Characterizing catch variability in a multispecies fishery - Canadian ...

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Characterizing catch variability in a multispecies fishery: implications for fishery management J.A.E. van Oostenbrugge, E.J. Bakker, W.L.T. van Densen, M.A.M. Machiels, and P.A.M. van Zwieten

Abstract: Exploiting several fish species simultaneously reduces variability in daily catches. The reduction depends on the number of species, the catch-frequency distributions of individual species, and the level of co-occurrence of species in the catch. We explore theoretically the reduction of variability (coefficient of variation; CV) in the total catch by combining the distributions of daily catches of individual fish species, including zero catches, into a total catch frequency distribution. Theoretical findings are tested with an example from a stationary lift-net fishery for schooling small pelagic species around Ambon Island in the Central Moluccas, Indonesia. This fishery catches over 30 species, all with high daily variability (CV = 2.2–13.4). The reduction of variability in the total catch (CV = 1.7) is a result of the dominance and independent occurrence of the three main species. We conclude that in this fishery the information value of the total catch as an indicator of the catches of the individual species is low. Résumé : L’exploitation simultanée de plusieurs espèces de poissons peut réduire la variabilité des captures journalières. L’importance de cette réduction dépend du nombre d’espèces, de la distribution de fréquence des espèces dans la récolte et du niveau de la co-occurrence des espèces dans la récolte. Nous examinons en théorie la réduction de la variabilité (coefficient de variation; CV) dans les captures totales en combinant les distributions des captures journalières d’espèces particulières, incluant les captures nulles, dans la distribution de fréquence des captures totales. Un exemple tiré d’une pêche commerciale à carrelet de petits poissons pélagiques vivant en bancs près de l’Îsle Amboine (Moluques, Indonésie) permet de tester les résultats théoriques. Les récoltes incluent plus de 30 espèces de poissons, chacune avec une variabilité journalière élevée (CV = 2,2–13,4). La réduction de la variabilité dans la capture totale (CV = 1,7) est le résultat de la dominance et de l’occurrence indépendante des trois espèces principales. Dans cette pêche commerciale, la valeur prédictive de la capture totale comme indicateur de la capture des espèces particulières est basse. [Traduit par la Rédaction]

van Oostenbrugge et al.

Introduction Together with the mean catch, variability in catch rate is one of the primary characteristics of a fishery, affecting many aspects of its functioning, such as its economy and the different options for its management (Platteau and Abraham 1987; van Oostenbrugge et al. 2001). Total variability in catch rate is determined by trends, cyclic patterns, persistence, and “random variation”. Random variation on a daily scale causes what we may call basic uncertainty and is the result of small-scale spatial and temporal patterns of fish abundance on the fishing ground and the inability of fishers to respond accurately to such patterns. Basic uncertainty is intrinsic to a fishery and its magnitude depends on the type of ecosystem, the state of the stocks, and the scale of the fishing operation (van Densen 2001). Variability in daily catches made by individual fishing units, ex-

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pressed as the coefficient of variation (CV), can be used as a standardized measure of basic uncertainty. For instance, the typical variability in daily catch for fisheries using gill nets and small-scale purse seines on the nonschooling cichlids of Lake Malombe in Burundi is CV = 0.7–0.8 (van Zwieten et al. 2002). The variability in daily catch for the small-scale purse-seine fishery targeting schooling pelagic species in the coastal waters around Ambon Island in the Central Moluccas, Indonesia, is extremely high (CV = 3.1) and only a small proportion can be explained by external factors such as time trends and effects of the lunar cycle (van Oostenbrugge et al. 2001). For individual species, variability in the catch depends on the dispersion (spatial pattern) of the targeted fish species, their temporal dynamics (dispersal) in relation to the scale of operation of the fishery, and the fishers’ strategy. The variability in the total catch of a combination of species is inevi-

Received 29 January 2002. Accepted 27 May 2002. Published on the NRC Research Press Web site at http://cjfas.nrc.ca on 25 July 2002. J16737 J.A.E. van Oostenbrugge,1 M.A.M. Machiels, and P.A.M. van Zwieten. Fish Culture and Fisheries Group, Wageningen Institute of Animal Science, Wageningen University and Research Centre, P.O. Box 338, 6700 AH, Wageningen, The Netherlands. E.J. Bakker. Mathematical and Statistical Methods Group, Department of Plant Sciences, Wageningen University and Research Centre, P.O. Box 9101, 6700 HB, Wageningen, The Netherlands. W.L.T. van Densen. Netherlands Institute for Fisheries Research P.O. Box 68, 1970 AB IJmuiden, The Netherlands. 1

Corresponding author (e-mail: [email protected]).

