結論與未來方向

本文主要的研究內容是以Hill 數值指標為基礎，結合系統演化樹的資 訊，建立一新的系統演化多樣性指標。新建立的指標具有生態直觀的解釋 意義“平均物種差異為 T 的有效物種數”，且滿足指標最基本的要求 “倍增 性質”。並且透過簡單的轉換公式，可以將其他非中性指標值轉換成“平均 物種差異為T 的有效物種數”的單位，如此即可解決之前非中性指標在解 釋上所面臨矛盾的現象。此外，本文以三個實例來介紹指標的應用性：（1）

由Shimatani ( 2001 )以橡樹為主的次生林資料，系統演化多樣性指標值反 應未受疏伐的森林具有較高的多樣性，這與Shimatani 的論文結果正好相 反。新指標值的結果反應在自然環境下，群落自然演替的多樣性比受人為 干擾的群落多樣性還來得高，而此結論亦較符合生態學家的預期。（2）第 二個實例是以新竹、苗栗地區三個河口的鳥類資料為依據，分析結果得 到，新的多樣性指標值與當地的自然環境的優劣成正比。（3）最後實例是 Pavoine et al. (2009) 論文中南加州 rockfish 屬的魚類資料，分析結果顯示，

無論傳統Hill 數值指標或新的系統演化多樣性指標都顯示，從 1980 至 2007 年，rockfish 屬魚類多樣性隨時間而遞減，且消失的物種是那些較古老稀 有的物種。

多群落系統演化多樣性指標的建立，是考慮系統演化樹的資訊下，透 過Whittaker ( 1972 ) 的定義，並且滿足 Jost ( 2007 ) 的五項公設，得到系 統演化Gamma、Alpha 和 Beta 多樣性指標族。另外透過四種觀點建立四種 系統演化分化、相似性指標，除了可以和傳統的分化、相似指標做連結，

並且校正

N

ST分化指標的缺點，進而提供一可以客觀量測群落分化的指 標。另外以兩個實例來對指標的應用做介紹：（1）以 Pavoine et al. (2009)

論文中南加州rockfish 屬的魚類資料為依據，分析結果顯示隨時間的差異 增大，其群落間的差異也隨之增加，結合單一群落的分析結果，得知此差 異主要是因為某些魚種的消失所造成，而非不同族群的移入所造成。（2）

第二例子是根據新竹、苗栗地區客雅溪、中港溪及後龍溪三個河口的鳥類 資料，得到彼此間的系統演化Beta 多樣性指標值，此三個指標值的大小差 異可透過資料的特性、調查地點自然環境和調查時間的差異，得到合理的 解釋。

對於指標的估計，根據實用性和估計量偏誤及均方根誤差的表現，本 文推薦二階不偏估計量及最小權重均方誤差估計量來做指標的估計，除了 可以修正傳統最大概似估計量低估的缺點外，在不同的模型下，此兩種估 計量亦可得到較穩健的估計值。其中，最小權重均方誤差估計量在

CV 大

的模型，可以得到較佳指標的估計曲線，而二階不偏估計量，則在

CV 大

的模型有較佳的表現。另外，當群落的物種大都屬於因近代種化事件而產 生時，當考慮位階

q > 1 的指標值時，此時最大概似估計量即可得到不錯

的估計值。

雖然本文對於多群落指標的估計僅就兩群落且等權重的條件下做討 論，然而對於更多群落及不等權重條件下，指標的估計仍可利用相同的方 法來進行估計。此外，對於系統演化樹為非超度量性質的指標估計亦是另 一重點。另一重點是，本文對於系統演化多樣性指標的估計，是在一前提 的假設下進行估計，即：部份物種的系統演化樹不會受其他物種的影響，

或是影響可以忽略，然而這是一理想的狀況，一般實際的應用可能並非如 此，因為大部分物種的系統演化樹的建構是透過物種的DNA 資訊，經由 一些演算法（如：UPGMA, Maximun Parsimony Method, Maximun Likelihood

Method,… ,等等）得到，因此可以視系統演化樹是一估計得到的系統演化 樹，因此上述的前提假設可能不成立。且每一種方法都有其優缺點，因此 在建構系統演化樹的不同演算法下，系統演化多樣性指標的估計，亦是另 一重要課題。

由於生物科技的進步，透過分子層面探討基因多樣性的研究，是一熱 門議題。然而，並未考慮基因間的差異，透過本文的研究，以期可以考量 此遺傳差異訊息，進而將新建立的指標應用至基因多樣性層面的研究，進 而讓我們可以了解基因多樣性的另一面向。

群落的穩定與否，取決於該群落的生態功能是否健全，因此生態功能 多樣性指標，是另一生態學家強調的議題，其定量的方法如同

PD 一樣。

所以，透過本文建立的多樣性指標的策略，亦可將功能多樣性指標，推廣 至考慮物種豐富度資訊的指標，進而讓我們對區域中群落的生態功能有更 進一步的瞭解。

附表

附表一：群落物種大多屬於近代種化事件而產生的模擬結果。

表 1-1-1 系統演化樹為結構 A，物種相對豐富度為模型一：

S=100, p

i

~1/S, Rep.=200 , Bootstrap=200, q=1 , True=3.9534 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 3.7106 -0.2428 0.1010 0.1121 0.2630 CBA 3.7672 -0.1862 0.1081 0.1213 0.2153 JK1 3.9010 -0.0524 0.1086 0.1203 0.1206 JK2 3.9322 -0.0212 0.1094 0.1212 0.1114 SH1 4.0004 0.0471 0.1049 0.1164 0.1150 SH2 3.9432 -0.0101 0.1102 0.1204 0.1106 60

SH3 3.9900 0.0367 0.1079 0.1205 0.1140

MLE 3.8103 -0.1431 0.0645 0.0781 0.1570 CBA 3.8408 -0.1126 0.0683 0.0820 0.1317

JK1 3.9403 -0.0131 0.0682 0.0817 0.0694 JK2 3.9590 0.0057 0.0692 0.0821 0.0694 SH1 4.0026 0.0493 0.0648 0.0795 0.0814 SH2 3.9590 0.0056 0.0691 0.0822 0.0693 100

SH3 3.9969 0.0435 0.0663 0.0826 0.0794

MLE 3.8495 -0.1038 0.0548 0.0626 0.1174 CBA 3.8889 -0.0645 0.0572 0.0644 0.0862

JK1 3.9487 -0.0047 0.0570 0.0647 0.0572 JK2 3.9603 0.0070 0.0578 0.0649 0.0582 SH1 3.9948 0.0415 0.0545 0.0634 0.0685 SH2 3.9572 0.0039 0.0569 0.0651 0.0571 140

SH3 3.9908 0.0375 0.0557 0.0655 0.0671

MLE 3.8678 -0.0855 0.0528 0.0540 0.1005 CBA 3.9057 -0.0477 0.0533 0.0549 0.0715

JK1 3.9469 -0.0064 0.0542 0.0555 0.0546 JK2 3.9535 0.0001 0.0544 0.0555 0.0544 SH1 3.9823 0.0289 0.0518 0.0546 0.0593 SH2 3.9505 -0.0028 0.0541 0.0557 0.0542 180

SH3 3.9795 0.0262 0.0531 0.0564 0.0592

表 1-1-2 系統演化樹為結構 A，物種相對豐富度為模型二：

S=100, p

i

~random unif, Rep.=200 , Bootstrap=200, q=1, True=3.8789 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 3.6551 -0.2238 0.1072 0.1263 0.2482 CBA 3.7112 -0.1677 0.1102 0.1341 0.2007 JK1 3.8361 -0.0428 0.1158 0.1349 0.1235 JK2 3.8628 -0.0160 0.1170 0.1356 0.1181 SH1 3.9342 0.0553 0.1099 0.1321 0.1230 SH2 3.8719 -0.0070 0.1176 0.1357 0.1178 60

SH3 3.9227 0.0438 0.1166 0.1364 0.1246

MLE 3.7406 -0.1383 0.0787 0.0917 0.1591 CBA 3.7608 -0.1181 0.0802 0.0947 0.1428 JK1 3.8625 -0.0164 0.0826 0.0957 0.0842 JK2 3.8773 -0.0016 0.0836 0.0959 0.0836 SH1 3.9327 0.0538 0.0811 0.0946 0.0973 SH2 3.8799 0.0011 0.0839 0.0965 0.0839 100

