34 Tou-Liao 277778 2747897 245 1245 52905 2594 042 35 Sha-Lun 275500 2769500 15 918 5454 1203 006 36 2_18 276500 2770300 65 968 6943 1288 007 37 2_2-1 274175 2770158 58 821 9658 1223 012 38 2_1-2 270398 2770362 53 1260 13402 1421 011 39 Heng-Shan 271672 2775953 52 1574 36950 1633 023
41 Chang-Pi 260088 2755995 159 249 4472 676 018 42 Yuan-Pen 259121 2760179 92 315 9189 763 029
X_Coord X coordination Y_Coord Y coordination Elevation (m) Perimeter (m) FCA Foliage Canopy Area (m2) PS Pond Size (Ha) FCA Ratio FCAPS10000
170
Appendix B-2 Environmental parameters in pondscape
ID Name X_Coord Y_Coord Farms (m2)ha
Builds(m2)ha
Ponds (m2)ha
Rivers(m2)ha
Roads (m2)ha
Distance to coastal line (m)
Distance to city limit (m)
01 Lo-Tso 268315 2765170 728489 90394 159248 0 21869 9841 3838
02 Cha-Liao 266027 2767377 786565 73050 101208 5560 33617 7315 6711
03 Ching-Pu-Tzu 264790 2768225 725907 66117 174844 0 33132 6192 8075
04 Pi-Nei 264480 2768155 699376 70371 197644 0 32610 6222 8386
05 Hsueh-Hsiao 263309 2767611 581657 245555 136140 3391 33257 6692 8804
06 Pu-Ting 258956 2770460 865373 16564 98974 0 19089 1816 14073
07 Ta-Pi-Chiao 259361 2769253 613178 118431 202606 0 65786 2999 12858
08 Chiu-Pi 263373 2769638 844617 10012 110637 2056 32678 4650 10235
09 Po-Kua-Tzu 263933 2770699 689493 92309 171671 0 46527 3732 10702
10 Hu-Ti 269578 2774459 766943 92751 71702 21266 47338 2405 6527
11 Hou-Hu-Tang 258450 2764000 764020 38372 186705 0 10902 7131 9644
12 Feng-Tien 256326 2765320 789556 25803 158661 8434 17547 4369 11579
13 Hou-Hu-Chih 253263 2766142 712475 15459 235931 0 36134 1367 14326
14 Lin-Wu 255820 2769339 681772 147799 125813 0 44617 1324 15178
15 Hung-Tang 258229 2767980 706106 29566 232710 2177 29441 3434 12458
16 Liao-Wu 258854 2762597 625262 216765 103992 8984 44997 7963 7783
17 Ta-Po 253834 2761225 869158 31631 68151 7554 23506 3484 10827
18 Lu-Wu 256666 2760433 820059 50538 100967 0 28436 6370 8053
19 Fu-Lien 256100 2759100 805635 126333 46001 0 22031 6577 7873
20 Wang-Wu 250826 2761709 857952 46790 42557 7727 44973 819 13856
21 Han-Pi 264924 2764212 709546 48762 213700 6221 21772 10436 6667
22 Liu-Liu 259707 2765463 778978 70572 81179 4051 65221 6338 9726
23 Tu-Lung-Kou 260145 2766455 772795 28012 153954 5758 39481 5686 10244
24 Keng-Wu 260205 2767318 820261 68659 72833 0 38246 5071 11076
25 Keng-Wei 259198 2767662 868093 24729 98355 0 8823 4174 12103
26 Tsao-Pi 265671 2761796 702379 180332 94549 2237 20503 12792 3732
27 Kuo-Ling-Li 265660 2761998 756011 138896 85899 2237 16958 12584 3684
28 Pei-Shih 262415 2762501 704298 86424 147942 6103 55233 11118 5585
29 Shih-Pi-Hsia 260748 2761961 688797 182989 89472 12664 26079 9912 6586
30 Mei-Kao-Lu 264191 2760924 424734 379157 131790 0 64319 12541 3287
31 Pa-Chang-Li 268476 2752997 763904 177152 41979 0 16965 20369 1397
32 Lung-Tan 270250 2750700 351370 464034 10857 101761 71979 23148 269
171
Appendix B-2 Continued
ID Name X_Coord Y_Coord Farms (m2)ha
Builds(m2)ha
Ponds (m2)ha
Rivers(m2)ha
Roads (m2)ha
Distance to coastal line (m)
Distance to city limit (m)
33 Feng-Kuei-
Kou 271250 2748300 860699 44805 78481 0 16016 25045 881
34 Tou-Liao 277778 2747897 722022 113701 158527 0 5750 29508 3611
35 Sha-Lun 275500 2769500 632011 139736 179469 1543 47241 2175 2802
36 2_18 276500 2770300 810541 47320 129035 0 13104 8728 1558
37 2_2-1 274175 2770158 783159 69387 105553 18719 23181 8323 2300
38 2_1-2 270398 2770362 624982 178180 166138 4869 25832 6184 6070
39 Heng-Shan 271672 2775953 779071 42809 128150 29083 20886 2162 5053
40 Po-Kung-
Kang 258646 2757445 755033 61549 163445 0 19974 9619 5156
41 Chang-Pi 260088 2755995 812892 74782 70638 0 41687 11659 3016
42 Yuan-Pen 259121 2760179 800921 38888 141945 0 18246 8758 5873
43 Hung-Wa-Wu 260475 2760784 449183 416572 105239 4141 24864 9921 5398
44 Hsia-Yin-Ying 258061 2760530 924773 40389 10163 0 24675 7666 7278
45 Pa-Chiao-Tan 269064 2755889 525204 395050 45467 4010 30269 19557 318
33 Feng-Kuei-
Kou 271250 2748300 860699 44805 78481 0 16016 25045 881
34 Tou-Liao 277778 2747897 722022 113701 158527 0 5750 29508 3611
35 Sha-Lun 275500 2769500 632011 139736 179469 1543 47241 2175 2802
36 2_18 276500 2770300 810541 47320 129035 0 13104 8728 1558
172
Appendix B-3 Environmental parameters in pondscape
ID Name X_Coord Y_Coord Consolidated LPI
MPS
MPFD
MSI
ED
Area (31)
(32)
(34)
(35)
(36)
01 Lo-Tso 268315 2765170 NO 392 1477 126 133 12291
02 Cha-Liao 266027 2767377 NO 150 563 128 131 19556
03 Ching-Pu-Tzu 264790 2768225 NO 137 517 126 118 18460
04 Pi-Nei 264480 2768155 NO 225 847 125 114 13898
05 Hsueh-Hsiao 263309 2767611 NO 217 818 131 167 20740
06 Pu-Ting 258956 2770460 NO 263 990 123 106 11924
07 Ta-Pi-Chiao 259361 2769253 YES 537 2022 123 116 9153
08 Chiu-Pi 263373 2769638 NO 294 1106 128 146 15589
09 Po-Kua-Tzu 263933 2770699 NO 273 1028 124 113 12453
10 Hu-Ti 269578 2774459 YES 164 618 125 112 15984
11 Hou-Hu-Tang 258450 2764000 NO 496 1868 123 113 9235
12 Feng-Tien 256326 2765320 YES 398 1498 122 104 9504
13 Hou-Hu-Chih 253263 2766142 YES 325 1224 123 108 10904
14 Lin-Wu 255820 2769339 NO 334 1258 123 109 10919
15 Hung-Tang 258229 2767980 YES 543 2047 123 114 8938
16 Liao-Wu 258854 2762597 YES 266 1004 125 121 13504
17 Ta-Po 253834 2761225 YES 155 585 128 133 19462
18 Lu-Wu 256666 2760433 YES 256 966 124 111 12625
19 Fu-Lien 256100 2759100 NO 027 101 133 127 44703
20 Wang-Wu 250826 2761709 YES 095 359 126 109 20444
21 Han-Pi 264924 2764212 NO 108 405 128 127 22330
22 Liu-Liu 259707 2765463 YES 065 244 132 141 31945
23 Tu-Lung-Kou 260145 2766455 YES 254 958 126 122 13990
24 Keng-Wu 260205 2767318 YES 193 728 126 118 15475
25 Keng-Wei 259198 2767662 YES 175 660 125 111 15280
26 Tsao-Pi 265671 2761796 NO 064 240 129 123 28170
27 Kuo-Ling-Li 265660 2761998 NO 035 133 131 121 37146
28 Pei-Shih 262415 2762501 NO 132 499 127 123 19535
29 Shih-Pi-Hsia 260748 2761961 NO 230 868 124 113 13629
30 Mei-Kao-Lu 264191 2760924 NO 133 500 131 152 24039
173
Appendix B-3 Continued
ID Name X_Coord Y_Coord Consolidated LPI
MPS
MPFD
MSI
ED
Area (31)
(32)
(34)
(35)
(36)
31 Pa-Chang-Li 268476 2752997 NO 005 020 136 112 88438
32 Lung-Tan 270250 2750700 NO 269 1015 137 245 27218
33 Feng-Kuei- Kou 271250 2748300 NO 124 468 131 151 24742
34 Tou-Liao 277778 2747897 NO 330 1245 134 207 20840
35 Sha-Lun 275500 2769500 YES 244 918 124 112 13107
36 2_18 276500 2770300 NO 257 968 125 117 13310
37 2_2-1 274175 2770158 NO 218 821 126 120 14896
38 2_1-2 270398 2770362 NO 334 1260 124 113 11279
