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Theoretical evaluation of trap capture for stock assessment
Fisheries Research, 19 ( 1 9 9 4 ) 3 4 9 - 3 6 2
349
0 1 6 5 - 7 8 3 6 / 9 4 / $ 0 7 . 0 0 © 1994 - Elsevier Science B.V. All rights reserved
Theoretical evaluation of trap capture for stock assessment Guillermo Arena, Luis Barea, Omar Defeo* Instituto Nacional de Pesca, Constituyen te 1497, P.O. Box 1612, Montevideo, Uruguay (Accepted 17 August 1993 )
Abstract
A method to estimate the size of benthic stocks catchable by traps is described. Such species cannot be accurately sampled by trawling gear, nor evaluated by the conventional 'swept area method'. A n assessment of this method is presented. The total area of influence of a line of traps is estimated, taking into account the possible overlapping area of influence of adjacent traps. Variations of m e a n yields for different lines with different separation between traps are modelled, also allowing for t h e choice of optimum separation. The possible effect of currents on the area of influence of traps is also discussed.
Introduction
Different methods have been developed to evaluate fish stocks. One of the best known procedures used to assess mid-water or demersal organisms is the 'swept area method' (Alverson and Pereyra, 1969), through which the biomass of each stratum of homogeneous distribution of the stock is evaluated by trawls as: Bj=
cpuej. 1. a
~ Aj
(1)
where: Bj is biomass in the stratum j; cpuej is mean yield obtained in a standard haul in stratum j; a is the swept area in the haul; Q is the catchability coefficient; and Aj is the area of stratum j. This method is not always applicable to mobile benthic stocks such as crabs or lobsters, owing to: ( 1 ) inappropriate bottoms for trawling (e.g. irregular, hard or muddy); (2) sharp slopes (Barea and Defeo, 1985, 1986); (3) species living in caves or tunnels, and consequently not vulnerable to the net (Miller, 1975; Breen et al., 1985; Melville-Smith, 1986). This paper proposes an alternative methodology conceptually similar to the * C o r r e s p o n d i n g author.
SSDI 0 1 6 5 - 7 8 3 6 ( 93 ) 0 0 2 5 5 - H
350
6. Arena et aL / Fisheries Research 19 (1994) 349-362
above, but assuming the use of traps instead of the trawl net. The traps are passive-attractive gears laid on the bottom and separated by equal distance on a groundline. This m e t h o d is directed at bottom species with moderate mobility, and thus assumes a bidimensional stock distribution. A circular area of influence for each trap in the groundline is also assumed, disregarding the effect of direction and speed of currents that could introduce bias in the estimation of the size and shape of the area of attraction (see McQuinn et al., 1988). Although the m e t h o d utilizes Eq. ( 1 ), some problems regarding traps are raised, as well as those inherent to the referred benthic species. When traps are employed, the determination of the area swept by the gear is not simple, because the total area of influence of a trap line is a function of the number of traps, the area of influence of each trap, and the eventual overlapping between the areas of influence of contiguous traps. Owing to the scarce knowledge on this subject (see Eggers et al., 1982; Boschi et al., 1984), the main objective of this work was to develop a methodology that allows the application of Eq. ( 1 ) adapted to trap characteristics.
Theory Calculation of mean yield per trap line Calculation of mean yield per trap line may be estimated as: n
cpue=~
(2)
where: cpue is mean yield of the line (number of individuals per trap); n is total n u m b e r of individuals per line of traps, used instead of weight to denote fluctuations in gear attraction; and N is the n u m b e r of traps on the line.
Calculation of the area covered by the trap line When each trap is separated from adjacent gears, so that in no case it overlaps their areas of influence ai, the area aT covered by the line will be the sum of the ai areas of influence. Usually, this situation does not occur, because of economic factors or those related to gear stability. Each gear competes with the adjacent ones for the individuals equidistant to both contiguous traps and therefore, its efficacy is lower than if it was alone. This p h e n o m e n o n was mentioned by Hamley and Skud (1978 ) with reference to successive hooks of a longline, passive-attractive gear like traps. This is why the area really covered by the line (Fig. 1 ) could be calculated as:
G. Arena et al. / Fisheries Research 19 (1994) 349-362
35 1
I. Fig. 1. Scheme showing the area ( a t ) covered by a line of traps in case of superposition of t h e area of influence between adjacent traps.
aT=N*ai-- (N-1).L
(3)
where L is the surface of the superposition zone of two adjacent areas of influence. Eq. ( 3 ) will be valid only when there are no currents or when these do not have dominant direction. Otherwise, instead of having a circular shape (Miller, 1975; McElman and Elner, 1982; Eggers et al., 1982), the areas of influence would have other forms, and the whole area covered by the line could more likely resemble a sector of a circle (Boschi et al., 1984), a rectangle (Melville-Smith, 1986 ) or an elliptical shape (Gros and Santarelli, 1986 ). Recent papers also highlight the importance of currents in determining the field of attraction and effective area of a baited trap or hook (Olsen and Laevastu, 1983; Sainte-Marie and Hargrave, 1987; Himmelman, 1988; McQuinn et al., 1988; Sainte-Marie, 1991; Lapointe and Sainte-Marie, 1992 ).
