Appendix A. Best fit parameters for all dispersal kernels.
One (c1) or two parameter (c1, c2) kernels were fit to the population dispersal data. Single parameter kernels have blanks in the c2 columns. k is the asymptotic density of seed in the source area, fitted to the data. Lower (e.g., c1lo) and upper (e.g., c1hi) 95% confidence limits are given for the c’s and k’s. LL is log likelihood. PERE is Pectocarya recurvata and SCBA is Schismus barbatus. Circle radius is the measured radius of the area shaded by the focal shrub for each transect in Shrub Suppression and Open Suppression treatments. Transects for the Both Suppression treatment were assumed to have a linear border so there is no circle radius. Distances were coded in cm.
All models were run using Poisson error fitting. Any fits that failed to converge or produced step functions have been excluded. Lognormal, Inverse Power, general exponential with one-parameter fixed, and the Tufto kernel fits are not presented due to a problems obtaining reasonable fits (step functions and non-convergence).
The following one-dimensional (radially integrated) dispersal kernels were fit to the population dispersal data:
1-Dimensional Exponential :
2-Dimensional Gaussian :
2-Dimensional Exponential :
Wallace :
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Student t, 1 parameter fixed:
Weibull, 1 parameter fixed :
Student t, 2 parameter:
Generalized Exponential:
Weilbull, 2 parameter :
Literature citations for these kernels are given in the Methods section.
TABLE A1. Dispersal kernel best fit parameters for down-slope dispersal into Both Suppression.
species rep kernel circle
radiusc1 c2 k c1lo c2lo klo c1hi c2hi khi LL PERE 1 1d Exp - 0.01 30.56 0.00 27.14 0.01 34.25 77.75 2d Exp - 68.04 30.78 54.50 27.34 88.38 34.50 78.39 2d Gaussian - 144.16 30.83 119.90 27.38 180.18 34.55 79.01 1P Student t - 11695.70 30.77 7160.65 27.33 20234.80 34.49 78.31 Gamma - 68.04 30.78 54.50 27.34 88.38 34.50 78.39 Wallace - 0.35 30.64 0.30 27.21 0.41 34.34 77.88 Weibull - 159.84 30.56 119.10 27.14 226.28 34.25 77.75 2 Par Weibull - 0.95 161.85 30.53 0.48 119.46 27.11 2.05 231.84 34.21 77.75 2P Student t - Gen Exp - 0.39 1.32 30.41 0.38 1.18 27.18 0.41 1.52 34.31 77.81 2 1d Exp - 0.01 39.27 0.01 35.29 0.02 43.55 68.31 2d Exp - 38.03 39.66 32.14 35.63 45.53 43.98 64.03 2d Gaussian - 85.90 39.91 75.05 35.86 99.28 44.26 62.87 1P Student t - 3519.28 39.39 2362.45 35.39 5301.99 43.68 65.18 Gamma - 38.03 39.66 32.14 35.63 45.53 43.98 64.03 Wallace - 0.49 39.27 0.44 35.29 0.54 43.55 67.34 Weibull - 80.02 39.27 64.36 35.29 101.35 43.55 68.31 2 Par Weibull - 2.14 86.67 39.95 1.42 76.21 35.90 3.06 99.63 44.30 62.83 2P Student t - 11.84 81241.10 39.89 8.92 6.13E+04 35.84 15.39 1.10E+05 44.23 62.84 Gen Exp - 2.01 7701.20 39.91 2.06 5866.08 35.86 1.95 10281.80 44.26 62.87 3 1d Exp - 0.02 24.88 0.01 21.54 0.02 28.55 88.74 2d Exp - 33.04 24.90 27.61 21.56 39.78 28.57 98.95 2d Gaussian - 93.99 24.48 82.27 21.19 108.60 28.08 112.21 1P Student t - 973.63 25.24 520.24 21.85 1747.93 28.96 85.83 Gamma - 33.04 24.90 27.61 21.56 39.78 28.57 98.95 Wallace - 0.61 25.00 0.54 21.65 0.69 28.69 87.64 Weibull - 56.11 24.88 45.03 21.54 70.54 28.55 88.74 2 Par Weibull - 2P Student t - Gen Exp - SCBA 2 1d Exp - 0.03 28.35 0.03 24.72 0.04 32.32 70.79 2d Exp - 2d Gaussian - 1P Student t - 175.42 28.40 78.28 24.76 365.89 32.38 62.30 Gamma - 18.91 28.39 15.13 24.76 23.29 32.37 81.36 Wallace - 0.86 28.39 0.75 24.75 1.00 32.36 67.89 Weibull - 30.52 28.35 23.40 24.72 39.44 32.32 70.79 2 Par Weibull - 2P Student t - Gen Exp - 3 1d Exp - 0.01 9.25 0.01 7.38 0.02 11.41 46.28 2d Exp - 33.21 9.34 23.71 7.45 48.19 11.52 44.15 2d Gaussian - 1P Student t - 2947.84 9.24 1337.13 7.37 6710.46 11.40 45.10 Gamma - 33.21 9.34 23.71 7.45 48.19 11.52 44.15 Wallace - 0.52 9.23 0.41 7.37 0.64 11.39 46.01 Weibull - 69.19 9.25 45.06 7.38 113.29 11.41 46.28 2 Par Weibull - 2P Student t - 6.85E+07 3.65E+11 9.42 3.72E+07 2.11E+11 7.51 1.18E+08 6.72E+11 11.62 42.75 Gen Exp - 5.74 2.88E+11 9.48 5.44 9.08E+10 7.56 5.99 1.24E+12 11.70 41.86 5 1d Exp - 0.02 17.77 0.01 15.35 0.03 20.44 64.22 2d Exp - 2d Gaussian - 1P Student t - 1228.17 17.77 557.04 15.34 2648.63 20.44 64.47 Gamma - 25.24 17.79 18.91 15.36 34.17 20.46 64.08 Wallace - 0.64 17.77 0.53 15.35 0.77 20.44 64.28 Weibull - 47.16 17.77 33.14 15.35 68.87 20.44 64.22 2 Par Weibull - 1.36 53.85 17.79 0.72 40.35 15.36 2.25 73.30 20.46 63.95 2P Student t - 108.69 4.15E+05 17.80 67.29 2.63E+05 15.37 170.69 6.73E+05 20.47 64.29 Gen Exp - 0.87 12.78 17.79 0.82 9.81 15.36 0.92 16.86 20.46 64.07
TABLE A2. Dispersal kernel best fit parameters for up-slope dispersal into Both Suppression.