39 Heng-Shan 271672 2775953 NO 418 1574 124 116 10371
40 Po-Kung-Kang 258646 2757445 YES 256 963 127 133 15156
41 Chang-Pi 260088 2755995 YES 066 249 129 121 27181
42 Yuan-Pen 259121 2760179 NO 084 315 128 121 24230
43 Hung-Wa-Wu 260475 2760784 NO 164 616 124 108 15371
44 Hsia-Yin-Ying 258061 2760530 YES 290 1092 124 112 12066
45 Pa-Chiao-Tan 269064 2755889 NO 006 021 151 198 153382 Notes (1) LPI Largest Pond Index (2) MPS Mean Pond Size (PS in this case if n = 1) (3) NP Number of Ponds (in this case equal to 45) (4) MPFD Mean Pond Fractal Dimension (5) MSI Mean Shape Index (6) ED Edge Density (7) TE Total Edge (in this case equal to 54994 m)
174
Appendix C Results of the Regression Models
Appendix C-1 The regression model of waterfowl individuals and foliage canopy area next to waterfront edge of a pond (FCA)(m2) Database
Y = Waterfowl Individuals X = FCAx Linear Regression Plot Section
-200
100
400
700
1000
00 150000 300000 450000 600000
Waterfowl_Individuals vs FCAx
FCAx
Wat
erfo
wl_
Indi
vidu
als
Run Summary Section Parameter Value Parameter Value Dependent Variable Waterfowl Individuals Rows Processed 100 Independent Variable FCAx Rows Used in Estimation 45 Frequency Variable None Rows with X Missing 0 Weight Variable None Rows with Freq Missing 0 Intercept -78266 Rows Prediction Only 55 Slope 00015 Sum of Frequencies 45 R-Squared 04583 Sum of Weights 450000 Correlation 06770 Coefficient of Variation 11705 Mean Square Error 2299428 Square Root of MSE 1516387
175
Linear Regression Report Database
Y = Waterfowl Individuals X = FCAx Summary Statement The equation of the straight line relating Waterfowl Individuals and FCAx is estimated as Waterfowl Individuals (Y) = (-78266) + (00015) FCAx using the 45 observations in this dataset The y-intercept the estimated value of Waterfowl Individuals (Y) when FCAx is zero is -78266 with a standard error of 41207 The slope the estimated change in Waterfowl Individuals per unit change in FCAx is 00015 with a standard error of 00002 The value of R-Squared the proportion of the variation in Waterfowl Individuals that can be accounted for by variation in FCAx is 04583 The correlation between Waterfowl Individuals and FCAx is 06770 A significance test that the slope is zero resulted in a t-value of 60320 The significance level of this t-test is 00000 Since 00000 lt 00500 the hypothesis that the slope is zero is rejected The estimated slope is 00015 The lower limit of the 95 confidence interval for the slope is 00010 and the upper limit is 00020 The estimated intercept is -78266 The lower limit of the 95 confidence interval for the intercept is -161368 and the upper limit is 04836 Descriptive Statistics Section Parameter Dependent Independent Variable Waterfowl Individuals FCAx Count 45 45 Mean 129556 138212667 Standard Deviation 203682 91706217 Minimum 00000 11930000 Maximum 860000 529050000
176
Linear Regression Report Database
Y = Waterfowl Individuals X = FCAx Regression Estimation Section Intercept Slope Parameter B (0) B (1) Regression Coefficients -78266 00015 Lower 95 Confidence Limit -161368 00010 Upper 95 Confidence Limit 04836 00020 Standard Error 41207 00002 Standardized Coefficient 00000 06770 T Value -18993 60320 Prob Level (T Test) 00642 00000 Reject H0 (Alpha = 00500) No Yes Power (Alpha = 00500) 04590 10000 Regression of Y on X -78266 00015 Inverse Regression from X on Y -323874 00033 Orthogonal Regression of Y and X -78267 00015 Estimated Model (-782663192598266) + (150363841337781E-03) (FCAx) Analysis of Variance Section Sum of Mean Power Source DF Squares Square F-Ratio (5) Intercept 1 7553089 7553089 Slope 1 836637 836637 363846 10000 Error 43 9887541 2299428 Adj Total 44 1825391 4148616 Total 45 25807 S = Square Root (2299428) = 1516387 Notes The above report shows the F-Ratio for testing whether the slope is zero the degrees of freedom and the mean square error The mean square error which estimates the variance of the residuals is used extensively in the calculation of hypothesis tests and confidence intervals
177
Linear Regression Report Database
Y = Waterfowl Individuals X = FCAx Tests of Assumptions Section Is the Assumption Test Prob Reasonable at the 02 AssumptionTest Value Level Level of Significance Residuals follow Normal Distribution Shapiro Wilk 09399 0021294 No Anderson Darling 08413 0030312 No DAgostino Skewness 23578 0018381 No DAgostino Kurtosis 09900 0322196 Yes DAgostino Omnibus 65395 0038017 No Constant Residual Variance Modified Levene Test 37662 0058873 No Relationship is a Straight Line Lack of Linear Fit F (0 0) Test 00000 0000000 No Notes A Yes means there is not enough evidence to make this assumption seem unreasonable This lack of evidence may be because the sample size is too small the assumptions of the test itself are not met or the assumption is valid A No means that the assumption is not reasonable However since these tests are related to sample size you should assess the role of sample size in the tests by also evaluating the appropriate plots and graphs A large dataset (say N gt 500) will often fail at least one of the normality tests because it is hard to find a large dataset that is perfectly normal Normality and Constant Residual Variance Possible remedies for the failure of these assumptions include using a transformation of Y such as the log or square root correcting data-recording errors found by looking into outliers adding additional independent variables using robust regression or using bootstrap methods Straight-Line Possible remedies for the failure of this assumption include using nonlinear regression or polynomial regression
178
Linear Regression Report Database
Y = Waterfowl Individuals X = FCAx Residual Plots Section
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00 150000 300000 450000 600000
Residuals of Waterfowl_Individuals vs FCAx
FCAx
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Histogram of Residuals of Waterfowl_Individuals
Residuals of Waterfowl_Individuals
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Normal Probability Plot of Residuals of Waterfowl_Individuals
Expected Normals
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180
Appendix C-2 The regression model of shorebird diversity (Hrsquo) and mudflat area in a pond (m2) Linear Regression Report Database
Y = Shorebird Diversity (Hrsquo) X = MUDAx Linear Regression Plot Section
00
04
07
11
14
00 350000 700000 1050000 1400000
Shorebird_Diversity__H__ vs MUDA
MUDA
Sho
rebi
rd_D
iver
sity
