Jorge A. L´opez-Roh, Frniso J. Fern´ndez-River Melo, Ernesto Gst´elum-Nv,Estefni Lrios-Cstro

aLaboratorio de An´alisis Espacial de Zonas Costeras, Unidad Multidisciplinaria de Docencia e Investigaci´on, Facultad de Ciencias, Universidad Nacional Aut´onoma de M´exico, Sisal, 97356, Yucat´an, Mexico

bComunidad y Biodiversidad A.C, Guaymas, 85448, Sonora, Mexico

cCentro de Investigaciones Biol´ogicas Del Noroeste, La Paz, 02320, BCS, Mexico

Keywords:

ABSTRACT

1.Introduction

Small-scale fisheries contribute approximately half of global catches while employing about 90% of the workforce that depends directly on this activity (FAO, 2018). Strengthening small-scale fisheries has been recognized not only as an important employment strategy, but also as a way to address issues of food security and poverty, while the mismanagement of these resources has ecological, socioeconomic, and governance implications (FAO, 2018). It is well-established that a proper fishery management system requires both the adequate exploitation of fish stocks and a balance among environmental, social, and economic objectives (Ahmed, 1991; Charles, 1988; Hanna, 1994).

The natural populations of many small-scale fisheries have decreased, a decline related primarily to the overexploitation of resources (DOF, 2012; DOF, 2018; Pauly & Zeller, 2006; Vasilakopoulos et al., 2014). In Mexico, this tendency has been reported for several fisheries, especially those populated by sessile resources such as bivalves(scallops, clams, oysters, etc.) (Saenz-Arroyo et al., 2005; Antarctic Studies Report, ; Narchi et al., 2018; DOF, 2018). Excessive fishing since the 1970s has caused a drastic decrease in catch volumes and the local extinction of some banks, while impeding the recovery of natural populations (Fern´andez-Rivera Melo et al., 2015). The main causes of the overexploitation of these resources are the lack of adequate regulations,open access, and an over-capitalization of fishing operation, in detriment to the economy of the communities that traditionally exploit these resources (Narchi et al., 2018).

Fig.1.The study region in the northwest area of the Gulf of California, near Puerto Libertad, Sonora, Mexico.

The clam species

Megapitaria aurantiaca

(golden callista),

M. squalida

(squalid callista) and

Dosinia ponderosa

(ponderous dosinia) have long been captured in northwest Mexico (L´opez-Rocha et al., 2010). These fisheries are small-scale and fishing operations are carried out using small boats with outboard motors and hooka diving equipment (DOF,2018). Although this history of exploitation in various areas of the Gulf of California and along Mexico’s Pacific coast, no specific management plans currently regulate these fisheries. Today, management of the squalid callista and golden callista fisheries is governed only by a few general guidelines issued by the National Fishery Charter, a document that proposes closures, minimum sizes and exploitation rates of 20%–25% for squalid callista and 15%–20% for golden callista (DOF, 2012;DOF, 2018). Despite these regulations, clam populations are deteriorating in most harvest zones (DOF, 2018; DOF, 2020) and management has been reactive rather than adaptive in nature.In 2010, commercially unexploited clam banks off the coast of the Puerto Libertad fishing community (Gulf of California) with

M. aurantiaca

,

M. squalida

and

D. ponderosa

were found. In order to adequately manage and exploit these banks it is necessary to generate basic knowledge about the size of the exploitation zones and species abundance, and then determine reference points to establish clear,simple harvest control regulations (Jardim et al., 2015; Smith & Rago,2004).

Fig.2.Distribution of transects for estimating density and abundance in Bank A for M. squalida and D. ponderosa; and in Bank B for M. aurantiaca, Gulf of California, Mexico.