species rep kernel circle
radiusc1 c2 k c1lo c2lo klo c1hi c2hi khi LL PERE 1 1d Exp - 0.01 7.07 0.00 5.57 0.01 8.82 60.46 2d Exp - 85.42 7.03 63.46 5.54 122.32 8.77 62.58 2d Gaussian - 201.96 6.87 160.43 5.41 265.65 8.57 63.75 Clark - 15436.20 7.13 7188.43 5.62 33219.90 8.90 61.92 Gamma - 86.19 7.01 65.02 5.53 118.45 8.75 62.27 Wallace - 0.34 7.11 0.27 5.60 0.41 8.87 60.89 Weibull - 172.59 7.07 118.37 5.57 272.44 8.82 60.46 2 Par Weibull - Clark2dt - 0.22 203.55 6.98 58.14 Gen Exp - 0.96 65.60 7.00 0.91 49.35 5.52 1.00 88.74 8.73 62.19 2 1d Exp - 0.03 68.75 0.02 63.34 0.03 74.45 85.62 2d Exp - 20.20 68.89 17.75 63.52 23.40 74.66 97.42 2d Gaussian - 56.09 69.00 50.50 63.57 62.63 74.72 115.08 Clark - 510.69 68.69 342.99 63.29 753.60 74.39 84.99 Gamma - 20.36 68.93 17.74 63.51 23.40 74.65 97.42 Wallace - 0.76 68.73 0.69 63.32 0.82 74.43 84.96 Weibull - 35.75 68.75 30.34 63.34 42.27 74.45 85.62 2 Par Weibull - 0.51 17.36 68.17 0.42 13.23 62.81 0.60 22.90 73.83 78.26 Clark2dt - 0.45 41.54 68.01 0.40 22.60 62.66 0.52 73.44 73.66 78.51 Gen Exp - 0.16 0.12 68.14 0.16 0.11 62.78 0.16 0.12 73.79 78.31 3 1d Exp - 0.02 34.24 0.02 30.66 0.03 38.08 86.31 2d Exp - 26.25 34.29 21.81 30.71 31.83 38.15 87.49 2d Gaussian - 64.79 34.34 56.26 30.75 75.30 38.20 89.91 Clark - 1294.80 34.23 769.17 30.65 2137.02 38.07 86.47 Gamma - 26.25 34.29 21.81 30.71 31.83 38.15 87.49 Wallace - 0.63 34.23 0.56 30.65 0.72 38.08 86.36 Weibull - 48.30 34.24 38.20 30.66 61.84 38.08 86.31 2 Par Weibull - 0.84 43.67 34.21 0.56 33.42 30.63 1.17 57.86 38.05 86.19 Clark2dt - 0.78 727.14 34.19 0.62 402.22 30.62 0.97 1274.96 38.03 86.38 Gen Exp - 0.36 0.66 34.20 0.35 0.59 30.62 0.38 0.73 38.04 86.24 SCBA 1 1d Exp - 0.03 11.06 0.02 8.99 0.04 13.44 108.61 2d Exp - 2d Gaussian - Clark - 657.64 11.02 209.97 8.95 1627.76 13.39 108.19 Gamma - 23.77 11.09 17.64 9.01 31.82 13.47 109.10 Wallace - 0.72 11.05 0.59 8.98 0.89 13.43 108.41 Weibull - 39.18 11.06 27.12 8.99 56.16 13.44 108.61 2 Par Weibull - 0.77 28.93 11.04 0.56 18.42 8.97 1.04 44.75 13.41 108.48 Clark2dt - 1.00 657.04 11.02 0.73 209.72 8.95 1.40 1626.55 13.39 108.19 Gen Exp - 0.39 0.69 11.04 0.37 0.57 8.96 0.42 0.81 13.41 108.37 2 1d Exp - 0.03 5.84 0.02 4.37 0.05 7.61 32.64 2d Exp - 21.62 5.85 13.91 4.38 34.20 7.63 33.86 2d Gaussian - 59.75 5.86 43.47 4.38 85.43 7.64 35.47 Clark - 491.48 5.84 92.36 4.37 1904.91 7.61 32.50 Gamma - 21.62 5.85 13.91 4.38 34.20 7.63 33.86 Wallace - 0.75 5.84 0.56 4.37 1.01 7.61 32.55 Weibull - 36.61 5.84 21.46 4.37 64.63 7.61 32.64 2 Par Weibull - Clark2dt - Gen Exp - 3 1d Exp - 0.01 7.24 0.01 5.68 0.02 9.07 48.41 2d Exp - 42.95 7.26 29.34 5.69 68.28 9.10 48.69 2d Gaussian - 95.72 7.28 71.08 5.70 140.75 9.11 48.87 Clark - 4402.91 7.25 1707.00 5.68 12103.10 9.08 48.66 Gamma - 42.95 7.26 29.34 5.69 68.28 9.10 48.69 Wallace - 0.47 7.24 0.35 5.68 0.60 9.08 48.54 Weibull - 88.32 7.24 53.77 5.68 163.17 9.07 48.41 2 Par Weibull - Clark2dt - Gen Exp - 0.50 2.15 7.26 0.46 1.72 5.68 0.54 2.80 9.08 48.18 4 1d Exp - 0.03 70.87 0.03 65.36 0.04 76.68 229.21 2d Exp - 16.71 70.90 14.20 65.39 19.63 76.71 225.64 2d Gaussian - 42.91 70.93 37.96 65.42 48.73 76.74 224.64 Clark - 484.98 70.82 302.10 65.32 755.98 76.62 229.05 Gamma - 16.71 70.90 14.20 65.39 19.63 76.71 225.64 Wallace - 0.82 70.85 0.74 65.35 0.91 76.66 229.38 Weibull - 28.83 70.87 23.62 65.36 35.19 76.68 229.21 2 Par Weibull - 2.00 43.04 70.93 1.55 38.03 65.42 2.52 48.77 76.74 224.64 Clark2dt - 9.57 15346.20 70.92 7.55 11641.70 65.41 12.17 20113.80 76.73 224.54 Gen Exp - 1.81 781.31 70.93 1.86 617.65 65.42 1.86 987.46 76.74 224.61 5 1d Exp - 0.05 65.55 0.04 59.53 0.06 71.97 98.52 2d Exp - 12.13 65.63 10.10 59.60 14.56 72.05 98.63 2d Gaussian - 35.10 65.66 30.85 59.63 40.28 72.08 107.37 Clark - 179.59 65.30 102.82 59.30 300.61 71.69 96.79 Gamma - 12.13 65.63 10.10 59.60 14.56 72.05 98.63 Wallace - 1.00 65.50 0.89 59.48 1.14 71.91 97.69 Weibull - 20.22 65.55 16.12 59.53 25.11 71.97 98.52 2 Par Weibull - 1.03 20.92 65.56 0.86 16.72 59.54 1.24 25.83 71.98 98.49 Clark2dt - 1.61 528.70 65.53 1.31 323.90 59.51 2.02 828.03 71.94 95.15 Gen Exp - 0.66 2.25 65.58 0.63 1.95 59.55 0.68 2.60 71.99 97.38
TABLE A3. Best fit parameters for down-slope dispersal from into the Open Suppression.
