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Differential Catchability by Zone, Fleet, and Size: The Case of the Red Octopus(Octopus maya) and Common Octopus (Octopus vulgaris) Fishery in Yucatan,MexicoAuthor(s): Iván Velázquez—Abunader , Silvia Salas and Miguel A. CabreraSource: Journal of Shellfish Research, 32(3):845-854. 2013.Published By: National Shellfisheries AssociationDOI: http://dx.doi.org/10.2983/035.032.0328URL: http://www.bioone.org/doi/full/10.2983/035.032.0328

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DIFFERENTIAL CATCHABILITY BY ZONE, FLEET, AND SIZE: THE CASE OF THE RED

OCTOPUS (OCTOPUS MAYA) AND COMMON OCTOPUS (OCTOPUS VULGARIS)

FISHERY IN YUCATAN, MEXICO

IVAN VELAZQUEZ–ABUNADER, SILVIA SALAS* AND MIGUEL A. CABRERA

Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional, Unidad Merida,Antigua carretera a Progreso km 6, CP 97310, Merida, Yucatan, Mexico

ABSTRACT Catchability (q) is a key parameter for the assessment and management of stocks because it is widely used to

estimate other parameters such as fishing mortality and resource abundance. However, the common assumption in fisheries

assessment that q remains constant through time, individual size, and space can mask the effect of fishing gear, or fleet, when

applicable, and the behavior of the organisms, especially when different behavior can be portrayed by different components of the

population structure. In the current study, the parameter q was evaluated for the octopus fishery (Octopus maya and Octopus

vulgaris) in Yucatan, Mexico, using two deterministic techniques. In the first, q is assumed to be constant by size, age, and type of

fleet, whereas the second technique assumes different sources of variation in q associated with the size of individuals, fleet

characteristics, and fishing zone. Results suggest that q estimated using the second technique provides information that allows

understanding the effect of fishing gear, fleets, and fishing sites at different levels of the population structure. Differences were

observed in the patterns of q among fishing zones, with a high vulnerability of small organisms in the central and western zones of

the study area throughout the fishing season, whereas the opposite was found in the eastern zone. Differences were also observed

in the catchability of octopuses by fleet and species. The results suggest the presence of multiple intra-annual cohorts, which are

not considered if q is assumed constant, as currently applies for the official assessment of the resources, with the corresponding

fisheries management implications. The results are explained within this framework, and the potential effects of sequential

externalities are discussed.

KEY WORDS: octopus fishery, catch per unit effort, fishing mortality, fleet interactions, differential catchability, Campeche

Bank, Octopus maya, Octopus vulgaris

INTRODUCTION

Fishing is one of the most important activities worldwide;almost 1 billion people benefit from aquatic resources because it

is their main source of food and employment (Gutierrez et al.2011, Salas et al. 2011). The global generation of productsderived from fishing and aquaculture reached approximately

168 million t in 2010 (FAO 2012). The increase in demand byhumans for products extracted from different aquatic systems,together with the considerable increase in the world�s popula-tion, has led to most of the worlds fisheries being fully exploited

or overexploited (Worm et al. 2009, FAO 2012).Faced with this situation, the use of different quantitative

methods and techniques to find out the state of the populations

has evolved, with the objective of obtaining better estimatesduring assessment and therefore the management of fisheries.Hilborn and Walters (1992) state that, for many decades, re-

searchers have considered the changes in populations to bemore of a result of the effects of fishing than environmentalchanges, and fishery managers have assumed they can manip-

ulate stocks using available information, bearing in mindsteady-state populations, resulting from the limited methodsavailable to address with precision such variability. Many tech-niques used for stock assessment have used models that assume

steady-state conditions (Sparre & Venema 1997, De Leon et al.2005, Ceballos-Chavez 2009, Nevarez-Martınez et al. 2010).Currently, to assess stocks, there are alternative methods to the

techniques that assume a steady state, (Arreguın-Sanchez et al.2012). Some techniques have been developed to account for

natural variability of the data resulting from different population

processes in the age or size of individuals, or from introducingstochasticity into the behavior of some variables introduced intothe models for stock assessment (Hilborn & Walters 1992,Fournier et al. 1998).

It is known that the schemes commonly used tomanage waterresources are the estimates of abundance and fishing mortality,for which catchability (q) is an important parameter (Ye &

Hussain 1999, Bahamon et al. 2009). The use of methods thatassume stability have demonstrated that they do not alwaysproduce reliable information because they can underestimate or

overestimate the abundance of stock, and hence do not calculatefishingmortality adequately (Hunter et al. 1986), which can leadto serious problems in the management of fisheries.