Harvest strategy regulations are specific guidelines that determine catch volumes, effort, and fishing mortality, based on current estimates of the state of the system, such as population abundance and the amount of spawning biomass (Deroba & Bence, 2008; Jardim et al., 2015). In light of the characteristics of the clam fisheries in the study area, this study argues that regulations must be tailored specifically to each fishing bank according to the level of biomass before the fishing season begins,and in consonance with the biological, economic, and social objectives of each fishing community. This study presents an evaluation of new clam fishing banks that will allow us to generate information during the initial stages of fishing, though in a limited data situation, based on estimates of abundance and an analysis of the life history of the species involved. This approach will then enable us to propose specific harvest control regulations for each population (by species and area), a process deemed fundamental for sustainable resource use, and one that concurs with the main precautions observed in fisheries to avoid postponing decision-making in fishery management (Dowling et al., 2019; FAO,1995; Mayfield et al., 2008).

The study estimated the abundance of the clams

M. aurantiaca

,

M. squalida

, and

D. ponderosa

in two new fishing banks in the Gulf of California using a geostatistical method that permits incorporating the spatial variability that characterizes clam populations. It also evaluates the effects of fishing on the biomass of a cohort according to different sizes of first capture in an effort to provide information that will help establish simple harvest control regulations, such as minimum catch size and the total catch quota for each population, two fundamental measures for sustainable fisheries management.

2.Materials & methods

2.1.Study site and sampling

Research was carried out at Puerto Libertad in the northern area of the Gulf of California (Fig.1). The study region has an annual average surface temperature of 22.6C, average salinity of 34.6 UPS (Locarnini et al., 2010), mean productivity of 1752 mg/cmday, and dissolved oxygen of 503 mL/L (García et al., 2010 a, b). In this area,

M. aurantiaca

,

M. squalida

and

D. ponderosa

have been located in banks found mainly at depths of 2–30 m.In March 2017, transects were conducted by semi-autonomous scuba diving on two clam banks that measured 50 m in length by 1 m in width,where all sample organisms were collected. In Bank A (Puerto Libertad),where

M. squalida

and

D. ponderosa

were distributed, 123 transects of

M. squalida

and 119 of

D. ponderosa

were performed. In Bank B (Cerro Bola), where

M. aurantiaca

was distributed, 46 transects were conducted. Total length measures were made on 1000 individuals of each species. The methodological details of the measuring process, and the results of the length frequency distributions were published in L´opez-Rocha et al. (2018). All transects were distributed between the coordinates 112.75W; 29.91N and 112.65W; 29.84N. Bank A has an area of 5437 km, while Bank B covers an area of 861 km(Fig.2).

2.2.Density and abundance estimates

To estimate the density by species, the number of individuals collected in each transect was divided by 50 (50 m=area of the transect) to provide an estimate of the number of individuals per square meter (ind./ m). Abundance estimates were acquired using a geostatistical method previously recommended for benthic invertebrate species (Ulate-Naranjo, 2011; Hern´andez-Flores et al., 2015). For this type of resource, a large number of sampling stations with zero individuals are commonly recorded, together with aggregation areas of organisms that can generate biases and large variance in estimates of total abundance (Pennington, 1996).

The Kriging geostatistical interpolation method was used (Isaaks &Srivastava, 1989). The first step consisted in an analysis that describes the spatial correlation of the data through semi variograms. Once a description of the autocorrelation structure was acquired using an experimental semi variogram, a theoretical model of spherical semi variance was fitted. An interpolation of the density in the study area was conducted using the ordinary Kriging method with the Surfer computer program.

Calculations of the per species abundance in each interpolation cell were performed by multiplying the estimates of the number of individuals per square meter by the area of the cell. The number and area of cells were determined as a function of the total area of the bank and the number and distribution of the transects. In Bank A, the area of each interpolation cell was 5465.68 mwith a total of 336 cells, in Bank B the area of each cell was 2116.76 mwith a total of 407 cells. Total abundance per species was then estimated by multiplying the median abundance by the total number of cells.