Estimation of L To apply Eq. (3), it is necessary to calculate L. This subject has been already analyzed by Eggers et al. (1982) on the basis of similar reasoning, but with completely different results. In fact, to calculate the surface S of a sector of a circle, Eggers et al. ( 1982 ) used an inappropriate equation:
2) --27~ where S is the area of a sector of the capture field; 0 is the angle of the sector; and R is the radius of a single capture field.This equation can be simplified as" 2
352
G. Arena et al. / Fisheries Research 19 (1994) 349-362
which is not the accurate equation to estimate the surface of a sector (see Eq. (5) below). This leads to a wrong calculation of the surface of the overlapping zone between two adjacent capture fields L. To calculate L let us consider Fig. 2, where: r equals RP the radius of the area of influence; d equals 2r the diameter; s equals OP the separation between two adjacent traps; and L is the surface of the overlapping zone. It is evident that:
L/2=U-V
(4)
where Uis the surface of the sector PRT in a capture field and Vis the surface of isosceles triangle PRT. The surface of a sector corresponding to an angle of 2or is calculated by: 2or
U=~-~nr 2
(5)
To find a:
PQ s/2
COSO~ = - -
-
-
-
s
s
2r
d
-
r
r
Consequently a = c o s - ' (s/d) Applying this value in Eq. (5) we obtain: U - cos - 1(s/d),rtr 2 180
(6)
On the other hand, the surface of the isosceles triangle PRT can be calculated as:
V=2PRQ
(7)
Fig. 2. Illustrative diagram to calculate the surface L covered by superposed areas of influence of two adjacent traps.
G. Arena et al. / FisheriesResearch 19 (1994) 349-362
3 53
But the area of the triangle PRQ is:
p R Q _ R Q * s / 2 _ R Q *s 2 4 Substituting this value in Eq. ( 7 ) we obtain:
v _ R Q *s 2
(8)
By the Pythagorean theorem:
r2= (s/2)2+RQ 2 Then RQ--
x/(4r2--S2) x / ( 2 r + s) • (2r-s) 4} -2 = 2
/(rz--S2~
N/ \
Applying RQ in Eq. (8) we obtain:
V_..s*,f(d+s) * ( d - s ) 4
(9)
Using Eqs. (6) and (9) in Eq. (4) results in:
L/2
COS --1
(s/d)rcr2
180
s* x/(d+s) • ( d - s) 4
Therefore L will be calculated as: L = cos -l(s/d) rcr2_S*x/(d+s) * ( d - s ) 90 2
(10)
Estimation of r To establish the radius of the area of influence per trap (r) utilized for the estimation of L, it is necessary to fish with lines of traps with different spacing between traps, taking into account the following conditions: ( 1 ) all traps must be equal, including the bait and, ideally, they must be simultaneously soaked; (2) all the lines must have an identical number of traps, in a statistically sig, nificant quantity (see Miller, 1983a); ( 3 ) the distance between traps should be constant in each line, being progressively greater in successive lines; (4) such increment should be moderate (e.g. 5 m), specially in the separating level between traps for which it is estimated that s=2r, (5) the experiment should take place in an area of homogeneous characteristics, assuming that the stock density is uniform; therefore, some previous sampling should be carried out (Miller, 1983a); (6) when (5) is not fully accomplished, the soaking of the lines should be done parallel to that variable assumed to be
354
G. Arena et al. / Fisheries Research 19 (1994) 349-362
affecting the distribution of the species (e.g. depth ) to the greatest extent; ( 7 ) the separation between lines should be greater than the diameter of the assumed area of influence, so as to minimize the risk of overlapping between two circular capturing fields corresponding to different lines, which would invalidate the experience; (8) elapsed time should avoid saturation of the gear, destruction or loss of efficacy of the bait, or escape of the individuals (Miller, 1979, 1981; Eggers et al., 1982). When increasing the separation between traps on each line, the overlapping areas of influence will decrease so will competition between traps (Fig. 3 ). Thus, the mean yield per line will increase, although with a progressively lower rate (Fig. 4) until it becomes constant in an asymptotic value (cpue = cpUema~ ) once the areas of influence become tangent (in s = 2r) or do not touch absolutely ( s > 2r). Although the concepts stated in this paper are strictly theoretical (it has not been possible yet to carry out the proposed experiments), Hamley and Skud ( 1978 ) observed a similar reaction between halibut yields and the degree of separation between hooks, and proposed a curve very similar to the one indicated here. In practice, it is acceptable to assign to cpuemax the value of the m a x i m u m
Fig. 3. Schemeof the proposed experiment to determine the radius (r) of the area of influence of a trap. The center of each circlecorrespondsto the position of the trap, and the circleencloses its area of influence.
355
G. Arena et al. /Fisheries Research 19 (1994) 349-362
Ill
=.,
I°
(J
f
cpu---es ~ c ~ . .
TRAP
SPACING
-
1
a+bs
(S)
Fig. 4. Theoretical curve of mean yields obtained by lines having different separation between traps.
mean yield obtained by a line with an important separation between traps, and which does not present significant differences with the yield of other lines where traps are also wide apart. Summarizing, it would be assumed that: r=
Smax
2
(11)
where r is the radius of the area of influence and S~,x is the separation between the traps of that line which obtained the m a x i m u m mean yield, in the aforementioned conditions. From ( 11 ) we have: d=smax
(12)
which can be applied in Eq. ( 10 ).
Optimum separation among traps (Sopt) The use of lines with an Smax separation between traps, even if it provides the m a x i m u m mean yield per line, could be non-economical owing to investment or operating costs (Miller, 1981, 1983b) or present problems regarding gear stability. For example, a reduction of s by half leads to a very low decrease in yield (Fig. 4). The increase in the mean yield per line could be expressed as a monotoni-
356
G. Arena et al. /Fisheries Research 19 (1994) 349-362
i
l
TRAP
SPACING (S)
Fig. 5. Relationship between the increase in the mean yield per line and trap spacing.
T-
J TRAP
SPACING
(S)
Fig. 6. Relationship between the inverse of the increase of theoretical mean yields and trap spacing, considering lines with different separation between traps. cally decreasing exponential function of the separation between traps (Fig. 5 ). Therefore, the mean yield of a line ( c ~ s ) whose separation between traps has an s value could result from:
cpUes
= cpUemax
--
1 a + b~s
( 13 )
where cpUemax is the m a x i m u m mean yield which can be obtained by the line, when s tends to infinity. In practice, m a x i m u m mean yield is obtained from experience; b is the curvature parameter which indicates the rate at which cpUemax is reached with increasing separation between traps; a is the positive parameter associated with the intercept cpueo. When a = 0, cpueo tends to - ~ ; when a = 1 / C ~ m a x cpueo = O; and if a tends to + ~ , cpueo tends to cpUernax. Thus, increasing a values determines decreasing differences between cpUema x and cpueo. ,
G. Arena et al. / Fisheries Research 19 (1994) 349-362
357
Values of a and b may be calculated by modifying Eq. ( 13 ) as (see also Fig.