species rep kernel circle
radiusc1 c2 k c1lo c2lo klo c1hi c2hi khi LL PERE 1 1d Exp 90 0.00 35.93 0.00 29.46 0.00 43.28 81.56 2d Exp 90 120.85 34.64 102.46 28.40 142.66 41.73 72.17 2d Gaussian 90 212.82 31.40 185.26 25.74 245.40 37.82 69.67 Clark 90 45583.70 37.06 33164.80 30.39 62425.80 44.65 72.87 Gamma 90 120.85 34.64 102.46 28.40 142.66 41.73 72.17 Wallace 90 0.23 38.83 0.21 31.84 0.25 46.78 77.37 Weibull 90 372.46 35.93 292.69 29.46 476.73 43.28 81.56 2 Par Weibull 90 2.13 205.94 30.98 1.71 180.52 25.41 2.62 235.93 37.33 69.59 Clark2dt 90 4.35E+07 1.97E+12 31.39 3.27E+07 1.49E+12 25.74 5.73E+07 2.62E+12 37.81 69.68 Gen Exp 90 3.34 9.02E+07 30.27 3.41 6.00E+07 24.82 3.26 1.39E+08 36.46 69.23 2 1d Exp 85 0.00 17.17 0.00 13.32 0.01 21.68 54.82 2d Exp 85 79.94 16.40 63.98 12.73 99.98 20.71 55.33 2d Gaussian 85 158.32 16.23 133.49 12.60 189.56 20.50 56.92 Clark 85 18938.30 17.17 11986.50 13.32 29454.80 21.68 56.28 Gamma 85 79.94 16.40 63.98 12.73 99.98 20.71 55.33 Wallace 85 0.30 17.38 0.26 13.49 0.35 21.95 55.35 Weibull 85 223.10 17.14 160.99 13.30 310.47 21.65 54.82 2 Par Weibull 85 1.25 192.91 16.74 0.87 147.58 12.99 1.71 253.40 21.15 54.33 Clark2dt 85 1.49 29934.50 16.68 1.05 19509.20 12.95 2.10 45595.30 21.07 56.20 Gen Exp 85 0.72 14.25 16.79 0.75 11.88 13.03 0.75 17.05 21.20 55.15 3 1d Exp 65 0.00 35.86 0.00 28.39 0.01 44.53 46.84 2d Exp 65 76.53 31.52 60.91 24.96 96.00 39.15 46.89 2d Gaussian 65 136.11 28.64 113.12 22.68 165.29 35.57 47.70 Clark 65 17477.30 32.96 11199.30 26.10 26996.20 40.94 47.31 Gamma 65 76.53 31.52 60.91 24.96 96.00 39.15 46.89 Wallace 65 0.29 35.41 0.25 28.03 0.33 43.97 46.94 Weibull 65 257.91 35.86 187.61 28.39 356.36 44.53 46.84 2 Par Weibull 65 1.29 194.97 33.46 0.96 149.87 26.49 1.69 254.07 41.55 46.21 Clark2dt 65 1.21 21344.90 32.24 0.85 13802.30 25.52 1.74 32758.90 40.04 47.30 Gen Exp 65 0.72 14.75 33.32 0.75 12.32 26.38 0.75 17.61 41.38 46.78 4 1d Exp 95 0.00 22.34 0.00 17.27 0.00 28.32 78.24 2d Exp 95 139.88 23.33 114.91 18.04 170.60 29.58 63.90 2d Gaussian 95 241.62 20.92 204.56 16.17 286.30 26.52 58.97 Clark 95 62650.40 25.24 43149.20 19.51 90931.80 31.99 63.49 Gamma 95 139.88 23.33 114.91 18.04 170.60 29.58 63.90 Wallace 95 0.21 26.04 0.19 20.13 0.24 33.01 71.25 Weibull 95 400.37 22.34 298.67 17.27 542.42 28.32 78.24 2 Par Weibull 95 Clark2dt 95 Gen Exp 95 SCBA 1 1d Exp 90 0.01 133.22 0.01 123.66 0.01 143.25 