2.3.Relative cohort biomass-at-length

To comparatively evaluate the effect on a cohort, first catch length(

L

) was set equal to the first maturity length (

L

) or optimal length (

L

)in a no-fishing situation. Three theoretical scenarios were simulated according to the estimates of relative cohort biomass-at-length. The control scenario refers to the total natural production of a cohort in the condition without exploitation (fishing mortality

F

=0). For the moderate fishing scenario,

F

=0.5

M

and

L

=

L

; while for the moderate optimal fishing scenario,

F

=0.5

M

and

L

=

L

. Estimating the cohort biomass-at-length involved the following procedure: first, the number of individuals in the cohort at age t (

N

) was estimated using equations from Froese et al. (2008):

where:

R

is recruitment;

M

is natural maturity (year);

t

is age (years);

t

is the parameter of von Bertalanffy’s growth equation (years);

t

is age of first capture (years); and

F

is mortality due to fishing (year).

R

=1 was taken as the total recruitment at the beginning of the cohort (100%),so all estimates of

N

are relative.The relative biomass of a cohort (

Br

) was also estimated in accordance with Froese et al. (2008), using the equation:

Br

=

a

⋅

L

⋅

N

where

Br

is the relative biomass at age

t

;

a

and

b

are parameters related to weight (g) – length (mm),

L

is total length at age

t

in mm; and

N

is population size at age

t

taken as the number of individuals. The lengths corresponding to each age (

L

) were estimated using Von Bertalanffy’s growth equation:

where

K

(year) is the coefficient of growth and

L

(mm) is the asymptotic length.The optimal catch length (

L

) was calculated by:

The parameters used in the models were taken from L´opez-Rocha et al. (2018), who provided the following values for the three species in the study area:

-

M. squalida

:

a

=0.002;

b

=2.553;

L

=106.31 (mm);

K

=0.439(year);

t

=0.000 (years);

L

=40.32 mm; values of M for juveniles

M

=1.966 yearsand for adults

M

=1.448 years;

D. ponderosa

:

a

=0.00008;

b

=3.3029;

L

=131.57 (mm);

K

=0.448 (years);

t

=-0.044 (years);

L

=103.44 mm;

M

=1.534 yearand

M

=0.728 year; -

M. aurantiaca

:

a

=0.00006;

b

=3.4277;

L

=126.49 (mm);

K

=0.421 (year);

t

=- 0.413 (years);

L

=77.2 mm;

M

=1.261 yearsand

M

=0.713 years.

2.4.Population and biomass structure

The total estimated abundance of each species was calculated by size interval, taking the length frequency distribution as a weighting factor.Abundance by size was then transformed into biomass through the weight-length relationship reported for these species by L´opez-Rocha et al. (2018).

2.5.Catch regulations

Based on the information obtained, two harvest regulations were established, the maximum catch quota (

C

objective), based on capturing a maximum of 10% of the lower confidence interval of the estimated abundance for a range above the first catch length,

L

; and the minimum catch size based on the

L

that provides the largest remainingbiomass of a cohort, either

L

=

L

or

L

=

L

. The maximum catch limit(

C

limit) was calculated as 10% of the average estimated abundance for a range above first catch length,

L

.

Table 1 Density estimates of M. squalida, D. ponderosa and M. aurantiaca in Puerto Libertad, Gulf of California. n =number of transects; S.D. =standard deviation; C.V. =coefficient of variation.

Fig.3.Distribution of the estimated abundance in number of individuals of A) Megapitaria squalida, and B) Dosinia ponderosa per square in Bank A.

Fig.4.Distribution of the estimated abundance in number of individuals of Megapitaria aurantiaca per square in Bank B.

3.Results

The 123 transects of

M. Squalida

were conducted at depths of 2–25 m. A total of 572 individuals were captured. The number of individuals captured per transect varied from 0 to 26 with an average of 4.65 (±6.14 S.D.). For

D. ponderosa

, 119 transects were conducted at depths of 2–25.5 m, capturing a total of 4232 individuals. The number of individuals captured varied from 0 to 110 per transect with an average of 35.6 (±27.81 S.D.). For

