A Method for Determining Asymptotes of Home-Range Area Curves
A Method for Determining Asymptotes of Home-Range Area Curves A Method for Determining Asymptotes of Home-Range Area Curves
Home-range AsymptotesTable 2: Model parameters resulting from fitting means of home range size (ha) of northern bobwhite coveys to the number of locationsusing 4 separate function models. Home ranges were calculated using the 95% fixed kernel least squares cross validation (LSCV) smoothingparameter and minimum convex polygon home range estimators, Jim Hogg County, Texas, USA, Sep-Nov, 2001-2003.YearEstimator Model parameters AsymptoteModel Function a b C Estimate (ha) SE −1SE +1SE AICC ∆AICC R 22001Fixed-KernelReciprocal f(x) = a + b x14.8 15.90 NA 14.8 0.38 14.5 15.2 29.1 0.0 0.85Exponential f(x) = C + a ∗ e (−b∗x) -53.0 0.80 15.7 15.7 0.32 15.4 16.0 42.7 13.6 0.86Logistic f(x) = C/(1 + a ∗ e (b∗x) ) 7.7 0.95 15.7 15.7 0.32 15.4 16.0 42.7 13.6 0.86Gompertz f(x) = 2C − C ∗ e (−e(a−b∗x) )109.3 36.76 15.7 15.7 0.29 15.4 16.0 43.0 13.9 0.85MCPExponential f(x) = C + a ∗ e (−b∗x) 18.1 0.08 15.6 15.6 0.46 15.1 16.1 37.0 0.0 0.99Reciprocal f(x) = a + b x14.6 -45.67 NA 14.6 1.04 13.6 15.6 41.0 4.0 0.89Logistic f(x) = C/(1 + a ∗ e (b∗x) ) 7.6 0.18 14.8 14.8 0.77 14.0 15.6 48.3 11.3 0.96Gompertz f(x) = C ∗ e (−e(a−b∗x) )8.3 0.82 13.8 13.8 1.08 12.7 14.9 58.7 21.7 0.822002Fixed-KernelExponential f(x) = C + a ∗ e (−b∗x) 7.9 2.94 11.2 11.2 0.12 11.1 11.3 37.8 0.0 0.99Logistic f(x) = C/(1 + a ∗ e (b∗x) ) 4.6 7.49 11.3 11.3 0.16 11.1 11.4 38.2 0.4 0.99Gompertz f(x) = 2C − C ∗ e (−e(a−b∗x) )27.0 6.51 11.3 11.3 0.16 11.1 11.5 38.2 0.4 0.99Reciprocal f(x) = a + b x9.4 34.12 NA 9.4 1.04 8.3 10.4 43.3 5.5 0.77MCPExponential f(x) = C + a ∗ e (−b∗x) 13.5 0.03 14.0 14.0 1.46 12.6 15.5 30.0 0.0 0.99Gompertz f(x) = C ∗ e (−e(a−b∗x) )0.8 0.06 11.8 11.8 0.89 10.9 12.7 35.0 5.0 0.99Logistic f(x) = C/(1 + a ∗ e (b∗x) ) 5.3 0.09 11.1 11.1 0.74 10.3 11.8 37.8 7.8 0.98Reciprocal f(x) = a + b x9.0 -26.81 NA 9.0 0.86 8.1 9.8 40.7 10.7 0.75May 31 - June 4, 2006 492 Gamebird 2006 | Athens, GA | USA
Home-range AsymptotesTable 3: Model parameters resulting from fitting coefficients of variation (CV) of home range size of northern bobwhite coveys to the numberof locations using 4 separate function models. Home ranges were calculated using the 95% fixed kernel least squares cross validation (LSCV)smoothing parameter and minimum convex polygon home range estimators, Jim Hogg County, Texas, USA, Sep-Nov, 2001-2003.YearEstimator Model parameters AsymptoteModel Function a b C Estimate (ha) SE −1SE +1SE AICC ∆AICC R-square2001Fixed-KernelExponential xf(x) = C + a ∗ e (−b∗x) 1.43 0.15 0.34 0.34 0.03 0.32 0.37 4.8 4.9 0.98Logistic f(x) = C/(1 + a ∗ e (b∗x) ) -0.88 -0.04 0.28 0.28 0.06 0.22 0.34 8.8 8.9 0.97Gompertz f(x) = C ∗ e (−e(a−b∗x) )17.67 1.82 0.5 0.5 0.04 0.46 0.53 19.4 19.5 0.84MCPReciprocal f(x) = a + b x0.52 0.71 NA 0.52 0.08 0.43 0.6 8.1 0 0.58Gompertz f(x) = C ∗ e (−e(a−b∗x) )6.57 0.72 0.53 0.53 0.02 0.5 0.55 