The size structure of
C. bellicosus caught during the 2000, 2011 and 2014 seasons were dissimilar, causing differences in exploitation rates, fishing mortality and selectivity. In the 2000 to 2011 male capture seasons, a reduction of larger organisms was observed, apparently as a result of overfishing of growth. During the 2000, 2011 and 2014 seasons, the estimated selectivity for females in the fishing period reveals that the size of the first catch (CW50%) was determined at 97.5 mm CW, indicating that the captured organisms have not reached the size of first maturity (CW50% = 103.73 mm) in the BSMR as reported by [
19], suggesting a high risk of overexploitation of growth [
20]. In males, the effect of CW50% in the 2000 and 2011 seasons began after reaching the first maturity height (117.5 and 107.5 mm vs 103.73 mm) as proposed by [
19], the opposite case for the 2014 season where the CW50% was determined at 102.5 mm. However, there are studies on
C. bellicosus, where it has been determined that they can mature to smaller sizes between 51 and 112.4 mm on the Mexican Pacific coasts [
14,
19,
21], which would have a greater impact on the stock of broodstock and, therefore, the resource's capacity to renew. An average fishing mortality for the 3 years was 0.67 for females (F
2000= 0.112, F
2011= 0.257, F
2014= 1.639) and 0.32 for males (F
2000= 0.117, F
2011= 0.560, F
2014= 0.287), which was lower than that reported by [
19,
22] estimated fishing mortality between 1.1-1.37, 1.92-1.13 and 1.06-1.62 respectively. However, fishing mortality by size range reaches up to 4.85 (122.5 mm) in females and 3.10 in males (127.5 mm), which are the main contributors to catches in 2011, which causes a negative effect on the length at first maturity [
23], because of exploitation rates of more than 70 and 60% in each age group. The weighted exploitation rate of the 2014 season (0.426) was like that reported for the 2014 season by [
19] for the same region, who calculated an exploitation rate of 0.42 in females, however, it differs from that calculated in males (0.132) with a higher exploitation rate (0.34). In the same vein, [
22] in BSMR, using a predictive model (Thomson Bell), determined that female crabs (
C. bellicosus) are above their maximum sustainable yield, which differs in the present work, with an exploitation rate greater than 0.5, causing a decrease in population size [
24], while male crabs were below the maximum sustainable yield (E < 0.5). It is worth mentioning that the catches of
Callinectes sp. during the 2003 season in BSMR were no more than 300 tons, lower than what was reported in 2014 (3978 tons). [
19], in regions such as Bahía Navachiste and BSMR, using different methods, have concluded that the aforementioned areas are relatively healthy, which agrees with the present work.
In previous studies [
4,
19] the crab stock assessment in BSMR was done using the method propose by [
25]. This method is known as Catch-MSY. A key assumption of the Catch-MSY approach is the ability to define a reasonable prior range for the parameters of the Schaefer model. In the studies of [
4,
19], prior values of
r were between 0.6 and 1.5, which are default values suggested by [
25] for highly resilient species. Although no estimates of
r for
C. bellicosus exist, some reported life history parameters, such as age at 50% maturity (
L50%) and growth rate (
k) from a von Bertalanfy Model, are consistent with those of a resilient species. FishBase classifies highly resilient fishes as those with
k>0.3 year
-1 and
L50% < 1 year. With this [
4] concluded that crab fishery in Sinaloa state is in its limit of sustainability. While [
19] mentioned that the crab fishery is under risk of overexploitation. The later argument in consistent with the findings in present study that conclude similar result with different method the CASA model.
All methods devoted to management fisheries stocks have several limitations, and assessments stock biomass are expensive; however, because the sustainability of fisheries is desired and data-poor stocks are common, a simple method such as the Catch-MSY method proposed by [
25] is useful for the management of crab fisheries in the Gulf of California [
19]. In present study the CASA method was applied to crab fishery in BSMR, advising that the crab fishery in this coastal lagoon in Sinaloa state of Mexico is not at risk of over exploitation. After the literature research we support the use of CASA method because use of structured in sizes instead of age for a strong biomass analysis.
Reference [
4,
19] mentioned that management strategy for crab fishery is the catch quota. Thus, a catch quota of 5500 tons was recommended for the fishery in Sinaloa; however, because the stock biomass is below B
MSY, a smaller quota was recommended until the stock get its restocked. A precautionary catch quota of 3500 tons and 1171 tons are recommended for the Sonoran stock and for BSMR, respectively. Reference [
19] mentioned that if the recommended catch quota for the Sinaloa stock is divided by zones based on how catches contributed to the overall production of the state, a catch quota of 1100 tons would correspond to BSMR like that obtained in the stock assessment for BSMR separately. Once again, the present study becomes important for the crab fishery management in the region in particular and national in general.
To prevent overexploitation, the knowledge in population biology is fundamental. The contribution of the results, presented in this study, tend to support the conservation of the species under study. Is important to recall that in organisms with a short life cycle that are subject to high fishing pressure, biological process that occurs in a particular year define the stock´s abundance in the same years. Crabs of
Portunidae family from the Gulf of California comprise this principle. Since 1982, the brown crab
C. bellicosus has become the focus of an important commercial fishery in Mexico, especially in the eastern Gulf of California, where a small-scale fishery for these crabs has been established [
19]. The most effective strategy to reduce the risks of adverse economic, and social effect in this fishery would be the continued gathering of biological studies such as the surveys presented here.