In the 34 progression lines all initial cohorts were identified (Figure 2), and after in each progression line TL was estimated taken into account the days that elapsed between initial and terminal cohort. In this case TL was expressed in months.

Estimated TL values were separated by recruitment seasons types, and with this information a classification neuronal model (CNm) was conducted with three train layers (Haykin, 1999 [9] ). Linear models were used in order to activate the synaptic signals and three train layers. CNm results were two probability trends with scale between 0 and 1 that were called dwell time inside lagoon during marine recruitment season P(TL_MR) and dwell time inside lagoon during lagoon recruitment season P(TL_LR). The first probabilistic trend was used for re-estimating the recruitment age and the second probabilistic trend was used in order to approximate youngest shrimp age inside CTJB-LS.

White shrimp length parameters were estimated with 3,955 records of Lt arranged in age classes from 1 to 5-m-olds (Et) (Figure 2). The Pitcher and McDonald, 1973 [10] model was used:

L t e = L i n f ⋅ ( 1 − exp [ − k ⋅ ( E t − t o ) + ( ( k ⋅ C ) / ( 2 π ) ) ⋅ sin ( 2 π ⋅ ( E t − t s ) ) ] ) + ε (1)

where L_te (estimated total length), L_inf (the asymptotic length), k (the metabolic growth rate in body length), t_o (the age at zero cm), C (oscillations magnitude), t_s (starting point of C), ε is the estimation error of L_te.

With estimated length parameters the L. vannamei length trend was conducted inside CTJB-LS. This length trend was complemented with a projection towards outside CTJB-LS where the adult shrimp population reaches the oldest age. According to Taylor 1958 [11] , the oldest age was estimated with:

A 0.95 = t o + ( 2.996 / k ) (2)

where the oldest age is called A_0.95 and 0.92 is the time required to obtain 95% of L_inf value.

White shrimp Lt-Pt relationship was evaluated with 6,148 records of Lt and Pt. According to Ricker 1975 [12] , this relationship was estimated with:

P t = a ⋅ L t b + ε (3)

where a is the intercept, b is the slope, and ε is the estimation error. Estimated b parameter was compared with b = 3 (isometric grow) in order to know how L. vannamei grew during marine and lagoon recruitment seasons. This analysis was evaluated with t-student distribution (Zar, 1999 [13] ), and according to Ricker 1975 [12] when shrimp bodies grow equally in length and weight, resulted growth is isometric (b = 3). On the other hand, when shrimp bodies grow more in length than in weight, resulted growth type is negative allometry (b < 3), and the inverse is positive allometry (b > 3).

To estimate the parameters in the Equations (1)-(3), the Bayesian method of likelihood was used with the ε fitted to log-normal distribution (Haddon, 2011 [14] ). Bayesian method of likelihood was conducted with PopTools 2.7.5 software, and CNm was executed with StatSoft® 7.0 software.

TL values are summarized in Table 1.

Results of this section are shown in Figure 3.

For the population of L. vannamei inside CTJB-LS, the real age structure resulted between 1 and 4-m-olds (Figure 2). During marine recruitment season it was observed that when age increased the P(TL_MR) gradually descended. Estimated P(TL_MR) = 0.50 was taken into account as the midpoint of change in order to understand how young shrimp with 3-m-olds started leaving the CTJB-LS (P(TL_MR) > 0.5), and how the rest remained inside CTJB-LS (P(TL_MR) < 0.5). Young shrimp in 4-m-olds showed the minimal P(TL_MR) value, and ages > 4-m-olds were not found inside CTJB-LS. Based on the aforementioned, it was concluded that young shrimp migration elapsed between 3 and 4-m-olds, with the highest recruit flow in 4-m-olds. This last age was called the recruitment age of L. vannamei.