6): 1
cpUemax -- cpues
- a + bs
Once a and b have been estimated, it is possible to choose (on the resulting curve) the separation between traps which seems to be more adequate from the economic and operating points of view. Problems related to catchability a n d gear efficiency
Estimating the catchability coefficient and gear efficiency (fraction of individuals caught by the gear within the area of influence) is a difficult task: whatever fishing unit is utilized. In the specific case of the trap lines, the following three features deserve particular consideration. (1) In contrast to what normally occurs with trawling gears with otter boards, gear efficiency values greater than one are possible with traps. Thisl would occur if, during soaking time, all the individuals within the area of influence of a trap are caught, plus others from outside which, during the same: period, arrived inside that area by chance, and not due to bait attraction. Therefore, soaking time during the experiment should not be too long. For this reason, our method is better for benthic organisms with moderate mobility, for example the red crab (Chaceon notialis) which has been evaluated with this method (Defeo et al., 1991; see section on validation of the method's applicability). (2) The vulnerability of the individuals to the gear within the area of influence of each trap is not the same at all points. It declines in inverse ratio to the square of the distance from the organisms to the bait (Elner, 1980). In fact, the attractive particles dilute as a function of nr 2.
100.
"r (') I--
~R
,
DISTANCE
FROM
THE TRAP
Fig. 7. Theoretical curve of the percentage catch of individuals present within the area of influ~ ence of a trap, as a function o f the distance kept by the individuals to the trap.
3 58
G. Arena et aL / Fisheries Research 19 (1994) 349-362
Plotting the percentage catch of individuals present within the area of influence of a trap, as a function of the distance kept by the individuals to the trap (Fig. 7 ), it can be observed that the curve cannot exist for values of x smaller than the trap radius (R), and that it becomes a monotonically decreasing exponential rate as a consequence of the vagueness of the radius of influence. (3) All individuals of a species are not equally responsive to bait, even if they are at the same distance from it. According to Miller (1983a), large decapods are more responsive than small ones; males more than females; lastmolt more than pre-molt; hungry more than well-fed, etc.
Determination of the area of the stratum (Aj) Usually, the stratum of homogeneous distribution of the stock for which biomass is estimated, lacks a regular shape; therefore the area Aj is not mathematically calculable, but it could be measured on the chart. However, in cases of a sharp slope (one of the aspects which may make necessary the evaluation through traps), the graphic representation is just a horizontal projection of horizontal
~
. . . . . . . . . . . . . . . . . . . . . . . . .
:a--+
......
....
....
~--=
.....
~ ....
....
,--"
....
4 ....
,___'_..
"
,
I
,
i
,
I
:
i
i
7
6
:
I
~
shape
/.real
~, . . . . . . .
7~
" . . . . . . . . . . .
i
4 i
,
"
t
I
// t
*
"--~
I "
/
0 /
Q
Fig. 8. Graphic procedure to obtain the real shape (B) of the referred stratum instead of its horizontal projection (A).
3 59
G. Arena et al. / Fisheries Research 19 (1994) 349-362
the real shape. As a consequence, biased values of Aj would underestimate the stratum biomass. Therefore, a graphic m e t h o d is proposed (Fig. 8 ), through which once the slope is known it is possible to obtain the real shape and size of the stratum. The slope ( a ) is estimated by: O
tgce = q
where o is the increment in depth between two isobaths and q is the m i n i m u m horizontal separation between isobaths in the analyzed stratum.Therefore: a=tg-'(o/q)
Validation of the method's applicability The correct application of the proposed m e t h o d presupposes areas of influence of circular shape, which is not valid where there are persistent currents (see e.g. Lapointe and Sainte-Marie, 1992 ). If the yield of each trap is plotted against the ordinal number of trap, a significant trend between them would be an indicator of the existence of a strong and persistent current parallel to the line (Figs. 9 (a) and 9 (b) ), which will spread the attractive effect of the baits in the form of a sector of a circle
• .-5 Q. U
co°
a e•
o•
• ee ee
•e
trap
• e
I
!1 c
N -°
• eeeoeeeeee
trap
o eo
trap
e
N -°
d q~ ¢'~
ee
e
•
•
trap
N -=
•
N°
D.. L~
trap
N -°
Fig. 9. Theoretical variations of the yield of the traps (ordered ordinally) in a line (see text for discussion).
360
G. Arena et al. / Fisheries Research 19 (1994) 349-362
250 350450
550 650
750
850
DEPTH ( m )
950
35 °00
Kg/Trap 35°20
0 - 0.99 I - 4.99
u4
0
35+40
5 - 9.99
I=-
~ 36°00
I
>, 10
36°20
36°40
Fig. 10. Relative abundance (kg per trap) of the red crab Chaceon notialis in the ArgentinianUruguayan Common Fishing Zone (spring 1985). Fixed strata are defined by depth and latitude (from Defeo et al., 1991 ).