The value of q is defined as the proportion of the populationcaught per fishing unit, or fishing mortality per fishing unit(Gulland 1964, Caddy 1979). Historically, q has been assumedto be constant in different procedures developed for stock assess-

ment (Sparre & Venema 1997, Seijo et al. 1998). One approach,for instance, uses a simple linear regression, which assumes thereare no changes in q at different sizes and ages of the individuals

in the analyzed population (Leslie & Davis 1939, De Lury 1947,Chien &Condrey 1985,Mackinson et al. 1997). However, otherstudies have demonstrated that this parameter can vary among

individuals of different size or age, and between different fleetsand zones (Arreguın-Sanchez 1996, Arreguın-Sanchez &Pitcher 1999, Irwin et al. 2008, Lopez-Rocha & Arreguın-

Sanchez 2008, Lopez-Rocha et al. 2009).In cephalopod species, authors such as Morales-Bojorquez

et al. (2001) calculated q differentiated by size for the jumbosquid Dosidicus gigas in the Gulf of California, Mexico. They

found that the advantage of estimating these parameters for*Corresponding author. E-mail: ssalas@mda.cinvestav.mx

DOI: 10.2983/035.032.0328

Journal of Shellfish Research, Vol. 32, No. 3, 845–854, 2013.

845

each size cohort was that it allowed the influence of fishinggear on the different components of the population structure to

be distinguished. It was even possible to identify variations inq in each cohort present in the fishery. Similarly, Yamashitaet al. (2012) determined the values of q for 2 species of squid(Photololigo edulis and Todarodes pacificus) in the Sea of Japan,

taking into account different sources of variation such as themoon phase during fishing operations and the characteristicsof the fishing gear. They stated the relevance of appropriate

estimates of q because the estimates can vary as a function ofsquid behavior, its habitat, and its abundance.

Work addressing estimates of q in octopus species is limited

(Leporati et al. 2009, Jurado-Molina 2010, Ono et al. 2012). Theassessment of appropriated values of q for mollusc species isrelevant for adequate estimates of resource abundance throughthe use of age- or size-structured models, incorporating differ-

ential values of q if applicable. In the current study, an analysiswas undertaken to account for differential behavior of thecatchability coefficient (q) given fishing zones, fleets (small scale

and large scale), and size of the organisms in the octopus fisheryinYucatan,Mexico. The implications of these estimates on stockassessment and fisheries management are discussed.

Octopus Fishery in Yucatan, Mexico

Yucatan is the state with the highest octopus production in

Mexico. The catch of this fishery comprises 2 species: Octopusmaya (Voss & Solıs-Ramırez 1966), known as the red octopus,and Octopus vulgaris Cuvier, 1797, known in the region as thecommon octopus (Solıs-Ramırez et al. 1997). Since the year

2000, octopus catches have changed substantially—from ap-proximately 6,000 t (in 2005 and 2008) to its maximum during2006, 2009, and 2011 at around 18,000 t/y (Fig. 1). From this

amount, Yucatan Peninsula production represents close to 80%of the national catch. Currently, the red octopus fishery iscategorized as fully exploited, whereas the common octopus is

considered a resource with potential development (DOF 2012).The fishing season extends from August to December and

the current management scheme is based on catch quotas(defined through biomass estimates obtained annually by gov-

ernment authorities during the closed season) and the legal sizeof individuals with a mantle length of 11 cm (Carta NacionalPesquera 2010). The fishing gear allowed is the gareteo, which

involves bamboo sticks (known as jimbas) placed at the bow andstern with lines attached, which in turn are tied to the bait (crabs)

for catching the octopus (Solıs-Ramırez et al. 1997, Salas et al.2009).

Officially, there are 2 fleets that participate on the extractionof octopus in Yucatan, a small-scale fleet with vessels between

8–10 m in length that make daily trips and a large-scale fleetwith larger vessels (length, >12 m) that make trips that last 13–18 days. The vessels of the small-scale fleet are usually equipped

with 1–3 small boats of 3 m in length called alijos (Salas et al.2006, Torres-Irineo et al. 2009). In contrast, the large-scale fleetcarries up to 12 alijos (Salas et al. 2008); each fishing operation

by an alijo lasts approximately 3–4 h, so they can have 2 op-erations a day. The small-scale fleet comprises close to 5,000 boatswhereas the large-scale fleet integrates 536 vessels.