During lagoon recruitment season it was observed that when age increased the P(TL_MR) gradually ascended. Estimated P(TL_MR) = 0.50 was taken into account as the midpoint of change in order to understand how young shrimp between 3 and 4-m-olds started to have a relevant presence inside CTJB-LS (P(TL_MR) > 0.5), and how the rest did not show a relevant presence (P(TL_MR) < 0.5). Young shrimp in 1-m-old recorded the value of 0.40 in P(TLMR), and based on this it was concluded that post-larval could not be detected inside CTJB-LS until they reach 1-m-old ( youngest shrimp age).

Results of this section are shown in Figure 4.

The ages that frequently entered and developed inside CTJB-LS were identified between 1 and 4-m-olds (Figure 3), and for this age structure the Lt ranked from 51 to 106 mm (Figure 4). The A_0.95 was estimated at 19-m-olds reaching the asymptotic length at 205 mm.

Results of this section are summarized in Table 2 and Figure 5.

White shrimp Lt-Pt relationship resulted almost equal in both recruitment seasons (F = 3.25, F_0.05(1,6146) = 3.84, p > 0.05). But based on estimated b parameters,

it was concluded that during marine recruitment season Lt-Pt relationship was isometric (ho: 3.04 = 3.00, t = 0.87, t_{0.05(1),3,953)} = 1.64, p > 0.05), and during lagoon recruitment season this relationship was negative allometry (ha: 2.88 < 3.00, t = 10.81, t_{0.05(1),2,191} = 1.64, p < 0.05).

The highest biomass production was recorded inside CTJB-LS during marine recruitment season (Figures 2-6), and this was explained by the high cohorts number that reached the recruitment age with 8.4 g and > 106 mm. The lowest biomass production was recorded inside CTJB-LS during lagoon recruitment season (Figures 2-6), and this was explained by the low cohorts number that reached the recruitment age with 7.6 g and > 106 mm.

The region of GT is influenced by northerly winds from the Gulf of Mexico, which produce intense upwelling during winter Tehuanos seasons between November and February (Fernández-Álamo et al., 2000 [15] ). The upwelling process generates an ascension of cooler deep water and an elevated concentration of nutrient due to the rupture of the thermocline (González-Silvera et al., 2004 [16] ). These characteristics induce a complex oceanographic pattern with cyclonic and anticyclonic eddies that affect the concentration of chlorophyll a (Cl-a), primary productivity, and spatial distribution of organisms (Gallegos-García and Barberán-Falcón, 1998 [17] ; Monreal-Gómez and Salas de León, 1998 [18] ; Farber-Lorda et al., 2004 [19] ). Lara-Lara et al., 1998 [20] mentioned that outside winter Tehuanos seasons (during rainy seasons between May and October), in the region of GT lower Cl-a and primary productivity values were documented, and these were generated mainly by the local fluvial discharge.

As was established for L. vannamei, marine recruitment seasons spanned from April to August, with the highest recruit flow during June/July. These seasons coincided with the rainy seasons, when lower reproductive activity was documented. Reproductive seasons spanned from July to November, with the highest post-larvae flow during October (Cervantes-Hernández et al., 2008 [4] ).

Inside lagoon systems rainfall and fluvial discharge impose osmoregulatory limitations that stimulate young shrimp migration toward marine environments (Ruello, 1973 [21] ; Cruz-Orozco and Ley-Lou, 1980 [22] ; García and Le Reste, 1986 [23] ; Cervantes-Hernández, 2015 [24] ). Browder and Moore 1981 [25] mentioned that fresh water flow into coastal body of water increases shrimp production because mineral, organic matter and turbidity increases (Penn and Caputi, 1986 [26] ), and salinity with water temperature are reduced. García and Le Reste 1986 [23] indicated that environmental changes might delay or hurry shrimp migration.

In the Bank of Campeche, Mexico, Cervantes-Hernández 1999 [27] showed that marine recruitment of pink shrimp Farfantepenaeus duorarum (Burkenroad 1939) has a relationship with accumulated rainfall and fluvial discharge since 2 and 1 months, respectively, before maximum recruitment occur. Similar results were documented by Gracia and Soto 1990 [28] in white shrimp Litopenaeus setiferus (Linnaeus 1767).