(Boschi et al., 1984 ). If scattered dots with no trend are obtained (Fig. 9 (c) ), it is quite right to assume that such currents do not exist; therefore, the application of the methodology may be considered valid. Distributions such as shown in Figs. 9 (d) and 9 (e) are indicators of efficiency problems of the gear derived from its location within the line (McElman and Elner, 1982). The p h e n o m e n o n shown in Fig. 9 ( d ) could be attributed to a lack of stability of the traps situated at the end of the line (Barea and Defeo, 1986 ). On the other hand, the m i n i m u m yields of the central traps in Fig. 9 (e) would be the outcome of extreme competition with adjacent traps. The application of the method in both cases is correct. The validation of the m e t h o d also implies that the experience directed to estimate the radius of the area of influence of each trap, can be carried out within a wide area with homogeneous yields and similar values of the catchability coefficient (see also Estimation of r). In fact, the m e t h o d was successfully applied in the case of two surveys of the red crab C. notialis, carried out in the Southwestern Atlantic Ocean (Defeo et al., 1991 ). Fig. 10 shows wide areas of Chaceon distribution that satisfy the assumptions of the method; a similar catchability coefficient was assumed owing to the use of the same type of gear, bait and relatively similar soak time. Considering the above aspects, the proposed experiments could be carried
G, Arena et al. /Fisheries Research 19 (1994) 349-362
361
out. Future research will aim to test our methodology, continuing the experiments and evaluating the fitness of the theoretical approach. Acknowledgements We especially thank Drs. Robert Elner and Robert Miller (Halifax Fisheries Research Laboratory) and Dr. Jorge Csirke (FAO) for critical readings of the early stages of this paper and their valuable suggestions for the final manuscript. References Alverson, D.L. and Pereyra, W.T., 1969. Demersal fish explorations in the northeastern Pacific Ocean - an evaluation of exploratory fishing methods and analytical approaches to stock size and yield forecasts. J. Fish. Res. Board Can., 26:1985-2001. Barea, L. and Defeo, O., 1985. Primeros ensayos de captura del crust~iceo batial Geryon quinquedens Smith, en el Area Comtin de Pesca Argentino-Uruguaya. Contrib. Dep. Oceanogr. (F.H.C.) Montevideo, 2(8): 189-203. Barea, L. and Defeo, O., 1986. Aspectos de la pesqueria del cangrejo rojo (Geryon quinquedens) en la Zona Comt~n de Pesca Argentino-Uruguaya. Publ. Com. Tec. Mix. Fr. Mar., 1 ( 1 ): 3846. Boschi, E.E., Bertuche, D.A. and Wyngaard, J.G., 1984. Estudio biol6gico-pesquero de la centolla (Lithodes antarcticus) del Canal Beagle, Tierra del Fuego, Argentina. I Parte. IN1DEP Contrib., 441 : 1-72. Breen, P.A., Carolsfeld, W. and Narver, D., 1985. Crab gear selectivity studies in Departure Bay. Can. Manage. Rep. Fish. Aquat. Sci., 1048:21-39. Defeo, O., Barea, L. and Little, V., 1991. Stock assessment of the red crab Chaceon notialis in the Argentinian-Uruguayan Common Fishing Zone. Fish. Res., 11: 25-39. Eggers, D.M., Rickard, N.A., Chapman, D.G. and Whitney, R.R., 1982. A methodology for estimating area fished for baited hooks and traps along a ground line. Can. J. Fish. Aqua~. Sci., 39: 448-453. Elner, R.W., 1980. Lobster gear selectivity - a Canadian overview. Can. Tech. Rep. Fish. Aquat. Sci., 932: 77-84. Gros, P. and Santarelli, L., 1986. M6thode d'estimation de la surface de peche d'un casier a l'aide d'une filiere exp6rimentale. Oceanol. Acta, 9 ( 1 ): 81-87. Hamley, J.M. and Skud, E., 1978. Factors affecting longline catch and effort. International Pacific Halibut Commission, Scientific Report, 64:16-24. Himmelman, J.H., 1988. Movement of whelks (Buccinum undatum) towards a baited trap. Mar. Biol., 97: 521-531. Lapointe, V. and Sainte-Marie, B., 1992. Currents, predators and the aggregation of the gastropod Buccinum undatum around bait. Mar. Ecol. Prog. Ser., 85: 245-257. McElman, J.F. and Elner, R.W., 1982. Red crab (Geryon quinquedens) trap survey along the edge of the Scotian Shelf, September 1980. Can. Tech. Rep. Fish. Aquat. Sci., 1084: iii + 12 PP. McQuinn, I.H., Gendron, L. and Himmelman, J.H., 1988. Area of attraction and effective area fished by a whelk (Buccinum undaturn) trap under variable conditions. Can. J. Fish. Aquat. Sci., 45: 2054-2060. Melville-Smith, R., 1986. Red crab (Geryon maritae) density in 1985 by the technique ofeffcc-
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G. Arena et al. / Fisheries Research 19 (1994) 349-362
tive area fished per trap on the northern fishing grounds of South West Africa. S. Afr. J. Mar. Sci., 4: 257-263. Miller, R.J., 1975. Density of the commercial spider crab, C h i o n o c e t e s opilio, and calibration of effective area fished per trap using bottom photography. J. Fish. Res. Board Can., 32:761768. Miller, R.J., 1979. Saturation of crab traps: reduced entry and escapement. J. Cons. Int. Explor. Mer, 38: 338-345. Miller, R.J., 1981. Strategies for improving crab trap hauls. World Fishing, 30 ( I 0 ): 51 -53. Miller, R.J., 1983a. Considerations for conducting field experiments with baited traps. Fisheries, 8(5): 14-17. Miller, R.J., 1983b. How many traps should a crab fisherman fish? N. Am. J. Fish. Manage., 3: 1-8. Olsen, S. and Laevastu, T., 1983. Fish attraction to baits and effects of currents on the distribution of smell from baits. NOAA Natl. Mar. Fish. Serv., NWAFC Processed Rep., 83-05. Sainte-Marie, B., 1991. Whelk ( B u c c i n u m u n d a t u m ) movement and its implications for the use of tag-recapture methods for the determination of baited trap parameters. Can. J. Fish. Aquat. Sci., 48:751-756. Sainte-Marie, B. and Hargrave, B.T., 1987. Estimation of scavenger abundance and distance of attraction to bait. Mar. Biol., 94:431-443.