__H
__
Run Summary Section Parameter Value Parameter Value Dependent Variable Shorebird Diversity Rows Processed 10 Independent Variable MUDA Rows Used in Estimation 99 Frequency Variable None Rows with X Missing 1 Weight Variable None Rows with Freq Missing 0 Intercept 00610 Rows Prediction Only 0 Slope 00000 Sum of Frequencies 99 R-Squared 02746 Sum of Weights 99 Correlation 05240 Coefficient of Variation 21849 Mean Square Error 5241032E-02 Square Root of MSE 0228933
181
Linear Regression Report Database
Y = Shorebird Diversity (Hrsquo) X = MUDAx
Summary Statement The equation of the straight line relating Shorebird Diversity (Hrsquo) and MUDA is estimated as )(10033871010356)( 62 MUDAxYHDiversityShorebird minusminus times+times= using the 99 observations in this dataset The y-intercept the estimated value of Shorebird Diversity (Hrsquo) when MUDA is zero is 21010356 minustimes with a standard error of 00241 The slope the estimated change in Shorebird Diversity (Hrsquo) per unit change in MUDA is
61003387 minustimes with a standard error of 00000 The value of R-Squared the proportion of the variation in Shorebird Diversity (Hrsquo) that can be accounted for by variation in MUDA is 02746 The correlation between Shorebird Diversity (Hrsquo) and MUDA is 05240 A significance test that the slope is zero resulted in a t-value of 60589 The significance level of this t-test is 00000 Since 00000 lt 00500 the hypothesis that the slope is zero is rejected Descriptive Statistics Section Parameter Dependent Independent Variable Shorebird Diversity (Hrsquo) MUDA Count 99 99 Mean 01048 62195051 Standard Deviation 02674 199204706 Minimum 00000 00000 Maximum 13624 1228390000
182
Linear Regression Report Database
Y = Shorebird Diversity (Hrsquo) X = MUDAx Regression Estimation Section Intercept Slope Parameter B(0) B(1) Regression Coefficients 00610 00000 Lower 95 Confidence Limit 00132 00000 Upper 95 Confidence Limit 01089 00000 Standard Error 00241 00000 Standardized Coefficient 00000 05240 T Value 25310 60589 Prob Level (T Test) 00130 00000 Reject H0 (Alpha = 00500) Yes Yes Power (Alpha = 00500) 07074 10000 Regression of Y on X 00610 00000 Inverse Regression from X on Y -00546 00000 Orthogonal Regression of Y and X 00610 00000 Estimated Model ( 610348280556879E-02) + ( 703381879341286E-06) (MUDAx)
183
Linear Regression Report Database
Y = Shorebird Diversity (Hrsquo) X = MUDAx Tests of Assumptions Section Is the Assumption Test Prob Reasonable at the 02 AssumptionTest Value Level Level of Significance Residuals follow Normal Distribution Shapiro Wilk 05710 0000000 No Anderson Darling 203696 0000000 No DAgostino Skewness 66816 0000000 No DAgostino Kurtosis 47129 0000002 No DAgostino Omnibus 668545 0000000 No Constant Residual Variance Modified Levene Test 44050 0038430 No Relationship is a Straight Line Lack of Linear Fit F(13 84) Test 22123 0015538 No Notes A Yes means there is not enough evidence to make this assumption seem unreasonable This lack of evidence may be because the sample size is too small the assumptions of the test itself are not met or the assumption is valid A No means the that the assumption is not reasonable However since these tests are related to sample size you should assess the role of sample size in the tests by also evaluating the appropriate plots and graphs A large dataset (say N gt 500) will often fail at least one of the normality tests because it is hard to find a large dataset that is perfectly normal Normality and Constant Residual Variance Possible remedies for the failure of these assumptions include using a transformation of Y such as the log or square root correcting data-recording errors found by looking into outliers adding additional independent variables using robust regression or using bootstrap methods Straight-Line Possible remedies for the failure of this assumption include using nonlinear regression or polynomial regression
184
Linear Regression Report Database
Y = Shorebird Diversity (Hrsquo) X = MUDAx Residual Plots Section
-05
-01
03
06
10
00 350000 700000 1050000 1400000
Residuals of Shorebird_Diversity__H__ vs MUDA
MUDA
Res
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__H
__
00
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750
1000
-05 -01 03 06 10
Histogram of Residuals of Shorebird_Diversity__H__
Residuals of Shorebird_Diversity__H__
Cou
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-05
-01
03
06
10
-30 -15 00 15 30
Normal Probability Plot of Residuals of Shorebird_Diversity__H__
Expected Normals
Res
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__H
__
186
Appendix C-3 The regression model of waterside (water edge) bird individuals and pond size (PS)(m2) Linear Regression Report Database
Y = Waterside Bird Individuals X = PSx Linear Regression Plot Section
00
1500
3000
4500
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00 625000 1250000 1875000 2500000
Water_edge_Bird_Individuals vs PS
PS
Wat
er_e
dge_
Bird
_Ind
ivid
uals
Run Summary Section Parameter Value Parameter Value Dependent Variable Waterside Bird Individuals Independent Variable PS Rows Used in Estimation 45 Frequency Variable None Rows with X Missing 0 Weight Variable None Rows with Freq Missing 0 Intercept 696039 Rows Prediction Only 0 Slope 00011 Sum of Frequencies 45 R-Squared 01700 Sum of Weights 450000 Correlation 04123 Coefficient of Variation 07609 Mean Square Error 1485544 Square Root of MSE 1218829
187
Linear Regression Report Database
Y = Waterside Bird Individuals X = PSx Summary Statement The equation of the straight line relating Waterside Bird Individuals and PS is estimated as Waterside Bird Individuals = (696039) + (00011) PS using the 45 observations in this dataset The y-intercept the estimated value of Waterside Bird Individuals when PS is zero is 696039 with a standard error of 355207 The slope the estimated change in Waterside Bird Individuals per unit change in PS is 00011 with a standard error of 00004 The value of R-Squared the proportion of the variation in Waterside Bird Individuals that can be accounted for by variation in PS is 01700 The correlation between Waterside Bird Individuals and PS is 04123 A significance test that the slope is zero resulted in a t-value of 29675 The significance level of this t-test is 00049 Since 00049 lt 00500 the hypothesis that the slope is zero is rejected The estimated slope is 00011 The lower limit of the 95 confidence interval for the slope is 00003 and the upper limit is 00018 The estimated intercept is 696039 The lower limit of the 95 confidence interval for the intercept is -20303 and the upper limit is 1412381 Descriptive Statistics Section Parameter Dependent Independent Variable Waterside Bird Individuals PS Count 45 45 Mean 1601778 837270889 Standard Deviation 1322533 504044108 Minimum 40000 20260000 Maximum 5660000 2047320000
