20 
Fishery Bulletin 106(1 ) 
1.0 
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female male 
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female male 
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female male both 
Sex transition younger 
female male both 
Sex transition older 
female male both 
Fecundity lower 
female male both 
Fecundity higher 
Figure 3 
Box-percentile plots of relative error (RE) in estimates of biological reference points from each mea- 
sure of spawning biomass (female, male, and both), computed in secondary analyses, where an incor- 
rect value of age at 50:50 sex ratio was assumed in the assessment model or where fecundity was 
incorrectly assumed to scale linearly with weight. Values of S MSY were calculated separately for each 
measure of spawning biomass as in Equation 9. The first column of panels corresponds to sex transi- 
tion occurring at a younger age than that assumed in the assessment (x p = 0.75), the second column 
to sex transition occurring at an older age than that assumed in the assessment (% =1.25), the third 
column to fecundity at age being lower than that assumed in the assessment (X/=0-75), and the fourth 
column to fecundity at age being higher than that assumed in the assessment (x^l-25). Width at each 
percentile is proportional to the percent of observations more extreme than that percentile. The 25 th , 
50 th , and 75 th percentiles are indicated by horizontal lines within each box-percentile plot. 
assessment model using spawning biomass of both sexes 
generally provided the best results. When we incor- 
porated additional misspecifications, the assessment 
model based on both sexes still performed best, with 
the exception of cases where the age of sex transition 
in the assessment model was biased towards an older 
age. Such bias could occur if sex change is adaptive (i.e., 
if fish alter the timing of sex transition). However, if 
the age of sex transition is derived from an exploited 
population, we would expect an estimate used in the 
assessment to already reflect any adaptation, and thus 
it seems more likely that any bias in the estimate would 
be towards a younger age. 
Of all the parameters in the factorial design, re- 
silience of fertilization to male depletion, quantified 
by k, explains the most variation in relative error of 
estimates. When x>0.8, an assessment model based on 
females only provides the best estimates of BRPs. This 
result is logical, because for the largest values of k, the 
proportion of males can be driven quite low before fer- 
tilization is limited, and therefore, the number of fertil- 
ized eggs will be exactly (x=l) or approximately ( k = 0 . 8 
or 0.9) proportional to S? (given that the exponents of 
weight at age and fecundity at age are equal). A value 
of K— 1 is a limiting case because it implies fertilization 
can occur even in the absence of males (x F =0). When k 
is in the range of about 0.4-0. 7, an assessment model 
based on both sexes provides the best results. For these 
levels of k, fertilization rates decline moderately with 
depletion of males — an effect that is captured by the 
use of S b . Only at the most limiting values of k (0.2, 
0.3), where fertilization rates decline dramatically with 
depletion of males, did an assessment model based on 
males provide the best estimates. 