M. aurantiaca

, 46 transects were conducted at depths of 10–14 m. A total of 1173 individuals were caught. The number of individuals captured per transect varied from 0 to 63 with an average of 25.5 (±14.82 S.D.) (Table 1).Regarding abundance estimates, a heterogenous distribution was observed with respect to the densities which suggests a distribution of the three species in patches. Two large zones with high densities of

M. squalida

were observed in the northern and southern areas of the study region with a well-defined zone marked by high abundance and low size in the center. Some zones in the central and northern areas of the study region had no presence of

M. squalida

or only a low abundance(Fig.3A). In the case of

D. ponderosa

, two well-defined, high-abundance zones were found in the northern and southern areas of the study region(Fig.3B), while for

M. aurantiaca,

a high-abundance zone was located in the area farthest from the coast in the southern area of the study region,with a second high-abundance zone near the coast in the northeastern area (Fig.4). Total estimated abundance for

M. squalida

was 324,086 individuals with 95% confidence intervals of 266,293–381,881; for

D.

ponderosa,

the figures are 3,117,356 individuals(2,779,100–3,455,597); while the abundance of

M. aurantiaca

was 428,088 individuals (408,783–447,391).

Fig.5.Relative biomass of a cohort with respect to the first catch length of: A) Megapitaria squalida; B) Dosinia ponderosa; and C) Megapitaria aurantiaca. Lm =length at first maturity; Lopt =optimal length; Lc =first catch length. F =fishing mortality. M =natural mortality.

Table 2 Abundance and biomass estimated by size structure of M. squalida, D. ponderosa and M. aurantiaca in Puerto Libertad, Gulf of California. Abundance corresponds to the value of the lower 95% confidence interval.Abundance andtotalbiomassarepresented, correspondingto thelength at first maturity Lm;andabovetheoptimallength Lopt. Gray shaded values representthebiomassused to determinetheharvestcontrol.Biomass (t)0.02 0.02 0.08 0.16 0.00 0.08 0.62 1.31 2.37 2.62 13.46 40.81 52.51 28.86 13.39 3.69 0.98 Abundance (number)817 817 2042 2859 0 817 4900 8167 11843 10618 44921 113120 122104 56764 22461 5309 1225 Sample frequency (number)22570212 20 29 26 110 277 299 139 55 13 3 Megapitaria aurantiaca Total weight (g)19 28 40 55 75 98 127 160 200 246 300 361 430 508 596 694 803 Total length (mm)40 45 50 55 60 65 70＊75 80＊＊85 90 95 100 105 110 115 120 Biomass (t)0.09 0.12 0.33 0.22 1.93 2.77 8.13 24.05 68.20 137.40 177.97 242.71 188.68 46.83 14.70 3.74 Abundance (number)2771 2771 5542 2771 19396 22166 52645 127456 299245 504283 551387 640052 426701 91436 24937 5542 Sample frequency (number)11217819 46 108 182 199 231 154 33 92 Dosinia ponderosa Total weight (g)33 45 60 78 99 125 154 189 228 272 323 379 442 512 589 674 Total length (mm)50 55 60 65 70 75 80 85＊＊90 95 100 105＊110 115 120 125 Biomass (t)0.00 0.01 0.00 0.01 0.07 0.15 0.39 0.91 1.46 1.66 3.58 8.09 9.27 4.01 0.31 0.06 0.00 0.08 Abundance (number)528 793 0793 2642 4491 8982 16379 21134 19549 34872 66045 64196 23776 1585 264 0264 Sample frequency (number)230310 17 34 62 80 74 132 250 243 90 6101 Megapitaria squalida Total weight (g)4712 17 25 33 44 55 69 85 103 122 144 169 195 224 255 289 Total length (mm)20 25 30 35 40＊45 50＊＊55 60 65 70 75 80 85 90 95 100 105 161 161 159 408,783 401,432 388,364 1001 983 951 918 497 904 2,779,100 1,188,668 2,671,039 1003 429 964 30.1 30.03 29.8 266,293 264,180 257,047 1008 1000 973 TotalLm＊>＊＊>Lopt

Regarding estimates of the relative cohort biomass-at-length, the values for optimal length were