188
Linear Regression Report Database
Y = Waterside Bird Individuals X = PSx Regression Estimation Section Intercept Slope Parameter B(0) B(1) Regression Coefficients 696039 00011 Lower 95 Confidence Limit -20303 00003 Upper 95 Confidence Limit 1412381 00018 Standard Error 355207 00004 Standardized Coefficient 00000 04123 T Value 19595 29675 Prob Level (T Test) 00566 00049 Reject H0 (Alpha = 00500) No Yes Power (Alpha = 00500) 04824 08266 Regression of Y on X 696039 00011 Inverse Regression from X on Y -3726719 00064 Orthogonal Regression of Y and X 696034 00011 Notes The above report shows the least squares estimates of the intercept and slope followed by the corresponding standard errors confidence intervals and hypothesis tests Note that these results are based on several assumptions that should be validated before they are used Estimated Model ( 69603919723589) + ( 108177483842041E-03) (PSx)
189
Linear Regression Report Database
Y = Waterside Bird Individuals X = PSx Analysis of Variance Section Sum of Mean Power Source DF Squares Square F-Ratio (5) Intercept 1 1154561 1154561 Slope 1 1308168 1308168 88060 08266 Error 43 6387838 1485544 Adj Total 44 7696006 1749092 Total 45 1924162 s = Square Root(1485544) = 1218829 Notes The above report shows the F-Ratio for testing whether the slope is zero the degrees of freedom and the mean square error The mean square error which estimates the variance of the residuals is used extensively in the calculation of hypothesis tests and confidence intervals
190
Linear Regression Report Database Y = Waterside Bird Individuals X = PS x Tests of Assumptions Section Is the Assumption Test Prob Reasonable at the 02 AssumptionTest Value Level Level of Significance Residuals follow Normal Distribution Shapiro Wilk 09563 0087965 No Anderson Darling 05800 0131535 No DAgostino Skewness 20719 0038271 No DAgostino Kurtosis 13924 0163786 No DAgostino Omnibus 62319 0044337 No Constant Residual Variance Modified Levene Test 30485 0087954 No Relationship is a Straight Line Lack of Linear Fit F(0 0) Test 00000 0000000 No Notes A Yes means there is not enough evidence to make this assumption seem unreasonable This lack of evidence may be because the sample size is too small the assumptions of the test itself are not met or the assumption is valid A No means the that the assumption is not reasonable However since these tests are related to sample size you should assess the role of sample size in the tests by also evaluating the appropriate plots and graphs A large dataset (say N gt 500) will often fail at least one of the normality tests because it is hard to find a large dataset that is perfectly normal Normality and Constant Residual Variance Possible remedies for the failure of these assumptions include using a transformation of Y such as the log or square root correcting data-recording errors found by looking into outliers adding additional independent variables using robust regression or using bootstrap methods Straight-Line Possible remedies for the failure of this assumption include using nonlinear regression or polynomial regression
191
Linear Regression Report Database
Y = Waterside Bird Individuals X = PSx Residual Plots Section
-4000
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00
2000
4000
00 625000 1250000 1875000 2500000
Residuals of Water_edge_Bird_Individuals vs PS
PS
Res
idua
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er_e
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Bird
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ivid
uals
00
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Histogram of Residuals of Water_edge_Bird_Individuals
Residuals of Water_edge_Bird_Individuals
Cou
nt
192
-4000
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00
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-30 -15 00 15 30
Normal Probability Plot of Residuals of Water_edge_Bird_Individuals
Expected Normals
Res
idua
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er_e
dge_
Bird
_Ind
ivid
uals
193
Appendix C-4 The regression model of waterside (water edge) bird richness and the ratio of permanent building areas within a circle of 100 hectares from pond geometric center (BUILD) Linear Regression Report Database
Y = Waterside Bird Richness X = BUILDx Linear Regression Plot Section
20
40
60
80
100
00 1250000 2500000 3750000 5000000
Water_Edge_Bird_Richness vs BUILD
BUILD
Wat
er_E
dge_
Bird
_Ric
hnes
s
Run Summary Section Parameter Value Parameter Value Dependent Variable Waterside Bird Richness Rows Processed 45 Independent Variable BUILD Rows Used in Estimation 45 Frequency Variable None Rows with X Missing 0 Weight Variable None Rows with Freq Missing 0 Intercept 64037 Rows Prediction Only 0 Slope 00000 Sum of Frequencies 45 R-Squared 02280 Sum of Weights 45 Correlation -04775 Coefficient of Variation 02279 Mean Square Error 1681245 Square Root of MSE 12966
194
Linear Regression Report
Database Y = Waterside Bird Richness X = BUILDx
Summary Statement The equation of the straight line relating Waterside Bird Richness and BUILD is estimated as )(102857640376)( 6 BUILDxYSpeciesBirdedgeWater minustimesminus=minus using the 45 observations in this dataset The y-intercept the estimated value of Waterside Bird Richness when BUILD is zero is 64037 with a standard error of 02786 The value of R-Squared the proportion of the variation in Waterside Bird Richness that can be accounted for by variation in BUILD is 02280 The correlation between Waterside Bird Richness and BUILD is -04775 A significance test that the slope is zero resulted in a t-value of -35636 The significance level of this t-test is 00009 Since 00009 lt 00500 the hypothesis that the slope is zero is rejected Descriptive Statistics Section Parameter Dependent Independent Variable Waterside Bird Richness BUILD Count 45 45 Mean 56889 1137221333 Standard Deviation 14589 1108221594 Minimum 20000 100120000 Maximum 90000 4640340000
195
