0.92 -1.78 1.44 1.57
Leontodon autumnalis
Fixed effects Grazing Height Flowering Density
df t t t t
Y2004 68 -0.41 -3.78 -3.60 0.68
Y2005 68 -0.41 -1.69 -0.08 0.94
Y2006 68 -0.41 -2.35 -1.94 0.75
Y2007 68 0.18 -3.15 -3.90 1.07
Low 6 1.09 -1.26 -3.05 1.26
High 6 5.17 -1.71 -1.50 -0.36
Y2004:Low vs No sheep 68 -0.84 1.28 2.75 0.51
Y2005:Low vs No sheep 68 0.53 0.50 1.75 0.65
Y2006:Low vs No sheep 68 -0.01 1.57 2.46 0.76
Y2007:Low vs No sheep 68 1.72 0.24 2.27 -0.59
Y2004:High vs No sheep 68 -2.61 1.39 1.07 0.53 Y2005:High vs No sheep 68 -1.95 1.18 2.67 0.73
Y2006:High vs No sheep 68 0.04 0.37 0.58 1.37
Y2007:High vs No sheep 68 0.56 0.01 1.69 0.98
Omalotheca norvegica
Fixed effects Grazing Height Flowering Density
df t t t t
Y2004 90 0.00 -3.96 -0.14 1.81
Y2005 90 0.00 0.76 1.32 -0.47
Y2006 90 0.26 -0.49 0.99 -0.49
Y2007 90 0.00 -4.05 -4.24 -0.03
Low 4 4.70 -4.21 -3.93 -1.02
High 4 6.47 -7.49 -3.68 -0.51
Y2004:Low vs No sheep 90 -2.26 1.88 0.66 -0.00
Y2005:Low vs No sheep 90 -1.61 -0.54 -0.14 0.34
Y2006:Low vs No sheep 90 -1.90 0.95 -0.10 0.81
Y2007:Low vs No sheep 90 -1.21 1.78 2.90 0.68
Y2004:High vs No sheep 90 -3.03 1.93 0.09 -1.05
Y2005:High vs No sheep 90 -2.42 1.80 -0.85 0.84
Y2006:High vs No sheep 90 -2.46 0.57 -0.64 0.54
Y2007:High vs No sheep 90 -1.06 2.48 2.72 -1.70
Omalotheca supina
Fixed effects Grazing Height Flowering Density
df t t t t
Y2004 84 0.00 -1.60 2.41 0.74
Y2005 84 0.00 -2.39 0.73 1.18
Y2006 84 0.00 -0.58 1.29 1.44
Y2007 84 0.00 -3.66 -0.31 -0.85
Low 6 1.58 -1.14 0.63 -0.56
High 6 0.90 0.38 3.36 0.34
Y2004:Low vs No sheep 84 -1.25 -0.60 -1.84 -0.82 Y2005:Low vs No sheep 84 -1.25 0.70 -0.85 -0.35
Y2006:Low vs No sheep 84 -1.25 -0.09 -0.55 -1.17
Y2007:Low vs No sheep 84 -1.25 1.85 -0.68 0.22
Y2004:High vs No sheep 84 -0.64 0.32 -2.68 -1.66
Y2005:High vs No sheep 84 0.45 1.70 -1.19 -1.65
Y2006:High vs No sheep 84 1.25 0.27 -1.46 -0.74
Y2007:High vs No sheep 84 -0.64 1.50 -1.39 0.20
Potentilla erecta
Fixed effects Grazing Height Flowering Density
df t t t t
Y2004 40 0.00 -2.17 -1.63 1.60
Y2005 40 0.00 -1.01 -2.63 1.06
Y2006 40 0.00 -0.90 -1.97 2.68
Y2007 40 0.41 -1.22 -1.69 -0.09
Low 2 0.90 -2.13 -3.07 -0.26
High 2 4.36 -0.57 -1.00 -0.97
Y2004:Low vs No sheep 40 -0.74 2.27 1.38 -0.99
Y2005:Low vs No sheep 40 0.68 2.12 2.06 -0.71
Y2006:Low vs No sheep 40 0.20 -0.19 0.08 -0.92