In this study, it was concluded that young recruits migration toward outside CTJB-LS elapsed between 3 and 4-m-olds, with the highest recruit flow in 4-m-olds. Thus this last age was called the recruitment age of L. vannamei (Figure 3). The young of L. vannamei from 83 to 120 mm were documented as present marine environment in front of the Mar Muerto, CTJB-LS, Chantuto-Panzacola y Carretas-Pereyra lagoon systems, Oaxaca-Chiapas, Mexico (Figure 1) (Ramos-Cruz, 2011 [29] ). Specific ages for these sizes were not reported but based on Figure 4, it was suggested that these ages should be between 3 and 5-m-olds.

A recruitment age in 4-m-olds was documented for brown shrimp Farfantepenaeus californiensis (Holmes 1900) in GT (Cervantes-Hernández, 2008 [1] ; Cervantes-Hernández et al., 2008 [4] ), and brown shrimp Farfantepenaeus aztecus (Ives, 1891) in Tamaulipas-Veracruz region, Gulf of Mexico (Cervantes-Hernández, 2015 [24] ). The young of L. vannamei and F. aztecus with 3-m-olds were documented as present in the marine environments from gulfs of GT and Mexico (Cervantes-Hernández et al., 2008 [4] ; Cervantes-Hernández, 2015 [24] ). Due to its lower finishing mortality rates (F) and abundances these ages were reported underexploited, and partially recruited to the adult population. Monthly F values were estimated at F = 0.01 (Ramos-Cruz et al., 2006 [3] ), and F = 0.02 (Cervantes-Hernández, 2015 [24] ), respectively. In this study, this specific age was considered such as the minimum recruitment age inside CTJB-LS.

Inside CTJB-LS the recruitment age of L. vannamei was reported between 4.5 and 5-m-olds (Cervantes-Hernández et al., 2012 [7] ), but in this study ages > 4-m-olds were not found in this lagoon system. These specific ages were considered as the maximum recruitment ages that can be found outside CTJB-LS (Ramos-Cruz, 2011 [29] ), completely recruited to the adult population (Lt~125 mm y Pt~14 g) (Figure 4 & Figure 5). The aforementioned was true, because the sexual maturity age is generally reached between 6 and 7-m-olds as in cases of F. californiensis (Cervantes-Hernández, 2008 [1] ), F. aztecus (Cervantes-Hernández, 2015 [24] ) y L. vannamei (Cervantes-Hernández et al., 2008 [4] ). For those species the entire population is sexually mature between 11 and 16-m-olds.

Based on the information mentioned in the literature a new conclusion was done. In brief, in optimal environmental conditions (mainly rainfall and fluvial discharge), in CTJB-LS young recruits migration occurs during marine recruitment seasons between 3 and 5-m-olds, with the highest recruit flow in 4-m-olds. Environmental changes might delay (dominant ages in 5-m-olds) or hurry (dominant age in 3-m-olds) young recruits migration. The first case was documented by different authors, and this was explained due to excesses in the built of reservoirs and environmental pollution (Cervantes-Hernández, 2015 [24] ; Cervantes-Hernández et al., 2012 [30] ; 2017 [31] ). The 5-m-olds age was documented in relation with delay young recruits migration (Solana-Sansores et al., 1989 [32] ; Hannah, 1999 [33] ). The second case has relationship with the prolonged development of rainfall and fluvial discharge periods.

As was established, during marine recruitment season the recruitment age recorded 8.4 g with Lt at 106 mm, and during recruitment season, the Pt reduced by 0.8 g at the same Lt value (Figure 6). Ramos-Cruz (2011) [29] recorded 6.0 g in the youngest recruits of L. vannamei. Specific age for this weight was not reported but based on Figure 4, it was suggested that this age should be 3-m-olds with Lt at 80 mm. This author did not consider differences between marine and lagoon recruitment seasons in order to estimate the following Lt-Pt relationship model: Pt = 0.0000283・Lt^3.22 + ε. The author did not conclude on this model but considering that b = 3.22, it was suggested that during study period Lt-Pt relationship was positive allometry (b > 3).