Linear Regression Report Database Y = Waterside Bird Richness X = BUILD x Regression Estimation Section Intercept Slope Parameter B(0) B(1) Regression Coefficients 64037 00000 Lower 95 Confidence Limit 58419 00000 Upper 95 Confidence Limit 69655 00000 Standard Error 02786 00000 Standardized Coefficient 00000 -04775 T Value 229884 -35636 Prob Level (T Test) 00000 00009 Reject H0 (Alpha = 00500) Yes Yes Power (Alpha = 00500) 10000 09361 Regression of Y on X 64037 00000 Inverse Regression from X on Y 88241 00000 Orthogonal Regression of Y and X 64037 00000 Estimated Model ( 640371457368543) + (-62857217310662E-06) (BUILDx)
196
Linear Regression Report Database Y = Waterside Bird Richness X = BUILD x Analysis of Variance Section Sum of Mean Power Source DF Squares Square F-Ratio (5) Intercept 1 1456356 1456356 Slope 1 213509 213509 126995 09361 Error 43 7229354 1681245 Adj Total 44 9364445 2128283 Total 45 1550 s = Square Root(1681245) = 1296628 Notes The above report shows the F-Ratio for testing whether the slope is zero the degrees of freedom and the mean square error The mean square error which estimates the variance of the residuals is used extensively in the calculation of hypothesis tests and confidence intervals
197
Linear Regression Report Database Y = Waterside Bird Richness X = BUILD x Tests of Assumptions Section Is the Assumption Test Prob Reasonable at the 02 AssumptionTest Value Level Level of Significance Residuals follow Normal Distribution Shapiro Wilk 09883 0924382 Yes Anderson Darling 02507 0742326 Yes DAgostino Skewness -02552 0798569 Yes DAgostino Kurtosis 03904 0696219 Yes DAgostino Omnibus 02176 0896927 Yes Constant Residual Variance Modified Levene Test 24851 0122261 No Relationship is a Straight Line Lack of Linear Fit F(0 0) Test 00000 0000000 No No Serial Correlation Evaluate the Serial-Correlation report and the Durbin-Watson test if you have equal-spaced time series data Notes A Yes means there is not enough evidence to make this assumption seem unreasonable This lack of evidence may be because the sample size is too small the assumptions of the test itself are not met or the assumption is valid A No means the that the assumption is not reasonable However since these tests are related to sample size you should assess the role of sample size in the tests by also evaluating the appropriate plots and graphs A large dataset (say N gt 500) will often fail at least one of the normality tests because it is hard to find a large dataset that is perfectly normal Normality and Constant Residual Variance Possible remedies for the failure of these assumptions include using a transformation of Y such as the log or square root correcting data-recording errors found by looking into outliers adding additional independent variables using robust regression or using bootstrap methods Straight-Line Possible remedies for the failure of this assumption include using nonlinear regression
198
Linear Regression Report Database Y = Waterside Bird Richness X = BUILDx Residual Plots Section
-40
-20
00
20
40
00 1250000 2500000 3750000 5000000
Residuals of Water_Edge_Bird_Richness vs BUILD
BUILD
Res
idua
ls o
f Wat
er_E
dge_
Bird
_Ric
hnes
s
00
30
60
90
120
-40 -20 00 20 40
Histogram of Residuals of Water_Edge_Bird_Richness
Residuals of Water_Edge_Bird_Richness
Cou
nt
199
-40
-20
00
20
40
-30 -15 00 15 30
Normal Probability Plot of Residuals of Water_Edge_Bird_Richness
Expected Normals
Res
idua
ls o
f Wat
er_E
dge_
Bird
_Ric
hnes
s
200
Appendix C-5 The regression model of waterside (water edge) bird richness and the ratio of farmland areas within a circle of 100 hectares from pond geometric center (FARM) Linear Regression Report Database Y = Waterside Bird Richness X = FARMx Linear Regression Plot Section
20
40
60
80
100
3000000 4500000 6000000 7500000 9000000
Water_Edge_Bird_Richness vs FARM
FARM
Wat
er_E
dge_
Bird
_Ric
hnes
s
Run Summary Section Parameter Value Parameter Value Dependent Variable Waterside Bird Richness Rows Processed 45 Independent Variable FARM Rows Used in Estimation 45 Frequency Variable None Rows with X Missing 0 Weight Variable None Rows with Freq Missing 0 Intercept 20933 Rows Prediction Only 0 Slope 00000 Sum of Frequencies 45 R-Squared 01581 Sum of Weights 45 Correlation 03976 Coefficient of Variation 0238 Mean Square Error 18335 Square Root of MSE 1354
201
Linear Regression Report Database Y = Waterside Bird Richness X = FARMx Summary Statement The equation of the straight line relating Waterside Bird Richness and FARM is estimated as )(109597409332)( 6 FARMxYRichnessBirdedgeWater minustimes+=minus using the 45 observations in this dataset The y-intercept the estimated value Waterside Bird Richness when FARM is zero is 20933 with a standard error of 12815 The value of R-Squared the proportion of the variation in Waterside Bird Richness that can be accounted for by variation in FARM is 01581 The correlation between Waterside Bird Richness and FARM is 03976 A significance test that the slope is zero resulted in a t-value of 28412 The significance level of this t-test is 00068 Since 00068 lt 00500 the hypothesis that the slope is zero is rejected Descriptive Statistics Section Parameter Dependent Independent Variable Waterside Bird Richness FARM Count 45 45 Mean 56889 7249611778 Standard Deviation 14589 1169412063 Minimum 20000 3513700000 Maximum 90000 8691580000
202
Linear Regression Report Database Y = Waterside Bird Richness X = FARMx Regression Estimation Section Intercept Slope Parameter B(0) B(1) Regression Coefficients 20933 00000 Lower 95 Confidence Limit -04911 00000 Upper 95 Confidence Limit 46777 00000 Standard Error 12815 00000 Standardized Coefficient 00000 03976 T Value 16335 28412 Prob Level (T Test) 01097 00068 Reject H0 (Alpha = 00500) No Yes Power (Alpha = 00500) 03585 07931 Regression of Y on X 20933 00000 Inverse Regression from X on Y -170597 00000 Orthogonal Regression of Y and X 20933 00000 Notes The above report shows the least squares estimates of the intercept and slope followed by the corresponding standard errors confidence intervals and hypothesis tests Note that these results are based on several assumptions that should be validated before they are used Estimated Model ( 209330450951941) + ( 495969231123658E-06) (FARM)
203
Linear Regression Report Database Y = Waterside Bird Richness X = FARMx Analysis of Variance Section Sum of Mean Power Source DF Squares Square F-Ratio (5) Intercept 1 1456356 1456356 Slope 1 1480121 1480121 80724 07931 Error 43 7884323 1833564 Adj Total 44 9364445 2128283 Total 45 1550 s = Square Root(1833564) = 1354091 Notes The above report shows the F-Ratio for testing whether the slope is zero the degrees of freedom and the mean square error The mean square error which estimates the variance of the residuals is used extensively in the calculation of hypothesis tests and confidence intervals
