© 2004 International Council for the Exploration of the Sea
Evaluation of average length as an estimator of exploitation status for the Florida coral-reef fish community
a University of Miami, Rosenstiel School of Marine and Atmospheric Science, Division of Marine Biology and Fisheries 4600 Rickenbacker Causeway, Miami, FL 33149, USA
b NOAA Fisheries, Southeast Fisheries Science Center 75 Virginia Beach Drive, Miami, FL 33149, USA
*Correspondence to J. S. Ault: tel: +1 305 421 4884; fax: +1 305 421 4791. e-mail: jault{at}rsmas.miami.edu.
Simulation and empirical analyses were conducted to evaluate the utility and robustness of average length (Lbar) of animals in the exploited population as an estimator of fishing mortality (F), and therefore as an indicator of exploitation status for Florida coral-reef fish. Simulation results showed that the Lbar estimator of fishing mortality was relatively insensitive to trends in recruitment, and demonstrated favourable properties for detecting statistical differences between sustainable and non-sustainable rates of exploitation. Rates of F estimated from fishery-dependent size composition data were comparable to F estimates from catch-and-effort time-series. Average length was also estimated from fishery-independent diver surveys for 22 species in the exploited snapper–grouper complex. A majority of snapper–grouper species are currently fished unsustainably in the Florida Keys, though overfishing appears most severe for long-lived, slow-growing fish.
Keywords: average size, coral-reef fish, exploitation, Florida Keys
Received 1 April 2004; accepted 1 November 2004.
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Introduction |
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 Top Introduction MethodsResultsDiscussionReferences |
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The Florida Keys coral-reef ecosystem (24.7°N 81.0°W) is inhabited by more than 400 fish species and supports multibillion-dollar fishing and tourism industries (Johns et al., 2001). Over recent decades, reef-fish populations have declined, owing to a variety of human-related stressors, most notably fishing and habitat alterations (Ault et al., in press). The fish are intensively exploited (Ault et al., 1998, 2003), but fishing mortality affects the species differentially (Coleman et al., 2000; Musick et al., 2000).
Our research focus has been to quantify the reef-fish community response to exploitation in the Florida Keys (Ault et al., 1998). The principal data source is fishery-independent, synoptic diver-based visual surveys of species composition, abundance, and size structure, including target and non-target species (Bohnsack et al., 1999; Ault et al., 2002). The principal stock assessment indicator variable to quantify population status is average length (Lbar) of the exploited part of the population, which is a metabolic-based indicator that is highly correlated with population size (Beverton and Holt, 1957; Ricker, 1963; Pauly and Morgan, 1987; Ault and Ehrhardt, 1991; Ehrhardt and Ault, 1992; Kerr and Dickie, 2001). For exploited species, Lbar reflects the rate of fishing mortality. Because body size is broadly correlated with trophic level, large individuals and species are often top predators. Biomass declines of such animals are usually the most marked community response to exploitation (Ault et al., 1998; Gislason and Rice, 1998; Pauly et al., 1998; Kerr and Dickie, 2001). Previous studies showed that the Lbar estimator of mortality rate is unbiased under conditions of constant annual recruitment to the exploited stock (Ehrhardt and Ault, 1992; Quinn and Deriso, 1999). However, resulting mortality estimates may exhibit positive bias under conditions of an increasing trend in recruitment. In the Florida Keys, recruitment of the most severely depleted stocks may be increasing at present, in response to a series of recent management actions for the snapper–grouper complex, including gear restrictions, minimum size and bag limits, and spatial closures (Ault et al., in press).
To evaluate the utility and robustness of average size as an estimator of exploitation status for Florida reef fish, our objectives here are to: (i) examine uncertainty in Lbar estimates of mortality rates and potential bias caused by trends in recruitment; (ii) compare estimates of mortality rates based on a variety of methods and different data sources; (iii) apply the Lbar estimator of mortality simultaneously to a suite of reef-fish species under the same nominal fishing effort, to evaluate its potential as a first-order indicator of community response to exploitation.
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Methods |
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TopIntroductionMethodsResultsDiscussionReferences |
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Table 1 shows the sources of length composition and catch-and-effort data used. Life history parameters for Florida reef fish (Table 2) were taken from Ault et al. (1998, 2002, 2003) and Claro et al. (2001). Natural mortality rate (M) was estimated from lifespan, applying the procedure of Alagaraga (1984).