MATERIALS AND METHODS

Study Area

The Yucatan Peninsula is situated in the southeast ofMexico. It is washed by the waters of the Gulf of Mexico andit presents a wide continental platform known as Campeche

Bank (width, 250 km) (Salas et al. 2006). The Yucatan coast hasan extension of 373 km, through which octopus catches arelanded in 8 fishing ports (Salas et al. 2006). The ports with the

greatest reported production from the east to the west coasts areCelestun, Progreso, Dzilam de Bravo, and Rıo Lagartos. In allports, small-scale fleets operate, whereas the large-scale fleetonly operates in Progreso (Fig. 2) (SAGARPA 2012). The

small-scale fleet fishes in surrounding areas near the port basewhereas the large-scale fleet has the capacity to travel fartherout to deeper waters, toward the eastern zone of Campeche

Bank, and is the only fleet to report the catch of the commonoctopus (Salas et al. 2009).

Information Sources

Fortnightly samplings were performed during the 2007 to2010 fishing seasons at 4 landing fishing ports (Celestun,

Figure 1. Production of red octopus (Octopusmaya) and common octopus

(Octopus vulgaris) in Yucatan, Mexico. Line with circles is red octopus

catch, line with triangles is common octopus catch, and line with boxes is

total catch.

Figure 2. Distribution of the main octopus landing zones in Yucatan. Sites

chosen for sampling.

VELAZQUEZ–ABUNADER ET AL.846

Progreso, Dzilam de Bravo, and Rıo Lagartos). These sites werechosen based on the following criteria—geographical location,

importance in terms of catch volume, and fleet operation—toobtain information representative of the 2 octopus specieslandings (Salas et al. 2009) and to capture fleet effect as well.Stratified sampling was performed per fleet and landing site. For

the small-scale fleet, the sampled boats were chosen at randomevery time, whereas sampling of the large-scale fleet was guidedbecause the fishing trips lasted more than 10 days.

The samplings consisted of measures of the ML (±0.1 cm)and total weight (±0.1 g) of the individuals. For the small-scalefleet, all the octopuses caught by each selected boat were

sampled, whereas for the larger boats approximately 10% ofthe total catch was sampled. Additional information was alsoobtained using surveys of the fishermen on arrival, gatheringinformation on weight of total catch per trip (in kilograms),

number of organisms, effective fishing time (in hours), andnumber of alijos for each boat.

Estimate of Constant Catchability

A traditional method was used to estimate an approximateq value by means of the model by Schaefer (1954), who

maintained that catch depends on fishing effort and populationabundance. Therefore, q would be proportional to the catchextracted per unit effort (CPUE). Using this assumption, the

value of the slope (b) resulting from the relationship betweenCPUE and effort ( f ) can be interpreted as an approximatevalue of q (Gulland 1977, Seijo et al. 1998).

Catch per unit effort was assumed to be an index of relative

abundance to obtain the relationship CPUE – f, and wasdefined as the number of organisms caught per alijo during anhour of fishing. The alijo per hour was used as a unit of effort to

standardize the information from the fleets.

Variable Catchability by Size

The values of q by size were estimated according to

Arreguın-Sanchez (1996) and Arreguın-Sanchez and Pitcher(1999), which is based on Leslie�s transition matrix (Shepherd1987) in the form

Nð‘; t þ 1Þ ¼ Að‘; kÞ Nð‘; tÞ; (1)

where k and ‘ are the successive ML intervals, N(‘ , t) is thestock size at time t, and A is the transition matrix, which de-

pends directly on growth andmortality. To perform this analysis,the monthlyML frequency distribution for each landing site wasestimated per fleet and species. The frequency distribution ofML

was expressed in terms of CPUE and was used instead ofN. Forthis study, CPUE was defined as the number of organism for thekth interval of ML caught per alijo during an hour of fishing.

The following function was used to estimate A (Shepherd1987):

Að‘; kÞ ¼ Gð‘; kÞ SðkÞ; (2)

where G is the matrix that indicates the effect of growth in theabsence of mortality and S(k) is the survival and effect of fishing

gear for the kth size interval. To estimateG, it was assumed thatboth octopus species presented growth that could be explainedby the von Bertalanffy function, and the matrix was constructed

by allocating growth probabilities to each of the ML intervals,according to the criteria proposed by Shepherd (1987). This was

done based on the results of Lopez-Rocha et al. (2012), whoanalyzed the growth of another octopus species using length–frequency data, and they concluded that the ML providesadequate estimates of growth parameters of these organisms.

Therefore, the growth parameters reported by Cabrera andSalas (2011) were used for q estimation of red octopus (LN ¼23.6 cm ML and K ¼ 0.87/y), and those reported by Sabido

(2012) were used for the common octopus (LN ¼ 21.9 cm MLand K ¼ 1.2/y).