SH3 3.9283 0.0495 0.0832 0.0979 0.0968

MLE 3.7789 -0.0999 0.0670 0.0757 0.1203 CBA 3.805 -0.0739 0.0708 0.0778 0.1023

JK1 3.8703 -0.0085 0.0697 0.0781 0.0703 JK2 3.8789 0.0000 0.0704 0.0782 0.0704 SH1 3.9251 0.0463 0.0712 0.0777 0.0849 SH2 3.8798 0.0010 0.0717 0.0787 0.0717 140

SH3 3.9212 0.0423 0.0746 0.0804 0.0858

MLE 3.8020 -0.0769 0.0718 0.0656 0.1052 3.838 -0.0409 0.0729 0.0681 0.0836 JK1 3.8752 -0.0037 0.0736 0.0672 0.0737 JK2 3.8804 0.0015 0.0737 0.0673 0.0737 SH1 3.9201 0.0412 0.0715 0.0673 0.0825 SH2 3.8810 0.0022 0.0733 0.0678 0.0734 180

SH3 3.9158 0.0369 0.0734 0.0698 0.0822

表 1-1-3 系統演化樹為結構 A，物種相對豐富度為模型三：

S =100, p

i

~c/(i+10), Rep.=200 , Bootstrap=200, q=1, True=3.815 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 3.5988 -0.2165 0.1219 0.1343 0.2485 CBA 3.6824 -0.1326 0.1352 0.1441 0.1894 JK1 3.7759 -0.0394 0.1320 0.1434 0.1378 JK2 3.8020 -0.0133 0.1337 0.1440 0.1344 SH1 3.8878 0.0725 0.1324 0.1434 0.1509 SH2 3.8088 -0.0065 0.1370 0.1449 0.1371 60

SH3 3.8662 0.0509 0.1405 0.1482 0.1494

MLE 3.6740 -0.1413 0.1036 0.1028 0.1752 CBA 3.7131 -0.1019 0.1107 0.1093 0.1505 JK1 3.7927 -0.0226 0.1087 0.1071 0.1110 JK2 3.8083 -0.0070 0.1094 0.1074 0.1096 SH1 3.8699 0.0546 0.1086 0.1086 0.1216 SH2 3.8066 -0.0087 0.1119 0.1090 0.1123 100

SH3 3.8468 0.0315 0.1153 0.1129 0.1195

MLE 3.7087 -0.1066 0.0823 0.0852 0.1347 CBA 3.7371 0.0779 0.0859 0.0881 0.1160

JK1 3.7982 -0.0171 0.0851 0.0878 0.0868 JK2 3.8081 -0.0072 0.0854 0.0879 0.0857 SH1 3.8553 0.0400 0.0854 0.0891 0.0944 SH2 3.8031 -0.0122 0.0868 0.0891 0.0877 140

SH3 3.8349 0.0196 0.0900 0.0923 0.0921

MLE 3.7341 -0.0812 0.0734 0.0738 0.1095 CBA 3.7732 -0.0418 0.0761 0.0782 0.0868 JK1 3.8067 -0.0087 0.0753 0.0756 0.0758 JK2 3.8137 -0.0016 0.0754 0.0757 0.0755 SH1 3.8543 0.0390 0.0768 0.0770 0.0861 SH2 3.8088 -0.0065 0.0768 0.0766 0.0771 180

SH3 3.8365 0.0212 0.0810 0.0796 0.0837

表 1-1-4 系統演化樹為結構 A，物種相對豐富度為模型四：

S =100, p

i

~c/(i+2), Rep.=200, Bootstrap=200, q=1, True=3.6636 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 3.4620 -0.2017 0.1516 0.1469 0.2523 CBA 3.5098 -0.1538 0.1691 0.1611 0.2286 JK1 3.6229 -0.0408 0.1632 0.1565 0.1682 JK2 3.6444 -0.0192 0.1645 0.1569 0.1656 SH1 3.7354 0.0718 0.1684 0.1600 0.1831 SH2 3.6399 -0.0237 0.1699 0.1589 0.1716 60

SH3 3.6995 0.0359 0.1750 0.1642 0.1786

MLE 3.5392 -0.1245 0.1107 0.1127 0.1666 CBA 3.5713 -0.0923 0.1213 0.1181 0.1524 JK1 3.6473 -0.0163 0.1162 0.1173 0.1173 JK2 3.6607 -0.0030 0.1169 0.1174 0.1169 SH1 3.7226 0.0590 0.1207 0.1203 0.1343 SH2 3.6493 -0.0143 0.1189 0.1189 0.1197 100

SH3 3.6930 0.0293 0.1239 0.1228 0.1273

MLE 3.5619 -0.1017 0.0897 0.0977 0.1356 CBA 3.5965 -0.0671 0.0939 0.1021 0.1154 JK1 3.6437 -0.0199 0.0928 0.1005 0.0950 JK2 3.6530 -0.0106 0.0930 0.1006 0.0937 SH1 3.6978 0.0342 0.0945 0.1034 0.1005 SH2 3.6404 -0.0232 0.0933 0.1018 0.0962 140

SH3 3.6715 0.0079 0.0952 0.1049 0.0956

MLE 3.5807 -0.0829 0.0831 0.0854 0.1174 CBA 3.6218 -0.0418 0.0871 0.0892 0.0966 JK1 3.6471 -0.0165 0.0855 0.0874 0.0871 JK2 3.6538 -0.0098 0.0859 0.0874 0.0864 SH1 3.6876 0.0239 0.0878 0.0898 0.0910 SH2 3.6409 -0.0227 0.0865 0.0883 0.0895 180

SH3 3.6646 0.0010 0.0883 0.0906 0.0884

表 1-1-5 系統演化樹為結構 A，物種相對豐富度為模型五：

S =100, p

i

~c/(i+0),CV=2.253, Rep.=200 , Bootstrap=200, q=1, True=3.4995 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 3.3220 -0.1775 0.1350 0.1422 0.2230 CBA 3.3573 -0.1422 0.1471 0.1529 0.2046

JK1 3.4681 -0.0315 0.1459 0.1514 0.1492 JK2 3.4881 -0.0115 0.1465 0.1516 0.1470 SH1 3.5635 0.0639 0.1494 0.1566 0.1625 SH2 3.4648 -0.0347 0.1464 0.1529 0.1505 60

SH3 3.5400 0.0404 0.1487 0.1572 0.1541

MLE 3.3795 -0.1200 0.1148 0.1101 0.1661 CBA 3.4072 -0.0923 0.1239 0.1152 0.1545 JK1 3.4775 -0.0220 0.1203 0.1144 0.1223 JK2 3.4900 -0.0096 0.1211 0.1144 0.1215 SH1 3.5329 0.0334 0.1242 0.1173 0.1286 SH2 3.4658 -0.0337 0.1210 0.1149 0.1256 100

SH3 3.5255 0.0259 0.1244 0.1159 0.1270

MLE 3.4092 -0.0903 0.0997 0.0952 0.1346 CBA 3.4313 -0.0682 0.1048 0.0973 0.1250 JK1 3.4838 -0.0158 0.1033 0.0979 0.1045 JK2 3.4919 -0.0076 0.1041 0.0979 0.1043 SH1 3.5191 0.0196 0.1056 0.0999 0.1074 SH2 3.4694 -0.0301 0.1035 0.0981 0.1078 140

SH3 3.5149 0.0153 0.1036 0.0982 0.1047

MLE 3.4141 -0.0855 0.0899 0.0849 0.1241 CBA 3.4456 -0.0539 0.0931 0.0873 0.1076 JK1 3.4746 -0.0249 0.0925 0.0868 0.0958 JK2 3.4810 -0.0186 0.0930 0.0868 0.0948 SH1 3.5000 0.0004 0.0938 0.0882 0.0938 SH2 3.4603 -0.0392 0.0923 0.0868 0.1003 180

SH3 3.4985 -0.0011 0.0929 0.0867 0.0929

表 1-1-6 系統演化樹為結構 A，物種相對豐富度為模型六：

S =100, p

i

~c/(i-0.5), Rep.=200, Bootstrap=200, q=1, True=3.3193 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 3.1568 -0.1625 0.1629 0.1451 0.2301 CBA 3.1911 -0.1282 0.1793 0.1579 0.2204

JK1 3.2891 -0.0302 0.1764 0.1540 0.1790 JK2 3.3070 -0.0123 0.1778 0.1539 0.1782 SH1 3.3513 0.0320 0.1850 0.1592 0.1878 SH2 3.2673 -0.0520 0.1771 0.1542 0.1845 60

SH3 3.3503 0.0310 0.1796 0.1560 0.1823

MLE 3.2001 -0.1193 0.1232 0.1163 0.1715 CBA 3.2162 -0.1031 0.1296 0.1229 0.1656 JK1 3.2893 -0.0300 0.1295 0.1206 0.1329 JK2 3.3001 -0.0192 0.1307 0.1205 0.1321 SH1 3.3183 -0.0010 0.1332 0.1235 0.1332 SH2 3.2649 -0.0544 0.1288 0.1204 0.1398 100

