The aim of the present study was to test the hypothesis that size variation among individuals of one particular age affects the precise assessment of anticipated growth curve trajectories and their parameters for the marine shrimp, Penaeus vannamei Boone, 1931. The data came from shrimp farmed in earthen ponds of an aquaculture farm located in the Gulf of California. Five asymptotic models were applied to averaged length-at-age data: specialized Von Bertalanffy, generalized Von Bertalanffy, Gompertz, Logistic and Johnson. These models were parametrized considering two criteria: (1) variability in length-at-age () decreases with age (growth compensation approach), (2) constant variance (“normal” and “fat tail”). The model parameters were computed with the maximum likelihood criterion. The corrected version of Akaike’s information criterion AIC_c, selected the Gompertz model and the growth compensation approach as those who fitted the data best. We conclude that the growth compensation approach allows the application of a very high performance objective function to analyse individual length-at-age variability without underestimation of the parameters, and also that the best model to describe the growth trajectory of P. vannamei in a farmed environment is a sigmoid curve with an inflection point at 34% of the life period analysed (the Gompertz model).

Length-frequency data of juveniles and sub-adults of Penaeus californiensis were analyzed, collected from January 2002 to January 2003 in the Agiabampo lagoon system and adjacent marine coastal zone. Six models were parameterized with four criteria, in addition to a mixed criterion (fat-tail and depensatory), to estimate the parameters that best fit the growth curve. The model that best fit was the Johnson model with the mixed criterion in females and males: k = 6.02 (5.93-6.12); L∞ = 188.8 (186.3-191.8); t0 = 0.0221 (0.0207-0.0234); and: k = 8.98 (8.85-9.12); L∞ =153.3 (151.7-155.0); t0 = 0.0386 (0.0378-0.0394), respectively. The conclusion is that: 1) the mixture approach found in this study as best leads to the application of a very high-performance objective function to analyze individual length-at-age variability, 2) shows that the best model to describe the growth trajectory of P. californiensis in marine and estuarine environments is a sigmoid curve with an inflection point near to cero age (Johnson model).

In Mexico, shrimp catch is the main fishing activity, and the second important species is the blue shrimp, Penaeus stylirostris. Specimens of P. stylirostris collected in 2016-2018 from inland waters (bay) and offshore (littoral) in the Santa María la Reforma lagoon (SMLR) system were analysed. The sexes were separated, and then individuals were measured in total length (L, mm) and weighed (W, g). The data were transformed into a natural logarithm and were adjusted to seven candidate models with a multi-model approach (Linear, Quadratic, Cubic, Broken stick, Two segments, Three segments and Four segments: the last two proposed in this study as new equations). A total of 30 439 specimens were analysed. Statistical differences were found in L between areas (KS test, ). Positive and negative allometry was observed according to biometric relationship and sex. The best model was selected with the lowest value of the Akaike information criterion, resulting in the choice of the Four segments model.

The species composition and variation in density (postlarvae m⁻³) of penaeid shrimp postlarvae were surveyed every 14 days in two zones of the Mexican Pacific coast; in the north (Mazatlán, 23°N 106°W) and south (Gulf of Tehuantepec, 15°N 95°W). Sampling coincided with full moon and new moon, and they were carried out with plankton net (0.3 m mouth diameter and 450 μm mesh size). Average sea surface temperature (SST) for 1985-1995 increased from Mazatlán (26.2 ± 0.2°C) to Tehuantepec (28.3 ± 0.5°C). The difference in SST between the coldest and warmest month was 7.8°C in Mazatlán and 3.3°C in Tehuantepec. Four species of penaeid shrimp postlarvae were identified: Litopenaeus vannamei (Boone, 1931), L. stylirostris (Stimpson, 1874), Farfantepenaeus californiensis (Holmes, 1900) and F. brevirostris (Kingsley, 1878). There was a regional variation in the species composition. L. vannamei was abundant at both coasts with 40% and F. californiensis varied from south to north from 45 to 36%; the less representative species were L. stylirostris and F. brevirostris, which varied from south to north from 15 to 24%. The occurrence period near Mazatlán is seven months, and it is year-round in Tehuantepec. This study suggests that warm water and low seasonal SST variability facilitate the presence of the shrimp larvae over a longer period.

The relative growth of Calappa convexa can be used to identify dimorphism or morphological change related to sexual maturation. The carapace width (CW) against width and length of the propodus of the right and left cheliped were tested to obtain a coefficient of allometry. CW against total wet weight WT values were analysed for length-weight relationships (LWR). Relative growth was analysed by a multi-model approach. Five models were tested and the best was selected due to the greater weight of the Akaike criterion (). Significant differences between sexes were found in CW (, ) and WT (, ). The negative or positive allometry varied according to the morphometric relationship and sex. No real winner model () was observed in the LWR analysis under a multi-model approach. The average model estimated a breakpoint at 118 mm CW in males and 132 mm CW in females.

A stock reduction analysis (SRA) of bigeye croaker Micropogonias megalops was performed based on commercial catch data. SRA solutions were restricted to a 2011 bigeye croaker stock biomass estimate of 14,412 t. The viable solution indicated a reduction in stock of 73.6% from 1983 to 2020 with an initial biomass of 22,186 t. In addition, a possible effect of hyperstability of the stock was evaluated by applying different versions of the Cobb–Douglas catch function. The most probable function based on a multi-model selection procedure was the one wherein the catch does not depend on biomass and is directly proportional to the applied fishing effort of small boats (~7 m) and vessels (~24 m). This situation suggests that in a free access regime, fishing can deplete the resource until it collapses, without observing a significant reduction in its catches until the event is very close.