349
0 1 6 5 - 7 8 3 6 / 9 4 / $ 0 7 . 0 0 © 1994 - Elsevier Science B.V. All rights reserved
Theoretical evaluation of trap capture for stock assessment Guillermo Arena, Luis Barea, Omar Defeo* Instituto Nacional de Pesca, Constituyen te 1497, P.O. Box 1612, Montevideo, Uruguay (Accepted 17 August 1993 )
Abstract
A method to estimate the size of benthic stocks catchable by traps is described. Such species cannot be accurately sampled by trawling gear, nor evaluated by the conventional 'swept area method'. A n assessment of this method is presented. The total area of influence of a line of traps is estimated, taking into account the possible overlapping area of influence of adjacent traps. Variations of m e a n yields for different lines with different separation between traps are modelled, also allowing for t h e choice of optimum separation. The possible effect of currents on the area of influence of traps is also discussed.
Introduction
Different methods have been developed to evaluate fish stocks. One of the best known procedures used to assess mid-water or demersal organisms is the 'swept area method' (Alverson and Pereyra, 1969), through which the biomass of each stratum of homogeneous distribution of the stock is evaluated by trawls as: Bj=
cpuej. 1. a
~ Aj
(1)
where: Bj is biomass in the stratum j; cpuej is mean yield obtained in a standard haul in stratum j; a is the swept area in the haul; Q is the catchability coefficient; and Aj is the area of stratum j. This method is not always applicable to mobile benthic stocks such as crabs or lobsters, owing to: ( 1 ) inappropriate bottoms for trawling (e.g. irregular, hard or muddy); (2) sharp slopes (Barea and Defeo, 1985, 1986); (3) species living in caves or tunnels, and consequently not vulnerable to the net (Miller, 1975; Breen et al., 1985; Melville-Smith, 1986). This paper proposes an alternative methodology conceptually similar to the * C o r r e s p o n d i n g author.
SSDI 0 1 6 5 - 7 8 3 6 ( 93 ) 0 0 2 5 5 - H
350
6. Arena et aL / Fisheries Research 19 (1994) 349-362
above, but assuming the use of traps instead of the trawl net. The traps are passive-attractive gears laid on the bottom and separated by equal distance on a groundline. This m e t h o d is directed at bottom species with moderate mobility, and thus assumes a bidimensional stock distribution. A circular area of influence for each trap in the groundline is also assumed, disregarding the effect of direction and speed of currents that could introduce bias in the estimation of the size and shape of the area of attraction (see McQuinn et al., 1988). Although the m e t h o d utilizes Eq. ( 1 ), some problems regarding traps are raised, as well as those inherent to the referred benthic species. When traps are employed, the determination of the area swept by the gear is not simple, because the total area of influence of a trap line is a function of the number of traps, the area of influence of each trap, and the eventual overlapping between the areas of influence of contiguous traps. Owing to the scarce knowledge on this subject (see Eggers et al., 1982; Boschi et al., 1984), the main objective of this work was to develop a methodology that allows the application of Eq. ( 1 ) adapted to trap characteristics.
Theory Calculation of mean yield per trap line Calculation of mean yield per trap line may be estimated as: n
cpue=~
(2)
where: cpue is mean yield of the line (number of individuals per trap); n is total n u m b e r of individuals per line of traps, used instead of weight to denote fluctuations in gear attraction; and N is the n u m b e r of traps on the line.
Calculation of the area covered by the trap line When each trap is separated from adjacent gears, so that in no case it overlaps their areas of influence ai, the area aT covered by the line will be the sum of the ai areas of influence. Usually, this situation does not occur, because of economic factors or those related to gear stability. Each gear competes with the adjacent ones for the individuals equidistant to both contiguous traps and therefore, its efficacy is lower than if it was alone. This p h e n o m e n o n was mentioned by Hamley and Skud (1978 ) with reference to successive hooks of a longline, passive-attractive gear like traps. This is why the area really covered by the line (Fig. 1 ) could be calculated as:
G. Arena et al. / Fisheries Research 19 (1994) 349-362
35 1
I. Fig. 1. Scheme showing the area ( a t ) covered by a line of traps in case of superposition of t h e area of influence between adjacent traps.
aT=N*ai-- (N-1).L
(3)
where L is the surface of the superposition zone of two adjacent areas of influence. Eq. ( 3 ) will be valid only when there are no currents or when these do not have dominant direction. Otherwise, instead of having a circular shape (Miller, 1975; McElman and Elner, 1982; Eggers et al., 1982), the areas of influence would have other forms, and the whole area covered by the line could more likely resemble a sector of a circle (Boschi et al., 1984), a rectangle (Melville-Smith, 1986 ) or an elliptical shape (Gros and Santarelli, 1986 ). Recent papers also highlight the importance of currents in determining the field of attraction and effective area of a baited trap or hook (Olsen and Laevastu, 1983; Sainte-Marie and Hargrave, 1987; Himmelman, 1988; McQuinn et al., 1988; Sainte-Marie, 1991; Lapointe and Sainte-Marie, 1992 ).