Y2007:Low vs No sheep 40 0.19 2.30 2.13 -0.77
Y2004:High vs No sheep 40 -0.84 0.08 0.68 -0.49
Y2005:High vs No sheep 40 -3.17 0.02 -0.23 -0.25
Y2006:High vs No sheep 40 -1.75 0.33 0.34 -1.03
Y2007:High vs No sheep 40 -2.67 -0.12 -0.34 0.25
Pyrola minor
Fixed effects Grazing Height Flowering Density
df t t t t
Y2004 67 0.00 2.23 0.08 0.78
Y2005 67 0.00 1.07 -0.81 1.15
Y2006 67 0.00 1.92 1.67 0.70 Y2007 67 0.00 1.92 0.05 0.97
Low 5 0.59 2.24 0.28 0.98
High 5 3.57 2.14 -0.87 -0.36
Y2004:Low vs No sheep 67 -0.52 -1.87 0.15 0.20
Y2005:Low vs No sheep 67 0.44 -1.68 -0.21 -0.90
Y2006:Low vs No sheep 67 -0.52 -1.66 -0.35 1.78
Y2007:Low vs No sheep 67 -0.52 -1.27 -0.66 -1.20
Y2004:High vs No sheep 67 -2.04 -1.94 0.53 0.04
Y2005:High vs No sheep 67 -1.83 -1.20 0.59 -0.61
Y2006:High vs No sheep 67 -1.48 -2.04 -0.38 -0.52
Y2007:High vs No sheep 67 0.13 -2.15 0.05 -0.57
Rumex acetosa
Fixed effects Grazing Height Flowering Density
df t t t t
Y2004 100 -0.86 -0.35 -1.59 0.84
Y2005 100 -0.86 0.26 -1.39 1.44
Y2006 100 -0.86 1.17 -0.20 1.47
Y2007 100 -0.86 0.49 -2.40 0.27
Low 5 1.44 -0.63 -2.31 -0.54
High 5 3.09 -1.93 -2.64 0.46
Y2004:Low vs No sheep 100 -0.64 0.53 1.84 0.16
Y2005:Low vs No sheep 100 0.37 -0.00 1.74 -0.63
Y2006:Low vs No sheep 100 -0.37 0.58 1.82 -0.50
Y2007:Low vs No sheep 100 0.04 0.07 2.05 0.20
Y2004:High vs No sheep 100 0.33 0.90 1.46 -0.58
Y2005:High vs No sheep 100 0.50 1.05 1.07 0.09
Y2006:High vs No sheep 100 -0.55 -0.43 0.92 -0.48
Y2007:High vs No sheep 100 1.12 -0.15 1.70 -0.52
Saussurea alpina
Fixed effects Grazing Height Flowering Density df t t t t
Y2004 52 0.00 0.18 -1.82 1.30
Y2005 52 0.00 -0.05 -2.89 0.68
Y2006 52 0.00 0.68 1.48 1.14
Y2007 52 0.00 0.37 -2.89 0.30
Low 5 0.51 -0.38 -2.34 0.02
High 5 4.11 -0.90 -2.13 -0.50
Y2004:Low vs No sheep 52 0.62 -1.07 1.49 -0.63
Y2005:Low vs No sheep 52 0.57 -0.59 2.36 -0.22
Y2006:Low vs No sheep 52 0.87 -1.16 -1.21 0.46
Y2007:Low vs No sheep 52 1.21 -0.95 2.36 -0.22
Y2004:High vs No sheep 52 -1.83 -0.00 1.29 -0.59
Y2005:High vs No sheep 52 -1.59 0.03 2.04 -0.41
Y2006:High vs No sheep 52 -0.72 -1.72 -1.05 -0.79
Y2007:High vs No sheep 52 -0.61 -0.90 2.04 -0.08
Sibbaldia procumbens
Fixed effects Grazing Height Flowering Density
df t t t t
Y2004 84 0.00 -0.97 0.31 2.10
Y2005 84 0.00 0.42 0.21 0.81
Y2006 84 0.00 0.32 0.48 -0.33
Y2007 84 0.00 -0.14 -0.46 -0.92