Can. J. Fish. Aquat. Sci. 59: 1032–1043 (2002)

J:\cjfas\cjfas59\cjfas5906\F02-078.vp Monday, July 22, 2002 2:59:12 PM

DOI: 10.1139/F02-078

© 2002 NRC Canada



tably lowered compared with the variability in catches of the individual species because of statistical averaging (Doak et al. 1998). Since, with a few exceptions, all tropical fisheries are multispecies fisheries, the variability in the total catch is reduced compared with the variability in catches of individual species. This reduction is important for the fishers as well as for the managers, as the variability in the catches influences the economic uncertainty for the fishers and their ability to perceive differences that affect the functioning of the fishery and its management. Moreover, the reduced variability in the total catch can conceal decreases in catches of individual species and possible overfishing. However, the extent to which the variability is lowered depends on the number of species caught, the characteristics of their individual catch-frequency distributions (CFDs), and the level of their co-occurrence. The effect of catching a multitude of species on the variability in the total catch is to a large extent comparable to the statistical effects of diversification as discussed in other fields of science. In economics the effect of diversification is well known as the “portfolio effect” and is widely used in the literature on both investment and livelihood diversification (Ellis 1998). In ecology, discussions on the statistical inevitability of stability–diversity relationships have received wide attention (Doak et al. 1998; Lehman and Tilman 2000). However, these discussions do not deal with a problem specific to small-scale multispecies fisheries: the large proportion of zero catches. In particular, small-scale fishers targeting schooling fish hardly ever catch more than a few schools per daily trip; therefore, subsequent catches of individual species include a large number of zero values (e.g., van Oostenbrugge et al. 2002). The probability of cooccurrence of species as well as the correlation in nonzero catches affect the covariance in catches of species; therefore, the reduction of variability is more complex than described in the literature. Because of this, earlier studies of variability in catches omitted zero values (Blanchard and Boucher 2001). In this study, we first elaborate theoretically how variability is reduced by combining the different frequency distributions of daily catch per species, including zero catches. Subsequently, the theoretical results are tested with a stationary medium-scale lift-net fishery that uses light to attract small pelagic species in the coastal waters around Ambon Island. This fishery is known for its very high variability in daily catches and its low probability of nonzero catch for all species combined (p = 0.55) (van Oostenbrugge et al. 2002). In the Discussion we elaborate on the ecological reasons for typical species compositions and the consequences for the management of multispecies fisheries.

Materials and methods Model Depending on the size of the spatial window of operation for a fisher and the dispersion and dispersal of his target, the proportion of zero catches in daily catches can be considerable. In these cases, the CFD can be described as a combination of the probability of encountering and capturing a school (p) and a continuous distribution, representing the size of the nonzero catch. The mean, variance, and CV of

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the size of the catch of species i, including zero catches, are given by (1)

E(Gi) = pi µ i

(2)

Var(Gi) = pi [(1 − pi)µ i2 + σ i2 ]

and (3)

CV(Gi) =

CVi2 + 1 − pi pi

where Gi is the size of the catch of species i (usually on a 1day fishing trip), pi is the probability of capture of species i, µ i is the mean size of the nonzero catch of species i, σ i is the standard deviation of the nonzero catch of species i, and CVi is the CV of the size of the nonzero catch of species i (σ i /µ i ). With decreasing pi the ratio between CV(Gi) and CVi increases and the variability in the total catch becomes larger (Fig. 1). If pi is equal to unity, then CV(Gi) and CVi are the same. Because of the lognormal CFD and the high probability of zero catches, estimators of the mean and variance from the delta distribution might be more efficient in the case of small sample sizes (Pennington 1996). These estimators are not used, as they are less straightforward and present difficulties when covariance in a multispecies context is considered. If we combine two species (i and j), the total catch size can be calculated as G = Gi + Gj. Its mean (E(G)) and variance (Var(G)) can be calculated as (4)

E(G) = E(Gi) + E(G j ) = pi µ i + p j µ j

and (5)

Var(G) = Var(Gi) + Var(Gj) + 2 Cov(Gi,Gj)

in which Cov(Gi ,Gj) is the covariance between Gi and Gj. Thus, the variability in the catch of the two species combined is calculated as (6)