Estimation of L To apply Eq. (3), it is necessary to calculate L. This subject has been already analyzed by Eggers et al. (1982) on the basis of similar reasoning, but with completely different results. In fact, to calculate the surface S of a sector of a circle, Eggers et al. ( 1982 ) used an inappropriate equation:
2) --27~ where S is the area of a sector of the capture field; 0 is the angle of the sector; and R is the radius of a single capture field.This equation can be simplified as" 2
352
G. Arena et al. / Fisheries Research 19 (1994) 349-362
which is not the accurate equation to estimate the surface of a sector (see Eq. (5) below). This leads to a wrong calculation of the surface of the overlapping zone between two adjacent capture fields L. To calculate L let us consider Fig. 2, where: r equals RP the radius of the area of influence; d equals 2r the diameter; s equals OP the separation between two adjacent traps; and L is the surface of the overlapping zone. It is evident that:
L/2=U-V
(4)
where Uis the surface of the sector PRT in a capture field and Vis the surface of isosceles triangle PRT. The surface of a sector corresponding to an angle of 2or is calculated by: 2or
U=~-~nr 2
(5)
To find a:
PQ s/2
COSO~ = - -
-
-
-
s
s
2r
d
-
r
r
Consequently a = c o s - ' (s/d) Applying this value in Eq. (5) we obtain: U - cos - 1(s/d),rtr 2 180
(6)
On the other hand, the surface of the isosceles triangle PRT can be calculated as:
V=2PRQ
(7)
Fig. 2. Illustrative diagram to calculate the surface L covered by superposed areas of influence of two adjacent traps.
G. Arena et al. / FisheriesResearch 19 (1994) 349-362
3 53
But the area of the triangle PRQ is:
p R Q _ R Q * s / 2 _ R Q *s 2 4 Substituting this value in Eq. ( 7 ) we obtain:
v _ R Q *s 2
(8)
By the Pythagorean theorem:
r2= (s/2)2+RQ 2 Then RQ--
x/(4r2--S2) x / ( 2 r + s) • (2r-s) 4} -2 = 2
/(rz--S2~
N/ \
Applying RQ in Eq. (8) we obtain:
V_..s*,f(d+s) * ( d - s ) 4
(9)
Using Eqs. (6) and (9) in Eq. (4) results in:
L/2
COS --1
(s/d)rcr2
180
s* x/(d+s) • ( d - s) 4
Therefore L will be calculated as: L = cos -l(s/d) rcr2_S*x/(d+s) * ( d - s ) 90 2
(10)
Estimation of r To establish the radius of the area of influence per trap (r) utilized for the estimation of L, it is necessary to fish with lines of traps with different spacing between traps, taking into account the following conditions: ( 1 ) all traps must be equal, including the bait and, ideally, they must be simultaneously soaked; (2) all the lines must have an identical number of traps, in a statistically sig, nificant quantity (see Miller, 1983a); ( 3 ) the distance between traps should be constant in each line, being progressively greater in successive lines; (4) such increment should be moderate (e.g. 5 m), specially in the separating level between traps for which it is estimated that s=2r, (5) the experiment should take place in an area of homogeneous characteristics, assuming that the stock density is uniform; therefore, some previous sampling should be carried out (Miller, 1983a); (6) when (5) is not fully accomplished, the soaking of the lines should be done parallel to that variable assumed to be
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G. Arena et al. / Fisheries Research 19 (1994) 349-362
affecting the distribution of the species (e.g. depth ) to the greatest extent; ( 7 ) the separation between lines should be greater than the diameter of the assumed area of influence, so as to minimize the risk of overlapping between two circular capturing fields corresponding to different lines, which would invalidate the experience; (8) elapsed time should avoid saturation of the gear, destruction or loss of efficacy of the bait, or escape of the individuals (Miller, 1979, 1981; Eggers et al., 1982). When increasing the separation between traps on each line, the overlapping areas of influence will decrease so will competition between traps (Fig. 3 ). Thus, the mean yield per line will increase, although with a progressively lower rate (Fig. 4) until it becomes constant in an asymptotic value (cpue = cpUema~ ) once the areas of influence become tangent (in s = 2r) or do not touch absolutely ( s > 2r). Although the concepts stated in this paper are strictly theoretical (it has not been possible yet to carry out the proposed experiments), Hamley and Skud ( 1978 ) observed a similar reaction between halibut yields and the degree of separation between hooks, and proposed a curve very similar to the one indicated here. In practice, it is acceptable to assign to cpuemax the value of the m a x i m u m
Fig. 3. Schemeof the proposed experiment to determine the radius (r) of the area of influence of a trap. The center of each circlecorrespondsto the position of the trap, and the circleencloses its area of influence.
355
G. Arena et al. /Fisheries Research 19 (1994) 349-362
Ill
=.,
I°
(J
f
cpu---es ~ c ~ . .
TRAP
SPACING
-
1
a+bs
(S)
Fig. 4. Theoretical curve of mean yields obtained by lines having different separation between traps.
mean yield obtained by a line with an important separation between traps, and which does not present significant differences with the yield of other lines where traps are also wide apart. Summarizing, it would be assumed that: r=
Smax
2
(11)
where r is the radius of the area of influence and S~,x is the separation between the traps of that line which obtained the m a x i m u m mean yield, in the aforementioned conditions. From ( 11 ) we have: d=smax
(12)
which can be applied in Eq. ( 10 ).
Optimum separation among traps (Sopt) The use of lines with an Smax separation between traps, even if it provides the m a x i m u m mean yield per line, could be non-economical owing to investment or operating costs (Miller, 1981, 1983b) or present problems regarding gear stability. For example, a reduction of s by half leads to a very low decrease in yield (Fig. 4). The increase in the mean yield per line could be expressed as a monotoni-
356
G. Arena et al. /Fisheries Research 19 (1994) 349-362
i
l
TRAP
SPACING (S)
Fig. 5. Relationship between the increase in the mean yield per line and trap spacing.
T-
J TRAP
SPACING
(S)
Fig. 6. Relationship between the inverse of the increase of theoretical mean yields and trap spacing, considering lines with different separation between traps. cally decreasing exponential function of the separation between traps (Fig. 5 ). Therefore, the mean yield of a line ( c ~ s ) whose separation between traps has an s value could result from:
cpUes
= cpUemax
--
1 a + b~s
( 13 )
where cpUemax is the m a x i m u m mean yield which can be obtained by the line, when s tends to infinity. In practice, m a x i m u m mean yield is obtained from experience; b is the curvature parameter which indicates the rate at which cpUemax is reached with increasing separation between traps; a is the positive parameter associated with the intercept cpueo. When a = 0, cpueo tends to - ~ ; when a = 1 / C ~ m a x cpueo = O; and if a tends to + ~ , cpueo tends to cpUernax. Thus, increasing a values determines decreasing differences between cpUema x and cpueo. ,
G. Arena et al. / Fisheries Research 19 (1994) 349-362
357
Values of a and b may be calculated by modifying Eq. ( 13 ) as (see also Fig.
