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Fishery Bulletin 120(2) 
The standard errors of L;,) and Lg, were calculated with 
the delta method by using the package msm (vers. 1.6.9; 
Jackson, 2011) in R, and a Wald-type confidence interval 
was also calculated. The differences between sexes in the 
maturity model parameters were examined by applying 
information theory. The Akaike information criterion 
(AIC) was calculated to select the best model: 
AIC = 2p — 2in(Lik), (4) 
where p = the number of parameters; and 
Lik = the maximum likelihood of the model. 
Candidate models were fitted with data for the sexes 
pooled or separated, and then the AIC values for the mod- 
els were compared. The model with the lowest AIC value 
was selected as the best working model. 
Histological techniques were used to record different 
phases during the development of gonads. The gonads 
from fresh specimens were removed, weighed, and fixed 
in Bouin solution for 2 h and preserved thereafter in abso- 
lute ethanol. By using an ATP1 automated tissue proces- 
sor, TBS? (VWR International, Radnor, PA), small portions 
(anterior, posterior, middle, oviduct, and vas deferens) of 
these gonads were dehydrated through the use of a series 
of graded ethanol solutions finalized with a clearing step 
in xylene. The gonad tissues were thereafter embedded in 
paraffin wax, sectioned at 5-6 pm with an automated TBS 
SHUR/Cut 4500 microtome (Cole-Parmer Instrument Co., 
Vernon Hills, IL), and stained with eosin and hematoxylin 
(Bancroft and Stevens, 1990) with a TBS SHURStain 3030 
automated slide stainer (General Data Co. Inc., Cincinnati, 
OH). The stained sections were examined under a binoc- 
ular microscope (Olympus BX51, Olympus Corp., Tokyo, 
Japan). The sections were photographed by using an 
Olympus DP72 microscope camera (Olympus Corp.). Iden- 
tification and description of the different maturity stages 
in the ovary and testis were done on the basis of the works 
of Haddy et al. (2005) and Kizhakudan (2014). 
Because aging data are not directly available for the 
flathead lobster, statistical techniques were used to deter- 
mine the number of cohorts sampled over 4 years that 
underlie the length—frequency data. The method involves 
1) a statistical model for estimating the number of cohorts 
underlying the length—frequency data on the basis of the 
multinomial distribution, 2) biological criteria to resolve 
the aging of the cohorts, and 3) a hierarchical statistical 
model based on the multivariate normal distribution to fit 
a growth model to the mean length and the assigned age 
of each cohort. Details of the mathematical and statisti- 
cal models and the software used to fit the models to data 
have been described in Roa-Ureta (2010). 
Statistical analysis of the age structure was conducted 
with aggregated data, without distinction by year or sex, 
owing to the small sample sizes (n) for all years (2013: 
n=21; 2014: n=15; 2015: n=31; 2016: n=235; total: n=302). 
? Mention of trade names or commercial companies is for identi- 
fication purposes only and does not imply endorsement by the 
National Marine Fisheries Service, NOAA. 
In selecting a model for estimation of the number of 
cohorts underlying the length—frequency data, we tested 
models that included 2, 3, 4,5, 6, 7, and 8 cohorts. This wide 
range of hypotheses for the number of cohorts was tested 
because nothing was known about the age structure of the 
stock in waters of Saudi Arabia in the Arabian Gulf. A low 
number of cohorts would indicate a short-lived stock, and 
a high number of cohorts would point to a long-lived stock. 
Among the 7 models fit to the length—frequency data, the 
best model was selected by using the AIC. Age assignment 
for the resulting number of cohorts was based on previ- 
ous biological knowledge about the number of spawning 
events, the duration of life at the larval stage, and size at 
settlement. 
Once the number of cohorts composing the length— 
frequency data and associated parameters were estimated 
and once age assignment was completed, we fitted the fol- 
lowing 2-parameter version of the von Bertalanffy growth 
function to the mean length and age data: 
L(a)=L,, i = [=| aa (5) 
where L(a) = carapace length at age a; 
L,, = asymptotic carapace length; 
Ly = carapace length at birth; and 
K = the growth coefficient. 
The model is used to estimate only 2 parameters, L,, and K, 
because L, is assumed to be known from previous biolog- 
ical information and is equal to 8 mm. Both the multino- 
mial model for length—frequency data and the multivariate 
normal model for the growth data were fitted by using in 
AD Studio, vers. 1.0, the AD Model Builder (vers. 12.0; 
Fournier et al., 2012) code in the supplementary material 
accompanying Roa-Ureta (2010). 
This method has been used in many previous studies 
and has been useful for studying the growth of other crus- 
taceans, such as the green tiger prawn (Rabaoui et al., 
2017) and a blue swimming crab, Portunus segnis (Rabaoui 
et al., 2015b, 2021b). 
Old bycatch fishery and stock assessment 
The official Saudi government fisheries statistics for land- 
ings and fishing effort (MEWA?) that were collected for the 
2 fleets of small boats (called tarad) and large boats (called 
dhow), in Saudi Arabia from 1995 through 2008, include 
landings of flathead lobster as valuable bycatch of the 
trawl fishery for the green tiger prawn, the main Saudi 
fishery in the Arabian Gulf, both by volume and value. The 
number of boats operating in this fishery is close to 2000 
(Roa-Ureta, 2015). Almost half of them are traditional 
Arabic dhows with lengths ranging from 15 to 20 m, and 
the other half are smaller tarad boats with lengths of less 
3 MEWA (Ministry of Environment, Water & Agriculture). 1995— 
2008. Official fisheries statistics of Saudi Arabia. [Available 
from Fish. Dep., Minist. Environ. Water Agric., Riyadh 11195, 
Saudi Arabia.] 