On the other hand, the survival matrix S(k) was estimated in

terms of mortality

SðkÞ ¼ e�ZðkÞt ¼ e� Mþqðk;tÞ sðkÞ f ðtÞ½ �; (3)

where Z(k, t) is the instantaneous mortality rate for the kth ML

interval at time t;M is the natural mortality, which was assumedto be constant throughout time (the value for the red octopusused wasM¼ 1.65/y (Cabrera & Salas 2011) andM¼ 2.15/y for

the common octopus (Sabido 2012)); s(k) is the fishing gearselection parameter, which in this case was assumed to beconstant (s¼ 1) because currently this information is unknown;

f(t) is fishing effort expressed in effective fishing hours at time t;and q(k,t) is the differentiated catchability for the kth MLinterval.

By substitution, the final equation becomes

Nð‘; t þ 1Þ ¼Xk

Gð‘; kÞe� Mþqðk;tÞ sðkÞ f ðtÞ½ �Nðk; tÞ: (4)

With knowledge of all the components in Eq (4), the value ofq(k,t) was estimated by numerical approximation until the value

of q equal to the equation was found. To do so, the softwareCatchability (Martınez-Aguilar et al. 1999) was used.

Similarly, an analysis was performed for each q at the size

proposed by Arreguın-Sanchez and Pitcher (1999) with respectto the average of each fishing zone, kind of fleet, and species. Itwas calculated by

lnCPUEð‘ÞCPUEð‘; �Þ

� �¼ ln

qð‘Þqð‘; �Þ

� �; (5)

where CPUE(‘) is the CPUE for each ML interval, CPUE(‘; �)is the average CPUE for each ML interval, q(‘) is the catch-

ability for each ML interval, and q(‘; �) is the average catch-ability for each ML interval.

Arreguın-Sanchez (1996) proposed that the ratio betweenCPUE and q is linear as a function of size and can therefore be

represented as follows:

lnCPUEð‘ÞCPUEð‘; �Þ

� �¼ aþ b‘; (6)

where the slope (b)

b ¼ lnqð‘þ 1; tÞqð‘; tÞ

� �� qð‘þ 1; �Þ

qð‘; �Þ� �

: (7)

Here, the intercept (a) is interpreted as the relative vulner-ability of small octopuses, and the slope (b) is the rate of change

DIFFERENTIAL CATCHABILITY OF OCTOPUS FISHERY 847

of q to the size of time twith respect to the average. Therefore, ifthe data trend is negative (–b), the small organisms are more

vulnerable, whereas the opposite suggests greater vulnerabilityof large specimens.

RESULTS

Catch Per Unit Effort

During the sampling period, a total of 20,420 red octopuses

and 3,178 common octopuses were measured. The lowest redoctopus CPUEs were recorded for the small-scale fleet (between0.08 organisms/alijo/h in August 2010 and 0.804 organisms/

alijo/h in November 2009), whereas the CPUEs for the large-scale fleet showed a wider range (from 0.092 organisms/alijo/hin November 2007 to 9.452 organisms/alijo/h in October 2009.As for the common octopus, the large-scale fleet exhibited values

between 0.042 organisms/alijo/h (September 2007) and 5.3661organisms/alijo/h, corresponding to October 2010.

Fishing of red octopus for both the small-scale and large-

scale fleets generally presented 2 periods of high values in CPUEcorresponding to the fishing seasons of 2008 and 2009, whereasfor the common octopus, the CPUE presented consistent peaks

during September and October, for the seasons when sampleswere obtained (Fig. 3).

Constant Catchability

In contrast to the classic relationship between CPUE – fproposed by Schaefer (1954), in this study the relationship didnot behave linearly for the red octopus in the case of the small-

scale fleet and the common octopus caught by the large-scalefleet; therefore, q was assumed to be nonlinear for both cases.For the red octopus caught by the small-scale fleet, the patternwas exponential (CPUE ¼ 0.566e–0.005f, R2 ¼ 0.69, P < 0.05).

Although fishing of red octopus by the large-scale fleet pre-sented a high q value and the best fit was linear, it was notstatistically significant (CPUE ¼ –0.023f + 5.833, R2 ¼ 0.32,

P > 0.05), which suggests there is no relationship betweenCPUE and fishing effort, possibly because of the high vari-ability in CPUE in the different fishing seasons for this fleet

(Fig. 3). On the other hand, q for the common octopus wasalmost as high as for the red octopus extracted by the large-scalefleet, although it did not behave linearly. Themodel of best fit for

this relationship was exponential (CPUE ¼ 23.668e–0.022f, R2 ¼0.74, P < 0.05; Fig. 4).