204
Linear Regression Report Database Y = Waterside Bird Richness X = FARMx Tests of Assumptions Section Is the Assumption Test Prob Reasonable at the 02 AssumptionTest Value Level Level of Significance Residuals follow Normal Distribution Shapiro Wilk 09806 0644821 Yes Anderson Darling 02769 0654764 Yes DAgostino Skewness -11666 0243390 Yes DAgostino Kurtosis 09288 0352984 Yes DAgostino Omnibus 22236 0328974 Yes Constant Residual Variance Modified Levene Test 00058 0939636 Yes Relationship is a Straight Line Lack of Linear Fit F(0 0) Test 00000 0000000 No Notes A Yes means there is not enough evidence to make this assumption seem unreasonable This lack of evidence may be because the sample size is too small the assumptions of the test itself are not met or the assumption is valid A No means the that the assumption is not reasonable However since these tests are related to sample size you should assess the role of sample size in the tests by also evaluating the appropriate plots and graphs A large dataset (say N gt 500) will often fail at least one of the normality tests because it is hard to find a large dataset that is perfectly normal Normality and Constant Residual Variance Possible remedies for the failure of these assumptions include using a transformation of Y such as the log or square root correcting data-recording errors found by looking into outliers adding additional independent variables using robust regression or using bootstrap methods Straight-Line Possible remedies for the failure of this assumption include using nonlinear regression or polynomial regression
205
Linear Regression Report Database Y = Waterside Bird Richness X = FARMx Residual Plots Section
-40
-20
00
20
40
3000000 4500000 6000000 7500000 9000000
Residuals of Water_Edge_Bird_Richness vs FARM
FARM
Res
idua
ls o
f Wat
er_E
dge_
Bird
_Ric
hnes
s
00
30
60
90
120
-40 -20 00 20 40
Histogram of Residuals of Water_Edge_Bird_Richness
Residuals of Water_Edge_Bird_Richness
Cou
nt
206
-40
-20
00
20
40
-30 -15 00 15 30
Normal Probability Plot of Residuals of Water_Edge_Bird_Richness
Expected Normals
Res
idua
ls o
f Wat
er_E
dge_
Bird
_Ric
hnes
s
207
Appendix D Results of the Non-linear Regression Models (Factor Elimination Approach)
The structure of the neural network used by the package of MATLAB 61 The input layer comprises four cells representing each of the four-pondscape parameters Xi (BUILD FARM PS and MPFD) The hidden layer comprises four neurons which calculate the dot products between its vector of weights wj =[wji i =14] and x = [xi i= BUILD FARM PS and MPFD] The factor elimination approach (FEA) was used to determine which factors xi [xi i = BUILD FARM PS and MPFD] are causally major influences on waterside birdrsquos diversity (Hrsquo) in a respective sequence Data input by a one-row two-row and three-row elimination was tested and simulated the final output to find differentiations between an original model and some elimination models Appendix D-1 One-row factor elimination approach1
If data input while BUILD = 0 then output
If data input while FARM = 0 then output
If data input while PS = 0 then output
If data input while MPFD =0 then output
Error for model (BUILD)
Error for model (FARM)
Error for model (PS)
Error for model (MPFD)
0717988 0717987 0717982 0082728
0717952 071799 0717968 0082715
0717988 0717987 0717976 0082736
0717988 0717988 0717975 0082741
0717987 071799 0717971 0082729
0717988 071799 0717968 008274
0717988 0717987 0717982 0082734
0717987 0717987 0717963 0082743
0717988 0717987 0717969 0082741
0717988 0717989 071797 0082742
0717988 0717989 0717982 0082734
0717987 0717986 0717969 0082743
0717987 0717988 0717951 0082744
0717988 0717989 0717957 0082743
0717987 0717987 0717958 0082745
0717987 0717985 0717976 0082735
0717987 0717989 0717964 0082744
0717987 0717989 0717979 0082735
0717988 0717988 0717963 0082723
208
Appendix D-1 Continued
If data input while BUILD = 0 then output
If data input while FARM = 0 then output
If data input while PS = 0 then output
If data input while MPFD =0 then output
Error for model (BUILD)
Error for model (FARM)
Error for model (PS)
Error for model (MPFD)
0717988 0717988 0717986 0082718
0717987 0717985 0717974 0082741
0717987 0717985 0717968 0082744
0717967 071799 0717975 0082742
0717988 0717988 0717969 0082738
0717987 0717985 0717978 008273
0717988 071799 0717971 008274
0717987 0717985 071798 008274
0717988 0717988 0717984 0082731
0717972 071799 0717986 0082675
0717988 0717988 0717959 0082739
0717987 0717987 0717966 0082743
0717987 0717987 071798 0082736
0717988 071799 0717948 0082744
0717988 0717989 0717971 0082741
0717987 0717986 0717966 0082735
0717987 0717989 0717947 0082744
0717987 0717987 0717969 0082742
0717988 0717988 0717977 0082739
0717988 0717987 0717984 0082727
0717988 0717989 0717967 0082742
0717988 0717989 0717977 0082737
0717987 0717988 0717969 008274
0717988 0717986 0717973 008274
0717975 071799 0717977 008273
0717988 0717989 0717963 0082744 Total Hrsquo predicted error 3230936 3230946 3230869 3723117 2 Mean Hrsquo predicted error 0717986 0717988 0717971 0082736
Note 1 One-row factor elimination approach (FEA) determined that the MPFD is the major factor to affect
waterside birdrsquos diversity 2 Mean Hrsquo predicted error from MPFD = 0082736 plusmn 116432E-05 n = 45
209
Non-linear Model Report
Appendix D-2 Two-row factor elimination approach2
Model for four variables (1)
If data input while BUILD = 0 and MPFD = 0 then output (2)
|(1) - (2)| Mean|(1) - (2)|
0187446 0082705 0104741 0359866
0260985 0122874 0138111
0539752 0082714 0457038
0596994 0082716 0514278
0428046 0082662 0345384
0627509 0082675 0544834
0676667 0082712 0593955
0479812 0082733 0397079
0437183 0082724 0354459
0525698 0082688 044301
0394329 0082676 0311653
0616483 0082731 0533752
0508955 0082735 042622
03686 0082705 0285895
0517141 008274 0434401
0496184 0082726 0413458
0531822 008274 0449082
0402353 0082721 0319632
0511992 0082683 0429309
0209802 0082662 012714
0532727 0082735 0449992
0439588 008274 0356848
040717 0082834 0324336
0516359 0082721 0433638
0411911 0082715 0329196
0328685 0082686 0245999
0337185 0082727 0254458
210
Appendix D-2 Continued
Model for four variables (1)
