160 
Fishery Bulletin 99(1 ) 
Table 2 
The conditional maximum likelihood point estimate for harbor porpoise population proportions composing the winter stock mix- 
ture, and its bootstrap standard error and 95% confidence bounds (nonsymmetric percentile method). Reported proportions do not 
necessarily sum to 1.0 because they are rounded. 
95% Confidence bounds 
Point 
Population 
estimate 
SE' 
Lower 
Upper 
Gulf of Maine-Bay of Fundy 
0.19 
0.14 
0.00 
0.37 
Gulf of St. Lawrence 
0.40 
0.16 
0.13 
0.77 
Newfoundland 
0.18 
0.15 
0.00 
0.35 
West Greenland 
0.24 
0.15 
0.00 
0.48 
1 These standard errors are reduced by 30% to 50% from those reported by Rosel et al. (1999). At our earlier recommendation, the authors pooled 
subsets of haplotypes without a well-grounded basis in order to avoid the small counts of individual haplotypes used here. The point estimate is 
unchanged, but the confidence intervals differ mainly because a new method was used in their computation. 
bounds were computed with an update of the program, 
spam 3.2 (Debevec et al., in press), available on the inter- 
net at http : / / www.cf.adfg.state.ak.us / geninfo / research / 
genetics / Software / SpamPage. htm . 
Both the pseudo-Bayes and conditional maximum likeli- 
hood methods are in agreement on the population compo- 
sition of the winter sample in five respects (Tables 1 and 
2). First, any of the populations could be involved in the 
stock mixture and comprise much (upper posterior bounds 
range from 0.46 to 0.84, and upper confidence bounds, 
from 0.35 to 0.77) of it. Second, the contributions by any 
of the populations are very imprecisely determined from 
the mtDNA counts (widths of all interval estimates exceed 
0.35, and standard deviations or standard errors range 
from 0.13 to 0.19). Third, more than one population seems 
to be present, given that none of the interval estimates in- 
cludes 1.0. Fourth, the most frequent estimates, or modes, 
of the Bayes posterior imply that the mix is almost entire- 
ly composed of the Gulf of St. Lawrence and West Green- 
land populations (Fig. 2). Fifth, and last, the Gulf of St. 
Lawrence population was almost certainly present (lower 
95% posterior bound for the proportion, 0.14; correspond- 
ing lower 95% confidence bound, 0.13). 
The claim that the Gulf of St. Lawrence population was 
wintering along the mid-Atlantic coast is important to the 
conservation issue. Is its presence conspicuous to a direct 
examination of the genetic samples? The answer is yes 
if one knows where to look. The Bayes method actually 
identifies the stock origins of the stock-mixture individu- 
als during generation of each sample from the posterior 
distribution, and so the posterior identity distribution — 
the relative frequency of assignment to each population — 
for each stock-mixture individual is available. The identi- 
ty distributions of mixture individuals showed 4 of the 33 
(12%) winter porpoise were more likely than not (posterior 
probabilities-0.60, 0.64, 0.67, 0.72) to be from the Gulf of 
St. Lawrence, and 4 more were more certainly (posterior 
probabilities=0.87, 0.88, 0.88, and 0.89) from that popula- 
tion. Corresponding probabilities (Eq. 5, Pella and Milner, 
1987) from the CML method for the first (0.62, 0.69, 0.70, 
0.81) and second groups (1, 1, 1, 1) agreed reasonably. The 
summer samples contained the following numbers of the 
same 8 haplotypes: Gulf of Maine-Bay of Fundy, 2 of 80 
(3%); Gulf of St. Lawrence, 14 of 40 (35%); Newfoundland, 
4 of 42 (10%); and West Greenland, 6 of 50 (12%). Except 
for the Gulf of St. Lawrence population, in which these 
haplotypes were fairly common, their observed RFs in the 
other populations were half or less of that (24%) in the 
winter sample. With the observed haplotype RFs assumed 
to be accurate, the probability is less than 0.05 that 8 of 
33 individuals with the haplotypes came from any popu- 
lation other than Gulf of St. Lawrence. The conjunction 
of necessary sampling errors — higher frequencies of the 
8 haplotypes in the other populations or lower frequency 
in the stock mixture — without the presence of Gulf of St. 
Lawrence is deemed highly improbable from the Bayes 
computations. Without the posterior probabilities of stock 
identities, a search for direct evidence of the presence of 
particular populations in the winter sample would have 
been futile. 
A total of 25 sets of simulated baseline and stock-mix- 
ture samples of harbor porpoise mtDNA haplotypes was 
generated for each of four experiments. Sizes of the sim- 
ulated samples equaled those of the actual data. The ex- 
perimental conditions that were controlled include the pro- 
portions from the four populations in the stock mixtures 
and their haplotype RFs. In three of the experiments, the 
Gulf of St. Lawrence population comprised 0.95 of the stock 
mixture, and the other stocks comprised equal thirds of 
the remaining 0.05. In the fourth experiment, the four pop- 
ulations contributed equal parts (0.25) to the stock mix- 
ture. The haplotypes of the samples were drawn with re- 
placement from either the original baseline samples (0% 
addition) or augmented baseline samples for which half 
(50% addition) or all (100% addition) of the missing hap- 
lotypes were replaced by singletons. The conditional maxi- 
mum likelihood method was applied to each set of simu- 
lated samples just as it had to the actual samples. The 
Bayes method was similarly applied, but with a single ex- 
ception — a long fixed sequence of 5000 samples (first 2500 
discarded as burn-in) was generated for all sets to reduce 
processing labor. Average point estimates among the 25 