6): 1
cpUemax -- cpues
- a + bs
Once a and b have been estimated, it is possible to choose (on the resulting curve) the separation between traps which seems to be more adequate from the economic and operating points of view. Problems related to catchability a n d gear efficiency
Estimating the catchability coefficient and gear efficiency (fraction of individuals caught by the gear within the area of influence) is a difficult task: whatever fishing unit is utilized. In the specific case of the trap lines, the following three features deserve particular consideration. (1) In contrast to what normally occurs with trawling gears with otter boards, gear efficiency values greater than one are possible with traps. Thisl would occur if, during soaking time, all the individuals within the area of influence of a trap are caught, plus others from outside which, during the same: period, arrived inside that area by chance, and not due to bait attraction. Therefore, soaking time during the experiment should not be too long. For this reason, our method is better for benthic organisms with moderate mobility, for example the red crab (Chaceon notialis) which has been evaluated with this method (Defeo et al., 1991; see section on validation of the method's applicability). (2) The vulnerability of the individuals to the gear within the area of influence of each trap is not the same at all points. It declines in inverse ratio to the square of the distance from the organisms to the bait (Elner, 1980). In fact, the attractive particles dilute as a function of nr 2.
100.
"r (') I--
~R
,
DISTANCE
FROM
THE TRAP
Fig. 7. Theoretical curve of the percentage catch of individuals present within the area of influ~ ence of a trap, as a function o f the distance kept by the individuals to the trap.
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G. Arena et aL / Fisheries Research 19 (1994) 349-362
Plotting the percentage catch of individuals present within the area of influence of a trap, as a function of the distance kept by the individuals to the trap (Fig. 7 ), it can be observed that the curve cannot exist for values of x smaller than the trap radius (R), and that it becomes a monotonically decreasing exponential rate as a consequence of the vagueness of the radius of influence. (3) All individuals of a species are not equally responsive to bait, even if they are at the same distance from it. According to Miller (1983a), large decapods are more responsive than small ones; males more than females; lastmolt more than pre-molt; hungry more than well-fed, etc.
Determination of the area of the stratum (Aj) Usually, the stratum of homogeneous distribution of the stock for which biomass is estimated, lacks a regular shape; therefore the area Aj is not mathematically calculable, but it could be measured on the chart. However, in cases of a sharp slope (one of the aspects which may make necessary the evaluation through traps), the graphic representation is just a horizontal projection of horizontal
~
. . . . . . . . . . . . . . . . . . . . . . . . .
:a--+
......
....
....
~--=
.....
~ ....
....
,--"
....
4 ....
,___'_..
"
,
I
,
i
,
I
:
i
i
7
6
:
I
~
shape
/.real
~, . . . . . . .
7~
" . . . . . . . . . . .
i
4 i
,
"
t
I
// t
*
"--~
I "
/
0 /
Q
Fig. 8. Graphic procedure to obtain the real shape (B) of the referred stratum instead of its horizontal projection (A).
3 59
G. Arena et al. / Fisheries Research 19 (1994) 349-362
the real shape. As a consequence, biased values of Aj would underestimate the stratum biomass. Therefore, a graphic m e t h o d is proposed (Fig. 8 ), through which once the slope is known it is possible to obtain the real shape and size of the stratum. The slope ( a ) is estimated by: O
tgce = q
where o is the increment in depth between two isobaths and q is the m i n i m u m horizontal separation between isobaths in the analyzed stratum.Therefore: a=tg-'(o/q)
Validation of the method's applicability The correct application of the proposed m e t h o d presupposes areas of influence of circular shape, which is not valid where there are persistent currents (see e.g. Lapointe and Sainte-Marie, 1992 ). If the yield of each trap is plotted against the ordinal number of trap, a significant trend between them would be an indicator of the existence of a strong and persistent current parallel to the line (Figs. 9 (a) and 9 (b) ), which will spread the attractive effect of the baits in the form of a sector of a circle
• .-5 Q. U
co°
a e•
o•
• ee ee
•e
trap
• e
I
!1 c
N -°
• eeeoeeeeee
trap
o eo
trap
e
N -°
d q~ ¢'~
ee
e
•
•
trap
N -=
•
N°
D.. L~
trap
N -°
Fig. 9. Theoretical variations of the yield of the traps (ordered ordinally) in a line (see text for discussion).
360
G. Arena et al. / Fisheries Research 19 (1994) 349-362
250 350450
550 650
750
850
DEPTH ( m )
950
35 °00
Kg/Trap 35°20
0 - 0.99 I - 4.99
u4
0
35+40
5 - 9.99
I=-
~ 36°00
I
>, 10
36°20
36°40
Fig. 10. Relative abundance (kg per trap) of the red crab Chaceon notialis in the ArgentinianUruguayan Common Fishing Zone (spring 1985). Fixed strata are defined by depth and latitude (from Defeo et al., 1991 ).
