累加性親屬係數距離分組法與加總法選留"代表性"種畜群

黃鈺嘉 林德育 張秀鑾

行政院農業委員會畜產試驗所

為保有畜群的遺傳變異，本試驗提出兩種選擇種畜的方法，方法一為利用距離分組的方法將(1-累加性親屬係數)視為距離，再利用彼此間最短距離進行分群(如single linkage 法)，最後再由各子群抽出代表，將此抽出的集合視為"代表性"種畜群。方法二為利用組合的方法，取出 C(N, n )組種畜群，N 為全部畜群數，n 為擬選留的"代表"個數，再加總兩兩間共 0.5n(n-1) 個累加性親屬係數(A 為上三角與對角線為0的矩陣，a..為所其有元素aij 加總)，即選出最小的a..，此組內的成員即視為選留的"代表"。方法一主要的困擾為子群內個體的選擇，方法二則需面臨一個以上的可代表群的選擇(a..相同，最小值不唯一)。雖然利用分生的遺傳多態性分組，如血型或是DNA指紋等，也可作為個體間分組選留"代表性"畜群的方法。然而採血、分生分析等工作需要相當的人力與物力。從機率的關點，分生的分組方法只是在一個子集合下(能被度量的性狀)的分組法之一，且亦需面臨所提方法一中所面臨的問題。本試驗『累加性親屬係數距離分組法與加總法選留"代表性"種畜群』提供了較經濟的選留方法，可用於有限資源下，種畜群留種的參考。

關鍵語：累加性親屬係數、分群、距離。

SELECT POPULATION REPRESENTATIVES BY MINIMIZING THE SUMMATION
OR CLUSTERING THE ADDITIVE RELATIONSHIP COEFFICIENTS

Y. C. Huang, D. Y. Lin, and H. L. Chang

Taiwan Livestock Research Institute, Council of Agriculture

In order to keep the population genetic variation, two methods are proposed to select representative breeding stocks in this study. Method I, distance matrix D=(1-A), where element dij=(1-aij), a function of additive relationship coefficient, aij , is used as distance between two individuals. With linkage methods can cluster animals into n groups, where n is the upper limit of number of selected animals. Each cluster chooses an animal to form the representative set. Method II is to minimize the summation of the additive relationship coefficients of the selected animals. C(N, n) combination sets need be computed for the minimization, and N is the number of candidates. In each set, there is 0.5n(n-1) elements from the lower triangular of matrix A for summation. Individuals in the set with minimum a.. , summation all lower triangular elements, will be the selected representatives. In method I, the main puzzle is how to choose representative for each cluster, and dilemma of the method II is the minimization might not be unique. Although biotechnology such as blood typing or DNA finger prints data can be used to select representatives, the puzzle of method I existed also and need cost for sampling and lab works. Comparing with the molecular methods, the methods proposed in this study are less expensive.

Key Words: Additive relationship coefficient, Cluster, Distance.