48 
Fishery Bulletin 107(1) 
PI P2 P3 P4 
P6 
P5 P7 
B 
0 
iF-ih 
0.2 
0.4 
PI 
P 2 
P 3 
P 4 
P 5 
P 6 
P 7 
P 8 
P 9 
P 10 
pi 
0 
0.03 
0.06 
0.11 
0.29 
0.31 
0.33 
0.50 
0.53 
0.64 
P 2 
0.03 
0 
0.03 
0.08 
0.27 
0.28 
0.30 
0.48 
0.51 
0.62 
P 3 
0.06 
0.03 
0 
0.05 
0.23 
0.24 
0.27 
0.44 
0.47 
0.58 
P 4 
0.11 
0.08 
0.05 
0 
0.18 
0.20 
0.22 
0.40 
0.43 
0.53 
P 5 
0.29 
0.27 
0.23 
0.18 
0 
0.01 
0.04 
0.21 
0.24 
0.35 
P 6 
0.31 
0.28 
0.24 
0.20 
0.01 
0 
0.02 
0.20 
0.23 
0.34 
P 7 
0.33 
0.30 
0.27 
0.22 
0.04 
0.02 
0 
0.18 
0.21 
0.31 
P 8 
0.50 
0.48 
0.44 
0.40 
0.21 
0.20 
0.18 
0 
0.03 
0.14 
P 9 
0.53 
0.51 
0.47 
0.43 
0.24 
0.23 
0.21 
0.03 
0 
0.11 
P 10 
0.64 
0.62 
0.58 
0.53 
0.35 
0.34 
0.31 
0.14 
0.11 
0 
P8 P9 P10 
~r— •- 
0.6 
0.8 
D 
E 
Partitions of simulated genetic distance data. (A) Populations P1-P10 are located randomly along a line 
from zero to one; (B) simulated proximity data were generated by using line distance between populations 
P1-P10; (C) results of the partitioning optimization using restricted growth strings (PORGS) analysis of 
simulated data, showing hierarchical group membership for k groupings and corresponding minimized cost 
function (CF) values; black, gray, and white represent status of the populations for a given cluster number. 
Black and white represent populations involved in partitions for a particular value of k, whereas gray 
populations were not involved; (D) expected CF values from the reference distribution and observed values 
plotted against number of groups k for the simulated data; and (E) the gap statistic plotted against number 
of groups, showing k = 3 as the optimum number of groups with the simulated data for 10 populations. 
optimal partitions and group membership obtained from 
the model. 
To simulate genetic distance data, ten populations 
were assumed to be randomly located along a horizontal 
line, where i = 1 to 10 for a population P(i) selected at 
random (Fig. 2A). 
0<P(i)<l. (6) 
A proximity matrix of i rows and j columns of simulated 
data was constructed from the distances cl between two 
populations (Fig. 2B) such that the values of each matrix 
element were 
d(ij)=\P(i) — P(J)\. (7) 
Using the PORGS method, we partitioned the proxim- 
ity matrix into optimal group membership for k - 1 to 
n groups by minimizing the cost function (Eq. 1; Fig. 
2C). Ten bootstrapped variants of the proximity matrix 
were treated similarly, and the mean of the bootstrapped 
values provided a reference distribution to compare with 