162.09 2d Exp 90 48.34 123.18 44.42 114.35 52.56 132.45 142.69 2d Gaussian 90 100.89 121.72 94.71 113.00 107.45 130.89 137.84 Clark 90 7506.06 131.87 6284.28 122.42 8917.70 141.80 143.02 Gamma 90 48.34 123.18 44.42 114.35 52.56 132.45 142.69 Wallace 90 0.39 135.43 0.37 125.72 0.41 145.63 154.74 Weibull 90 126.47 133.22 111.79 123.66 142.98 143.25 162.09 2 Par Weibull 90 2.05 100.88 121.86 1.72 94.83 113.12 2.42 107.30 131.04 137.80 Clark2dt 90 7.60 71151.70 121.37 6.69 62057.40 112.67 8.62 81476.50 130.51 137.28 Gen Exp 90 1.85 4723.83 121.54 1.88 4187.06 112.83 1.88 5327.31 130.70 137.76 2 1d Exp 85 0.04 54.26 0.03 49.32 0.04 59.51 57.98 2d Exp 85 15.91 54.09 13.12 49.17 19.20 59.33 60.45 2d Gaussian 85 44.21 55.01 38.47 50.00 50.74 60.34 69.93 Clark 85 441.11 54.56 253.80 49.59 731.48 59.85 58.52 Gamma 85 15.91 54.09 13.12 49.17 19.20 59.33 60.45 Wallace 85 0.84 54.25 0.74 49.31 0.95 59.50 57.90 Weibull 85 28.27 54.26 22.41 49.32 35.52 59.51 57.98 2 Par Weibull 85 0.87 25.41 54.36 0.65 19.61 49.41 1.10 32.83 59.63 57.75 Clark2dt 85 1.17 608.14 54.30 0.92 362.81 49.36 1.50 975.76 59.56 58.47 Gen Exp 85 0.45 0.88 54.34 0.43 0.78 49.39 0.47 0.99 59.60 57.86 3 1d Exp 65 0.02 63.99 0.01 56.70 0.02 71.88 53.17 2d Exp 65 27.28 63.69 23.59 56.43 31.50 71.55 57.12 2d Gaussian 65 64.45 65.67 58.15 58.19 71.42 73.77 64.64 Clark 65 1755.23 64.03 1185.80 56.74 2515.40 71.93 55.49 Gamma 65 27.28 63.69 23.59 56.43 31.50 71.55 57.12 Wallace 65 0.58 64.06 0.52 56.76 0.65 71.96 53.49 Weibull 65 57.14 63.99 46.34 56.70 70.65 71.88 53.17 2 Par Weibull 65 0.87 57.92 64.91 0.60 45.26 57.52 1.24 74.19 72.92 52.89 Clark2dt 65 0.43 433.20 69.19 0.35 255.73 61.30 0.54 692.77 77.72 53.89 Gen Exp 65 0.33 0.59 65.93 0.34 0.54 58.42 0.34 0.64 74.06 52.99 4 1d Exp 95 0.01 4.83 0.01 3.32 0.02 6.73 40.76 2d Exp 95 39.62 4.76 26.91 3.28 58.33 6.64 41.45 2d Gaussian 95 91.79 4.86 70.68 3.35 121.29 6.78 43.00 Clark 95 3580.07 4.76 1145.89 3.28 8828.63 6.64 40.88 Gamma 95 39.62 4.76 26.91 3.28 58.33 6.64 41.45 Wallace 95 0.48 4.81 0.37 3.31 0.64 6.71 40.73 Weibull 95 84.21 4.83 47.96 3.32 150.84 6.73 40.76 2 Par Weibull 95 0.74 85.25 4.96 0.23 38.68 3.42 1.78 185.36 6.92 40.59 Clark2dt 95 0.52 1230.20 5.06 0.29 256.23 3.48 0.95 3723.19 7.05 40.66 Gen Exp 95 0.29 0.50 4.97 0.27 0.40 3.42 0.33 0.62 6.93 40.60
TABLE A4. Best fit parameters for up-slope dispersal into the Open Suppression.