CV(G) =

Var (Gi) + Var (G j ) + 2 Cov(Gi, G j ) E(Gi ) + E(G j )

In the simplest situation, i.e., that the two species caught have equal CFDs (pi, µ i , σ i , and thus E(Gi) and Var(Gi)) and the two species are caught independently, so Cov(Gi,Gj) = 0, eq. 6 is reduced to (7)

CV(G) =

1 × CV(Gi) 2

If the CFDs differ between the two species, as they will in practice, the resulting CV is influenced by the characteristics of the CFDs of the individual species and will be determined mostly by the species with a high mean catch and (or) a high variance (eq. 6). We show the changes in variability of the total catch, as a fraction of the variability in the catch of species i, in relation to the characteristics of the CFDs of two independently occurring species (i and j; Fig. 2). In Fig. 2 the effect of differences in each of the characteristics of the CFDs (pi, µ i , σ i ) is shown, whereas all other characteristics are kept constant and the same for the two species. When the CFDs of the two species are the same, the variability in the © 2002 NRC Canada



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Can. J. Fish. Aquat. Sci. Vol. 59, 2002

25

2.5

20

2.0

SD

CV 15

1.5

10

1.0

Mean, SD

CV (= SD/Mean)

Fig. 1. Mean, standard deviation (SD), and coefficient of variation in the total catch (CVtot = SD/mean) in relation to the probability of capture (p). The mean and standard deviation of nonzero catches are constant: µ nonzero = 1, σ nonzero = 2.

Mean 5

0 0.00

0.5

0.25

0.50

0.75

0.0 1.00

p

(8)

CV(G) =

2Var(Gi) + 2Cov(Gi, G j ) 2 E(Gi)

If the species are highly correlated and thus Cov(Gi,Gj) is close to Var(Gi), then CV(G) will approximate CV(Gi). If Gi and Gj are not highly correlated, then CV(G) will be considerably smaller than CV(Gi). CV(Gi) can even become zero if Cov(Gi,Gj) = –Var(Gi), a perfect negative correlation between Gi and Gj. In such an extreme situation, Gi is low whenever Gj is high and vice versa. Because the CFD of the individual species (i and j) includes zero catches (eqs. 1 and 2) it can be shown that (9)

Cov(Gi,Gj) = pi[(pj|i – pj) µ i µ j + pj|irσ i σ j ]

where pj|i is the conditional probability of capture of species j, given the capture of species i, and r is the correlation coefficient of nonzero catches of species i and j. When species i and j are caught independently of each other, pj|i = pj and r = 0. When species i and j are caught alternately, pj|i = 0, so the total variance is reduced by a constant, which is affected by the probability of capture and the mean nonzero catch of both species. When there are more than two, say n, species, and n

Gtot =

∑ Gi, then i =1

total catch is reduced by a factor 1/ 2, as was shown before (eq. 7). Differences in individual characteristics have particular effects: (i) Probability of capture (p) (Fig. 2a): the influence of a species with a low p value on the variability in the total catch is low compared with that of a species with a larger p value, because a lowered p value reduces the variance and mean catch, including zero values (eq. 6). Therefore, the smaller pj is compared with pi, the more the CV of the total catch (CVtot) resembles the variability in the catch of species i. Conversely, the larger pj is compared with pi, the more CVtot resembles the variability in the catch of species j. Because CVi increases with decreasing pi (Fig. 1), CVtot becomes smaller relative to CVi. (ii) Mean nonzero catch (µ) (Fig. 2b): CVtot increases with decreasing µ j (eq. 6); conversely, if µ j is much larger than µ i , the reduction in CVtot relative to CVi can be substantial. (iii) Standard deviation (σ) (Fig. 2c): with decreasing σ j compared with σ i, CVtot becomes smaller; conversely, with increasing σ j compared with σ i , CVtot becomes larger (eq. 6). Although the magnitude of the effect on total variability differs for other values of the characteristics illustrated (Fig. 2), the effect itself does not. In conclusion, we can state that the variability in the total catch will resemble the variability in the most common species in the catch with the largest standard deviation, while the large variability of rare species hardly contributes to the reduction in variability in the total catch of both species. When the species are not caught independently, the covariance between the catches of the species affects the reduction of variability as well. To show this, we will consider the specific situation that the CFDs of the two species have the same characteristics (Var(Gi) and E(Gi)). In that case, eq. 6 reduces to

n

n

∑ Var(Gi) + ∑ ∑ Cov(Gi, G j ) (10)

