Hesp et a\ . Age and size composition, growth rate, reproductive biology, and liabitats of Glaucosoma hebraiaim 



217 



would maximize the log-likelihood function, by fitting the 

 equations to the combined set of length-at-age data for 

 both females and males. 



The growth curves for the fish of each sex were com- 

 pared following the Hkelihood ratio method described by 

 Ivimura (1980) and Cerrato (1990). The test of the like- 

 lihood ratio, A. that was applied was to reject the null 

 hypothesis il (that there was no difference between the 

 cui-v'es) at the « level of significance when 



fM+ff 



-F", 



ih,*U 



where A = 



. 2 \-"f '2 



' Fil ) 



and where n - /; ,, + nf, 

 f = n - 3; and 



q = the number of linear constraints of the form 

 0J^^ = Op, where 6 is one of the parameters 



M and F = males and females, respectively. 



This test was developed by Gallant (1975), as described by 

 Cerrato (1990). 



The gi'owth curves were fitted under all possible para- 

 meter sets, and the best of both the 4- and 5-parameter, 

 models, i.e. those that maximized the log-likelihood, were 

 selected. The resulting 3-, 4- and 5-parameter models were 

 compared with the 6-parameter model by using the above 

 test to determine which of these three models, w. was of 

 minimum complexity and not significantly different from 

 the 6-parameter model i2. The model selected on the basis 

 of these tests was the simplest model that, in the statisti- 

 cal sense, provided the best description of the data. 



Reproductive biology 



The gonads of each fish that could be sexed macroscopi- 

 cally were removed and weighed to the nearest 0.01 g. 

 Each gonad was allocated to a maturity stage, based on 

 the scheme of Laevastu (1965), but which, in the case of 

 females, also took into account the histological character- 

 istics of the ovaries (see "Results" section). 



The percentage contributions made by the different go- 

 nadal stages in sequential 50-mm length intervals were 

 calculated for both female and male G. hebraicum. The 

 lengths at which 50'7f of female and male G. hebraicum 

 reach sexual maturity (L50' were determined by fitting the 

 logistic curve to the percentage of female and male fish 

 which, during the spawning period, possessed gonads at 

 stages III to VIII (see "Results" section for rationale for us- 

 ing these six stages for this purpose). The logistic curve 

 was fitted by employing a nonlinear technique (Saila et 

 al., 1988) and by using a routine statistical method pro- 

 vided in SPSS (SPSS Inc., 1988). The logistic equation is 

 Pf^ = 1/(1 -H e'"*'''-'), where P^ is the proportion offish with 

 mature gonads at the mid-point of the length class, L, and 

 a and b are constants. The L-,, for each sex was derived 



from the equation Lr,,, = y . The ages at which 50% of fe- 

 males and males reached maturity, i.e. the Ar,,,, were esti- 

 mated, as follows, from the inverse von Bertalanffy growth 

 equations for the two sexes (see Stergiou, 1999): 



■^0 ~ 'i 



■o-(i|log 



h. 



Gonadosomatic indices (GSIs) of females and males >Lr^Q 

 at first maturity were determined from the equation 



W1/W2 X 100, 



where W\ = wet weight of the gonad; and 

 W2 = wet weight of the whole fish. 



Mortality 



PreliminaiT analysis of catch curves demonstrated that 

 the mortality estimates derived for commercially and rec- 

 reationally caught fish that were greater than the MLL of 

 500 mm and eight years old and thus fully recruited (see 

 "Results" section) were similar. Thus, the data from the 

 commercial and recreational samples were pooled for esti- 

 mating mortality. An estimate of the instantaneous coef- 

 ficient of natural mortality, M, was determined from the 

 von Bertalanffy gi'owth coefficient, k. with the regression 

 equation developed by Ralston (1987), i.e. M = 0.0189 -i- 

 2.06/;. The instantaneous coefficient of total mortality, Z, 

 was determined by maximizing the likelihood, when fitting 

 the estimated age composition resulting from that mortal- 

 ity to the observed age composition data for those dhufish 

 that were gi'eater than the MLL of 500 mm and eight years 

 old. In order to assess whether the observed age composi- 

 tion data reflected decreasing levels of total mortality in 

 earlier years, the catch cui-ve analysis was repeated with 

 different initial ages, ranging from 10 to 30 years. Values of 

 Z were also estimated by using the observed maximum age 

 '^jiov* fo'' *'^^ sampled dhufish, employing both the regres- 

 sion equation reported for fish by Hoenig ( 1983), i.e. 



log(Z)= 1.46- 1.01 log(C„,,,,^), 



and the equation for the expected value of the maximum 

 age in a sample of size n, i.e. 



£(C) = 



1 V- 1 



Ir'^' 



where /, = the age at which fish become fully recruited to 

 the fishery (Johnson and Kotz, 1970, p. 216, as 

 reported by Hoenig, 1983). 



Results 



Habitats of Glaucosoma hebraicum 



Glaucosoma hebraicum <150 mm TL and <14 months 

 old were caught regularly by trawlers offshore in water 