species rep kernel circle
radiusc1 c2 k c1lo c2lo klo c1hi c2hi khi LL PERE 1 1d Exp 85 0.03 27.05 0.02 23.30 0.03 31.17 54.67 2d Exp 85 20.71 26.88 16.42 23.16 25.94 30.97 55.07 2d Gaussian 85 51.05 27.07 42.71 23.33 60.89 31.19 56.84 Clark 85 955.57 27.39 509.74 23.60 1683.54 31.56 55.06 Gamma 85 20.71 26.88 16.42 23.16 25.94 30.97 55.07 Wallace 85 0.70 27.16 0.60 23.40 0.82 31.30 54.82 Weibull 85 39.21 27.05 29.13 23.30 52.81 31.17 54.67 2 Par Weibull 85 1.09 40.65 26.97 0.64 30.86 23.24 1.61 53.52 31.08 54.63 Clark2dt 85 1.28 1450.66 27.12 0.93 815.80 23.37 1.76 2455.66 31.25 55.00 Gen Exp 85 0.63 2.96 27.00 0.60 2.48 23.27 0.66 3.52 31.12 54.75 2 1d Exp 85 0.02 21.72 0.01 18.19 0.02 25.69 49.03 2d Exp 85 31.40 21.35 24.46 17.88 39.86 25.25 51.07 2d Gaussian 85 73.40 21.68 61.16 18.15 87.52 25.64 52.54 Clark 85 2542.63 21.92 1310.37 18.35 4490.47 25.92 51.14 Gamma 85 31.40 21.35 24.46 17.88 39.86 25.25 51.07 Wallace 85 0.54 21.75 0.46 18.21 0.64 25.72 49.69 Weibull 85 66.08 21.72 46.74 18.19 93.08 25.69 49.03 2 Par Weibull 85 0.52 122.55 26.99 0.31 67.47 22.60 0.81 214.34 31.92 47.84 Clark2dt 85 0.17 85.14 29.62 0.13 24.75 24.80 0.22 231.57 35.03 49.20 Gen Exp 85 0.10 0.08 27.89 0.11 0.07 23.35 0.11 0.08 32.99 48.09 3 1d Exp 65 0.01 32.15 0.01 27.22 0.02 37.65 42.08 2d Exp 65 31.80 31.45 26.23 26.62 38.37 36.82 41.91 2d Gaussian 65 71.87 32.42 62.71 27.44 82.31 37.96 44.39 Clark 65 2843.15 32.43 1799.45 27.45 4303.18 37.98 41.56 Gamma 65 31.80 31.45 26.23 26.62 38.37 36.82 41.91 Wallace 65 0.51 32.46 0.45 27.48 0.58 38.02 41.91 Weibull 65 72.57 32.15 54.71 27.22 96.23 37.65 42.08 2 Par Weibull 65 1.24 69.32 31.49 0.74 55.43 26.66 1.87 86.83 36.88 41.76 Clark2dt 65 1.09 3190.84 32.21 0.82 2041.03 27.27 1.47 4790.56 37.73 41.55 Gen Exp 65 0.73 7.39 31.62 0.76 6.27 26.76 0.76 8.67 37.03 41.72 4 1d Exp 95 0.01 24.07 0.01 20.58 0.01 27.93 51.10 2d Exp 95 44.17 22.17 35.99 18.96 53.56 25.73 53.78 2d Gaussian 95 95.32 22.01 82.09 18.82 110.09 25.54 55.54 Clark 95 5715.95 23.22 3564.89 19.85 8639.72 26.94 53.76 Gamma 95 44.17 22.17 35.99 18.96 53.56 25.73 53.78 Wallace 95 0.42 23.60 0.37 20.18 0.49 27.39 52.05 Weibull 95 111.50 24.07 84.12 20.58 145.78 27.93 51.10 2 Par Weibull 95 0.61 