And Age-Dependence in Batch Spawning: Implications for Stock Assessment of Fish Species Exhibiting Indeterminate Fecundity

Review of size- and age-dependence in batch spawning: implications for stock assessment of fish species exhibiting indeterminate fecundity Item Type article Authors Fitzhugh, Gary R.; Shertzer, Kyle W.; Kellison, G. Todd; Wyanski, David M. Download date 24/09/2021 13:04:50 Link to Item http://hdl.handle.net/1834/30348 413 Abstract—Most assessments of fish Review of size- and age-dependence stocks use some measure of the reproductive potential of a population, such in batch spawning: implications as spawning biomass. However, the correlation between spawning bio- for stock assessment of fish species mass and reproductive potential is exhibiting indeterminate fecundity not always strong, and it likely is weakest in the tropics and subtropics, where species tend to exhibit inde- Gary R. Fitzhugh (contact author)1 terminate fecundity and release eggs Kyle W. Shertzer2 in batches over a protracted spawn- 2 ing season. In such cases, computing G. Todd Kellison annual reproductive output requires David M. Wyanski3 estimates of batch fecundity and the Email address for contact author: [email protected] annual number of batches—the latter subject to spawning frequency and 1 Southeast Fisheries Science Center duration of spawning season. Batch National Marine Fisheries Service fecundity is commonly measured by 3500 Delwood Beach Road age (or size), but these other vari- Panama City, Florida 32408 ables are not. Without the relevant 2 Southeast Fisheries Science Center data, the annual number of batches National Marine Fisheries Service is assumed to be invariant across 101 Pivers Island Road age. We reviewed the literature and Beaufort, North Carolina 28516 found that this default assumption 3 Marine Resources Research Institute lacks empirical support because both South Carolina Department of Natural Resources spawning duration and spawning fre- 217 Fort Johnson Road quency generally increase with age or Charleston, South Carolina 29412 size. We demonstrate effects of this assumption on measures of reproductive value and spawning potential ratio, a metric commonly used to gauge stock status. Model applications showed substantial sensitivity to age dependence in the annual number The relationship between reproductive Much of the work to date on repro- of batches. If the annual number of output and subsequent recruitment ductive potential and stock assess- batches increases with age but is of new individuals is fundamental to ments comes from investigations on incorrectly assumed to be constant, population dynamics. In stock assess- gadoids, pleuronectids, and other stock assessment models would tend ments, this relationship is typically high-latitude species that typically to overestimate the biological refer- quantified by using a spawner–recruit have determinate fecundity patterns ence points used for setting harvest model. Such models were originally (Trippel, 1999; Murawski et al., rates. This study underscores the need to better understand the age- developed with population fecundity 2001; Morgan, 2008; Witthames and or size-dependent contrast in the as the measure of spawners, but most Marshall, 2008; Morgan et al., 2009). annual number of batches, and we current applications use spawning bio- Fewer studies have been conducted conclude that, for species without mass, calculated as the total weight of on fish species with indeterminate evidence to support invariance, the mature females (Rothschild and Fog- fecundity, in part because the data default assumption should be replaced arty, 1989). A critical assumption with requirements can be more daunt- with one that accounts for age- or this approach is that spawning bio- ing (Lowerre-Barbieri et al., 2011a, size-dependence. mass accurately represents the repro- 2011b). Many warm-water marine ductive potential of a stock. However, species from the subtropics (lati- this assumption does not always hold tudes <40°) spawn multiple batches (Trippel, 1999; Marshall et al., 2003, per year, usually over a protracted 2006) and, when violated, can inject spawning season. For example, spe- error into assessment models and sub- cies off the southeastern United sequent management advice (Roth- States typically spawn several times schild and Fogarty, 1989; Murawski within a 3–4 month duration (Cuellar Manuscript submitted 22 December 2011. et al., 2001; Scott et al., 2006). Thus, et al., 1996; McGovern et al., 1998; Manuscript accepted 15 August 2012. recognition is growing for the need to Waggy et al., 2006). Near the trop- Fish. Bull. 110:413–425 (2012). integrate more reproductive biology ics, spawning seasons are even longer into stock assessments by replacing and often associated with peak (but The views and opinions expressed spawning biomass with more accurate variable) activity when local condi- or implied in this article are those of the author (or authors) and do not necessarily measures of reproductive potential tions favor transport and survival of reflect the position of the National Marine (Trippel, 1999; Morgan, 2008; Wit- offspring (Johannes, 1978; Thresher, Fisheries Service, NOAA. thames and Marshall, 2008). 