46 
Fishery Bulletin 107(1 ) 
Figure 1 
Location of the 18 sites on the west coast of Vancouver Island where Chinook salmon (Oncorhynchus 
tshawytsclxa ) populations were sampled. Numbers correspond to stock codes in Table 1. The same 
population was sampled for Somas River (12A) and Robertson Hatchery (12B). Shapes around loca- 
tion numbers denote an genetic affiliation with one of the four regional groups: Quatsino Sound 
(diamonds), Nootka Sound (squares), Clayoquot+Barkley aounds (circles), and southwest Vancouver 
Island (triangles). 
into smaller ones (divisive). A number of algorithms 
are available to decide which small clusters are 
merged or which larger clusters are split (e.g., Swof- 
ford et al., 1996; Jain et al., 1999). Groupings can be 
depicted as a branching tree or dendrogram where 
branch length is scaled to represent genetic distance. 
A drawback with the hierarchical approach is that 
the result is sensitive to initial groupings, which 
are not permitted to change once an assignment has 
been made. Furthermore, arbitrary tie-breaking ac- 
tions, either in the original proximity data or dur- 
ing agglomeration, can cause instability in the tree 
structure (van der Kloot et al., 2005). Consensus from 
multiple tree constructions by bootstrapping across 
loci provides a measure of robustness of the appar- 
ent dominant tree structure (Felsenstein, 1985). A 
majority-rule consensus tree can provide a phylogeny 
with groups that occur in a majority of the bootstrap 
samples. However, the incorporation of variation from 
consensus trees appears to have limited quantitative 
application, and the optimum cluster number is not 
obvious. 
This article provides a new method for partitioning 
genetic distance data by finding the optimal group 
membership and number of groupings. We validate 
the method using simulated data. To demonstrate the 
utility of this partition method, we applied it to genetic 
distance data calculated from samples taken from 18 
Chinook salmon populations along the west coast of 
Vancouver Island, British Columbia (Fig. 1). The group- 
ings determined by this method were evaluated with 
respect to known transfers of broodstock and histo- 
ries of stock enhancement. Furthermore, results from 
both the simulated and Chinook salmon data sets were 
compared to results from a commonly used clustering 
method for genetic data. 
Materials and methods 
Pairwise cost function 
A pairwise cost function used in the field of pattern rec- 
ognition (Roth et al. 2003) minimizes the sum of mean 
intracluster distances. Minimized intracluster distance 
appears most desirable in grouping populations where 
two or more populations assigned to the same group 
contribute to total cost. Other clustering algorithms 
have been proposed which emphasize separation, com- 
binations of compactness and separation, or conductivity 
measures (Buhmann, 2002). 
Given row ( i ) and column (j) indices of an (nxn) dis- 
similarity matrix D of populations with k groups, the 
pairwise cost function ( CF ) is 
