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Fishery Bulletin 1 10(4) 
spawning, or extended readiness to spawn, are typical 
of indeterminate spawners with asynchronous oocyte 
development patterns (Hunter et al., 1985; Murua et 
ah, 2003). Although many species that exhibit deter- 
minate fecundity also spawn in batches, quantifying 
annual fecundity for indeterminate spawners requires 
estimates of batch fecundity (i.e., eggs per batch) and 
number of batches per year, each as a function of pa- 
rental age or size (Murua et ah, 2003). Estimating 
the number of batches per year requires knowledge 
about spawning season duration and spawning fre- 
quency within the season (or average time between 
batches), including any temporal patterns of that fre- 
quency (Murua et ah, 2003). Then, annual fecundity of 
indeterminate species can be calculated as the product 
of the number of eggs per batch and the number of 
batches per year. 
Estimation of batch fecundity by age is relatively 
straightforward (Porch et ah, 2007). In fact, these 
estimates tend to relate linearly to body weight, and 
this relationship has been the rationale for the use of 
spawning biomass as a proxy for total egg production. 
However, estimation of spawning season duration and 
spawning frequency by size or age is much more dif- 
ficult. Despite recognition from individual studies that 
frequency and duration of spawning may increase with 
age and size (Lowere-Barbieri et ah, 2011a), much of 
this information is lacking for many species. Without 
information, the typical default assumption in stock 
assessment is that both spawning duration and fre- 
quency are invariant across age. Widespread appli- 
cation of this assumption of invariance raises 2 key 
questions. Is the assumption justified? If not, what are 
the consequences for stock assessment and resulting 
management advice? We address the first question 
through a review of the literature and the second one 
by modeling effects of age-dependent spawning activ- 
ity (annual number of batches) on spawning potential 
ratio (Goodyear, 1993; Shertzer et ah, 2008) and re- 
productive value (both of these metrics are defined in 
the next section). 
Materials and methods 
Review of scientific literature — spawning frequency 
and duration 
To examine whether or not age and size effects on spawn- 
ing duration and frequency were common, we reviewed 
scientific literature on fishes, including aquaculture 
studies that investigated natural spawning (nonhormon- 
ally induced), as well as field studies. Although most of 
these studies were of marine species, freshwater spe- 
cies were not excluded from this review. In addition, 
our search included species not necessarily classified 
as indeterminate spawners because relatively few stud- 
ies distinguish fecundity pattern (Murua et ah, 2003). 
Our review proceeded in 2 stages. First, we selected 
articles in which batch spawning frequency was exam- 
ined, either as spawning fraction (proportion of mature 
fish actively spawning), number of batches within a fixed 
time period, or average time interval between batches. 
From these articles, we further narrowed the list to 
those that reported the relationship (or lack thereof) 
between spawning frequency and age or size. Second, 
we selected articles in which spawning duration was 
examined by age or size. Numerous articles reported 
the season or duration of spawning, but duration by age 
or size was examined in relatively few of them. Thus, 
in this second review, we did not restrict our search 
to batch spawners; instead, we noted any study that 
reported spawning duration by age or size. 
Implications for stock assessment and management 
To examine how the age-dependent annual number of 
batches affects stock assessment results and manage- 
ment advice, we used classical per-recruit analyses 
(Shertzer et al., 2008) of spawning potential ratio and 
reproductive value. Standard fishery equations described 
equilibrium abundance of females at age (N a ), weight 
at age (W a ), maturity at age (m a ), fecundity at age of 
mature fish (/ a ), and selectivity of fishing gear (s a ) (Table 
1). These analyses are “per recruit” by virtue of scaling 
to an initial abundance of one (N^l). To populate our 
model with parameter values representing warm-water 
marine fishes, we used average life-history characteris- 
tics reported for the Gulf of Mexico (Table 2). Fishes of 
this region tend to be characterized by indeterminate 
fecundity and batch spawning, in contrast to fishes 
from higher latitudes where determinate fecundity is 
more common. 
Annual fecundity at age was determined as the prod- 
uct of eggs produced per batch (assumed to be pro- 
portional to body weight) and the annual number of 
batches, which implicitly accounted for joint effects of 
spawning frequency and spawning duration. The an- 
nual number of batches at age followed 1 of 4 qualita- 
tive patterns: constant, increasing, decreasing, or dome 
shaped (Fig. 1A). To create these patterns, we first set 
the constant pattern to a value of 1, and then we scaled 
the remaining patterns such that the 4 patterns had 
equal integration (i.e., area under the curve). Although 
not all these patterns were prevalent in the literature 
review, we included all for completeness and compari- 
son. In this article, we report spawning potential ratio 
and reproductive value across these 4 patterns. 
Spawning potential ratio Spawning potential ratio 
(Goodyear, 1993; Shertzer et al., 2008) was computed 
by using standard fishery equations (Table 1): 
(1) 
The numerator {(j > F ) of this ratio quantified expected 
reproductive output (e.g., fecundity) per recruit under 
fishing rate F, 
= X 
a=l 
(2) 