Low 6 1.42 3.11 -1.21 -0.10
High 6 1.89 0.59 -0.20 0.46
Y2004:Low vs No sheep 84 -1.39 -1.45 1.00 -1.19
Y2005:Low vs No sheep 84 -1.08 -1.71 0.42 -0.31
Y2006:Low vs No sheep 84 -1.08 -1.28 1.76 0.40
Y2007:Low vs No sheep 84 -0.67 -1.42 0.11 0.66
Y2004:High vs No sheep 84 -1.84 -0.89 0.91 -1.78
Y2005:High vs No sheep 84 0.99 -1.28 -0.31 -1.67
Y2006:High vs No sheep 84 -0.96 -2.31 0.72 0.06 Y2007:High vs No sheep 84 -0.48 -2.19 -0.41 -0.71
Solidago virgaurea
Fixed effects Grazing Height Flowering Density
df t t t t
Y2004 64 -1.22 -0.60 1.03 1.77
Y2005 64 -1.22 1.06 2.23 0.09
Y2006 64 -1.22 -0.48 4.78 0.14
Y2007 64 -1.22 0.57 0.42 0.31
Low 5 1.35 0.08 -0.45 0.22
High 5 5.14 -2.74 -0.88 1.83
Y2004:Low vs No sheep 64 1.42 -0.77 -0.94 -0.75
Y2005:Low vs No sheep 64 -0.18 -1.87 -1.63 0.26
Y2006:Low vs No sheep 64 0.32 -0.82 -3.11 -0.01
Y2007:Low vs No sheep 64 0.64 -0.82 -0.59 -0.57
Y2004:High vs No sheep 64 -1.30 -0.10 -0.85 -1.82
Y2005:High vs No sheep 64 -0.34 -0.78 -1.66 -0.05
Y2006:High vs No sheep 64 -0.26 0.08 -3.41 0.82
Y2007:High vs No sheep 64 -2.00 -0.58 -0.43 -1.83
Trientalis europaea
Fixed effects Grazing Height Flowering Density
df t t t t
Y2004 96 0.00 -1.60 -2.62 0.11
Y2005 96 0.00 -3.13 -1.96 0.64
Y2006 96 0.75 -1.90 -1.31 1.13
Y2007 96 0.00 0.52 -0.59 0.51
Low 6 0.00 0.66 -1.85 0.64
High 6 0.00 1.37 -2.26 0.42
Y2004:Low vs No sheep 96 0.00 0.32 1.39 0.71
Y2005:Low vs No sheep 96 0.00 0.63 2.52 1.37
Y2006:Low vs No sheep 96 0.00 0.24 0.63 -0.61 Y2007:Low vs No sheep 96 0.50 0.58 0.81 -0.83
Y2004:High vs No sheep 96 -1.04 2.23 0.73 0.53
Y2005:High vs No sheep 96 -0.05 -0.22 1.97 0.74
Y2006:High vs No sheep 96 1.48 -1.07 0.56 -0.64
Y2007:High vs No sheep 96 2.88 -3.89 -0.22 -0.88
Viola palustris
Fixed effects Grazing Height Flowering Density
df t t t t
Y2004 48 0.00 -4.93 -2.40 -1.84
Y2005 48 0.00 -2.19 -1.77 -1.62
Y2006 48 0.90 -2.24 -0.11 -1.90
Y2007 48 0.90 -3.00 -2.40 -1.49
Low 5 1.56 0.14 -0.85 -1.71
High 5 3.47 -0.74 -2.18 -1.40
Y2004:Low vs No sheep 48 -1.11 1.05 0.60 1.62
Y2005:Low vs No sheep 48 -1.11 -0.40 0.13 1.23
Y2006:Low vs No sheep 48 -1.77 -0.74 2.25 -1.83
Y2007:Low vs No sheep 48 0.22 0.99 1.30 -1.22
Y2004:High vs No sheep 48 -2.46 2.39 1.60 1.45
Y2005:High vs No sheep 48 -0.71 0.79 1.18 1.32
Y2006:High vs No sheep 48 -3.06 -0.19 0.07 3.58
Y2007:High vs No sheep 48 -0.64 0.45 1.60 1.86