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Total instantaneous mortality rate (Z) was estimated using the method of Ehrhardt and Ault (1992), which is based on length at first capture (Lc), maximum length in the stock (L
), and average length in the exploited stock (Lbar), in conjunction with the Bertalanffy growth parameters K and L
. Estimates of Z were computed using an iterative numerical algorithm (LBAR; Ault et al., 1996; FAO, 2003), and annual estimates of F were obtained by subtracting M from Z. All input values are given in Table 2.
Theoretically, Lbar in year t is expressed as
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the oldest age in the stock, N(a,t) the abundance for age class a, L(a,t) the length-at-age, and F(t) is the instantaneous fishing mortality rate at time t. In practice, Lbar is usually estimated in the length range Lc–L. Estimates of average length and the corresponding variances were obtained from fishery-dependent and -independent length composition data, applying standard statistical procedures (Sokal and Rohlf, 1981). Non-normality of length observations was corrected by log-transformation. Fishery-dependent estimates were obtained by weighting recreational and commercial fleet estimates by their respective proportions of the catch, and fishery-independent estimates by weighting estimates of population abundance from data collected inside and outside marine protected areas by their respective proportions. In addition, two methods were used to estimate F from Florida-wide catch-and-effort time-series: the ASPIC non-equilibrium surplus production model (Prager, 1994), and a continuous formulation (i.e. no age or size structure) of a general stock-synthesis model (Methot, 1990; Quinn and Deriso, 1999), employing maximum-likelihood procedures (Haddon, 2001). These time-series methods generally produce more reliable estimates for the most recent years. Effort among fleets and gears was standardized using the fishing power method of Robson (1966).
Finally, a numerical cohort-structured model (Ault and Olson, 1996; Ault et al., 1998) was used to compute management benchmarks of stock status and to conduct simulation analyses of uncertainty and bias properties of F estimates based on average size. The benchmarks used to evaluate sustainable exploitation in terms of a limit control rule were: Fmsy (F generating maximum sustainable yield, MSY); Bmsy (population biomass at MSY); and SPR (spawning potential ratio; Mace, 1997; Restrepo and Powers, 1999). We define Fmsy as F = M.
The bias in F resulting from potentially increasing trends in recruitment to the exploited stock was evaluated for hogfish (Lachnolaimus maximus) with the cohort-structured model. Hogfish was used here because reliable long-term fishery-dependent and -independent data were available for methodological comparisons, and because its life history demographics are characteristic of the snapper–grouper complex. Simulations were run over a range of exploitation rates (F = 0.0–0.8) and increasing recruitment trends (0–10% y–1). Recruitment of fish entering the population at age tr was assumed to have an exponential trend (with recruitment rate parameter r; 
), and was presumed to occur over the entire lifespan (Quinn and Deriso, 1999). These analyses represent a "worst-case" scenario for potential bias in F estimates.
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Results |
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TopIntroductionMethodsResultsDiscussionReferences |
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The analytical relationship between Lbar and F, some aspects of uncertainty in average length mortality estimates, and the expected stochastic population length compositions at three levels of fishing mortality (F = 0; F = Fmsy; F = F2001) are depicted in Figure 1. The most recent Florida-wide estimate of F is about four times higher than Fmsy. Means and 95% confidence intervals (CI) of Lbar for the cases Fmsy and F2001 were used to estimate the respective means and 95% CIs of F. Although the CI of Lbar is larger at Fmsy than at F2001, the corresponding CI of F is higher at F2001 owing to the non-linear relationship between Lbar and F. The non-linear relationship also results in asymmetric CIs of F that are more pronounced at higher exploitation rates.
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A contour diagram of the proportional bias in Z estimates at different rates of recruitment r and F (Figure 2) shows that bias increases with decreasing F and increasing r. Based on the F-range observed in Florida-wide estimates during the past 10 years and an upper bound of r = 0.04 (corresponding to a 251% increase over a full lifespan; at most a 200% increase has been observed for snapper–grouper species over 20 years of the fishery-independent surveys), the feasible realm of bias for hogfish ranges from 3% to 7%. At values of F near Fmsy = 0.13, the bias is <15%, and probably much lower, because recruitment would be expected to increase less for a stock fished sustainably.