CV(Gtot ) =

i =1

i =1 j ≠1

n

∑ E(Gi ) i =1

The reduction of variability is governed here by three factors that influence each other: (1) the total number of species caught, (2) the CFDs of the individual species, and (3) the homogeneity of species composition in subsequent catches, expressed as the covariance between individual species. When CFDs are equal and the catches of any pair of species are independent, the variability in the total catch can be given by (11)

CV(Gtot ) =

1 × CV(Gi) n

This means that when a large number of independently occurring species are combined, CV(Gtot) approaches zero. In real-life situations this total reduction of variability does not occur, as the CFDs of species caught by multispecies fisheries vary, which makes calculating the reduction in variability highly complex. Doak et al. (1998) tried to simplify this situation in their discussion of the relation between species diversity and the temporal stability of ecosystems. They assumed that the CVs for all species were similar and that species varied independently. Further, they assumed that the relative abundance of each subsequent species declined exponentially by rank number, so that (Doak et al. 1998) (12)

m i = m1 × e− a ( i −1) © 2002 NRC Canada




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Fig. 2. Isopleth diagrams of CVs of the total catch of two species relative to the CV of species i (CVtot/CVi) in relation to the probability of capture of the two individual species (pi, pj) (a), the mean nonzero catch of the two individual species (µ i , µ j ) (b), and the SDs of the nonzero catches of the two individual species (σ i , σ j ) (c). The two species were independently caught, and the parameters that are not included in the graphs are constant and the same for the two individual species and are indicated below the graph.

When applied to the problem of a reduction of variability in a multispecies catch, these parameters signify the following: m1 is the relative abundance of the most common species, i is the species rank when species are ranked according to their relative importance to the total weight of the catch, and a is a coefficient that indicates the rate of decline in the relative importance of each subsequent species, or the coefficient of abundance inequality (CAI). Using eq. 12 we can rewrite eq. 10 as (eq. 3 in Doak et al. 1998) 12

(13)

 (1 – e–a )(1 + e–an)  CV(Gtot ) = CV(G1) ×  –a –an   (1 + e )(1 – e ) 

where we can see that the reduction in CV is asymptotic and that with a larger value of a, i.e., a greater relative importance of the most abundant species, the maximum reduction in CV that can be attained is lowered (Fig. 3a). Finally, if the CFDs of all species are equal, but the level of co-occurrence between species varies, eq. 10 reduces to n

nVar(Gi ) + 2∑ ∑ Cov(Gi, G j ) (14)

CV(Gtot ) =

i =1 j ≠1

nE(Gi )

CV(Gtot) is equal to CV(Gi) if all catches have a perfect positive correlation, i.e., Cov(Gi,Gj) = Var(Gi) for all i,j. In that case, no reduction in CV would be attained by catching more than one species (Fig. 3b). CV(Gtot) is zero in the case of the most negative covariance between the species, so the total catch is constant. Study site The research was conducted on a pelagic fishery with lift nets, located in two areas on the southeastern and eastern sides of Ambon Island (Fig. 4). Baguala Bay (3°38′S, 128°17′E) has a total surface area of approximately 17 km² and Haruku Strait (3°35′S, 128°20′E) has a total surface area of approximately 38 km². With water depths not more than 200 m in the mouth of Baguala Bay and in the western part of Haruku Strait (approximately 10 km²), these areas are suitable for a lift-net fishery from stationary anchored platforms. The coastal lift-net fishery for small pelagic species around Ambon and Lease islands has regional importance. In 1995, the 326 lift-net units contributed 21% of the total catch of coastal fisheries in the Central Moluccas (Anonymous 1981– 1997). In addition to human consumption, a large proportion of the 3600 t of mainly anchovies and sardines caught was used as live bait for the offshore pole-and-line fishery for

skipjack tuna (Katsuwonus pelamis). The tuna fishery represented 12% of the total weight and 29% of the total value of the catch from the Central Moluccas in 1995. Price differences among species caught by the lift-net fishery are negligible, © 2002 NRC Canada



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Can. J. Fish. Aquat. Sci. Vol. 59, 2002

Fig. 3. CV of total catch relative to the CV of the individual species (CVtot / CVsp) resulting from a combination of n distributions with equal CVs and varying coefficients of abundance inequality (CAIs; i.e., the decrease in abundance of individual species with increasing rank (eq. 12)) (a) and varying covariance (b). The line with a = 0 denotes a situation in which all species are equally abundant. With increasing CAI, the abundances of individual species are more unequal and the species that occur most often are more important (eq. 13). Adapted from Doak et al. (1998). Numbers in b are correlation coefficients (r).

