12 
Abstract — In stock assessments, 
recruitment is typically modeled as 
a function of females only. For pro- 
togynous stocks, however, dispropor- 
tionate fishing on males increases 
the possibility of reduced fertiliza- 
tion rates. To incorporate the impor- 
tance of males in protogynous stocks, 
assessment models have been used 
to predict recruitment not just from 
female spawning biomass (SO, but 
also from that of males (S m ) or both 
sexes ( S b ). We conducted a simulation 
study to evaluate the ability of these 
three measures to estimate biologi- 
cal reference points used in fishery 
management. Of the three, St pro- 
vides best estimates if the potential 
for decreased fertilization is weak, 
whereas S'" is best only if the poten- 
tial is very strong. In general, S b esti- 
mates the true reference points most 
closely, which indicates that if the 
potential for decreased fertilization 
is moderate or unknown, S b should be 
used in assessments of protogynous 
stocks. Moreover, for a broad range 
of scenarios, relative errors from St 
and S b occur in opposite directions, 
indicating that estimates from these 
measures could be used to bound 
uncertainty. 
Manuscript submitted 25 April 2007. 
Manuscript accepted 1 August 2007. 
Fish. Bull 106:12-23 (2008). 
The views and opinions expressed or 
implied in this article are those of the 
author and do not necessarily reflect 
the position of the National Marine 
Fisheries Service, NOAA. 
Stock assessment of protogynous fish: 
evaluating measures of spawning biomass 
used to estimate biological reference points 
Elizabeth N. Brooks (contact author) 
Email addresss: Liz.Brooks@noaa.gov 
National Marine Fisheries Service, NOAA 
Southeast Fisheries Science Center 
75 Virginia Beach Drive 
Miami, Florida 33149 
Present address: National Oceanic and Atmospheric Administration 
National Marine Fisheries Service, Northeast Fisheries Science Center 
166 Water Street 
Woods Hole, Massachusetts 02543 
Kyle W. Shertzer 
National Marine Fisheries Service, NOAA 
Southeast Fisheries Science Center 
Center for Coastal Fisheries and Habitat Research 
101 Pivers Island Road 
Beaufort, North Carolina 28516 
Todd Gedamke 
Virginia Institute of Marine Science 
College of William and Mary 
PO. Box 1346, Route 1208 Greate Road 
Gloucester Point, Virginia 23063 
Douglas S. Vaughan 
National Marine Fisheries Service, NOAA 
Southeast Fisheries Science Center 
Center for Coastal Fisheries and Habitat Research 
101 Pivers Island Road 
Beaufort, North Carolina 28516 
Populations persistence requires that 
losses from mortality must at least be 
matched by gains from the production 
of new individuals (i.e., recruitment). 
The theory of stock reproduction 
relates recruitment to total egg pro- 
duction (Beverton and Holt, 1957). 
In practice, however, stock assess- 
ment often relates recruitment to 
the biomass of mature females rather 
than to total egg production. The two 
predictors are functionally similar if 
egg production of a mature female is 
highly correlated to body mass (Roth- 
schild and Fogarty, 1989), as observed 
or assumed for many stocks. 
With the use of either predictor — 
biomass of mature females or total 
egg production — the proportion of 
eggs fertilized is assumed to be con- 
stant. This assumption is believed 
to be valid for stocks with little fluc- 
tuation in sex ratio, as in most gono- 
choristic stocks (fish that remain the 
same sex throughout life). However, 
this assumption may be inappropri- 
ate for protogynous stocks (fish that 
begin life as female and later become 
male). Under natural mortality alone, 
sex ratios of protogynous stocks are 
expected to be skewed toward fe- 
males (Allsop and West, 2004). The 
addition of fishing mortality could 
skew the ratio even further (Cole- 
man et al., 1996; McGovern et al., 
1998; Armsworth, 2001), particularly 