219.42 30.39 0.43 149.58 25.98 0.82 318.67 35.26 49.64 Clark2dt 95 0.19 422.18 31.86 0.15 194.40 27.24 0.23 814.96 36.97 51.96 Gen Exp 95 0.13 0.12 31.16 0.13 0.12 26.64 0.13 0.13 36.16 50.15 SCBA 1 1d Exp 85 0.00 5.06 0.00 2.78 0.01 8.33 20.67 2d Exp 85 97.55 4.45 57.72 2.45 161.78 7.32 20.57 2d Gaussian 85 170.08 3.95 107.96 2.17 265.99 6.50 20.73 Clark 85 27259.30 4.55 9543.38 2.50 72327.40 7.49 20.67 Gamma 85 97.55 4.45 57.72 2.45 161.78 7.32 20.57 Wallace 85 0.25 5.02 0.19 2.76 0.35 8.26 20.60 Weibull 85 335.06 5.06 163.33 2.78 715.55 8.33 20.67 2 Par Weibull 85 1.39 235.87 4.69 0.67 134.59 2.58 2.41 417.52 7.71 20.46 Clark2dt 85 1.26 34527.30 4.43 0.55 12390.40 2.44 2.89 90291.80 7.30 20.67 Gen Exp 85 0.78 24.54 4.65 0.72 15.93 2.56 0.85 37.23 7.66 20.55 2 1d Exp 85 0.06 3.00 0.02 1.91 3.37E+17 4.43 29.04 2d Exp 85 12.72 3.04 0.69 1.94 27.41 4.49 28.85 2d Gaussian 85 37.46 3.09 2.97 1.97 63.04 4.57 28.53 Clark 85 137.25 3.01 0.00 1.92 2108.54 4.44 29.19 Gamma 85 12.72 3.04 0.69 1.94 27.41 4.49 28.85 Wallace 85 Weibull 85 17.18 3.00 0.00 1.91 51.94 4.43 29.04 2 Par Weibull 85 Clark2dt 85 Gen Exp 85 2.41 8965.05 3.11 2.17 11.61 1.99 3.89 27738.90 4.60 28.43 3 1d Exp 65 0.01 10.56 0.01 7.85 0.02 13.84 49.71 2d Exp 65 31.29 10.26 22.59 7.62 42.84 13.44 47.69 2d Gaussian 65 71.83 10.65 57.38 7.92 90.20 13.96 48.71 Clark 65 2623.31 10.47 1193.43 7.78 5208.40 13.72 47.21 Gamma 65 31.29 10.26 22.59 7.62 42.84 13.44 47.69 Wallace 65 0.51 10.75 0.41 7.99 0.63 14.08 48.64 Weibull 65 72.44 10.56 45.59 7.85 115.58 13.84 49.71 2 Par Weibull 65 1.58 69.28 10.37 0.94 51.95 7.70 2.36 92.50 13.58 48.17 Clark2dt 65 1.52 4412.02 10.17 0.93 2137.44 7.56 2.48 8366.80 13.33 47.10 Gen Exp 65 1.05 41.16 10.26 0.99 29.45 7.63 1.12 56.84 13.44 47.68 4 1d Exp 95 0.06 5.21 0.03 3.94 0.15 6.72 44.08 2d Exp 95 9.60 5.20 4.68 3.94 20.69 6.72 45.08 2d Gaussian 95 28.73 5.23 16.91 3.96 53.52 6.76 46.11 Clark 95 51.11 5.18 2.38 3.92 514.88 6.69 43.83 Gamma 95 9.60 5.20 4.68 3.94 20.69 6.72 45.08 Wallace 95 1.17 5.20 0.73 3.93 1.91 6.71 44.00 Weibull 95 16.20 5.21 6.89 3.94 38.87 6.72 44.08 2 Par Weibull 95 Clark2dt 95 Gen Exp 95
TABLE A5. Best fit parameters for down-slope dispersal into Shrub Suppression.
