413 
Review of size- and age-dependence 
in batch spawning: implications 
for stock assessment of fish species 
exhibiting indeterminate fecundity 
David M. Wyanski 3 
Email address for contact author: gary.fitzhugh@noaa.gov 
1 Southeast Fisheries Science Center 
National Marine Fisheries Service 
3500 Delwood Beach Road 
Panama City, Florida 32408 
2 Southeast Fisheries Science Center 
National Marine Fisheries Service 
101 Pivers Island Road 
Beaufort, North Carolina 28516 
3 Marine Resources Research Institute 
South Carolina Department of Natural Resources 
217 Fort Johnson Road 
Charleston, South Carolina 29412 
Abstract — Most assessments of fish 
stocks use some measure of the repro- 
ductive potential of a population, such 
as spawning biomass. However, the 
correlation between spawning bio- 
mass and reproductive potential is 
not always strong, and it likely is 
weakest in the tropics and subtropics, 
where species tend to exhibit inde- 
terminate fecundity and release eggs 
in batches over a protracted spawn- 
ing season. In such cases, computing 
annual reproductive output requires 
estimates of batch fecundity and the 
annual number of batches — the latter 
subject to spawning frequency and 
duration of spawning season. Batch 
fecundity is commonly measured by 
age (or size), but these other vari- 
ables are not. Without the relevant 
data, the annual number of batches 
is assumed to be invariant across 
age. We reviewed the literature and 
found that this default assumption 
lacks empirical support because both 
spawning duration and spawning fre- 
quency generally increase with age or 
size. We demonstrate effects of this 
assumption on measures of reproduc- 
tive value and spawning potential 
ratio, a metric commonly used to 
gauge stock status. Model applica- 
tions showed substantial sensitivity to 
age dependence in the annual number 
of batches. If the annual number of 
batches increases with age but is 
incorrectly assumed to be constant, 
stock assessment models would tend 
to overestimate the biological refer- 
ence points used for setting harvest 
rates. This study underscores the 
need to better understand the age- 
or size-dependent contrast in the 
annual number of batches, and we 
conclude that, for species without 
evidence to support invariance, the 
default assumption should be replaced 
with one that accounts for age- or 
size-dependence. 
Manuscript submitted 22 December 2011. 
Manuscript accepted 15 August 2012. 
Fish. Bull. 110:413-425 (2012). 
The views and opinions expressed 
or implied in this article are those of the 
author (or authors) and do not necessarily 
reflect the position of the National Marine 
Fisheries Service, NOAA. 
Gary R. Fitzhugh (contact author ) 1 
Kyle W. Shertzer 2 
G. Todd Kellison 2 
The relationship between reproductive 
output and subsequent recruitment 
of new individuals is fundamental to 
population dynamics. In stock assess- 
ments, this relationship is typically 
quantified by using a spawner-recruit 
model. Such models were originally 
developed with population fecundity 
as the measure of spawners, but most 
current applications use spawning bio- 
mass, calculated as the total weight of 
mature females (Rothschild and Fog- 
arty, 1989). A critical assumption with 
this approach is that spawning bio- 
mass accurately represents the repro- 
ductive potential of a stock. However, 
this assumption does not always hold 
(Trippel, 1999; Marshall et ah, 2003, 
2006) and, when violated, can inject 
error into assessment models and sub- 
sequent management advice (Roth- 
schild and Fogarty, 1989; Murawski 
et ah, 2001; Scott et ah, 2006). Thus, 
recognition is growing for the need to 
integrate more reproductive biology 
into stock assessments by replacing 
spawning biomass with more accurate 
measures of reproductive potential 
(Trippel, 1999; Morgan, 2008; Wit- 
thames and Marshall, 2008). 
Much of the work to date on repro- 
ductive potential and stock assess- 
ments comes from investigations on 
gadoids, pleuronectids, and other 
high-latitude species that typically 
have determinate fecundity patterns 
(Trippel, 1999; Murawski et ah, 
2001; Morgan, 2008; Witthames and 
Marshall, 2008; Morgan et ah, 2009). 
Fewer studies have been conducted 
on fish species with indeterminate 
fecundity, in part because the data 
requirements can be more daunt- 
ing (Lowerre-Barbieri et ah, 2011a, 
2011b). Many warm-water marine 
species from the subtropics (lati- 
tudes <40°) spawn multiple batches 
per year, usually over a protracted 
spawning season. For example, spe- 
cies off the southeastern United 
States typically spawn several times 
within a 3-4 month duration (Cuellar 
et ah, 1996; McGovern et ah, 1998; 
Waggy et ah, 2006). Near the trop- 
ics, spawning seasons are even longer 
and often associated with peak (but 
variable) activity when local condi- 
tions favor transport and survival of 
offspring (Johannes, 1978; Thresher, 
1984). Such extended patterns of 