If data input while BUILD = 0 and MPFD = 0 then output (2)
|(1) - (2)| Mean|(1) - (2)|
0419735 0082685 033705
0455566 0171857 0283709
0417423 0082714 0334709
0338905 0082733 0256172
0434793 0082724 0352069
0491163 0082713 040845
0526723 0082724 0443999
0448619 0082731 0365888
0514072 0082737 0431335
0251645 0082731 0168914
0459589 0082721 0376868
054215 0082683 0459467
0536566 0082719 0453847
036816 0082712 0285448
0419471 0082733 0336738
0465609 0082722 0382887
0225209 0082919 014229
043893 0082704 0356226
Model for four variables (1)
If data input while FARM = 0 and MPFD = 0 then output (3)
|(1) - (3)| Mean|(1) - (3)|
0187446 0119762 0067684 0190609
0260985 0082665 017832
0539752 0295036 0244716
0596994 0408341 0188653
0428046 008274 0345306
0627509 00982 0529309
0676667 0327516 0349151
0479812 0481802 000199
0437183 0446435 0009252
0525698 0238242 0287456
211
Appendix D-2 Continued
Model for four variables (1)
If data input while FARM = 0 and MPFD = 0 then output (3)
|(1) - (3)| Mean|(1) - (3)|
0394329 0096696 0297633
0616483 0506644 0109839
0508955 0493653 0015302
03686 0141107 0227493
0517141 0535493 0018352
0496184 0452838 0043346
0531822 0408257 0123565
0402353 0115738 0286615
0511992 008366 0428332
0209802 0083815 0125987
0532727 0511091 0021636
0439588 0530891 0091303
040717 0082839 0324331
0516359 0270776 0245583
0411911 0346511 00654
0328685 0094077 0234608
0337185 0488498 0151313
0419735 0117446 0302289
0455566 0082659 0372907
0417423 0250451 0166972
0338905 0487894 0148989
0434793 0326796 0107997
0491163 012676 0364403
0526723 0257555 0269168
0448619 0412632 0035987
0514072 0393359 0120713
0251645 0493673 0242028
0459589 0222926 0236663
054215 0139283 0402867
0536566 0270283 0266283
036816 013834 022982
212
Appendix D-2 Continued
Model for four variables (1)
If data input while FARM = 0 and MPFD = 0 then output (3)
|(1) - (3)| Mean|(1) - (3)|
0419471 039382 0025651
0465609 0464695 0000914
0225209 0082681 0142528
043893 0310171 0128759
Model for four variables (1) If data input while PS = 0 and MPFD = 0 then output (4)
|(1) - (4)| Mean|(1) - (4)|
0187446 0082728 0104718 0361753
0260985 0082715 017827
0539752 0082737 0457015
0596994 0082743 0514251
0428046 008273 0345316
0627509 0082751 0544758
0676667 0082735 0593932
0479812 0082792 039702
0437183 0082751 0354432
0525698 0082749 0442949
0394329 0082734 0311595
0616483 0082755 0533728
0508955 0086509 0422446
03686 0082994 0285606
0517141 0083064 0434077
0496184 0082736 0413448
0531822 0082797 0449025
0402353 0082736 0319617
0511992 0082727 0429265
0209802 0082718 0127084
0532727 0082744 0449983
0439588 0082762 0356826
040717 0082745 0324425
0516359 0082743 0433616
213
Appendix D-2 Continued
Model for four variables (1) If data input while PS = 0 and MPFD = 0 then output (4)
|(1) - (4)| Mean|(1) - (4)|
0411911 008273 0329181
0328685 0082744 0245941
0337185 008274 0254445
0419735 0082731 0337004
0455566 0082675 0372891
0417423 0082804 0334619
0338905 0082764 0256141
0434793 0082736 0352057
0491163 009757 0393593
0526723 0082748 0443975
0448619 0082742 0365877
0514072 0106905 0407167
0251645 0082752 0168893
0459589 008274 0376849
054215 0082727 0459423
0536566 0082758 0453808
036816 0082738 0285422
0419471 0082748 0336723
0465609 0082743 0382866
0225209 008273 0142479
043893 0082802 0356128
Note
2 The smaller value between Mean|(1) - (2)| Mean|(1) - (3)| and Mean|(1) - (4)|is Mean|(1) - (3)| 0190609 It means that FARM is the major factor to affect waterside birdrsquos diversity second to MPFD
214
Non-linear Model Report
Appendix D-3 Three-row factor elimination approach3
Model for four variables (1) If data input while PS = 0 then output (5) |(1) - (5)| Mean|(1) - (5)|
0187446 0133191 0054255 0177395 0260985 036112 0100135 0539752 0311963 0227789 0596994 0394981 0202013 0428046 0088134 0339912 0627509 0101445 0526064 0676667 0398676 0277991 0479812 0442911 0036901 0437183 04224 0014783 0525698 0266918 025878 0394329 0137559 025677 0616483 0490963 012552 0508955 0449274 0059681 03686 0101951 0266649 0517141 0506424 0010717 0496184 048638 0009804 0531822 0375387 0156435 0402353 0104514 0297839 0511992 0086163 0425829 0209802 0180751 0029051 0532727 0510508 0022219 0439588 0521787 0082199 040717 0151181 0255989 0516359 0239217 0277142 0411911 0436041 002413 0328685 0089211 0239474 0337185 0512409 0175224 0419735 0202116 0217619 0455566 0448426 000714 0417423 0207832 0209591
215
Appendix D-3 Continued
Model for four variables (1) If data input while PS = 0 then output (5) |(1) - (5)| Mean|(1) - (5)|
0338905 0456638 0117733 0434793 0321924 0112869 0491163 0095369 0395794 0526723 019056 0336163 0448619 0414597 0034022 0514072 0340959 0173113 0251645 047338 0221735 0459589 0180769 027882 054215 0387556 0154594 0536566 0188782 0347784 036816 0116483 0251677 0419471 0363481 005599 0465609 0486035 0020426 0225209 0139851 0085358 043893 0229862 0209068
Model for four variables (1) If data input while BUILD = 0 then output (6)
|(1) - (6)| Mean|(1) - (6)|
0187446 0274949 0087503 0117559 0260985 0082704 0178281 0539752 0490462 004929 0596994 0538866 0058128 0428046 0232105 0195941 0627509 0589941 0037568 0676667 0446631 0230036 0479812 0548573 0068761 0437183 0535868 0098685 0525698 0577974 0052276 0394329 0215564 0178765 0616483 0527835 0088648 0508955 0564772 0055817 03686 0616616 0248016 0517141 056208 0044939
216
Appendix D-3 Continued
Model for four variables (1) If data input while BUILD = 0 then output (6)
|(1) - (6)| Mean|(1) - (6)|
0496184 0478083 0018101 0531822 0589654 0057832 0402353 0399068 0003285 0511992 0441631 0070361 0209802 0084544 0125258 0532727 0504365 0028362 0439588 0513029 0073441 040717 0135948 0271222 0516359 0522604 0006245 0411911 0460899 0048988 0328685 0562533 0233848 0337185 0505554 0168369 0419735 0199027 0220708 0455566 0082656 037291 0417423 0545984 0128561 0338905 054011 0201205 0434793 0464991 0030198 0491163 0629243 013808 0526723 0571718 0044995 0448619 0462239 001362 0514072 0594199 0080127 0251645 0529846 0278201 0459589 0511951 0052362 054215 0213175 0328975 0536566 0586547 0049981 036816 0476408 0108248 0419471 0531681 011221 0465609 0513163 0047554 0225209 0082793 0142416 043893 0600789 0161859 Note 3 The smaller value between Mean|(1) - (5)|and Mean|(1) - (6)|is Mean|(1) - (6)| 0117559 It means that PS is the major factor compared with BUILD to affect waterside birdrsquos diversity next to MPFD FARM respectively
217
Non-linear Model Report