13.4 5.3 0.88Exponential f(x) = C + a ∗ e (−b∗x) 0.76 0.07 0.43 0.43 0.13 0.3 0.56 17.3 9.2 0.79Logistic f(x) = C/(1 + a ∗ e (b∗x) ) -0.79 -0.01 0.24 0.24 0.4 -0.16 0.64 17.6 9.5 0.782002Fixed-KernelGompertz f(x) = C ∗ e (−e(a−b∗x) )2.52 0.31 0.39 0.39 0.01 0.39 0.4 -11.6 0 0.99Reciprocal f(x) = a + b x0.39 1.31 NA 0.39 0.03 0.36 0.42 -5.7 5.9 0.85Exponential f(x) = C + a ∗ e (−b∗x) 0.58 0.12 0.39 0.39 0.02 0.37 0.41 -0.3 11.3 0.96Logistic f(x) = C/(1 + a ∗ e (b∗x) ) -0.64 -0.06 0.37 0.37 0.03 0.34 0.41 1.8 13.4 0.94MCPReciprocal f(x) = a + b x0.22 2.29 NA 0.22 0.02 0.2 0.25 -10.0 0 0.97Logistic f(x) = C/(1 + a ∗ e (b∗x) ) -1.15 -0.17 0.31 0.31 0.01 0.3 0.32 -9.0 1 0.99Exponential f(x) = C + a ∗ e (−b∗x) 2.16 0.37 0.32 0.32 0.01 0.31 0.33 -4.2 5.8 0.99Gompertz f(x) = C ∗ e (−e(a−b∗x) )17.02 3.02 0.41 0.41 0.04 0.37 0.45 16.9 26.9 0.80Gamebird 2006 | Athens, GA | USA 493 May 31 - June 4, 2006
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<strong>Home</strong>-range <strong>Asymptotes</strong>Table 2: Model parameters resulting from fitting means <strong>of</strong> home range size (ha) <strong>of</strong> northern bobwhite coveys to the number <strong>of</strong> locationsusing 4 separate function models. <strong>Home</strong> ranges were calculated using the 95% fixed kernel least squares cross validation (LSCV) smoothingparameter and minimum convex polygon home range estimators, Jim Hogg County, Texas, USA, Sep-Nov, 2001-2003.YearEstimator Model parameters AsymptoteModel Function a b C Estimate (ha) SE −1SE +1SE AICC ∆AICC R 22001Fixed-KernelReciprocal f(x) = a + b x14.8 15.90 NA 14.8 0.38 14.5 15.2 29.1 0.0 0.85Exponential f(x) = C + a ∗ e (−b∗x) -53.0 0.80 15.7 15.7 0.32 15.4 16.0 42.7 13.6 0.86Logistic f(x) = C/(1 + a ∗ e (b∗x) ) 7.7 0.95 15.7 15.7 0.32 15.4 16.0 42.7 13.6 0.86Gompertz f(x) = 2C − C ∗ e (−e(a−b∗x) )109.3 36.76 15.7 15.7 0.29 15.4 16.0 43.0 13.9 0.85MCPExponential f(x) = C + a ∗ e (−b∗x) 18.1 0.08 15.6 15.6 0.46 15.1 16.1 37.0 0.0 0.99Reciprocal f(x) = a + b x14.6 -45.67 NA 14.6 1.04 13.6 15.6 41.0 4.0 0.89Logistic f(x) = C/(1 + a ∗ e (b∗x) ) 7.6 0.18 14.8 14.8 0.77 14.0 15.6 48.3 11.3 0.96Gompertz f(x) = C ∗ e (−e(a−b∗x) )8.3 0.82 13.8 13.8 1.08 12.7 14.9 58.7 21.7 0.822002Fixed-KernelExponential f(x) = C + a ∗ e (−b∗x) 7.9 2.94 11.2 11.2 0.12 11.1 11.3 37.8 0.0 0.99Logistic f(x) = C/(1 + a ∗ e (b∗x) ) 4.6 7.49 11.3 11.3 0.16 11.1 11.4 38.2 0.4 0.99Gompertz f(x) = 2C − C ∗ e (−e(a−b∗x) )27.0 6.51 11.3 11.3 0.16 11.1 11.5 38.2 0.4 0.99Reciprocal f(x) = a + b x9.4 34.12 NA 9.4 1.04 8.3 10.4 43.3 5.5 0.77MCPExponential f(x) = C + a ∗ e (−b∗x) 13.5 0.03 14.0 14.0 1.46 12.6 15.5 30.0 0.0 0.99Gompertz f(x) = C ∗ e (−e(a−b∗x) )0.8 0.06 11.8 11.8 0.89 10.9 12.7 35.0 5.0 0.99Logistic f(x) = C/(1 + a ∗ e (b∗x) ) 5.3 0.09 11.1 11.1 0.74 10.3 11.8 37.8 7.8 0.98Reciprocal f(x) = a + b x9.0 -26.81 NA 9.0 0.86 8.1 9.8 40.7 10.7 0.75May 31 - June 4, 2006 492 Gamebird 2006 | Athens, GA | USA
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