1984). Such extended patterns of 414 Fishery Bulletin 110(4) spawning, or extended readiness to spawn, are typical ined, either as spawning fraction (proportion of mature of indeterminate spawners with asynchronous oocyte fish actively spawning), number of batches within a fixed development patterns (Hunter et al., 1985; Murua et time period, or average time interval between batches. al., 2003). Although many species that exhibit deter- From these articles, we further narrowed the list to minate fecundity also spawn in batches, quantifying those that reported the relationship (or lack thereof) annual fecundity for indeterminate spawners requires between spawning frequency and age or size. Second, estimates of batch fecundity (i.e., eggs per batch) and we selected articles in which spawning duration was number of batches per year, each as a function of pa- examined by age or size. Numerous articles reported rental age or size (Murua et al., 2003). Estimating the season or duration of spawning, but duration by age the number of batches per year requires knowledge or size was examined in relatively few of them. Thus, about spawning season duration and spawning fre- in this second review, we did not restrict our search quency within the season (or average time between to batch spawners; instead, we noted any study that batches), including any temporal patterns of that fre- reported spawning duration by age or size. quency (Murua et al., 2003). Then, annual fecundity of indeterminate species can be calculated as the product Implications for stock assessment and management of the number of eggs per batch and the number of batches per year. To examine how the age-dependent annual number of Estimation of batch fecundity by age is relatively batches affects stock assessment results and manage- straightforward (Porch et al., 2007). In fact, these ment advice, we used classical per-recruit analyses estimates tend to relate linearly to body weight, and (Shertzer et al., 2008) of spawning potential ratio and this relationship has been the rationale for the use of reproductive value. Standard fishery equations described spawning biomass as a proxy for total egg production. equilibrium abundance of females at age (Na), weight However, estimation of spawning season duration and at age (Wa), maturity at age (ma), fecundity at age of spawning frequency by size or age is much more dif- mature fish (fa), and selectivity of fishing gear (sa) (Table ficult. Despite recognition from individual studies that 1). These analyses are “per recruit” by virtue of scaling frequency and duration of spawning may increase with to an initial abundance of one (N1=1). To populate our age and size (Lowere-Barbieri et al., 2011a), much of model with parameter values representing warm-water this information is lacking for many species. Without marine fishes, we used average life-history characteris- information, the typical default assumption in stock tics reported for the Gulf of Mexico (Table 2). Fishes of assessment is that both spawning duration and fre- this region tend to be characterized by indeterminate quency are invariant across age. Widespread appli- fecundity and batch spawning, in contrast to fishes cation of this assumption of invariance raises 2 key from higher latitudes where determinate fecundity is questions. Is the assumption justified? If not, what are more common. the consequences for stock assessment and resulting Annual fecundity at age was determined as the prod- management advice? We address the first question uct of eggs produced per batch (assumed to be pro- through a review of the literature and the second one portional to body weight) and the annual number of by modeling effects of age-dependent spawning activ- batches, which implicitly accounted for joint effects of ity (annual number of batches) on spawning potential spawning frequency and spawning duration. The an- ratio (Goodyear, 1993; Shertzer et al., 2008) and re- nual number of batches at age followed 1 of 4 qualita- productive value (both of these metrics are defined in tive patterns: constant, increasing, decreasing, or dome the next section). 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 Materials and methods equal integration (i.e., area under the curve). Although not all these patterns

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