M. squalida L

=50.63 mm,

D. ponderosa L

=85.34 mm, and

M. aurantiaca L

=80.85 mm.The graph curves in Fig.5 show the effects of a cohort by assuming different values of

L

compared to the control scenario (

F

=0). In the case of

M. squalida

(Fig.5A), adopting

L

=

L

(optimal moderate fishing) would mean a remaining cohort biomass of 72% of the total biomass, compared to 57% if

L

=

L

(moderate fishing) is adopted. In the case of

D. ponderosa

(Fig.5B), adopting

L

=

L

would mean a remaining cohort biomass of 73% of the total biomass, compared to 90%if

L

=

L

is adopted. This is a special case because

L

is slightly lower than

L

; however, the estimated

L

was lower than

L

. For

M. aurantiaca

(Fig.5C), adopting

L

=

L

would mean a remaining cohort biomass of 72% of the total biomass, compared to 67% if

L

=

L

is adopted.Table 2 displays the estimates of abundance and biomass for the population structure using the lower value of the total abundance confidence interval. For

M. squalida,

a biomass of 30.1 t was estimated. For purposes of comparison, the values of abundance and biomass for the sizes above

L

and

L

are also shown. In the case of

D. ponderosa

, a biomass of 918 t was estimated, while the biomass of

M. aurantiaca

was 161 t.With respect to harvest control regulations, Table 3 shows the

C

and

L

values for each species. According to the results for the relative remaining biomass of the cohort, when different

L

values were adopted the minimum catch sizes for both

M

.

squalida

and

M. aurantiaca

were established as

L

=

L

; whereas for

D. ponderosa

the figure was

L

=

L

,since the estimated value of

L

was lower than

L

. Regarding the establishment of

C

, no large differences were observed whether

L

=

L

or

L

=

L

was adopted; except in the case of

D. ponderosa

but, as mentioned above, the

L

=

L

scenario cannot be considered.

4.Discussion

These results clearly show differences in the abundance and distribution of the three clam populations (Bivalvia: Veneridae) in two new fishing banks in the northern area of the Gulf of California. This information, together with the life history of the species permit establishing an evaluation prior to initial exploitation based on the limited data available, thus allowing us to progress towards compliance with a precautionary management approach without having to postpone decisions for fishery management (Dowling et al., 2019; FAO, 1995; Mayfield et al., 2008).

The catch is regulated by a harvesting strategy based on a quota,which determines the catch that can be permitted in a year, divided into three values: 1) constant catch rate (mortality by fishing, established as a proportion of the population); 2) constant escape or population size; and 3) constant catch. Another harvesting strategy is to restrict capture to only part of the population, such as the males of a species (in crab populations, for example), or only those organisms larger than a certain minimum size. Catch levels can also be specified according to the population size of the target species (Hoggarth et al., 2006).

Catch strategies employed in Mexico include permits, closed seasons,minimum sizes, and quotas (Fernandez-River Melo et al., 2018).Currently, catch quotas for clams are defined as the explicit constant catch rate stipulated in the National Fishery Charter, which establishes an exploitation rate of 20–25% for squalid callista and 15–20% for golden callista (DOF, 2012; DOF, 2018). The exploitation rate for bivalves varies from 1 to 30% in different fisheries around the world(Gorman et al., 2011; Jones et al., 2009), with percentages below 20%considered most adequate (Khan, 2006; Gorman et al., 2011; Tarbath &Gardner, 2013). Over the last decade, these values have been calculated taking into account data on the growth, mortality, and recruitment of the species of interest in an effort to obtain more precise estimates.

Table 3 Harvest strategy for M. squalida, D. ponderosa y M. aurantiaca in Puerto Libertad, Gulf of California. Maximum catch, Cmax, estimated as 10% of abundance considering two options of length at first catch. Suggested values shaded in gray. First capture length Lc; length of first maturity Lm; optimal length Lopt.