SH3 3.3326 0.0133 0.1304 0.1198 0.1311

MLE 3.2265 -0.0928 0.0982 0.1002 0.1351 CBA 3.2482 -0.0711 0.1031 0.1032 0.1252 JK1 3.2943 -0.0251 0.1019 0.1029 0.1049 JK2 3.3015 -0.0178 0.1028 0.1028 0.1044 SH1 3.3106 -0.0088 0.1046 0.1046 0.1050 SH2 3.2720 -0.0473 0.1018 0.1026 0.1122 140

SH3 3.3277 0.0084 0.1047 0.1012 0.1051

MLE 3.2408 -0.0785 0.0912 0.0888 0.1203 CBA 3.2664 -0.0529 0.0944 0.0903 0.1082 JK1 3.2959 -0.0234 0.0938 0.0906 0.0967 JK2 3.3017 -0.0176 0.0943 0.0906 0.0959 SH1 3.3057 -0.0136 0.0957 0.0919 0.0967 SH2 3.2756 -0.0437 0.0937 0.0905 0.1034 180

SH3 3.3241 0.0048 0.0968 0.0891 0.0969

表 1-1-7 系統演化樹為結構 A，物種相對豐富度為模型七：

S =100, p

i

~Broken-Stick, Rep.=200, Bootstrap=200, q=1, True=3.8436 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 3.6326 -0.2110 0.0958 0.1134 0.2317 CBA 3.6703 -0.1733 0.1033 0.1237 0.2018

JK1 3.8062 -0.0374 0.1048 0.1216 0.1113 JK2 3.8301 -0.0135 0.1060 0.1223 0.1069 SH1 3.9161 0.0725 0.1013 0.1205 0.1245 SH2 3.8342 -0.0094 0.1053 0.1227 0.1057 60

SH3 3.9049 0.0613 0.1050 0.1252 0.1216

MLE 3.7113 -0.1323 0.0736 0.0805 0.1514 CBA 3.7327 -0.1109 0.0749 0.0841 0.1338 JK1 3.8254 -0.0182 0.0774 0.0841 0.0795 JK2 3.8372 -0.0064 0.0774 0.0842 0.0776 SH1 3.9043 0.0607 0.0741 0.0837 0.0958 SH2 3.8374 -0.0062 0.0767 0.0848 0.0770 100

SH3 3.8990 0.0554 0.0758 0.0869 0.0939

MLE 3.7496 -0.0940 0.0540 0.0650 0.1084 CBA 3.7631 -0.0805 0.0541 0.0683 0.0970 JK1 3.8349 -0.0087 0.0557 0.0670 0.0564 JK2 3.8419 -0.0017 0.0559 0.0671 0.0560 SH1 3.8967 0.0531 0.0534 0.0671 0.0753 SH2 3.8406 -0.0030 0.0549 0.0675 0.0550 140

SH3 3.8929 0.0492 0.0545 0.0696 0.0735

MLE 3.7648 -0.0788 0.0550 0.0564 0.0961 CBA 3.7948 -0.0488 0.0558 0.0582 0.0741 JK1 3.8326 -0.0111 0.0565 0.0577 0.0576 JK2 3.8372 -0.0065 0.0568 0.0577 0.0572 SH1 3.8838 0.0401 0.0553 0.0577 0.0684 SH2 3.8358 -0.0079 0.0565 0.0580 0.0571 180

SH3 3.8810 0.0373 0.0550 0.0594 0.0664

表 1-2-1 系統演化樹為結構 A，物種相對豐富度為模型一：

S =100, p

i

~1/S , Rep.=200, Bootstrap=200, q=2, True= 2.923 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 2.8322 -0.0908 0.1238 0.1243 0.1535 CBA 2.8370 -0.0860 0.1241 0.1245 0.1509 JK1 2.9052 -0.0178 0.1367 0.1368 0.1378 JK2 2.9106 -0.0124 0.1381 0.1382 0.1387 SH1 2.9495 0.0265 0.1198 0.1246 0.1227 SH2 2.9118 -0.0112 0.1265 0.1288 0.1270 60

SH3 2.9391 0.0162 0.1216 0.1272 0.1227

MLE 2.8739 -0.0491 0.0801 0.0932 0.0939 CBA 2.8756 -0.0474 0.0802 0.0932 0.0931 JK1 2.9205 -0.0025 0.0859 0.0993 0.0859 JK2 2.9230 0.0000 0.0864 0.0998 0.0864 SH1 2.9557 0.0327 0.0765 0.0936 0.0832 SH2 2.9258 0.0029 0.0812 0.0956 0.0812 100

SH3 2.9501 0.0271 0.0770 0.0949 0.0816

MLE 2.8866 -0.0364 0.0723 0.0774 0.0809 CBA 2.8873 -0.0357 0.0723 0.0774 0.0806 JK1 2.9206 -0.0024 0.0761 0.0812 0.0761 JK2 2.9221 -0.0009 0.0763 0.0814 0.0763 SH1 2.9500 0.0270 0.0715 0.0780 0.0765 SH2 2.9250 0.0020 0.0737 0.0790 0.0737 140

SH3 2.9460 0.0231 0.0724 0.0787 0.0759

MLE 2.8894 -0.0336 0.0718 0.0681 0.0793 CBA 2.8897 -0.0332 0.0718 0.0681 0.0791 JK1 2.9161 -0.0069 0.0747 0.0708 0.0750 JK2 2.9170 -0.0060 0.0748 0.0709 0.0751 SH1 2.9413 0.0184 0.0724 0.0689 0.0747 SH2 2.9197 -0.0033 0.0732 0.0694 0.0733 180

SH3 2.9381 0.0151 0.0730 0.0695 0.0745

表 1-2-2 系統演化樹為結構 A，物種相對豐富度為模型二：

S =100, p

i

~random unif, Rep.=200, Bootstrap=200, q=2, True= 2.830 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 2.7460 -0.0838 0.1384 0.1513 0.1618 CBA 2.7503 -0.0796 0.1388 0.1516 0.1600 JK1 2.8095 -0.0204 0.1531 0.1654 0.1544 JK2 2.8137 -0.0161 0.1547 0.1668 0.1556 SH1 2.8686 0.0387 0.1396 0.1571 0.1449 SH2 2.8255 -0.0044 0.1451 0.1589 0.1452 60

SH3 2.8576 0.0277 0.1430 0.1592 0.1456

MLE 2.7873 -0.0426 0.1146 0.1177 0.1222 CBA 2.7888 -0.0411 0.1147 0.1178 0.1218 JK1 2.8281 -0.0018 0.1221 0.1248 0.1221 JK2 2.8301 0.0003 0.1226 0.1253 0.1226 SH1 2.8697 0.0399 0.1175 0.1215 0.1241 SH2 2.8374 0.0076 0.1186 0.1219 0.1189 100

SH3 2.8637 0.0338 0.1188 0.1224 0.1235

MLE 2.8002 -0.0297 0.0962 0.0994 0.1007 CBA 2.8008 -0.0290 0.0962 0.0994 0.1005 JK1 2.8300 0.0001 0.1008 0.1038 0.1008 JK2 2.8312 0.0013 0.1011 0.1041 0.1011 SH1 2.8631 0.0332 0.0992 0.1024 0.1046 SH2 2.8367 0.0069 0.0992 0.1022 0.0994 140

SH3 2.8593 0.0294 0.1001 0.1031 0.1043

MLE 2.8128 -0.0171 0.0910 0.0864 0.0925 CBA 2.8131 -0.0167 0.0910 0.0864 0.0925 JK1 2.8366 0.0067 0.0944 0.0895 0.0947 JK2 2.8373 0.0075 0.0946 0.0896 0.0949 SH1 2.8634 0.0335 0.0935 0.0887 0.0993 SH2 2.8415 0.0116 0.0932 0.0884 0.0939 180

SH3 2.8609 0.0311 0.0940 0.0893 0.0990

表 1-2-3 系統演化樹為結構 A，物種相對豐富度為模型三：

S =100, p

i

~c/(i+10), Rep.=200, Bootstrap=200, q=2, True=2.8089 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 2.7364 -0.0725 0.1471 0.1493 0.1640 CBA 2.7408 -0.0680 0.1476 0.1495 0.1625 JK1 2.7988 -0.0101 0.1630 0.1634 0.1633 JK2 2.8025 -0.0063 0.1649 0.1648 0.1650 SH1 2.8630 0.0541 0.1489 0.1554 0.1584 SH2 2.8155 0.0066 0.1545 0.1567 0.1547 60