Since 1976 in lagoon systems located in GT, the artisanal catch of L. vannamei and F. californiensis has been done with atarraya nets with mesh opening of 25.4 mm (Ramos-Cruz, 2011b [8] ). PESCA 1997 [34] indicated that the artisanal catch must be done with atarraya nets with mesh opening of 38.1 mm, but this mesh opening really have never been used in GT. With the first mesh opening mentioned by [8] the length catch ranked from 60 and 120 mm, and with suggested ages between 1.5 and 4.5-m-olds (Figure 4). On the other hand, with an atarraya nets with mesh opening <25.4 mm the length catch was <80 mm (<3-m-olds). It was considered that these mentioned data were not correct because the artisanal catch of this study was obtained with mesh opening of 19 mm, and the age catch ranked from 1 and 5-m-olds. Thus, it was concluded that atarraya nets with mesh opening between 19 to 25.4 mm generate the same range of catch for shrimp length and age. Ramos-Cruz, 2011 [8] reported in activity atarraya nets with mesh opening from 9.5 to 25.4 mm.

The discussion about which mesh opening should be used to protect shrimp recourse in GT is open, and in this study we did not recommend a mesh opening to use inside lagoon systems because we do not have a scientific base to support this, instead shrimp artisanal catch can carry on like ever, but the following should be taken into account:

1) Atarraya nets with mesh opening of 25.4 mm can be used during complete lagoon recruitment seasons because as was established before, in CTJB-LS biomass production was lower. This same should be done in the other lagoon systems located in GT.

2) During marine recruitment seasons atarraya nets with mesh opening of 25.4 mm only can be use from April to May when biomass production and young recruits migration begin to increase. All fishing methods shall be prohibited from June to July because in this period maximum young recruits migration occurs (Figure 2). Details in the literature (Cervantes-Hernández, 1999 [27] ; 2008 [1] ; 2015 [24] ; Cervantes-Hernández et al., 2008 [4] ; 2012 [7] ; 2017 [31] ).

The marine shrimp fishery has been regulated in Mexican Pacific through closure systems, and these were documented as follow: from July to September (between 1979 and 1987), from May/April to September (between 1993 and 1997) (Cervantes-Hernández et al., 2008 [4] ), from April to September 1999, and afterwards of 2001 from March/April to September (INAPESCA, 2007 [35] ). In GT, closure periods have not worked because these periods were focused on protecting marine recruitment seasons, and lagoon recruitment seasons were only partially included. In the literature if was found that L. vannamei reproductive seasons spanned from June to November, with the highest post-larvae flow during October (Cervantes-Hernández et al., 2008a [4] ). In the case of F. californiensis reproductive seasons spanned July to February, with the highest post-larvae flow during October/November (Cervantes-Hernández, 2008 [1] ; Cervantes-Hernández et al., 2008 [4] ).

The last authors mentioned proposed a new closure system to protect shrimp reproductive seasons exclusively in GT. This closure system was reported from June/July to October, and afterward this was ratified by Cervantes-Hernández et al. 2017 [31] from July to November. To manage the artisanal shrimp catch, the second choice should be better because during July a lagoon closure can be established inside lagoon systems located in GT. This new proposal will allow for artisanal fishermen to use atarraya nets with mesh opening of 25.4 mm during complete June, and they will obtain a good biomass production level as support (Figure 6).

From the beginning, the results published on marine closure system changes in GT were not accepted by the fishery community in Oaxaca because those studies did not include lagoon recruitment information in their fishery models. At present, shrimp fishery in GT is reported on a critical level of overexploitation (Cervantes-Hernández et al., 2006 [36] ). A lagoon closure was proposed by Barrera-Huerta in 1976 [37] , and this was not taken into account due to a lack of ecological, biological and fishery analysis. Now, L. vannamei fishery has complete population analysis in order to influence possible closure system changes. This information is a guide to plan F. californiensis fishery because both fisheries in GT reproduce almost at the same time.