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Fishery Bulletin 107(1) 
tidimensional scaling); therefore, the underlying struc- 
ture of the distance data remains intact, and resultant 
clusters can be compared between sets of populations. 
Successive increases in cluster numbers automatically 
lead to a hierarchical representation of the group struc- 
ture. The gap statistic determines optimal number of 
groupings. In this example, k = A was the first optimum 
number of groupings for Chinook salmon populations 
from the west coast of Vancouver Island. Except for 
populations impacted by straying fish and transferred 
fish, these groupings correspond to four geographic ar- 
eas: Quatsino Sound, Nootka Sound, Clayoquot+Barkley 
sounds, and southwest Vancouver Island. Similar group- 
ings were identified by agglomerative clustering seen in 
the UPGMA tree. 
It was determined that random set partitions do not 
prevent visits to the same group memberships; therefore 
redundancy in cost function evaluations wastes process- 
ing time. Random search proves ineffective, except for 
very small n, because the prohibitively large number of 
iterations requires an unreasonable amount of time to 
find an optimal solution. However, an exhaustive search 
of the data space provided by a simple random search or a 
pass-through of all set partitions ensures that a globally 
optimized solution is found. By a globally optimal solu- 
tion, we mean that no smaller cost function evaluations 
are possible for each k from a particular data set. Depend- 
ing on available computational speed and the number of 
populations, PORGS can require an unreasonable amount 
of time. An alternative approach reduces the search by 
sequentially splitting into groups (bi-PORGS method) and 
evaluating subgrouping combinations to minimize the 
cost function. But like other hierarchical clustering meth- 
ods, the nested search approach (bi-PORGS) means that 
prior cluster groups cannot be undone; therefore finding 
the optimal values may not always be possible. However, 
for the simulated data, PORGS and bi-PORGS methods 
produced the same results, indicating a globally optimal 
solution is possible with the nested search. The faster 
search method with bi-PORGS may forgo the guarantee 
of an optimal solution, but it can tackle larger problems, 
with the limitation being the number of populations in 
the first bipartition. 
For large, coastwide data sets, a nested search re- 
quires bipartitioning a large number of populations 
simultaneously. Sparse data sets or optimization heuris- 
tics, such as thouse derived from deterministic anneal- 
ing and mean field approximation, may be necessary 
when an exhaustive search is not possible (Puzicha et 
ah, 1999). However, regional groupings could be recog- 
nized where each region could be run independently. 
This “divide and conquer” method requires that the 
subproblems be naturally disjoint, and that divisions be 
appropriate and of manageable size (Kirkpatrick et al., 
1983). Ultimately, given the same set of genetic markers 
and distance measures, researchers will have a means 
of establishing groupings of varying size but represent- 
ing similar levels of intracluster genetic variation. 
Analysis of coded-wire tag data has indicated that 
straying Chinook salmon occur at a higher frequency 
between nearby spawning sites (e.g., Quinn, 1993; Can- 
dy and Beacham, 2000). Consequently, geographic dis- 
tance between populations may be a good approximator 
of gene flow in salmon species; however, inferring barri- 
ers to migration on the basis of geographical or physi- 
cal features alone can be misleading (Waples, 1991). 
The Gold River Chinook salmon population stands out 
by not conforming to the general rule of concordant ge- 
netic and geographic distance. According to geographic 
distance alone, Gold River Chinook salmon should be 
most genetically similar to Burman River Chinook 
salmon because less than 10 km separate the mouths 
of the two river systems. However, cluster analysis indi- 
cates that Gold River fish are most genetically similar 
to Barkley Sound fish, 125 km to the south (Fig. 1). 
Because the nearby Burman River population remains 
clustered with the Nootka Sound group, straying Bark- 
ley Sound fish must be extremely precise; apparently 
remaining in the Gold River only to spawn. 
A number of factors could contribute to this restricted 
straying between Barkley Sound and the Gold River. 
Olfactory imprinting on waters near natal streams dur- 
ing out-migration is known to be important for success- 
ful homeward navigation (Harden Jones, 1968; Quinn, 
1984). Consequently, the presence of pulp mills at the 
heads of both Muchalat (Gold River) and Alberni (So- 
mas River) Inlets, and their effects on water chemistry, 
may increase straying between these two systems. Both 
systems lie at the head of long inlets, where the Gold 
and Somas Rivers have similar inlet and stream ori- 
entation. Also, both are lake-headed systems, possibly 
resulting in similarly modified river temperatures and 
flow regimes. Finally, approach to natal stream may be 
important for determining stray patterns. During the 
return migration to spawn, Barkley Sound, Chinook 
salmon heading south must first pass Nootka Sound, 
which provides an opportunity for these fish to eventu- 
ally stray into the Gold River. The Gold River tissue 
samples collected in the early to mid-1980s, along with 
recent recoveries of thermally marked Robertson Hatch- 
ery fish in the Gold River, indicate that straying into 
the Gold River has likely occurred for quite a number 
of years. 
Populations receiving transfers (Toquart, Thornton, 
and Sooke Rivers; Table 2) remain grouped to their re- 
spective donor stocks rather than to nearby populations, 
indicating that transfer history also plays an important 
role in establishing regional stock structure. The initial 
transfer of Robertson Creek fish to the Toquart River 
is not apparent from the bi-PORGS analysis, where 
Toquart River grouped with the second transfer source, 
Nitinat River. If native stocks existed in Toquart and 
Sooke Rivers before transfers into these systems, their 
continued existence there is not evident from the pres- 
ent study. However, populations with mixed ancestry 
may be better analyzed with individual-based cluster- 
ing methods (Pritchard et al., 2000; Corander et al., 
2003). The remaining two southwest Vancouver Island 
populations, where no transfers have occurred, remain 
quite distinctive. 