species rep kernel circle
radiusc1 c2 k c1lo c2lo klo c1hi c2hi khi LL PERE 1 1d Exp 115 0.05 41.82 0.04 38.22 0.06 45.63 126.96 2d Exp 115 13.25 41.76 11.21 38.17 15.61 45.57 133.03 2d Gaussian 115 38.85 41.45 33.45 37.88 44.16 45.23 145.80 Clark 115 140.73 41.85 76.68 38.25 241.93 45.67 123.99 Gamma 115 13.25 41.76 11.21 38.17 15.61 45.57 133.03 Wallace 115 1.00 41.85 0.90 38.25 1.11 45.67 125.73 Weibull 115 21.32 41.82 17.53 38.22 25.76 45.63 126.96 2 Par Weibull 115 Clark2dt 115 Gen Exp 115 2 1d Exp 85 0.05 37.21 0.04 33.69 0.06 40.96 76.90 2d Exp 85 13.03 37.23 11.02 33.71 15.35 40.98 76.07 2d Gaussian 85 35.60 37.05 31.16 33.54 40.57 40.79 79.41 Clark 85 246.13 36.99 149.94 33.49 391.51 40.72 77.17 Gamma 85 13.03 37.23 11.02 33.71 15.35 40.98 76.07 Wallace 85 0.95 37.16 0.86 33.65 1.06 40.91 77.05 Weibull 85 21.87 37.21 17.95 33.69 26.58 40.96 76.90 2 Par Weibull 85 1.27 26.61 37.23 1.04 22.44 33.70 1.53 31.45 40.98 76.24 Clark2dt 85 2.07 1108.09 37.23 1.68 754.39 33.71 2.56 1597.80 40.99 75.56 Gen Exp 85 0.86 6.66 37.23 0.89 5.72 33.71 0.89 7.72 40.99 75.97 3 1d Exp 45 0.06 17.90 0.04 15.84 0.08 20.13 57.84 2d Exp 45 10.21 17.92 7.88 15.85 13.27 20.15 57.09 2d Gaussian 45 25.27 17.93 20.70 15.87 30.93 20.17 56.24 Clark 45 200.46 17.85 92.57 15.79 408.62 20.07 58.04 Gamma 45 10.21 17.92 7.88 15.85 13.27 20.15 57.09 Wallace 45 1.03 17.88 0.86 15.82 1.23 20.11 57.96 Weibull 45 18.05 17.90 13.09 15.84 25.27 20.13 57.84 2 Par Weibull 45 Clark2dt 45 Gen Exp 45 6.68 3.84E+10 17.97 54.82 SCBA 1 1d Exp 115 0.05 9.95 0.03 8.25 0.08 11.88 80.06 2d Exp 115 12.43 9.93 7.27 8.23 18.21 11.85 81.78 2d Gaussian 115 41.11 9.80 29.46 8.12 54.16 11.69 85.65 Clark 115 82.63 9.99 17.28 8.28 288.44 11.92 78.51 Gamma 115 12.43 9.93 7.27 8.23 18.21 11.85 81.78 Wallace 115 1.08 9.98 0.84 8.27 1.44 11.90 79.43 Weibull 115 19.34 9.95 11.93 8.25 29.72 11.88 80.06 2 Par Weibull 115 Clark2dt 115 0.89 57.88 9.98 0.62 10.89 8.27 1.36 211.86 11.90 78.48 Gen Exp 115 2 1d Exp 85 0.10 26.95 0.07 23.93 0.18 30.20 78.50 2d Exp 85 5.93 26.94 3.69 23.93 8.98 30.20 78.10 2d Gaussian 85 15.40 26.93 10.43 23.92 22.45 30.19 77.86 Clark 85 35.01 26.89 8.21 23.88 101.02 30.14 79.94 Gamma 85 5.93 26.94 3.69 23.93 8.98 30.20 78.10 Wallace 85 1.46 26.94 1.16 23.93 1.94 30.20 78.80 Weibull 85 9.68 26.95 5.61 23.93 15.01 30.20 78.50 2 Par Weibull 85 2.29 16.15 26.93 1.14 11.25 23.92 4.44 23.21 30.18 77.85 Clark2dt 85 0.00 0.00 26.77 0.00 0.00 23.78 0.00 2.24E+08 30.01 84.45 Gen Exp 85 3.13 11673.10 26.92 2.83 4068.68 23.91 3.46 34901.10 30.18 77.83 3 1d Exp 45 0.09 24.48 0.07 22.03 0.13 27.10 85.07 2d Exp 45 6.84 24.46 4.99 22.01 9.08 27.08 85.24 2d Gaussian 45 19.23 24.40 15.08 21.96 23.94 27.02 85.70 Clark 45 45.40 24.48 13.18 22.03 118.13 27.10 85.37 Gamma 45 6.84 24.46 4.99 22.01 9.08 27.08 85.24 Wallace 45 1.38 24.48 1.14 22.03 1.71 27.10 85.15 Weibull 45 10.77 24.48 7.42 22.03 15.14 27.10 85.07 2 Par Weibull 45 1.03 11.10 24.48 0.75 7.70 22.03 1.38 15.51 27.10 85.07 Clark2dt 45 1.39 117.82 24.48 1.00 43.72 22.03 1.97 260.88 27.10 85.32 Gen Exp 45 0.61 1.25 24.48 0.57 0.98 22.03 0.67 1.54 27.10 85.14
TABLE A6. Best fit parameters for up-slope dispersal into Shrub Suppression.