(a) 1.0

CVtot/CVsp

0.8 0.6 0.4 0.2 0.0 0

10

20

30

40

a = 0.5 a = 0.4 a = 0.3 a = 0.2 a = 0.1 a = 0.0 (Equal abundance)

Number of species

(b) 1.0

1.0

CVtot/CVsp

0.8

0.5

0.6 0.4 0.0

0.2 -1

- 0.5

0.0 1

6

11

16

Number of species

Fig. 4. Ambon and Lease islands showing the locations of Baguala Bay (1) and Haruku Strait (2).

as most of the catch is sold as live bait at a constant price, and market prices of the species caught are similar. The lift-net units in the Central Moluccas consist of a

square wooden platform about 200 m2 in area mounted on an anchored body. A square lift net is attached under the platform. The surface area of the net opening is equal to the size of the platform; the net has a mesh size of around 3 mm. The stationary lift-net units are operated during 1night trips made by the crew to and from the platform. The fishing process consists of two phases. First, small pelagic fish are attracted to the unit using all lamps on the platform. When the fishers conclude from direct observation that enough fish have clustered under the platform, all lamps are slowly extinguished except for one in the centre of the unit. Fish concentrate around it and are caught by lifting the net using windlasses, each operated by one of the two to six fishers working on the unit. In this way up to three hauls are made per night. The variability in total catch per night of individual lift-net units is large: CV = 2.5. Only 55% of the trips result in a catch, and only nonzero catches still show large variability: CV = 1.7. Data collection A sampling program was carried out from mid-September 1998 (the end of the southeast monsoon) to February 1999. Samples of fish weighing 0.5–4 kg were taken three times a week from 06:30 to 07:30 as the fishers landed their nightly catches at the main landing site in each of the two areas. One to four samples were taken per day, depending on the number of landings. In addition, the total catch was recorded either by counting the baskets (18 kg) when the fish were landed or asking the fishers about the number of buckets (4 kg) sold when the fish were sold as live bait at sea. All small pelagic species (e.g., sardines, anchovies, sprats) were identified to species following Whitehead (1985); juveniles of larger pelagic species such as scads, mackerels, and tunas were identified to genus. All demersal fish were grouped into one category (“other”). Testing the model Probability of capture (p), mean catch per day (µ; kg·day–1), standard deviation (σ; kg), and variability (CV), both including and excluding zero catches, were calculated for all individual species caught. Total zero catches included both hauls when no catch was made and cases when no haul was made, usually because the amount of fish attracted under the liftnet platform was negligible. No distinction could be made between these two situations and thus it was not known whether total zero catches were real zero values or low values. Because this distinction is important in terms of the characteristics of the CFD, all total zero catches were excluded from the data set; p is therefore the conditional probability of catching a certain species when the total catch is larger than zero. To test whether pairs of species occurred independently in daily catches, a χ 2 test was used to test the proportion of catches in which a pair of species occurred together against the theoretical probability of co-occurrence of the two species. This theoretical probability was based on the probabilities of occurrence of the two individual species. Finally, the effects of the characteristics of the CFDs of individual species and the level of co-occurrence among species on the reduction of variability in the total catch were © 2002 NRC Canada




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Table 1. Species composition of lift-net catches from Baguala Bay and Haruku Strait, Ambon Island, Central Moluccas, Indonesia, with descriptive statistics for each species taken from nonzero catches.

Sardines Ambligaster clupeoides Ambligaster sirm Dussumieria elopsoides Escualosa sp. Herklotsichthys quadrimaculatus Ilisha sp. Sardinella albessa Sardinella atricauda Sardinella fimbriata Sardinella gibbosa Sardinella melanura Spratelloides delicatulus Spratelloides gracilis Anchovies Encrasicholina devisi Encrasicholina heteroloba Encrasicholina punctifer Stolephorus commersonii Stolephorus indicus Stolephorus waitei Thrissa baelama Thrissa setirostris Other species Atherina spp. Auxis spp. Caesio spp. Decapterus spp. Rastrelliger spp. Selar spp. Sphyraena sp. Other

% of total weight

p