Nelson: Age, growth; mortality; and distribution of Lagodon rhombotdes 



585 



ability of pinfish being mature was modeled as a logistic 

 function of the following form: 



V(Z) = 



sa-sf 



p.= 



exp 



1+exp 



iu+fi*x, 



- + £,< 



where P = the response probability; 



-v = the standard length (mm) of the / th fish; 

 a = the intercept; 



P = the slope coefficient of standard length; and 

 f, = the error term. 



Model regression coefficients were estimated using maxi- 

 mum likelihood (SAS, 1997). Goodness-of-fit was assessed 

 with the chi-square test. 



Chi-square analyses were used to test for deviations 

 from a theoretical 50:50 sex ratio. 



Length-weight relationships 



Because of the seasonality of reproduction, data on body 

 length and weight were separated into two groups rep- 

 resenting two time periods to construct length-weight 

 relationships that reflected seasonal changes in gonad 

 weight. Data collected during March-August composed 

 the data group representing the spring-summer period, 

 and data collected during September-February composed 

 the data group representing the fall-winter period. Sea- 

 sonal regression equations for logj^-transformed standard 

 length and body weight (total and gonad-free weight) 

 were generated by the least-squares regression. One-way 

 analysis of covariance (Sokal and Rohlf, 1981), conducted 

 by using SAS PROC MIXED (Littell et al, 1996), was 

 used to test for differences between regression slopes and 

 adjusted means of the length-weight relationships by sex 

 and season. 



Mortality 



Total instantaneous mortality (Z) was estimated in Tampa 

 Bay and the Gulf of Mexico from pinfish numbers-at-age 

 data by using the Chapman-Robson equation for survival 

 (S) estimation: 



-Z = ln(S) = ln 



I<^ 



\ i=i J 



the natural log; 

 , - the number of years the / th fish is older than 



where In 



x^ 



the age-at full-recruitment 



S = annual survival; and 



n = the total number of fully recruited fish (Chap- 

 man and Robson, 1960). 



The variance of Z was estimated from the variance of S 

 by 



(Jensen, 1985). The Chapman-Robson estimator was used 

 because it is more robust to sample siz.e variation in num- 

 bers-at-age (Jensen, 1996; Murphy, 1997). 



In addition to Z, natural mortality (A/) of pinfish was 

 estimated by using a multiple regression equation relat- 

 ing M to L. (TL in cm) and k (per yr) of the von Berta- 

 lanffy equation, and to mean annual water temperature 

 ("C)(Pauly, 1980). To estimate the growth parameters used 

 in the equation, the von Bertalanffy function was refitted 

 to total length and age data. Mean annual water tempera- 

 ture was estimated from temperature data of the Tampa 

 Bay survey. 



Distribution 



To determine if pinfish catch rates in the Gulf of Mexico 

 were associated with depth, a generalized linear model 

 (McCullagh and Nelder, 1989) was used to model the 

 random trawl catches during the April survey from 1994 

 to 1997. Catch data were transformed by using ln(.r+l) to 

 stabilize the variance and reduce the influence of sam- 

 pling variability between tows. Year, average depth of the 

 trawl tow, and their first-order interaction were included 

 in the model. Only depth was analyzed because surface 

 readings of temperature and salinity were thought to 

 not reflect bottom conditions where the trawl tows were 

 made. Size structure of pinfish caught during the Gulf of 

 Mexico survey was also examined by calculating summary 

 statistics (mean and percentiles) of length data to identify 

 patterns related to depth. 



Results 



Biology 



Length-conversion equations are listed in Table 2. All 

 slopes and intercepts were significantly different from 

 zero. 



Age and growth 



Age determination was based on sagittae from 658 pinfish 

 (66-255 mm SL). Alternating opaque and hyaline zones, 

 which composed an annual growth increment, were evi- 

 dent on whole pinfish otoliths (Fig. 2A). Only 13 otoliths 

 were considered unreadable. Agreement between the 

 number of opaque bands counted on whole otoliths and 

 the number counted on sections of the same otoliths (Fig. 

 2B) was 96.3% (26/27), indicating that whole otoliths can 

 be used to reliably age pinfish. The high percentage of 

 agreement (89.6%) between the author's final annulus 

 counts and those made by a second reader, and no appar- 

 ent bias towards a particular aging error, indicated that 

 ages were consistently interpreted. 



Plots of the monthly proportions of otolith with opaque 

 edges for pinfish ages 1 to 3 indicated that an opaque ring 