SH3 2.8465 0.0376 0.1551 0.1586 0.1596

MLE 2.7611 -0.0478 0.1233 0.1191 0.1322 CBA 2.7627 -0.0462 0.1234 0.1192 0.1318 JK1 2.7998 -0.0090 0.1315 0.1265 0.1319 JK2 2.8014 -0.0074 0.1322 0.1270 0.1324 SH1 2.8463 0.0375 0.1265 0.1234 0.1320 SH2 2.8105 0.0017 0.1280 0.1233 0.1280 100

SH3 2.8321 0.0232 0.1303 0.1259 0.1324

MLE 2.7740 -0.0349 0.0982 0.1012 0.1042 CBA 2.7747 -0.0342 0.0982 0.1012 0.1040 JK1 2.8022 -0.0067 0.1031 0.1059 0.1033 JK2 2.8031 -0.0058 0.1034 0.1062 0.1036 SH1 2.8385 0.0297 0.1014 0.1045 0.1057 SH2 2.8098 0.0009 0.1012 0.1040 0.1012 140

SH3 2.8273 0.0184 0.1042 0.1064 0.1058

MLE 2.7843 -0.0246 0.0947 0.0896 0.0978 CBA 2.7847 -0.0242 0.0947 0.0896 0.0978 JK1 2.8066 -0.0022 0.0985 0.0929 0.0985 JK2 2.8073 -0.0016 0.0987 0.0930 0.0987 SH1 2.8359 0.0270 0.0976 0.0922 0.1013 SH2 2.8123 0.0035 0.0971 0.0916 0.0971 180

SH3 2.8266 0.0178 0.1001 0.0937 0.1016

表 1-2-4 系統演化樹為結構 A，物種相對豐富度為模型四：

S =100, p

i

~c/(i+2), Rep.=200, Bootstrap=200, q=2, True= 2.7239 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 2.6563 -0.0676 0.1582 0.1593 0.1721 CBA 2.6603 -0.0636 0.1587 0.1595 0.1709 JK1 2.7104 -0.0135 0.1743 0.1740 0.1748 JK2 2.7125 -0.0114 0.1761 0.1754 0.1765 SH1 2.7833 0.0594 0.1648 0.1679 0.1752 SH2 2.7308 0.0069 0.1669 0.1676 0.1670 60

SH3 2.7573 0.0334 0.1697 0.1710 0.1730

MLE 2.6904 -0.0335 0.1286 0.1240 0.1329 CBA 2.6918 -0.0321 0.1288 0.1241 0.1327 JK1 2.7246 0.0007 0.1369 0.1315 0.1369 JK2 2.7255 0.0016 0.1375 0.1320 0.1375 SH1 2.7742 0.0503 0.1342 0.1295 0.1433 SH2 2.7365 0.0127 0.1335 0.1285 0.1341 100

SH3 2.7553 0.0314 0.1366 0.1314 0.1401

MLE 2.6894 -0.0345 0.1015 0.1101 0.1072 CBA 2.6900 -0.0338 0.1015 0.1101 0.1070 JK1 2.7136 -0.0103 0.1063 0.1150 0.1068 JK2 2.7141 -0.0098 0.1066 0.1152 0.1070 SH1 2.7515 0.0277 0.1057 0.1145 0.1093 SH2 2.7224 -0.0015 0.1044 0.1132 0.1044 140

SH3 2.7366 0.0127 0.1066 0.1158 0.1074

MLE 2.6998 -0.0241 0.0963 0.0962 0.0993 CBA 2.7002 -0.0237 0.0964 0.0962 0.0993 JK1 2.7189 -0.0049 0.1000 0.0997 0.1001 JK2 2.7193 -0.0046 0.1002 0.0998 0.1003 SH1 2.7492 0.0253 0.0998 0.0995 0.1030 SH2 2.7257 0.0018 0.0987 0.0984 0.0987 180

SH3 2.7368 0.0129 0.1007 0.1003 0.1015

表 1-2-5 系統演化樹為結構 A，物種相對豐富度為模型五：

S =100, p

i

~c/(i+0), Rep.=200, Bootstrap=200, q=2, True= 2.7074 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 2.6461 -0.0613 0.1251 0.1368 0.1393 CBA 2.6496 -0.0578 0.1254 0.1370 0.1381 JK1 2.7017 -0.0057 0.1378 0.1494 0.1379 JK2 2.7035 -0.0039 0.1391 0.1506 0.1391 SH1 2.7650 0.0576 0.1262 0.1431 0.1387 SH2 2.7144 0.0070 0.1286 0.1428 0.1288 60

SH3 2.7433 0.0359 0.1287 0.1455 0.1336

MLE 2.6691 -0.0383 0.1075 0.1025 0.1142 CBA 2.6704 -0.0370 0.1077 0.1025 0.1138 JK1 2.7036 -0.0038 0.1141 0.1084 0.1142 JK2 2.7042 -0.0032 0.1145 0.1088 0.1145 SH1 2.7471 0.0397 0.1097 0.1059 0.1167 SH2 2.7124 0.0050 0.1102 0.1054 0.1104 100

SH3 2.7335 0.0261 0.1108 0.1070 0.1138

MLE 2.6775 -0.0299 0.0893 0.0873 0.0941 CBA 2.6782 -0.0292 0.0893 0.0873 0.0940 JK1 2.7024 -0.0050 0.0933 0.0911 0.0935 JK2 2.7027 -0.0047 0.0935 0.0912 0.0936 SH1 2.7364 0.0290 0.0916 0.0898 0.0961 SH2 2.7095 0.0021 0.0916 0.0893 0.0916 140

SH3 2.7261 0.0187 0.0922 0.0903 0.0941

MLE 2.6718 -0.0356 0.0772 0.0780 0.0850 CBA 2.6721 -0.0353 0.0772 0.0780 0.0849 JK1 2.6908 -0.0166 0.0798 0.0807 0.0816 JK2 2.6910 -0.0164 0.0799 0.0808 0.0816 SH1 2.7182 0.0108 0.0786 0.0800 0.0793 SH2 2.6965 -0.0109 0.0786 0.0795 0.0793 180

SH3 2.7099 0.0025 0.0790 0.0804 0.0790

表 1-2-6 系統演化樹為結構 A，物種相對豐富度為模型六：

S =100, p

i

~c/(i-0.5), Rep.=200, Bootstrap=200, q=2, True= 2.6483 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 2.5887 -0.0596 0.1093 0.1214 0.1245 CBA 2.5921 -0.0562 0.1096 0.1215 0.1232 JK1 2.6414 -0.0069 0.1181 0.1320 0.1184 JK2 2.6427 -0.0056 0.1188 0.1329 0.1189 SH1 2.6874 0.0390 0.1160 0.1253 0.1224 SH2 2.6454 -0.0029 0.1142 0.1251 0.1143 60

SH3 2.6722 0.0239 0.1135 0.1262 0.1160

MLE 2.6031 -0.0452 0.0826 0.0882 0.0941 CBA 2.6044 -0.0439 0.0827 0.0882 0.0936 JK1 2.6354 -0.0129 0.0865 0.0928 0.0875 JK2 2.6359 -0.0125 0.0867 0.0930 0.0876 SH1 2.6636 0.0153 0.0847 0.0902 0.0860 SH2 2.6372 -0.0111 0.0836 0.0898 0.0844 100

SH3 2.6566 0.0083 0.0831 0.0901 0.0835

MLE 2.6125 -0.0358 0.0658 0.0737 0.0749 CBA 2.6132 -0.0352 0.0658 0.0737 0.0746 JK1 2.6357 -0.0126 0.0681 0.0764 0.0692 JK2 2.6360 -0.0123 0.0681 0.0765 0.0692 SH1 2.6576 0.0093 0.0676 0.0749 0.0683 SH2 2.6379 -0.0104 0.0669 0.0746 0.0677 140

SH3 2.6533 0.0050 0.0666 0.0746 0.0668

MLE 2.6177 -0.0306 0.0577 0.0640 0.0653 CBA 2.6181 -0.0303 0.0577 0.0640 0.0652 JK1 2.6358 -0.0125 0.0592 0.0658 0.0605 JK2 2.6360 -0.0123 0.0593 0.0659 0.0605 SH1 2.6527 0.0044 0.0595 0.0649 0.0596 SH2 2.6373 -0.0110 0.0588 0.0647 0.0598 180