species rep kernel circle
radiusc1 c2 k c1lo c2lo klo c1hi c2hi khi LL PERE 1 1d Exp 115 0.02 19.93 0.01 17.77 0.02 22.26 138.55 2d Exp 115 31.51 20.05 26.89 17.88 37.20 22.40 139.49 2d Gaussian 115 74.46 20.15 65.89 17.96 84.65 22.51 138.93 Clark 115 2200.76 19.79 1431.95 17.64 3376.58 22.11 140.35 Gamma 115 31.51 20.05 26.89 17.88 37.20 22.40 139.49 Wallace 115 0.57 19.89 0.51 17.73 0.63 22.21 139.23 Weibull 115 59.63 19.93 48.72 17.77 74.02 22.26 138.55 2 Par Weibull 115 Clark2dt 115 Gen Exp 115 5.52 1.50E+11 20.13 5.62 9.40E+10 17.99 5.41 2.53E+11 22.55 138.00 2 1d Exp 85 0.04 60.50 0.03 56.20 0.04 65.02 142.18 2d Exp 85 15.12 60.72 13.29 56.40 17.21 65.25 141.91 2d Gaussian 85 38.90 60.60 35.03 56.29 43.22 65.12 146.08 Clark 85 392.14 60.30 276.52 56.01 554.17 64.81 141.01 Gamma 85 15.12 60.72 13.29 56.40 17.21 65.25 141.91 Wallace 85 0.85 60.42 0.78 56.12 0.92 64.93 141.89 Weibull 85 27.22 60.50 23.32 56.20 31.86 65.02 142.18 2 Par Weibull 85 1.21 30.54 60.65 0.98 26.64 56.34 1.47 35.07 65.18 141.61 Clark2dt 85 1.18 560.13 60.46 1.01 402.23 56.16 1.38 776.18 64.97 140.89 Gen Exp 85 0.71 3.62 60.62 0.73 3.27 56.31 0.73 4.01 65.15 141.37 3 1d Exp 45 0.06 26.18 0.04 23.74 0.08 28.79 65.96 2d Exp 45 9.16 26.22 6.88 23.77 12.42 28.83 65.77 2d Gaussian 45 21.89 26.22 17.33 23.77 28.24 28.83 66.06 Clark 45 175.08 26.16 83.52 23.72 367.87 28.77 65.64 Gamma 45 9.16 26.22 6.88 23.77 12.42 28.83 65.77 Wallace 45 1.05 26.17 0.86 23.73 1.26 28.78 65.88 Weibull 45 17.52 26.18 12.30 23.74 25.86 28.79 65.96 2 Par Weibull 45 1.41 19.84 26.22 0.47 14.94 23.77 2.57 26.93 28.83 65.79 Clark2dt 45 1.17 236.04 26.18 0.79 117.53 23.73 1.69 478.45 28.79 65.63 Gen Exp 45 0.91 6.28 26.21 0.85 4.80 23.76 0.98 8.35 28.83 65.76 SCBA 1 1d Exp 115 0.04 32.44 0.03 29.52 0.05 35.54 128.78 2d Exp 115 14.41 32.42 12.00 29.51 17.23 35.52 134.14 2d Gaussian 115 41.65 32.20 35.81 29.31 48.15 35.28 143.34 Clark 115 209.61 32.41 118.58 29.50 355.70 35.51 129.06 Gamma 115 14.41 32.42 12.00 29.51 17.23 35.52 134.14 Wallace 115 0.93 32.45 0.84 29.53 1.05 35.55 128.56 Weibull 115 23.73 32.44 19.27 29.52 29.10 35.54 128.78 2 Par Weibull 115 Clark2dt 115 Gen Exp 115 2 1d Exp 85 0.07 39.76 0.05 36.25 0.08 43.50 71.04 2d Exp 85 8.93 39.78 7.20 36.26 11.06 43.51 73.13 2d Gaussian 85 24.56 39.68 20.71 36.17 29.33 43.41 78.06 Clark 85 93.80 39.68 50.33 36.17 166.99 43.41 71.00 Gamma 85 8.93 39.78 7.20 36.26 11.06 43.51 73.13 Wallace 85 1.16 39.75 1.02 36.24 1.33 43.49 70.91 Weibull 85 15.09 39.76 11.77 36.25 19.20 43.50 71.04 2 Par Weibull 85 0.82 12.16 39.73 0.66 9.21 36.22 1.01 15.91 43.47 70.73 Clark2dt 85 1.00 94.51 39.68 0.82 50.75 36.17 1.24 168.14 43.41 71.00 Gen Exp 85 0.40 0.51 39.72 0.38 0.46 36.21 0.43 0.57 43.46 70.80 3 1d Exp 45 0.11 23.00 0.08 20.70 0.18 25.47 59.16 2d Exp 45 5.16 23.01 3.54 20.71 7.39 25.48 58.96 2d Gaussian 45 13.14 23.01 9.62 20.71 18.21 25.48 59.17 Clark 45 39.39 22.96 12.80 20.67 100.64 25.42 59.71 Gamma 45 5.16 23.01 3.54 20.71 7.39 25.48 58.96 Wallace 45 1.51 22.99 1.21 20.69 1.91 25.46 59.34 Weibull 45 8.73 23.00 5.63 20.70 13.22 25.47 59.16 2 Par Weibull 45 1.42 11.31 23.01 0.87 7.83 20.71 2.53 16.15 25.48 58.92 Clark2dt 45 4.02 493.77 23.01 2.45 240.45 20.71 6.87 992.53 25.48 59.04 Gen Exp 45 1.11 7.78 23.01 1.01 5.18 20.71 1.23 11.51 25.48 58.95