Despite the fact that these types of methods have commonlybeen used in stock assessment, this form of estimating a relevantparameter such as q is limited because, under these conditions, itis assumed as a constant value. Therefore, the possible differ-

ences in the influence of fishing fleet at different levels of theoctopus population structure cannot be distinguished.

Variable Catchability by ML

Catchability by Size and Fleet

The values of q per fleet presented average variations thatranged from 1.92310–5–0.001 for the small-scale fleet and from

4.83 10–5–0.001 for the large-scale fleet. Hence, the order ofmagnitude was similar for both fleets, although the behavior wasreversed; for the small-scale fleet, q decreased with increasing size

whereas the opposite effect was observed for the large-scale fleet.For both fleets, the pattern in q was explained by a potentialmodel (R2 ¼ 0.61 and P < 0.05) for the small-scale fleet:

�q ¼ 205:85ML�5:252: (8)

For the large-scale fleet the best fit model was (R2¼ 0.59,P <0.05; Fig. 5)

�q ¼ 1 3 10�5ML2:361: (9)

It was observed that the small-scale fleet had an importanteffect on organisms smaller than the minimum legal catch size

(ML, <11 cm) (DOF 1993), whereas the large-scale fleet mainlyaffected organisms larger than 18 cm in ML. These resultsconfirm the potential sequential effect of this fishery given the

participation of 2-fleet fishery (Seijo et al. 1998), as suggestedby Salas et al. (2009).

For the temporal analysis, because it only concerned 2 fleets,

the CPUE anomalies considered in Eq (6) between the small-scale and the large-scale fleets, the results demonstrated that,in 84.2% of the months sampled for the small-scale fleet, thesmall organisms were highly vulnerable compared with the

large-scale fleet. The values of the parameters a andb corresponding to Eq (6) are shown in Table 1. The positiveb values indicate greater vulnerability of larger octopuses,

whereas negative b values indicate high vulnerability of organisms

Figure 3. Monthly catch per unit effort (CPUE; organisms alijo per hour) for the large-scale fleet in the 2007 to 2010 fishing season for the red octopus

(Octopus maya) and the common octopus (Octopus vulgaris) in Yucatan, Mexico. The solid line indicates fishing of Octopus maya by the small-scale

fleet, the dashed line indicates the catch of O. maya by the large-scale fleet, and the line with circles indicates the catch of O. vulgaris by the large-scale

fleet.

VELAZQUEZ–ABUNADER ET AL.848

of small sizes (Lopez-Rocha & Arreguın-Sanchez 2008). During

the fishing seasons 2007, 2008, and 2009, in all months, the smallindividuals were the most vulnerable (b < 0) to the small-scalefleet, possibly because of spatial segregation by size for this

species, with larger specimens in zones far from the coast notvisited by the small-scale fleet.

Catchability by Zone

The average q for all months of the 4 fishing seasons by size

was estimated for each landing site, and the analysis by zonealone was performed for the small-scale fleet and only for thered octopus because the common octopus is only landed in 1

port, and reference of the fishing rounds was not available. The

average q showed a decreasing trend for Celestun and Dzilamde Bravo, with high catchability of small individuals (ML,<11 cm). These trends are explained by a potential model for

both sites with significant fits ð�q¼ 1310–7ML–8.811, R2 ¼ 0.70,P < 0.05 in Celestun and �q¼ 214.4ML–4.896,R2¼ 0.71,P < 0.05in Dzilam de Bravo). Although the trends presented by these 2zones were similar, greater values of q were observed in

Celestun (from 4.09 3 10–5–0.037) and lower values ofthis parameter were estimated for Dzilam de Bravo (2.73 310–5–0.005).

In the case of Rıo Lagartos, greater values of qwere recordedfor large sizes of the red octopus, with an ascending patternexplained by a power model (�q ¼ 23 10–12ML8.566, R2 ¼ 0.92,

P < 0.05). The values of q for Rıo Lagartos were of the sameorder of magnitude as for Celestun, and were greater than thosein Dzilam de Bravo (from 3.01310–5–0.04; Fig. 6).

The 3 sampling sites presented months with high variability

of small organisms; the zone with the greatest percentage ofmonths where this pattern was exhibited was Dzilam de Bravowith 60%, followed by Celestun with 53.33%, andRio Lagartos

with 35.71%.Seasonally, Celestun presented high vulnerability of small

octopuses (b < 0) at the start of each fishing season (August to

September) for all years except 2010. In Dzilam de Bravo, forvirtually 3–4 of the 5 mo of the fishing season, high vulnerabilityof small organisms was observed, except in 2008, when this

Figure 5. Average catchability by size for the small-scale and large-scale

fleets in the catch of the red octopus (Octopus maya) in Yucatan, Mexico.