SH3 2.6495 0.0012 0.0585 0.0646 0.0586

表 1-2-7 系統演化樹為結構 A，物種相對豐富度為模型七：

S =100, p

i

~Broken-Stick, Rep.=200, Bootstrap=200, q=2, True= 2.9309 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 2.8534 -0.0776 0.0806 0.1083 0.1119 CBA 2.8576 -0.0734 0.0808 0.1084 0.1092 JK1 2.9291 -0.0019 0.0896 0.1194 0.0897 JK2 2.9345 0.0036 0.0907 0.1206 0.0908 SH1 2.9673 0.0363 0.0745 0.1069 0.0829 SH2 2.9309 0.0000 0.0814 0.1114 0.0814 60

SH3 2.9538 0.0228 0.0748 0.1081 0.0782

MLE 2.8795 -0.0515 0.0607 0.0741 0.0796 CBA 2.8808 -0.0501 0.0607 0.0741 0.0787 JK1 2.9268 -0.0041 0.0647 0.0790 0.0648 JK2 2.9291 -0.0018 0.0650 0.0794 0.0650 SH1 2.9589 0.0280 0.0585 0.0733 0.0648 SH2 2.9293 -0.0017 0.0615 0.0754 0.0615 100

SH3 2.9487 0.0178 0.0562 0.0724 0.0589

MLE 2.8937 -0.0373 0.0485 0.0599 0.0612 CBA 2.8943 -0.0366 0.0485 0.0599 0.0608 JK1 2.9282 -0.0027 0.0510 0.0628 0.0511 JK2 2.9295 -0.0014 0.0511 0.0630 0.0512 SH1 2.9545 0.0235 0.0471 0.0596 0.0527 SH2 2.9304 -0.0006 0.0493 0.0607 0.0493 140

SH3 2.9462 0.0153 0.0454 0.0582 0.0479

MLE 2.8945 -0.0365 0.0500 0.0531 0.0619 CBA 2.8948 -0.0361 0.0500 0.0531 0.0617 JK1 2.9214 -0.0095 0.0520 0.0552 0.0528 JK2 2.9223 -0.0087 0.0521 0.0552 0.0528 SH1 2.9447 0.0138 0.0494 0.0534 0.0513 SH2 2.9236 -0.0073 0.0507 0.0539 0.0512 180

SH3 2.9378 0.0069 0.0470 0.0520 0.0475

附表二 群落物種大多屬於古老物種的模擬結果。

表 2-1-1 系統演化樹為結構 B，物種相對豐富度為模型一：

S =100, p

i

~1/S , Rep.=200, Bootstrap=200, q=1, True= 88.365 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 39.4093 -48.9558 2.8937 2.2296 49.0413 CBA 80.7767 -7.5884 22.2030 5.7112 23.4639 JK1 63.9142 -24.4509 6.6716 3.9790 25.3447 JK2 78.6239 -9.7411 10.3641 4.9996 14.2233 SH1 92.7815 4.4164 23.7503 7.1820 24.1574 SH2 87.6261 -0.7390 19.3399 5.5737 19.3541 60

SH3 90.1729 1.8079 23.2428 6.7500 23.3130 MLE 52.6147 -35.7504 2.9150 2.5216 35.8690 CBA 74.3431 -14.0220 9.7416 4.8924 17.0738 JK1 77.8729 -10.4922 5.9103 4.1437 12.0423 JK2 88.6266 0.2615 8.2174 4.9050 8.2216 SH1 90.5191 2.1540 12.0094 6.4691 12.2011 SH2 87.0710 -1.2941 10.1455 5.1799 10.2277 100

SH3 87.5976 -0.7675 11.0568 6.2701 11.0834 MLE 61.1236 -27.2415 2.9581 2.5850 27.4017 CBA 73.5005 -14.8646 5.8362 4.3322 15.9692 JK1 84.3965 -3.9685 5.2204 3.9605 6.5576 JK2 91.2334 2.8683 6.4022 4.4722 7.0154 SH1 90.6802 2.3151 7.7954 5.6710 8.1319 SH2 87.7219 -0.6432 6.6215 4.6727 6.6527 140

SH3 88.1175 -0.2476 7.2583 5.6864 7.2626 MLE 66.0722 -22.2929 2.6512 2.5567 22.4500 CBA 73.6538 -14.7113 4.8076 4.0943 15.4769 JK1 86.2327 -2.1323 4.3474 3.6915 4.8422 JK2 90.2385 1.8734 5.2001 4.0177 5.5272 SH1 90.5965 2.2314 6.9837 4.9614 7.3315 SH2 87.5487 -0.8164 5.6994 4.1910 5.7576 180

SH3 88.4803 0.1152 6.6295 5.1149 6.6305

表 2-1-2 系統演化樹為結構 B，物種相對豐富度為模型二：

S =100, p

i

~random unif, Rep.=200, Bootstrap=200, q=1, True= 74.2715 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 35.6915 -38.5800 2.9273 2.1351 38.6909 CBA 63.6491 -10.6224 15.2042 5.0285 18.5474 JK1 55.6314 -18.6401 6.2933 3.6649 19.6738 JK2 66.3337 -7.9378 9.1697 4.4743 12.1281 SH1 75.4687 1.1972 16.8172 6.2895 16.8597 SH2 70.2344 -4.0371 13.5112 4.8809 14.1014 60

SH3 72.6616 -1.6100 16.3633 5.9611 16.4423

MLE 46.6372 -27.6343 2.9978 2.3888 27.7965 CBA 61.8895 -12.3821 8.3009 4.4203 14.9071 JK1 66.3312 -7.9403 5.6480 3.7509 9.7441 JK2 73.6477 -0.6239 7.4324 4.3064 7.4586 SH1 77.0806 2.8091 10.6142 5.5781 10.9796 SH2 72.2673 -2.0042 8.5819 4.5195 8.8128 100

SH3 73.8615 -0.4100 9.9143 5.5066 9.9227

MLE 53.0213 -21.2503 2.9311 2.4063 21.4515 CBA 62.2560 -12.0155 5.2604 4.1935 13.1166 JK1 70.5020 -3.7696 4.8432 3.5126 6.1373 JK2 75.0591 0.7876 5.6986 3.8544 5.7528 SH1 78.1161 3.8446 7.1858 4.8374 8.1497 SH2 73.2844 -0.9871 5.9056 4.0235 5.9875 140

SH3 75.1522 0.8807 6.9961 4.9229 7.0514

MLE 56.8052 -17.4663 2.5316 2.3663 17.6488 CBA 62.6142 -11.6573 4.5689 4.2143 12.5206 JK1 71.8644 -2.4071 3.8038 3.2559 4.5015 JK2 74.6405 0.3689 4.2575 3.4620 4.2735 SH1 78.3252 4.0537 5.5108 4.2831 6.8411 SH2 73.3151 -0.9564 4.4620 3.6397 4.5633 180

SH3 75.6127 1.3412 5.5255 4.4693 5.6860

表 2-1-3 系統演化樹為結構 B，物種相對豐富度為模型三：

S =100, p

i

~c/(i+10), Rep.=200, Bootstrap=200, q=1, True= 73.1812 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 35.0669 -38.1143 3.3087 2.1566 38.2577 CBA 64.1908 -8.9904 18.7054 5.0215 20.7537 JK1 54.5152 -18.6661 7.0002 3.6705 19.9355 JK2 65.0371 -8.1442 10.1227 4.4632 12.9922 SH1 76.4863 3.3051 20.4230 6.3080 20.6887 SH2 69.3228 -3.8584 15.7269 4.8894 16.1933 60

SH3 73.0071 -0.1741 20.2383 6.0150 20.2391

MLE 44.8669 -28.3143 3.2692 2.4480 28.5024 CBA 62.8057 -10.3755 9.6506 4.3540 14.1698 JK1 63.7630 -9.4182 6.0293 3.7791 11.1828 JK2 71.3758 -1.8054 7.8487 4.3012 8.0536 SH1 79.1225 5.9413 11.7701 5.5523 13.1846 SH2 70.6679 -2.5134 8.9601 4.5315 9.3059 100

SH3 74.3741 1.1928 11.1809 5.5390 11.2443

MLE 51.4035 -21.7778 2.8872 2.5176 21.9683 CBA 62.7237 -10.4575 5.9603 4.0592 12.0368 JK1 68.7365 -4.4447 4.7073 3.6299 6.4741 JK2 73.9931 0.8118 5.5467 3.9649 5.6058 SH1 79.9789 6.7977 7.4211 4.9471 10.0639 SH2 71.8063 -1.3749 5.8025 4.1614 5.9632 140