Appendix D-4 Testing for MPFDrsquos trends with waterside birdrsquos diversity (neurons = 4 testing at a plusmn10 range)45
+10
Model for four variables (real value )
Model for four variables (value +10 for MPFD)
Error Error Absolute Error Absolute Error
0187446 0086846 -01006 -5367 01006 5367
0260985 0419103 0158118 6059 0158118 6059
0539752 0241327 -029843 -5529 0298425 5529
0596994 0409666 -018733 -3138 0187328 3138
0428046 0126446 -03016 -7046 03016 7046
0627509 0478065 -014944 -2382 0149444 2382
0676667 0121843 -055482 -8199 0554824 8199
0479812 0418704 -006111 -1274 0061108 1274
0437183 0507477 0070294 1608 0070294 1608
0525698 062896 0103262 1964 0103262 1964
0394329 0113587 -028074 -7119 0280742 7119
0616483 0499311 -011717 -1901 0117172 1901
0508955 0363725 -014523 -2853 014523 2853
03686 0442154 0073554 1995 0073554 1995
0517141 0392819 -012432 -2404 0124322 2404
0496184 0547495 0051311 1034 0051311 1034
0531822 0397962 -013386 -2517 013386 2517
0402353 0083391 -031896 -7927 0318962 7927
0511992 0449082 -006291 -1229 006291 1229
0209802 0243291 0033489 1596 0033489 1596
0532727 05219 -001083 -203 0010827 203
0439588 0454133 0014545 331 0014545 331
040717 027637 -01308 -3212 01308 3212
0516359 039338 -012298 -2382 0122979 2382
0411911 0343719 -006819 -1656 0068192 1656
0328685 0120889 -02078 -6322 0207796 6322
0337185 0482327 0145142 4305 0145142 4305
0419735 0107504 -031223 -7439 0312231 7439
218
Appendix D-4 Continued
+10
Model for four variables (real value )
Model for four variables (value +10 for MPFD)
Error Error Absolute Error Absolute Error
0455566 0477773 0022207 487 0022207 487
0417423 0477161 0059738 1431 0059738 1431
0338905 0437777 0098872 2917 0098872 2917
0434793 0100243 -033455 -7694 033455 7694
0491163 0361597 -012957 -2638 0129566 2638
0526723 0225592 -030113 -5717 0301131 5717
0448619 0465423 0016804 375 0016804 375
0514072 0379417 -013466 -2619 0134655 2619
0251645 0483704 0232059 9222 0232059 9222
0459589 0096827 -036276 -7893 0362762 7893
054215 0138836 -040331 -7439 0403314 7439
0536566 0352103 -018446 -3438 0184463 3438
036816 0087037 -028112 -7636 0281123 7636
0419471 038156 -003791 -904 0037911 904
0465609 0581141 0115532 2481 0115532 2481
0225209 0286337 0061128 2714 0061128 2714
043893 0562228 0123298 2809 0123298 2809 Mean Absolute Error = 0160848 Mean Absolute Error = 3720
Mean Error = -009954 Mean Error = -1883
-10
Model for four variables (real value )
Model for four variables (value -10 for MPFD)
Error Error Absolute Error Absolute Error
0187446 0535527 0348081 18570 0348081 18570
0260985 0465616 0204631 7841 0204631 7841
0539752 0549607 0009855 183 0009855 183
0596994 0561024 -003597 -603 003597 603
0428046 0531174 0103128 2409 0103128 2409
219
Appendix D-4 Continued
-10
Model for four variables (real value )
Model for four variables (value -10 for MPFD)
Error Error Absolute Error Absolute Error
0627509 0495453 -013206 -2104 0132056 2104
0676667 0545614 -013105 -1937 0131053 1937
0479812 0614344 0134532 2804 0134532 2804
0437183 0575875 0138692 3172 0138692 3172
0525698 0507576 -001812 -345 0018122 345
0394329 0553225 0158896 4030 0158896 4030
0616483 0588588 -00279 -452 0027895 452
0508955 0630609 0121654 2390 0121654 2390
03686 0568743 0200143 5430 0200143 5430
0517141 0637883 0120742 2335 0120742 2335
0496184 0555125 0058941 1188 0058941 1188
0531822 0659972 012815 2410 012815 2410
0402353 0601145 0198792 4941 0198792 4941
0511992 0463043 -004895 -956 0048949 956
0209802 0663442 045364 21622 045364 21622
0532727 0591605 0058878 1105 0058878 1105
0439588 0611965 0172377 3921 0172377 3921
040717 0725582 0318412 7820 0318412 7820
0516359 0578344 0061985 1200 0061985 1200
0411911 0526542 0114631 2783 0114631 2783
0328685 0525251 0196566 5980 0196566 5980
0337185 0569102 0231917 6878 0231917 6878
0419735 0547502 0127767 3044 0127767 3044
0455566 0319199 -013637 -2993 0136367 2993
0417423 0559975 0142552 3415 0142552 3415
0338905 0610003 0271098 7999 0271098 7999
0434793 0581464 0146671 3373 0146671 3373
0491163 0606986 0115823 2358 0115823 2358
0526723 0611576 0084853 1611 0084853 1611
0448619 0584086 0135467 3020 0135467 3020
220
Appendix D-4 Continued
-10
Model for four variables (real value )
Model for four variables (value -10 for MPFD)
Error Error Absolute Error Absolute Error
0514072 0654742 014067 2736 014067 2736
0251645 0593954 0342309 13603 0342309 13603
0459589 05942 0134611 2929 0134611 2929
054215 0569574 0027424 506 0027424 506
0536566 0597571 0061005 1137 0061005 1137
036816 0576004 0207844 5645 0207844 5645
0419471 0617513 0198042 4721 0198042 4721
0465609 0556435 0090826 1951 0090826 1951
0225209 0255199 002999 1332 002999 1332
043893 0541991 0103061 2348 0103061 2348 Mean Absolute Error = 0142779 Mean Absolute Error = 4003
Mean Error = 0119205 Mean Error = 3586
Note
4 The value of MPFD (range = [1 2] ) has a strongly negative relationship with waterside birdrsquos diversity MPFD approaches 1 for shapes with very simple perimeters such as circles or squares then waterside birdrsquos diversity increases and approaches 2 for shapes with highly convoluted and plane-filling perimeters then waterside birdrsquos diversity declines If the value of added +10 occurs the value of mean error (= -009954) reduces and vice versa 5 The training sets (r = 0725537 n = 35) and validated sets (r = 0722752 n = 10) were able to meet the underlying rules embedded for real values in the true Hrsquo
221
Appendix E The Location of Taiwan
222
VITA
Wei-Ta Fang was born in Kaohsiung Taiwan on February 14 1966 He received a
BA degree in land economics and administration from National Taipei University
Taipei Taiwan ROC in 1989 He received his first masterrsquos degree in environmental
planning (MEP) from Arizona State University in 1994 and second masterrsquos degree in
landscape architecture in design studies (MDesS) from the Graduate School of Design
Harvard University in 2002 He served as a specialist in the Taipei Land Management
Bureau from 1991 to 1992 and a specialist in charge of environmental education
(1994~1999) and environmental impact assessment (EIA) case reviews (1999~2000) at
the Taiwan EPArsquos headquarters from 1994 to 2000 During 2000 he received a three-
year scholarship from the Taiwanese government to promote knowledge on wetland
restoration and pursue a further degree in the United States He is currently in charge of
national EIA case reviews at the Taiwan EPArsquos headquarters
Permanent Address 5F 63-3 Hsing-An St Taipei Taiwan 104
Email wtfangsunepagovtw