The lines indicate the exponential trend in the observed data.

Figure 4. Relationship between the catch per unit effort (CPUE) and

fishing effort (f; effective fishing hours) for the large-scale and small-scale

fleets in the fishing of red octopus (Octopus maya) and common octopus

(Octopus vulgaris) in Yucatan, Mexico. The solid line indicates the best

trend in the observed data.

TABLE 1.

Relative monthly (t) vulnerability of small octopuses (a) andanomalies in the average monthly (t) catchability by size

outputs (b) by fleet for the red octopus Octopus maya in

Yucatan, Mexico.

Month and year

Small-scale/large-scale fleet

P valuea(t) b(t) R2

2007

August

September 1.69 –0.30 0.82 *

October 3.68 –0.25 0.67 *

November 7.02 –0.69 0.99 *

December 7.15 –0.58 0.99 *

2008

August –0.70 –0.12 0.39 NS

September 8.56 –0.77 0.85 *

October 3.71 –0.44 0.72 *

November 5.06 –0.51 0.92 *

December 9.87 –0.68 0.93 *

2009

August 2.21 –0.46 0.81 *

September –3.59 –0.36 0.74 *

October –11.06 0.01 0.24 NS

November 9.41 1.14 0.93 *

December –1.89 –0.54 0.91 *

2010

August –4.49 0.11 0.52 *

September 0.52 –0.26 0.34 NS

October 2.16 –0.35 0.75 *

November 3.44 –0.47 0.94 *

December 8.40 0.72 0.94 *

* P < 0.05. NS, not significant (P > 0.05).

DIFFERENTIAL CATCHABILITY OF OCTOPUS FISHERY 849

pattern was observed only for 2 of the 5 mo. Last, in Rıo

Lagartos during the catch period, high vulnerability of smallindividuals was found in August for 2007 and 2009, and inSeptember and October for 2010. For logistics reasons, datawere not obtained in the 2008 season for this site (Table 2).

Catchability of Common Octopus

The average q presented a wide range of values, with a min-imum of 5.453 10–7, which corresponded to an ML of 6–7 cm

and a maximum q of 0.14, corresponding to organisms of thelargest mantle length interval of 18–19 cm. Trends in q valuesindicated that this parameter increases with increase in mantlelength. Themodel that explained the relationship q –MLwas �q¼4310–14ML10.253, withR2 ¼ 0.72 (P < 0.05; Fig. 7). Throughoutthe different months of the 4 fishing periods analyzed, highvulnerability of small octopuses was observed from September

to November (b < 0), whereas the opposite was observed at thestart and end of each catch season (b > 0; Table 3).

DISCUSSION

This study showed that estimates of q at different sizes pro-vides greater information on the octopus fishing patterns thanthose that assume constant q values. The calculations of q be-

come important because they are necessary to perform assess-ment of parameters linked closely to management, such asfishing mortality (F), and, in turn, the fishing effort required to

exploit a resource (Morales-Bojorquez et al. 2001, Haddon 2001Benoıt & Swain 2011). Differential values by size on q estimatesmade it possible to realize which component of the population is

being most affected by different fleets in this study, unlikemethods that assume balanced conditions in which some of theprocesses that could influence changes in stock could be not

accounted for (Hilborn & Walters 1992, Seijo et al. 1998). It istherefore important to recognize that to obtain adequate esti-

mates of q and, furthermore, fishing mortality, several sources ofvariation need to be taken into account, such as organism size,population structure, differences between fishing fleets, popula-tion density, and amount fished, as well as environmental factors

and operational tactics and fishing gear used (Arreguın-Sanchez1996, Yamashita et al. 2012).

In the current study, the CPUE – f relationship did not be-

have linearly for the cases of the small-scale fleet (red octopus),or for the large-scale fleet in the case of common octopus. Theobserved pattern in this case fits better the model proposed

by Fox (1970), which assumes that the relationship is moreexponential than linear, as suggested by Schaefer (1954). Onlyin the case of the large-scale fleet for red octopus did a linearrelationship apply. The observed differences may be the result

of the behavior of the fleets in terms of the number of tripsmade, method of operation, and duration of the fishing trips.For the case of the common octopus, because the fishery is more

recent, less effort seems to be allocated to this species (Salaset al. 2009), although as shown in the Figure 1, the productionof common octopus has tended to increase in recent years.