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A comparison of estimates for hogfish based on different methods and data sources (Figure 3) indicates that annual F for the non-equilibrium production and stock-synthesis models were nearly identical over the period 1993–2001, whereas Florida-wide Lbar estimates of F from fishery-dependent data for the years 2001 and 2002 generally corresponded with the estimates from catch-and-effort time-series. Florida Keys estimates from fishery-independent data were higher than the Florida-wide estimates for 2001 and 2002. One likely reason for this is that the Florida Keys comprises most of the coral-reef habitats in Florida, so generating most of the commercial and recreational landings of this species (Ault et al., 2003).
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Lbar mortality estimates, based on fishery-independent size composition data collected between 2000 and 2002, and management benchmarks for 22 species of reef fish, are provided in Table 2. Values of the F/Fmsy ratio plotted against the B/Bmsy ratio (Figure 4) suggest that most species of the snapper–grouper complex experience overfishing (F-ratio > 1, B-ratio < 1; Restrepo and Powers, 1999) and have been subject to unsustainable rates of exploitation in recent years. Notable exceptions are two small grunt species not targeted by the fishery (French grunt, Haemulon flavolineatum, and tomtate, H. aurolineatum), and the goliath grouper (Epinephelus itajara), which has been under a fishing moratorium since 1990. Overfishing appears most severe for long-lived, slow-growing fish (cf. Table 2, Figure 4).
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Discussion |
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TopIntroductionMethodsResultsDiscussionReferences |
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The Lbar method for estimating total mortality exhibits relatively robust properties for assessing exploitation impacts on the Florida coral-reef community. Apart from being unique by having zero-bias properties at equilibrium (Ehrhardt and Ault, 1992; Quinn and Deriso, 1999), the method appears to be relatively insensitive to trends in likely recruitment for Florida Keys reef-fish species (Ault et al., 1998, 2001, 2002). Temporal variation in recruitment, in contrast to a deterministic trend, would result in an even smaller bias than the simulated extreme trends. The estimator also showed desirable properties for detecting statistical differences at the lower range of exploitation rates that should allow discrimination between sustainable and non-sustainable rates. Finally, estimates of F from fishery-dependent size composition data were comparable to those from catch-and-effort time-series.
The use of Lbar as an estimator of fishing mortality, and therefore indirectly as an indicator of exploitation, has several practical advantages: (i) relatively simple data requirements (i.e. accurate and precise information on the age-and-size relationship, length frequency compositions for the exploited stock, and estimates of M); (ii) the method applies to both fishery-independent and -dependent data, and therefore may help to resolve incongruencies that exist among individual data sets; (iii) relatively simple computational requirements for the Lbar algorithm, because length-to-age transformation is not required, unlike most contemporaneous age-based mortality estimators (Quinn and Deriso, 1999); (iv) the method might be used to generate a "community control rule" indicator of exploitation status, when used in the context of synoptic fishery-independent survey data.
The principal fleet targeting the reef-fish complex of approximately 50 species is recreational, and the principal gear is hook and line, which is relatively non-selective (Ault et al., 2003). Because many of the species co-occur in similar habitats, capture probability for most species on any given trip at any location is greater than zero. Therefore, nominal fishing effort in the Florida Keys affects the snapper–grouper complex as a whole, but acts differentially on individual species, depending on their life history characteristics. The impact of exploitation was more severe for the slow-growing, long-lived groupers and hogfish than for other species (Figure 4). In addition, exploitation rates appear to differ throughout Florida, but are most intense in the Florida Keys. Because of these factors, management to build sustainable fisheries may need to consider the entire reef-fish complex and perhaps invoke a spatial context to interventions.
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Acknowledgements |
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We thank D. Harper, R. McBride, M. Murphy, and J. O'Hop for assistance in obtaining fishery-dependent databases. We appreciate the critical reviews of this manuscript by J. Munyandorero, G. Scott, J. Powers, A. Chester, and B. Mackenzie. The research was supported by funding from the NOAA Coastal Ocean Program South Florida Program Grant NA17RJ1226, the NOAA Fisheries Coral Reef Program Grant No. NA17RJ1226, the NOAA Caribbean Reef Ecosystem Study Grant NA17OP2919, NOAA National Sea Grant RLRB47, and the National Park Service Cooperative Ecosystem Studies Unit Grant H500000B494.
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