1.65 year-I. Natural mortality was estimated by Ralston's empirical formula: M = 0.527 year-I. Fishing mortality ... (Pauly and David, 1981). The resulting response ...
BULLETIN OF MARINE SCIENCE. 50(2): 282-291. 1992
ESTIMA TION OF GROWTH, MORTALITY AND YIELD PER RECRUIT FOR LUTJANUS SYNAGRIS (LINNAEUS) IN PUERTO RICO Alejandro Acosta and Richard S. Appeldoorn ABSTRACT Growth and mortality parameters of lane snapper Lutjanus synagris were estimated from length-frequency data collected from the Puerto Rican commercial fisheries using the ELEFAN method. The von Bertalanffy growth parameters were estimated as K = 0.23 year-I and Loo= 450 mm. The length-weight relationship was W (g) = 0.000061 FU 75. The growth parameters from Puerto Rico fall within reported growth values for lane snapper and lutjanids elsewhere. Total mortality rate was estimated using length-converted catch curve analysis Z = 1.65 year-I. Natural mortality was estimated by Ralston's empirical formula: M = 0.527 year-I. Fishing mortality, F, was 1.13 year-'. A Beverton-Holt yield-per-recruit model indicated that the current fishery harvests approximately 91 % of the potential yield.
The lane snapper Lutjanus synagris (Family: Lutjanidae) is among the most important lutjanids caught in Puerto Rico and throughout the Caribbean. Lane snapper is tropical, commonly occurring in the western Atlantic from northern Florida to southern Brazil (Manooch and Mason, 1984). It is reported to occur in a number of habitats, from coral reefs to murky brackish water, and over mud bottom (Randall, 1967). In Puerto Rico this species is fished commercially by hook and line, traps, trammel nets and gillnets. Several authors have reported on the biology and ecology of lane snapper (Thompson and Munro, 1983; Claro and Reshetnikov, 1981; Manooch and Mason, 1984; Manickchand-Dass, 1987). Age, growth and mortality oflane snapper have been estimated using different techniques for ageing (otoliths, vertebrae and scales). However, estimating growth rate of the species by length-frequency analysis has not been attempted. The objectives of this study are to evaluate the use oflength-frequency analysis, specifically the COMPLEAT ELEFAN (Gayanilo et a1., 1989), on the biostatistical data collected by the Fisheries Research Laboratory (FRL) of the Puerto Rico Department of Natural Resources (DNR), to estimate growth and mortality parameters and the length-weight relationship for lane snapper, and to construct a corresponding yield-per-recruit analysis. METHODS Length-frequency data collected from January to December 1988 by FRL port samplers were used in this study. The number of samples varied from two to seven per month. The sample size varied from 22 to 199 individuals and the total number of fish sampled was 1,308. For all individuals fork length (FL) was measured to the nearest millimeter. Data Preparation. - These data were collected from several fishing gears; however, only two gears were predominant (hook and line, and traps). Comparison of the length-frequency distributions by gear (Fig. I) using a Kolmogorov-Smimov two-sample test (Sokal and Rohlf, 1981) showed no significant differences among gears (P = 0.991). The depth range fished by traps was 3 to 85 fathoms (5.4-153 m) with a mean of 26 fathoms (46 m). For hook and line the depth range was 3 to 100 with a mean of 13 fathoms (5.4-153 m, x = 23.4 m). No significant depth size distribution was found that could have possibly biased the combined length-frequency distribution. As a result, the gear-specific data were pooled and used in subsequent analyses. Samples were pooled by month and given a single midmonth date. A size class of 10 mm was used. In an attempt to control for possible biases due to low sample sizes in some months, the analysis was conducted for two data sets: a) all samples (12 months), 282
ACOSTA AND APPELDOORN:
LUTJANUS
SYNAGRIS
283
and b) a subsample of 7 months with large sample sizes (over 100). Data were also corrected for gear selection and the analysis run for both the corrected and uncorrected distribution. Estimates of L~, K and Z were obtained for both data sets. Length-converted catch curve analysis was performed by converting the data of each monthly sample to percent frequency and then weighting by square root of the sample size. Giving all monthly samples equal weight prevents a single large monthly sample from being a major source of bias or from overly affecting the total annual sample. This approach is desirable when all samples are large, but strong differences between sample sizes occur. However, if some samples sizes are low, equal weighting could overemphasize data of lesser quality. Estimation of Growth Parameters and Mortality. - The analysis assumes von Bertalanffy growth L,