SH3 74.9758 1.7946 7.3943 5.0740 7.6089

MLE 55.3342 -17.8470 3.0821 2.4827 18.1112 CBA 62.7254 -10.4558 4.5409 4.0137 11.3993 JK1 70.6006 -2.5806 4.5876 3.3938 5.2636 JK2 74.0704 0.8892 5.1255 3.6134 5.2020 SH1 79.1706 5.9894 6.1878 4.4801 8.6117 SH2 71.6771 -1.5041 5.3993 3.8112 5.6049 180

SH3 74.4870 1.3058 6.3912 4.6607 6.5232

表 2-1-4 系統演化樹為結構 B，物種相對豐富度為模型四：

S =100, p

i

~c/(i+2), Rep.=200, Bootstrap=200, q=1, True=55.6104 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 28.5236 -27.0868 3.6952 2.0794 27.3376 CBA 49.6477 -5.9627 14.9558 4.3018 16.1006 JK1 42.1190 -13.4913 6.9077 3.2760 15.1569 JK2 48.9735 -6.6369 9.1515 3.7980 11.3048 SH1 60.2777 4.6673 16.2295 5.1384 16.8872 SH2 50.0421 -5.5683 12.1641 4.0631 13.3781 60

SH3 55.9024 0.2920 15.2907 5.0046 15.2935

MLE 35.3659 -20.2444 3.4713 2.3862 20.5399 CBA 49.3741 -6.2362 7.9571 3.7770 10.1097 JK1 48.4556 -7.1548 5.7050 3.4189 9.1508 JK2 53.7562 -1.8542 6.9602 3.7512 7.2029 SH1 60.4744 4.8640 9.7726 4.7037 10.9162 SH2 50.7910 -4.8194 7.4402 3.8880 8.8647 100

SH3 55.9418 0.3314 9.8733 4.6183 9.8788

MLE 39.7268 -15.8835 3.2802 2.4645 16.2187 CBA 49.1922 -6.4181 5.7673 3.5770 8.6287

JK1 51.7016 -3.9088 5.0083 3.3304 6.3531 JK2 55.6093 -0.0011 5.7930 3.5469 5.7930 SH1 59.7505 4.1401 7.4291 4.3401 8.5048 SH2 51.5975 -4.0129 5.7610 3.6288 7.0209 140

SH3 55.2212 -0.3892 7.1256 4.1925 7.1362

MLE 42.5429 -13.0675 3.3522 2.4526 13.4906 CBA 49.3022 -6.3082 4.8344 3.5190 7.9476

JK1 53.2515 -2.3589 4.6737 3.1728 5.2353 JK2 56.0863 0.4759 5.1452 3.3187 5.1671 SH1 58.9432 3.3328 6.5936 4.0061 7.3881 SH2 52.0644 -3.5460 5.2944 3.3822 6.3722 180

SH3 54.7649 -0.8455 6.1839 3.8219 6.2414

表 2-1-5 系統演化樹為結構 B，物種相對豐富度為模型五：

S =100, p

i

~c/(i+0), Rep.=200, Bootstrap=200, q=1, True=37.6467 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 20.4510 -17.1958 3.7071 1.9645 17.5908 CBA 33.5170 -4.1298 10.9056 3.6121 11.6613 JK1 28.5571 -9.0897 6.1759 2.8113 10.9893 JK2 32.4347 -5.2120 7.6769 3.0989 9.2790 SH1 37.1187 -0.5280 12.0348 3.9439 12.0464 SH2 29.9963 -7.6504 8.5193 3.1842 11.4502 60

SH3 36.7756 -0.8711 13.0359 3.7564 13.0650

MLE 24.6340 -13.0128 3.2370 2.2096 13.4093 CBA 33.6424 -4.0044 6.6042 3.1894 7.7234

JK1 32.4067 -5.2400 4.9520 2.9368 7.2097 JK2 35.5178 -2.1290 5.8263 3.1224 6.2031 SH1 36.2277 -1.4190 6.8854 3.6542 7.0302 SH2 31.0347 -6.6121 5.1995 3.0414 8.4116 100

SH3 37.3522 -0.2945 7.9869 3.3262 7.9924

MLE 27.4820 -10.1647 3.0341 2.2766 10.6079 CBA 34.3420 -3.3047 4.6686 2.9938 5.7199

JK1 34.8104 -2.8364 4.3035 2.9007 5.1541 JK2 37.3513 -0.2954 4.8070 3.0264 4.8160 SH1 36.5717 -1.0751 5.0995 3.3780 5.2116 SH2 32.4527 -5.1940 4.1512 2.8847 6.6491 140

SH3 38.3384 0.6916 5.5520 3.0225 5.5949

MLE 29.2210 -8.4258 3.1927 2.2539 9.0104 CBA 34.0292 -3.6175 4.4130 2.8747 5.7062 JK1 35.8072 -1.8395 4.2699 2.7779 4.6493 JK2 37.6926 0.0458 4.6505 2.8646 4.6508 SH1 36.3489 -1.2978 4.9771 3.1301 5.1435 SH2 33.0932 -4.5535 4.1609 2.7258 6.1683 180

SH3 37.5352 -0.1115 4.8757 2.7875 4.8770

表 2-1-6 系統演化樹為結構 B，物種相對豐富度為模型六：

S =100, p

i

~c/(i-0.5), Rep.=200, Bootstrap=200, q=1, True=25.7654 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 14.7885 -10.9769 3.1546 1.7879 11.4212 CBA 23.4421 -2.3233 7.5686 3.0299 7.9172

JK1 19.8527 -5.9127 4.8682 2.4080 7.6590 JK2 22.2235 -3.5419 5.8088 2.5822 6.8034 SH1 22.7587 -3.0067 7.2752 3.0106 7.8720 SH2 19.1084 -6.6570 5.4082 2.4886 8.5769 60

SH3 25.0588 -0.7065 8.6953 2.7857 8.7240

MLE 17.3434 -8.4220 2.6522 1.9347 8.8297 CBA 23.4090 -2.3564 4.6609 2.6769 5.2227 JK1 22.1683 -3.5971 3.8449 2.4579 5.2652 JK2 24.1103 -1.6551 4.4045 2.5713 4.7052 SH1 22.5031 -3.2623 4.1695 2.7179 5.2941 SH2 20.1123 -5.6531 3.4464 2.3564 6.6208 100

SH3 27.2481 1.4827 6.8358 2.5113 6.9948

MLE 19.0652 -6.7001 2.5784 1.9443 7.1792 CBA 23.6502 -2.1152 4.0660 2.4417 4.5833 JK1 23.5745 -2.1909 3.5520 2.3885 4.1733 JK2 25.1640 -0.6013 3.9699 2.4664 4.0152 SH1 23.0262 -2.7392 3.7042 2.5078 4.6070 SH2 21.1853 -4.5800 3.1686 2.2413 5.5693 140

SH3 28.5239 2.7585 5.5725 2.3387 6.2179

MLE 20.3254 -5.4400 2.5881 1.9058 6.0242 CBA 23.9187 -1.8467 3.5778 2.2906 4.0263 JK1 24.4964 -1.2689 3.3873 2.2805 3.6171 JK2 25.7843 0.0189 3.6896 2.3345 3.6896 SH1 23.5668 -2.1986 3.5128 2.3411 4.1441 SH2 22.0551 -3.7103 3.0753 2.1324 4.8191 180

SH3 28.7877 3.0224 4.6867 2.1997 5.5767

表 2-1-7 系統演化樹為結構 B，物種相對豐富度為模型七：

S =100, p

i

~Broken-Stick, Rep.=200, Bootstrap=200, q=1, True=59.2193 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 30.7958 -28.4235 2.7477 2.0587 28.5560 CBA 51.2691 -7.9502 12.6368 4.6385 14.9296 JK1 45.8546 -13.3648 5.4008 3.3328 14.4148 JK2 53.1907 -6.0286 7.3953 3.9129 9.5412 SH1 62.9651 3.7458 14.3242 5.3696 14.8058 SH2 55.0366 -4.1827 10.1858 4.1985 11.0111 60

SH3 59.2290 0.0097 14.0107 5.1909 14.0107

MLE 38.1442 -21.0751 3.0103 2.2446 21.2890 CBA 49.4965 -9.7228 6.5333 4.1453 11.7140 JK1 51.9004 -7.3189 5.0717 3.2885 8.9044 JK2 56.7087 -2.5106 6.1916 3.6340 6.6812 SH1 62.8649 3.6456 8.3902 4.6493 9.1480 SH2 55.2608 -3.9585 6.7978 3.8162 7.8664 100