The parameter q makes it possible to identify the character-istics related to the species� behavior, its biology, as well as themethod of operation, seasonality, and sites of catch of the fishing

units (Arreguın-Sanchez & Pitcher 1999).Changes in size and species composition can indicate

changes in the vulnerability of the organisms under differentconditions (Ziegler et al. 2003, Benoıt & Swain 2011)—in this

case, the effect of different type of fleets and biogeographicalconditions where the organisms inhabit (Salas et al. 2009). Thechoice of the model used to explain the pattern of q by size

depends, to a great extent, on the behavior of the species and ofthe fishery rather than a purely statistical fit (Martınez-Aguilaret al. 2009). For the red octopus and the common octopus, clear

patterns were observed in q, given the different sizes of theindividuals targeted by both fleets (e.g., the power model bestexplained the trend in q with respect to octopus size). It isassumed here that the patterns in q observed for the red

octopus are linked closely to the animal�s behavior and theoperating zone where the fleets that exploit it. The small-scalefleet caught only red octopus in shallow waters close to the coast,

where the presence of small specimens has been reported,whereas the large-scale fleet caught both species and operatedin mid and deeper waters, where larger individuals have been

recorded (Salas et al. 2009).Most studies have addressed the analysis of q for fish;

however, this parameter has rarely been evaluated in inverte-

brates (Ziegler et al. 2003, Leporati et al. 2009, Jurado-Molina2010, Ono et al. 2012). In several cases, the value of the para-meter is used to determine biomass, omitting the variability ofthis parameter with size and time and its effects on the manage-

ment of the resource. In invertebrate species, q is considered animportant parameter because these resources present high vul-nerability to fishing gear in certain zones and at different sizes

(Morales-Bojorquez et al. 2001, Ziegler et al. 2003). For example,several authors have suggested that q presents inverse behaviorwith abundance and density (i.e., when abundance and density

decrease, q increases and vice versa (Shardlow & Hilborn 1985,Zhou et al. 2007). Octopus species present semelparous repro-ductive behavior and, as their size or age increases, the organisms

Figure 6. Average catchability by size by landing site for the catch of red

octopus (Octopus maya) in Yucatan, Mexico. The lines indicate the

exponential trend in the observed data.

VELAZQUEZ–ABUNADER ET AL.850

mature and seem to segregate according to size for reproductionand spawning (Boyle&Rodhouse 2005,Rocha et al. 2001). In the

Yucatan Peninsula, spatial segregation has also been reported(Salas et al. 2009).

As shown in Figures 6 and 7, the values of q for the common

octopus were higher than for the red octopus in larger animals;these results were expected. Similar results were achieved byZiegler et al. (2003), who indicated that larger lobsters areassociated with greater catchability. Currently, population pa-

rameters of the common octopus in the study zone are limited,and estimates of abundance, spatial distribution, and reproduc-tive pattern, among others, are nil. It is known that this species

presents a larval period (Boyle & Rodhouse 2005), unlike the redoctopus, which presents a direct development and is endemic tothe region (Solıs-Ramrez et al. 1997); furthermore, differences in

abundance and density are expected, which affects vulnerability.Spatial and temporal catchability using Eq (6) shows that 2

small-organism recruitment zones exist—Celestun and Dzilamde Bravo—with greater vulnerability of small octopuses in most

of the months, particularly at the start off the fishing season(August). These issues demand attention to enforce regulations,with special attention in these 2 zones to prevent overfishing,

as forewarned previously by Salas et al. (2009), who reporteda high incidence of juveniles in the octopuses caught in thesezones.

The results show the relevance of this study given the factthat regulations in the region are based on quotas for whichcatchability is assumed constant, and differences by fleet are not

accounted for (Perez-Perez et al. 2011). The high catchability ofsmall animals is significant, and the enforcement system that

operates in the region seems to be misrepresenting this fact.In this context, the importance of evaluating the patterns of qbased on the incidence of 2 fleets and 2 species in the octopus

fishery in Yucatan becomes relevant for the management of thisfishery in Yucatan. It is also important to highlight that stockassessment to define management regulation in Yucatan is

TABLE 2.

Relative monthly (t) vulnerability of small octopuses (a) and anomalies in the average monthly (t) catchability by size outputs (b) bylanding site for the red octopus Octopus maya in Yucatan, Mexico.