=
L~(\ -
e-Kll-lO})
where L, is length at time t, L~ is the asymptotic length an individual would reach ifit lived indefinitely, and K is the rate at which L~ is approached. The parameter to is a location parameter, necessary to relate size to absolute age, and cannot be estimated using length frequency analysis. The growth parameters L~ and K were estimated using ELEFAN I of the COMPLEAT ELEFAN (Gayanilo et aI., 1989), which incorporates Wetherall et aI.'s (1987) method used to obtain preliminary estimates of L~ and Z/K ratio, where Z is the instantaneous rate of total mortality. Using different combinations of L~ and K, ELEFAN I was used to generate a response surface of Rn, the goodness of fit index (Pauly and David, 1981). The resulting response surface was inspected to find the combination ofL~ and K that best fit the data; using these results a narrow search with different starting points was conducted until the maximum Rn value was found and corresponding values ofL~ and K determined. The jackknife method was used to estimate the 95% confidence limits for L~ and K (Pauly, 1984). The basis of the jackknife as applied to ELEFAN I is the reanalysis of the data, and in each analysis a different month's sample is omitted. This results in estimates of L~ and K equal in number to the total number of samples. The standard deviation of these estimates can be used to generate 95% confidence intervals. In order to compare different estimatcs of growth parameters, the empirical equation ofo = LoglOK - 2 Log,o(L~) of Pauly and Munro (\ 984) was used. Estimation of instantaneous natural mortality (M) was by Ralston's (\ 987) equation for snappers and groupers: M
=
-0.0666
+
2.53(K).
Ralston (1987) found this equation to better predict M for snappers and groupers than using Pauly's (1980) more general equation, which uses estimates ofK and L~ together with the local sea temperature. The length-converted catch curve (Ricker, 1975; Pauly, 1985) was used to estimate Z, length at first capture (lJ, and to correct the length-frequency distribution for gear selection. A regression line was fitted to points immediately to the right of the highest point on the catch curve, excluding points representing less than five individuals (N = 5). The slope of the regression line is an estimate of Z. The standard deviation of the slope was used to calculate 95% confidence limits around Z. Annual recruitment pattern was obtained using ELEFAN II, which projects the length-frequency data back on the time axis using the estimated values of the growth parameters. This approach gives only relative results; because to is not known, the absolute time of recruitment within the year is not known. The length-weight relationship was determined by the equation W
= a(L)b
where W is weight of an individual fish in grams and L is fork length (mm). This was calculated using least squares regression on log-transformed data with bias correction (Saila et aI., 1988). A total of 200 fish randomly selected from the whole data set, ranging from 145 mm to 330 mm FL, were employed for this analysis. A Be.verton-Holt (1957) yield-per-recruit model for lane snapper was constructed using the Sluczanowski (1985) implementation.
RESULTS
Length-frequency data used are presented in Table 1. Figure 1 gives the lengthfrequency distribution by gear and the total distribution pooled over all gears. The corresponding optimum values of Loo(mm FL) were 450 and 448, respectively, for 12 and 7 samples without selection correction and 450 for both cases with selection correction. K was found to be 0.23 year-I for all situations except
284
BULLETIN OF MARINE SCIENCE, YOLo 50, NO.2,
1992
200 180 ..c:: U)
•.-1 4-l 4-l
160
All gears Hook and line
140
Traps
0
120
~ Q)
100
~ ;:j
80
Z
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60
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40
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1.0
0
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