(Boschi et al., 1984 ). If scattered dots with no trend are obtained (Fig. 9 (c) ), it is quite right to assume that such currents do not exist; therefore, the application of the methodology may be considered valid. Distributions such as shown in Figs. 9 (d) and 9 (e) are indicators of efficiency problems of the gear derived from its location within the line (McElman and Elner, 1982). The p h e n o m e n o n shown in Fig. 9 ( d ) could be attributed to a lack of stability of the traps situated at the end of the line (Barea and Defeo, 1986 ). On the other hand, the m i n i m u m yields of the central traps in Fig. 9 (e) would be the outcome of extreme competition with adjacent traps. The application of the method in both cases is correct. The validation of the m e t h o d also implies that the experience directed to estimate the radius of the area of influence of each trap, can be carried out within a wide area with homogeneous yields and similar values of the catchability coefficient (see also Estimation of r). In fact, the m e t h o d was successfully applied in the case of two surveys of the red crab C. notialis, carried out in the Southwestern Atlantic Ocean (Defeo et al., 1991 ). Fig. 10 shows wide areas of Chaceon distribution that satisfy the assumptions of the method; a similar catchability coefficient was assumed owing to the use of the same type of gear, bait and relatively similar soak time. Considering the above aspects, the proposed experiments could be carried
G, Arena et al. /Fisheries Research 19 (1994) 349-362
361
out. Future research will aim to test our methodology, continuing the experiments and evaluating the fitness of the theoretical approach. Acknowledgements We especially thank Drs. Robert Elner and Robert Miller (Halifax Fisheries Research Laboratory) and Dr. Jorge Csirke (FAO) for critical readings of the early stages of this paper and their valuable suggestions for the final manuscript. References Alverson, D.L. and Pereyra, W.T., 1969. Demersal fish explorations in the northeastern Pacific Ocean - an evaluation of exploratory fishing methods and analytical approaches to stock size and yield forecasts. J. Fish. Res. Board Can., 26:1985-2001. Barea, L. and Defeo, O., 1985. Primeros ensayos de captura del crust~iceo batial Geryon quinquedens Smith, en el Area Comtin de Pesca Argentino-Uruguaya. Contrib. Dep. Oceanogr. (F.H.C.) Montevideo, 2(8): 189-203. Barea, L. and Defeo, O., 1986. Aspectos de la pesqueria del cangrejo rojo (Geryon quinquedens) en la Zona Comt~n de Pesca Argentino-Uruguaya. Publ. Com. Tec. Mix. Fr. Mar., 1 ( 1 ): 3846. Boschi, E.E., Bertuche, D.A. and Wyngaard, J.G., 1984. Estudio biol6gico-pesquero de la centolla (Lithodes antarcticus) del Canal Beagle, Tierra del Fuego, Argentina. I Parte. IN1DEP Contrib., 441 : 1-72. Breen, P.A., Carolsfeld, W. and Narver, D., 1985. Crab gear selectivity studies in Departure Bay. Can. Manage. Rep. Fish. Aquat. Sci., 1048:21-39. Defeo, O., Barea, L. and Little, V., 1991. Stock assessment of the red crab Chaceon notialis in the Argentinian-Uruguayan Common Fishing Zone. Fish. Res., 11: 25-39. Eggers, D.M., Rickard, N.A., Chapman, D.G. and Whitney, R.R., 1982. A methodology for estimating area fished for baited hooks and traps along a ground line. Can. J. Fish. Aqua~. Sci., 39: 448-453. Elner, R.W., 1980. Lobster gear selectivity - a Canadian overview. Can. Tech. Rep. Fish. Aquat. Sci., 932: 77-84. Gros, P. and Santarelli, L., 1986. M6thode d'estimation de la surface de peche d'un casier a l'aide d'une filiere exp6rimentale. Oceanol. Acta, 9 ( 1 ): 81-87. Hamley, J.M. and Skud, E., 1978. Factors affecting longline catch and effort. International Pacific Halibut Commission, Scientific Report, 64:16-24. Himmelman, J.H., 1988. Movement of whelks (Buccinum undatum) towards a baited trap. Mar. Biol., 97: 521-531. Lapointe, V. and Sainte-Marie, B., 1992. Currents, predators and the aggregation of the gastropod Buccinum undatum around bait. Mar. Ecol. Prog. Ser., 85: 245-257. McElman, J.F. and Elner, R.W., 1982. Red crab (Geryon quinquedens) trap survey along the edge of the Scotian Shelf, September 1980. Can. Tech. Rep. Fish. Aquat. Sci., 1084: iii + 12 PP. McQuinn, I.H., Gendron, L. and Himmelman, J.H., 1988. Area of attraction and effective area fished by a whelk (Buccinum undaturn) trap under variable conditions. Can. J. Fish. Aquat. Sci., 45: 2054-2060. Melville-Smith, R., 1986. Red crab (Geryon maritae) density in 1985 by the technique ofeffcc-
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G. Arena et al. / Fisheries Research 19 (1994) 349-362
tive area fished per trap on the northern fishing grounds of South West Africa. S. Afr. J. Mar. Sci., 4: 257-263. Miller, R.J., 1975. Density of the commercial spider crab, C h i o n o c e t e s opilio, and calibration of effective area fished per trap using bottom photography. J. Fish. Res. Board Can., 32:761768. Miller, R.J., 1979. Saturation of crab traps: reduced entry and escapement. J. Cons. Int. Explor. Mer, 38: 338-345. Miller, R.J., 1981. Strategies for improving crab trap hauls. World Fishing, 30 ( I 0 ): 51 -53. Miller, R.J., 1983a. Considerations for conducting field experiments with baited traps. Fisheries, 8(5): 14-17. Miller, R.J., 1983b. How many traps should a crab fisherman fish? N. Am. J. Fish. Manage., 3: 1-8. Olsen, S. and Laevastu, T., 1983. Fish attraction to baits and effects of currents on the distribution of smell from baits. NOAA Natl. Mar. Fish. Serv., NWAFC Processed Rep., 83-05. Sainte-Marie, B., 1991. Whelk ( B u c c i n u m u n d a t u m ) movement and its implications for the use of tag-recapture methods for the determination of baited trap parameters. Can. J. Fish. Aquat. Sci., 48:751-756. Sainte-Marie, B. and Hargrave, B.T., 1987. Estimation of scavenger abundance and distance of attraction to bait. Mar. Biol., 94:431-443.