SH3 58.5101 -0.7092 8.3553 4.6713 8.3853

MLE 42.7712 -16.4481 2.9466 2.2673 16.7099 CBA 50.7368 -8.4825 5.0452 4.0588 9.8695

JK1 55.0224 -4.1969 4.4576 3.1066 6.1225 JK2 58.3758 -0.8435 5.0975 3.3164 5.1668 SH1 63.9939 4.7746 6.8580 4.1672 8.3564 SH2 56.5904 -2.6289 5.4289 3.4850 6.0319 140

SH3 59.8332 0.6139 6.7972 4.2414 6.8249

MLE 45.4067 -13.8126 2.7315 2.2631 14.0801 CBA 51.3795 -7.8398 3.9580 3.9654 8.7823

JK1 56.1835 -3.0358 3.7908 2.9509 4.8566 JK2 58.6339 -0.5854 4.1382 3.0837 4.1794 SH1 63.8144 4.5951 5.6533 3.8378 7.2852 SH2 56.8064 -2.4129 4.5398 3.2352 5.1412 180

SH3 59.8278 0.6085 5.8103 3.8962 5.8420

表 2-2-1 系統演化樹為結構 B，物種相對豐富度為模型一：

S =100, p

i

~1/S , Rep.=200, Bootstrap=200, q=2, True=83.5129 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 35.3046 -48.2083 3.1507 2.4317 48.3111 CBA 63.8353 -19.6777 15.0980 3.8198 24.8024 JK1 55.1340 -28.3789 6.8110 4.2848 29.1848 JK2 66.3472 -17.1657 9.9488 5.3405 19.8404 SH1 88.8368 5.3239 20.4186 6.0688 21.1012 SH2 79.9139 -3.5991 16.1812 5.4739 16.5766 60

SH3 74.2987 -9.2142 15.0929 5.7669 17.6832

MLE 46.0483 -37.4646 3.0406 2.7614 37.5878 CBA 59.5595 -23.9534 6.8057 3.5754 24.9015 JK1 66.4055 -17.1075 5.8181 4.5359 18.0698 JK2 75.5084 -8.0045 7.7033 5.3895 11.1091 SH1 87.7980 4.2851 10.7289 5.6722 11.5530 SH2 81.3099 -2.2031 9.1438 5.5780 9.4055 100

SH3 76.6124 -6.9005 9.0685 6.0334 11.3954

MLE 52.9911 -30.5218 3.1754 2.8735 30.6865 CBA 60.0332 -23.4797 4.4955 3.3441 23.9062 JK1 72.3134 -11.1995 5.5608 4.4747 12.5040 JK2 79.4790 -4.0339 6.9005 5.1445 7.9931 SH1 87.9516 4.4386 6.8998 5.2082 8.2042 SH2 82.2758 -1.2372 6.6045 5.3370 6.7194 140

SH3 78.4696 -5.0433 7.0849 5.8977 8.6966

MLE 57.1967 -26.3162 2.8174 2.8469 26.4666 CBA 61.1405 -22.3725 3.5982 3.1213 22.6600 JK1 74.7379 -8.7750 4.5841 4.2338 9.9002 JK2 80.2346 -3.2783 5.4148 4.7421 6.3299 SH1 87.6675 4.1546 6.0680 4.7811 7.3540 SH2 81.8622 -1.6508 5.3453 4.9072 5.5944 180

SH3 79.6390 -3.8739 6.0259 5.5278 7.1637

表 2-2-2 系統演化樹為結構 B，物種相對豐富度為模型二：

S =100, p

i

~random unif, Rep.=200, Bootstrap=200, q=2, True=65.3754 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 31.9094 -33.4660 2.9013 2.3434 33.5916 CBA 50.4474 -14.9281 11.1582 3.3814 18.6374 JK1 47.9842 -17.3912 5.9869 4.0222 18.3928 JK2 56.1474 -9.2280 8.4086 4.9222 12.4844 SH1 73.4131 8.0376 16.2241 5.3975 18.1059 SH2 64.4306 -0.9449 12.1530 4.9621 12.1896 60

SH3 60.9480 -4.4274 11.7643 5.2688 12.5698

MLE 39.8990 -25.4764 3.2303 2.6423 25.6804 CBA 48.6060 -16.7694 5.6514 3.1989 17.6961 JK1 55.0623 -10.3131 5.8078 4.1801 11.8360 JK2 60.9012 -4.4742 7.3380 4.8500 8.5945 SH1 74.4149 9.0395 8.7761 5.1241 12.5989 SH2 65.2377 -0.1377 8.1270 5.0140 8.1282 100

SH3 62.9113 -2.4642 8.6344 5.4340 8.9792

MLE 45.2949 -20.0806 3.1212 2.6865 20.3217 CBA 49.8528 -15.5227 4.0566 2.9913 16.0440 JK1 59.3147 -6.0607 5.1158 4.0202 7.9312 JK2 63.7332 -1.6422 6.0667 4.5168 6.2851 SH1 74.5185 9.1431 6.6132 4.7341 11.2841 SH2 66.2706 0.8951 6.3464 4.6709 6.4092 140

SH3 64.7366 -0.6389 6.9481 5.1898 6.9774

MLE 48.0098 -17.3656 2.7212 2.6385 17.5775 CBA 50.6611 -14.7143 3.0830 2.8056 15.0338 JK1 60.2754 -5.1001 4.1731 3.7649 6.5898 JK2 63.4765 -1.8989 4.7517 4.1263 5.1171 SH1 73.6438 8.2684 4.8498 4.3746 9.5857 SH2 65.1624 -0.2130 4.9930 4.2288 4.9976 180

SH3 64.8691 -0.5063 5.4205 4.8045 5.4441

表 2-2-3 系統演化樹為結構 B，物種相對豐富度為模型三：

S =100, p

i

~c/(i+10), Rep.=200, Bootstrap=200, q=2, True=59.3195 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 30.5902 -28.7293 3.6679 2.3823 28.9625 CBA 47.9204 -11.3991 12.4341 3.3772 16.8686 JK1 45.3816 -13.9379 7.4110 4.0452 15.7857 JK2 52.6038 -6.7157 10.2623 4.9170 12.2644 SH1 71.6266 12.3071 17.0550 5.4154 21.0319 SH2 60.8743 1.5548 13.9365 5.0022 14.0229 60

SH3 57.6202 -1.6993 14.0705 5.3455 14.1728

MLE 37.6432 -21.6763 3.4702 2.7346 21.9523 CBA 45.9119 -13.4076 6.0657 3.2522 14.7159 JK1 51.0912 -8.2283 6.0883 4.2676 10.2359 JK2 55.9305 -3.3891 7.5608 4.9116 8.2856 SH1 72.3544 13.0349 9.8149 5.2710 16.3169 SH2 60.0416 0.7221 8.7037 5.1063 8.7336 100

SH3 58.3832 -0.9363 9.1563 5.5483 9.2040

MLE 42.3498 -16.9697 3.1984 2.8609 17.2684 CBA 46.9373 -12.3822 4.0435 3.1568 13.0257 JK1 54.5224 -4.7971 5.1503 4.2179 7.0383 JK2 58.0441 -1.2755 6.0398 4.7001 6.1730 SH1 72.2112 12.8917 6.6371 5.1539 14.4999 SH2 60.4794 1.1599 6.5530 4.8538 6.6548 140

SH3 59.1262 -0.1933 7.2067 5.4096 7.2093

MLE 45.1593 -14.1602 3.4513 2.8476 14.5747 CBA 47.8310 -11.4885 4.0060 3.0317 12.1669 JK1 55.9542 -3.3653 5.1921 4.0115 6.1874 JK2 58.5596 -0.7599 5.8501 4.3685 5.8993 SH1 70.8102 11.4907 6.6181 4.9110 13.2603 SH2 60.1058 0.7863 6.1433 4.4605 6.1935 180

SH3 59.2156 -0.1039 7.0000 5.0800 7.0007

表 2-2-4 系統演化樹為結構 B，物種相對豐富度為模型四：

S =100, p

i

~c/(i+2), Rep.=200, Bootstrap=200, q=2, True=34.5589 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 22.9710 -11.5879 4.0975 2.3268 12.2910 CBA 30.9366 -3.6223 8.9446 2.8917 9.6502

JK1 31.0250 -3.5340 7.2768 3.6803 8.0895 JK2 33.8318 -0.7271 9.1050 4.2752 9.1340 SH1 49.3632 14.8042 14.3872 4.7656 20.6435 SH2 37.7867 3.2278 11.1840 4.3838 11.6405 60

