Grandcourt et al : Biology and assessment of Diagramma pictum and Lethrinus nebulosus in the southern Arabian Gulf 



77 



was removed and subsequently weighed to 0.1 g with 

 an electronic balance. 



Sagittal otoliths were extracted, cleaned in water, 

 dried, and stored in seed envelopes. One of each pair 

 of sagittae was weighed to 0.1 mg, burnt on a hotplate 

 until it changed to a dark brown color, and embedded 

 in epoxy resin. Transverse sections through the nucleus 

 (of approximately 200-300 jim thickness) were obtained 

 by using a twin blade saw. Sections were mounted on 

 glass slides and examined with a low-power microscope 

 and transmitted light. 



Age and growth 



The number of opaque bands in transverse sections was 

 recorded in addition to the optical characteristics of the 

 outer margin (opaque or translucent). The proportion 

 of samples with opaque or translucent margins was 

 calculated for each month and used to infer the timing 

 and periodicity of increment formation. The age at which 

 the first opaque band formed was calculated as the time 

 between the mean birth date and the time of formation 

 of opaque bands. Subsequently, the absolute age was 

 calculated as the age at formation of the first band plus 

 the number of opaque bands outside the first band and 

 the time between the formation of the last band and cap- 

 ture. In order to establish the relationship of the timing 

 of opaque zone formation with trends in sea water tem- 

 perature, time series data were converted by using the 

 scaling process given in Newman and Dunk (2003). 



Growth was investigated by fitting the von Berta- 

 lanffy growth function (von Bertalanffy, 1938) to size- 

 at-age data using standard nonlinear optimization 

 methods. The model was fitted to pooled data and each 

 sex separately. The von Bertalanffy growth function is 

 defined as follows: 



L, = L., il -e 



-k U-l„) 



«'), 



where L, = length at time t\ 



L^= the asymptotic length; 

 k = the instantaneous growth coefficient; and 

 t^ = the hypothetical time at which length is 

 equal to 0. 



Growth curves were compared between sexes for each 

 species by using the analysis of residual sums of squares 

 method of Chen et al. (1992). 



The growth performance index (P (Gayanilo and Pau- 

 ly, 1997) was calculated in order to provide a basis for 

 the comparison of growth characteristics in terms of 

 length: 



*' = <J>- 2/3 logio (a), 



where <J> = logjg ik) + 0.67 logm iWj and W, = aLj. 



The constant, a, was derived from length-weight rela- 

 tionships and k and L^ were obtained from the von 

 Bertalanffy growth function. 



Parameters of the length-weight relationship were ob- 

 tained by fitting the power function W = oLp* to length 

 and weight data where W is the total wet weight, a is a 

 constant determined empirically, Lp is the fork length, 

 and b is close to 3.0 for species with isometric growth. 

 Ratios of total length (Lj) to fork length (Lp) were also 

 calculated for each species. 



Reproduction 



The mean size at first sexual maturity was estimated for 

 females by fitting the logistic function to the proportion 

 of mature fish in 2-cm (Lp) size categories. The mean 

 size at first maturity was taken as that at which 50% 

 of individuals were mature. Gonadosomatic indices, 

 calculated by expressing gonad weight as a proportion 

 of total body weight, were plotted against the sample 

 period by month to establish the timing and seasonality 

 of spawning. The mean birth date was estimated from 

 patterns in reproductive indices. 



Population sex ratios were examined by using x" good- 

 ness-of-fit tests. Independent tests were conducted to 

 determine whether sex ratios differed significantly from 

 unity for whole samples and for size and age categories 

 within samples. The probability level was set at 0.05 

 (a=0.05) and Yates's correction factor was used on ac- 

 count of there being only one degree of freedom for each 

 comparison. Juvenile retention was calculated as the 

 proportion of fish in aggregated size-frequency samples 

 below the mean size at first sexual maturity. 



Mortality and selectivity 



Size-at-age data were used to construct age-length keys 

 following the method of Ricker (1975) and these were 

 used to convert aggregated length-frequency data into 

 age-frequency distributions. The number of fish above 

 the age at which fish were fully recruited to the fishery 

 was calculated as a proportion of the total number of 

 fish. The annual instantaneous rate of total mortality 

 (Z) was subsequently determined with the age-based 

 catch curve method (Beverton and Holt, 1957). The 

 natural logarithm of the number of fish in each age 

 class was plotted against the corresponding age, and 

 Z <±95% CI) was estimated from the descending slope 

 of the best fitting line by using least-squares linear 

 regression. Initial ascending points representing fish 

 that were not fully recruited to the fishery were excluded 

 from the analyses. 



The annual instantaneous rate of total mortality was 

 also estimated with the length-converted catch method 

 of Pauly (1983). Pooled length-frequency samples were 

 converted into relative age-frequency distributions by 

 using parameters of the von Bertalanffy growth func- 

 tion. The natural logarithm of the number of fish in 

 each relative age group divided by the change in rela- 

 tive age was plotted against the relative age, and Z 

 (±95% CI) was estimated from the descending slope of 

 the best fitting line with least-squares linear regres- 

 sion. The estimates of Z from age-based and length- 