Month and year

Celestun Dzilam de Bravo Rıo Lagartos

a(t) b(t) R2 P value a(t) b(t) R2 P value a(t) b(t) R2 P value

2007

August 1.99 –0.27 0.88 * 3.12 –0.32 0.78 * 4.70 –0.34 0.94 *

September –0.14 –0.03 0.02 NS –1.04 0.09 0.24 NS –1.51 0.10 0.26 NS

October –2.00 0.18 0.79 * –1.79 0.13 0.26 NS

November –1.72 0.15 0.41 * –8.59 0.95 0.89 * –1.35 0.16 0.71 *

December 1.27 –0.03 0.21 NS 1.46 –0.24 0.59 * –4.28 0.18 0.43 NS

2008

August 1.89 –0.13 0.51 * 0.59 –0.04 0.60 *

September –1.47 0.11 0.35 NS 0.78 –0.09 0.29 NS

October 1.60 –0.15 0.68 *

November –5.04 0.37 0.71 * 0.20 –0.01 0.01 NS

December –2.27 0.17 0.72 *

2009

August 1.76 –0.20 0.84 * –1.61 0.13 0.54 NS 2.58 –0.20 0.87 *

September 2.02 –0.14 0.68 * 1.76 –0.13 0.76 * –1.50 0.11 0.71 *

October –9.10 0.69 0.79 * 0.36 –0.02 0.04 NS –1.39 0.11 0.66 *

November 1.01 –0.06 0.46 NS

December 3.29 –0.34 0.64 * –1.09 0.04 0.013 NS 1.12 –0.08 0.41 NS

2010

August –6.57 0.44 0.90 * –6.92 0.45 0.91 * –3.66 0.21 0.66 *

September –6.12 0.44 0.76 * –0.83 0.09 0.58 * 0.78 –0.02 0.06 NS

October –5.76 0.33 0.87 * 4.26 –0.35 0.91 * 1.51 –0.11 0.33 NS

November 1.61 –0.03 0.91 * 2.29 –0.18 0.39 NS –0.96 0.09 0.59 *

December 1.57 –0.14 0.44 NS –2.01 0.11 0.74 *

In the months with no data, it was not possible to obtain records of sizes because of logistical problems. * P < 0.05. NS, not significant (P > 0.05).

Figure 7. Average catchability by size for the large-scale fleet for the

catch of the common (Octopus vulgaris) in Yucatan, Mexico. The lines

indicate the exponential trend in the observed data.

DIFFERENTIAL CATCHABILITY OF OCTOPUS FISHERY 851

based on red octopus only, but applies to both species. In this

respect, for some species of cephalopods, a management schemebased on a proportional escapement has been suggested, whichis defined as Kp ¼ exp–F, where a value of Kp ¼ 40% isrecommended to reach a sustainable fishery, taking advantage

of the short life cycle of the cephalopods and the fact that the

structure of the population is of interannual cohorts (Rosenberget al. 1990, Morales-Bojorquez et al. 2001, Ichii et al. 2006,

Xinjun et al. 2008, Nevarez-Martınez et al. 2010). However,management schemes such as the establishment of quotasthrough estimates of biomass and proportional escapementare limited because they have to be calculated for species for

which the recruitment period is well defined. The high vulner-ability of small organisms (b parameter) of red octopus duringthe fishing season confirms the statement made by Solıs-

Ramırez et al. (1997) regarding the possibility that 2 recruitmentperiods occur in the study area. One of them, however, does notmaintain the same pattern year by year, and these changes could

have an impact on the fishery if they are not taken intoconsideration when defining management strategies.

With the results of the current study, it is possible to see thatthe fleets that operate in Yucatan catch different components of

the octopus populations, giving to this fishery a sequential effectin which different components of the same population are tar-geted by different fleets (Seijo et al. 1998). This probably occurs

as a result of spatial segregation by resource size as result offeeding and reproduction processes, and different habitatavailability by zones could be in place as well. The larger fleet

catches mainly adult organisms that possibly present reproduc-tive behavior in zones of greater depths; if this is the case, therewill be differences in the distribution of the resource, perhaps

leading to an effect of hyperstability or hyperdepletion con-cepts, as mentioned by Hilborn and Walters (1992) and Quinnand Deriso (1999). This potential effect, which would be re-flected in the CPUE of each fleet and each species, opens a

window for research to be addressed in future studies toimprove stock assessment and fisheries regulations.

ACKNOWLEDGMENTS

We thank the fieldwork team (E. Puerto, P. Sabido, E. Torres,L. Palomo, and P. Ortegon) for data collection. We also thank

the Fondo Mixto de Fomento a la Investigacion Cientıfica yTecnologica by the National Council of Science and Technol-ogy (Conacyt) and the state government of Yucatan for financialsupport.

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