SH3 36.7748 2.2159 11.1189 4.6363 11.3375

MLE 26.3103 -8.2487 3.8350 2.6852 9.0966 CBA 29.7327 -4.8262 5.1394 2.9690 7.0502 JK1 32.5297 -2.0292 5.8668 3.8479 6.2078 JK2 33.9453 -0.6137 6.6492 4.2220 6.6774 SH1 45.0505 10.4915 9.5432 5.0746 14.1825 SH2 35.7143 1.1553 7.0723 4.3423 7.1660 100

SH3 34.9442 0.3853 7.2976 4.5622 7.3078

MLE 28.4500 -6.1090 3.4024 2.7638 6.9926 CBA 30.3334 -4.2255 3.9786 2.9266 5.8038 JK1 33.6112 -0.9478 4.7994 3.7283 4.8920 JK2 34.5008 -0.0582 5.2113 3.9756 5.2116 SH1 42.9822 8.4233 7.1414 4.8867 11.0432 SH2 35.6149 1.0559 5.3807 4.0341 5.4833 140

SH3 34.7299 0.1710 5.4323 4.1993 5.4350

MLE 29.7323 -4.8266 3.7358 2.7493 6.1035 CBA 30.8951 -3.6638 4.0796 2.8529 5.4833 JK1 34.1239 -0.4351 4.9855 3.5521 5.0044 JK2 34.7411 0.1822 5.2855 3.7239 5.2886 SH1 41.5391 6.9802 6.8784 4.5423 9.7998 SH2 35.5509 0.9919 5.3725 3.7526 5.4633 180

SH3 34.6948 0.1359 5.4046 3.8847 5.4063

表 2-2-5 系統演化樹為結構 B，物種相對豐富度為模型五：

S =100, p

i

~c/(i+0), Rep.=200, Bootstrap=200, q=2, True=16.3018 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 13.7550 -2.5469 3.6248 2.1205 4.4301 CBA 15.8266 -0.4752 5.2851 2.3592 5.3064 JK1 16.1987 -0.1031 5.3060 2.9805 5.3070 JK2 16.5220 0.2201 5.8375 3.2379 5.8417 SH1 22.7972 6.4954 9.4041 4.0100 11.4293 SH2 18.0488 1.7469 6.4225 3.3490 6.6558 60

SH3 18.0305 1.7287 6.6158 3.3778 6.8380

MLE 14.6083 -1.6935 2.7012 2.2431 3.1882 CBA 15.4348 -0.8670 3.0555 2.3526 3.1761 JK1 16.1147 -0.1872 3.4275 2.8388 3.4326 JK2 16.1914 -0.1104 3.5378 2.9441 3.5395 SH1 19.7517 3.4498 4.8253 3.7200 5.9317 SH2 17.0534 0.7515 3.7028 3.0166 3.7783 100

SH3 17.0074 0.7056 3.5396 2.9196 3.6092

MLE 15.2181 -1.0837 2.4375 2.1800 2.6676 CBA 15.6996 -0.6022 2.5997 2.2418 2.6685 JK1 16.3563 0.0545 2.9292 2.6127 2.9297 JK2 16.3925 0.0907 2.9830 2.6667 2.9843 SH1 18.9503 2.6484 3.7815 3.2576 4.6167 SH2 17.0122 0.7104 3.0789 2.7186 3.1598 140

SH3 16.9462 0.6444 2.8892 2.6102 2.9601

MLE 15.5363 -0.7656 2.6660 2.0915 2.7737 CBA 15.8316 -0.4702 2.7807 2.1308 2.8202 JK1 16.4533 0.1515 3.0940 2.4226 3.0977 JK2 16.4753 0.1735 3.1309 2.4544 3.1357 SH1 18.4776 2.1757 3.7797 2.9061 4.3612 SH2 16.9613 0.6595 3.2011 2.4932 3.2683 180

SH3 16.8201 0.5183 3.0452 2.3989 3.0890

表 2-2-6 系統演化樹為結構 B，物種相對豐富度為模型六：

S=100, p

i

~c/(i-0.5), Rep.=200, Bootstrap=200, q=2, True=8.7313 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 8.3165 -0.4149 2.4813 1.6887 2.5158 CBA 8.9135 0.1821 3.0018 1.7905 3.0074

JK1 8.9096 0.1783 3.1340 2.1297 3.1390 JK2 8.8738 0.1425 3.2286 2.2012 3.2318 SH1 11.1701 2.4388 4.7698 2.8377 5.3571 SH2 9.6625 0.9312 3.5333 2.3115 3.6540 60

SH3 10.1265 1.3952 3.6240 2.2250 3.8832

MLE 8.3756 -0.3558 1.5440 1.5650 1.5845 CBA 8.6074 -0.1239 1.6369 1.6051 1.6416 JK1 8.6557 -0.0756 1.7172 1.7854 1.7189 JK2 8.6281 -0.1032 1.7132 1.7954 1.7163 SH1 9.8358 1.1045 2.1411 2.1973 2.4092 SH2 9.0806 0.3493 1.8283 1.8741 1.8613 100

SH3 9.6903 0.9590 1.9071 1.7797 2.1346

MLE 8.5464 -0.1849 1.4132 1.4234 1.4253 CBA 8.6821 -0.0492 1.4665 1.4449 1.4673 JK1 8.7445 0.0132 1.5271 1.5619 1.5271 JK2 8.7288 -0.0025 1.5243 1.5643 1.5243 SH1 9.5883 0.8570 1.7975 1.8267 1.9914 SH2 9.0542 0.3229 1.5983 1.6196 1.6306 140

SH3 9.5560 0.8247 1.5816 1.5484 1.7837

MLE 8.7350 0.0036 1.4978 1.3225 1.4978 CBA 8.8247 0.0933 1.5346 1.3357 1.5375 JK1 8.8964 0.1651 1.5986 1.4226 1.6071 JK2 8.8864 0.1551 1.5973 1.4236 1.6048 SH1 9.5698 0.8385 1.8177 1.6124 2.0018 SH2 9.1439 0.4126 1.6529 1.4639 1.7036 180

SH3 9.5850 0.8537 1.6336 1.4084 1.8432

表 2-2-7 系統演化樹為結構 B，物種相對豐富度為模型七：

S =100, p

i

~Broken-Stick , Rep.=200, Bootstrap=200, q=2, True = 48.7429 n 方法 Estimate Bias Sample

s.e.

Estimated

s.e RMSE MLE 27.3629 -21.3800 3.4726 2.2886 21.6602 CBA 38.6628 -10.0801 8.8080 3.0259 13.3862 JK1 39.0284 -9.7145 6.6103 3.7723 11.7502 JK2 44.0416 -4.7014 8.6978 4.4944 9.8871 SH1 59.5860 10.8431 13.1854 4.8728 17.0712 SH2 49.5182 0.7753 10.8633 4.5502 10.8909 60

SH3 47.2866 -1.4563 10.5044 4.8146 10.6048

MLE 33.7169 -15.0261 3.4596 2.5433 15.4192 CBA 38.9811 -9.7619 5.2086 2.9165 11.0645 JK1 44.3881 -4.3548 5.7822 3.8589 7.2386 JK2 47.7998 -0.9432 6.9364 4.3686 7.0002 SH1 60.5635 11.8205 8.7009 4.7545 14.6776 SH2 50.5836 1.8407 7.6483 4.5115 7.8666 100

SH3 49.0974 0.3544 7.7928 4.8731 7.8008

MLE 36.5932 -12.1497 3.4810 2.5850 12.6385 CBA 39.3652 -9.3777 4.2603 2.7764 10.3001 JK1 45.5751 -3.1679 5.2874 3.6782 6.1638 JK2 47.8090 -0.9339 5.9827 4.0246 6.0552 SH1 58.7204 9.9775 7.3211 4.5177 12.3753 SH2 49.4010 0.6581 6.3093 4.1184 6.3436 140

SH3 48.6440 -0.0990 7.0166 4.5370 7.0173

MLE 38.6937 -10.0492 3.2446 2.5981 10.5600 CBA 40.3669 -8.3761 3.5655 2.7136 9.1034

JK1 46.5040 -2.2390 4.6429 3.5349 5.1546 JK2 48.1034 -0.6396 5.0929 3.7879 5.1329 SH1 57.5235 8.7805 5.9598 4.3443 10.6121 SH2 49.1355 0.3926 5.2351 3.8397 5.2498 180

SH3 48.6531 -0.0899 5.9135 4.2654 5.9142

附表三 以實際資料為母體模型的模擬結果

表 3-1 後龍溪溪口鳥類資料:

S =150, CV=1.483, Rep.=200, Bootstrap=200, q=1, True=24.2078

方法 Estimate Bias Sample

在文檔中 系統演化多樣性指標之建立與統計估計 (頁 125-156)