The suggested catch strategies based on our results are a specific catch quota for each species of 10% of the estimated abundance (catch rate), as is often suggested for benthic resources with little mobility(Mayfield et al., 2008; Zhang & Campbell, 2002), and a minimum size to jointly ensure that the catch is composed only of individuals whose size is above the length at first maturity and so minimize the impact on the remaining abundance of a cohort.

A subsequent strategy require determining per bank abundance and sampling the size structure of populations before each fishing season as the basis for establishing the catch quota for that season. This would ensure that fishing mortality will always be proportional to population size, though catch quotas would vary from season-to-season according to the total estimated biomass. These measures, however, must be strongly-linked to community-based management, where each locality involved takes decisions as to how to distribute the quota among its fishers, accompanied by strategies designed to follow, record, and monitor catches, all within a framework of the territorial use rights of fisheries.

The distributions of ponderous dosinia and squalid callista were similar because they shared the same areas (Fig.1). These two species populate fine, smooth seabeds (Baqueiro-C´ardenas, 1979). Golden callista, in contrast, is found in banks with coarse sand or gravel seabeds(Baqueiro-C´ardenas, 1979). Although ponderous dosinia and squalid callista share the same banks, their densities differed (Fig.3.). Patterns of spatial distribution can be affected by various factors (environment,food, competition, predation, etc.) that will control the density and biomass of the clams in a bank (Charef et al., 2011; Derbali et al., 2015;Lomovasky et al., 2016). For organisms with little mobility it is important to understand not only their size but also the density and biomass of the exploited species, since harvest will be an additional effect that modifies the bank in terms of both size and density including, possibly,serial spatial depletion, a phenomenon recognized in the progressive depletion of the areas of greatest density as a consequence of extractive pressure (Kirby, 2004; Orensanz et al., 1998). Tracking these changes will make it possible to design tools –site rotation, for example– and seasonal no-fishing areas to prevent overfishing.

It is also important to recognize that information on the abundance of banks is constrained by seasonal variations. For this reason, it is important to evaluate abundance frequently during each fishing season to monitor seasonal variations and population structures. Another recommendation is to conduct these assessments before and after each fishing season or period and accompany them with stock reduction studies to evaluate the relative vulnerability of stocks. The timing and variability of recruitment is another key aspect because it will depend on the factors of abundance and catch quotas (Baqueiro & Aldana, 2003;Silva-Cavalcanti et al., 2018).

Over the last 10 years, bivalve fisheries in Mexico have suffered a drastic decrease in catch volumes, including the local extinction of certain banks, conditions that have impeded the natural recovery of species (DOF, 2012; DOF, 2017; DOF, 2018). The over-exploitation of these resources has been generated primarily due to insufficient regulation, situations of open access, and an over-capitalization of fishing enterprises (Fern´andez-Rivera Melo et al., 2015). The results of this study provide baseline information on the abundance, density, biomass,and harvest strategy for three commercial species of clam in the Gulf of California, as a contribution to the management and sustainable exploitation of the fisheries in this region.

CRediT authorship contribution statement

Jorge A. L

´

opez-Rocha:

Conceptualization, Methodology, Formal analysis, Writing - original draft, Visualization.

Francisco J. Fern

´

andez-Rivera Melo:

Conceptualization, Investigation, Resources, Writing- original draft, Supervision, Funding acquisition.

Ernesto Gast

´

elum-Nava:

Investigation, Writing - review & editing.

Estefani Larios-Castro:

Investigation, Writing - review & editing.

Declaration of competing interest

None.

Acknowledgements

This study was funded by the Walton Family Foundation (101951)and the Fondo Mexicano para la Conservaci´on de la Naturaleza(M1906002). The authors thank Juan Gabriel Lopez Hermosillo, Alfredo Lopez Hermosillo, Jesus Rafael Lopez Hermosillo, Christian Enrique Gonzalez Roman, Felix Guadalupe Carranza Romero, Juan Gabriel Carranza Cervantes, Hugo Valdivieso, Carlos Collins Jimenez (Pitayon),Imelda Amador, Lorena Rocha, and Margarita Bracamontes for their support in the field.