Contemporaneous Multistage Sampling for Age and ...

Optimizing Sampling from Trawl Catches: Contemporaneous Multistage Sampling for Age and Length structures Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by Guangzhou Jinan University on 06/03/13 For personal use only.

jukka Horppila Lahti Research and Braining Centre and Department sf Limnolsgy, University of Helsinki, Kikki, SF-00790 Helsinki, Finland

and k-leikkfleeltonen Department sf Limnslogy, University sf Helsinki, Viikki, SF-007 10 Helsinki, Finland

Horppila, J., and H. Peltonen. 1992. Optimizing sampling from trawl catches: contemporaneous multistage sampling for age and length structures. Can. J. Fish. Aquat, Sci. 49: 1555-1 559. The objective of this study was to find out the optimal sampling strategy for contemporaneousmultistage sampling of age and length structures of trawl catches. Samples were taken from a roach (Rutilus rutilus) stock of Lake Vesijarvi, southern Finland. Two-stage sampling proved to be superior to three-stage sampling (i.e. su bsamples from the trawl catches are unnecessary). Assuming that all the age and length groups are equally important, the optimal strategy is to sample 34 fish from each of 46 loads. Compared with the present scheme (500 fish from each of 10 loads),this design cuts down the total variance of the estimated proportions of different age and length groups to about one third. An age-length key was used when estimating the proportions of the age groups. The benefits of the applied agelength key were obvious. The estimates of the proportions sf different age grsups were more accurate than those obtained with age readings only. Increasing the fraction of age-deterrnined fish increases the costs, diminishes the optimal number sf samples, and consequently increases the variance of the estimated proportions of different groups. On a tent6 d'etablir la strategie sptimale d'echanti llsnnage en plusieurs &apes en vue de determiner la structure des iges et des longueurs dans les prises au chalut. Les echantil Ions ant ete prelevks d'un stock de gardon (Rutilus rutilus) du lac Vesijgrvi, situe dans le secteur sud de la Finlande. L'khantillonnage en deux &tapess'est rkv6le sup6rieur i I'4chantillonnage en trois etaps (c'est-&-direqu'il n'est pas necessaire de prelever des sous-6chantillows des prises au chalut). Si I'on suppose que tous Bes groupes d'i?ige et de longueur ssnt egalement importants, I'6chantillonnage de 34 poissons dans chacune de 46 charges constitue la strategie optirnale. Par rapport au sch&rned16chantilIsnnage courant, soit 500 poissons dans chacune de 40 charges, le prksent plan rkduit la variance totale des pourcentages estimks des differents groupes d'zge et de longueur i3 environ u n tiers. On s'est servi d'une cle 2gelsngueur pour etablir le p~urcentagedes groupes d'sge. bes avantages d'une telle cl6 etaient evidents. Ainsi, les estimations des pourcentages des differents grsupes d'sge etaient plus prkcises que celles obtenues par lecture des Ages. Une augmentation du nombre echanti ltonne de poissons df%gedetermine m&ne 5 une augmentation des coots, erne baisse du nombre optimal d'echantillons et, par consequent, i3 une augmentation de la variance du pourcentage estimatif des differents groupes. Received April 8, 199 3 Accepted February 7, 7 992 (JAY82)

T

he importance of well-planned sampling programmes in fisheries research is often underestimated, especially in freshwaters. Some authors (e.g. Ketchen 8950; Schweigert and Sibert 1982) have published methods for multistage sampling in fisheries research, but in practice these methods are not always used. Additionally, most of the published sampling strategies have dealt with the age structure of fish stocks. Although age structure is one of the basic sources of infomation in fish stock assessment, from the biological point of view the length distribution is in some cases a more reasonable subject for research. It is possible that sampling resources should be allocated differently if length structure is also taken into consideration. 911e material for this study was collected from roach (Rutilus rueilus) catches in 1990 from Lake V e s i j h i , southern Finland. Fishing with trawls in the Enonselkii basin (26 km', mean depth 6.8 rn) at the southern end sf the lake has k e n started to ~ d u c e the negative effects of the very dense roach and smelt (Osmerus. eperlanus) stocks on the water quality and to restore the lake by biomanipulation. It has been observed that trawl fishing Can. J . Fish. Aquas. Sci., $101. 49, 1992

effectively removes roaches from the trawling area (Peltonen and Horppila 1992). The Enonselka basin can be considered as a separate lake, since only narrow straits connect it with other parts of the lake. Lake Vesijiirvi was eutrophicated by the City of Lahti during the 1968's a d early 1970's. The municipal sewage loading was diverted from the lake in 1976 and the lake started to recover, However, in the 1980's, blue-green algal blooms increased again and the recovery of the lake faded. Enclosure experiments carried out in the lake demonstrated that high roach biomass is one of the key factors maintaining high algal productivity and biomass (Horppila and Kairesdo 1990). Roaches can change the water quality by size-selective predation on zooplankton, by bioturbation, and by their excretory products (Andersson et al. 1978; Henrikson et al. 1980; Brabrawd et al. 1890; Hoppila and Kairesals 1990). In the enclosure experiments carried out in Lake Vesijimi, bioturbation of sediments and recycling of nutrients, rather than zooplanktivory, seemed to be the main factors linking roaches to water quality. Roaches have omnivorous feeding habits; they B 555

Can. J. Fish. Aquat. Sci. Downloaded from www.nrcresearchpress.com by Guangzhou Jinan University on 06/03/13 For personal use only.

are plahnktivoms as juveniles, but become more bentthivorous as adults (Niederholzer and Hsfer 1980; Bmbrand 1985; Jamet et d. 1990). Since the diet of m individual fish is determined by its size rather than by its age, the length structure of the stock is of great importance to a study which investigates the cowakibution of the roach stock on the quality of the water. On the other hmd, in stock assessment the age structure is of primary importance. In this study, we are trying to find out the optimum strategy for contemporaneous sampling for length and age structures of the mach catches in the EnonselkH basin and to compare the 1990 sampling with an optimal scheme. Additiondly, the benefits of the applied age-length key are studied.

gives the value of rn, which minimizes the product of variance and cost. In the equation, c, is the cost of obtaining a load and c, is the cost of obtaining a sample from a load. If the value of m Pfor all the age or length groups is near 1, two-stage sampling can be used. In this situation, the estimate of variance is given by

where n is the number sf the loads sampled and k is the number of fish sampled per load. The variance component due to among-load variation is given bv

Materids and Methods In 1990, trawling took place from May to August. The mach catch was about 8'7 meakic tons (48% of the total catch). Samples were taken from the landed catches 10 times during the &mmer. Each sample included five randomly selected subsamples of a b u t 180 roaches. The total length of each fish was measured. Addi%ionally , four times (May 29, June 18, July 23, and August 21) during the sampling period, about 100 roaches were selected for age determination. Using the age-determined s a ples md a derived age-leng%hkey (Ketchen B950), the length distributions were used to estimate age distributions. To estimate the proportions, variance components, and optimal number of smpling units, we used the equations of Cochran (1977) as in Sehweigert and Sibert (1983). The vaimee of the mean proportion of fish at age or length group & can be estimated with equation

where n is the number of loads sampled, m is the number of samples from a load, and k is the number of fish at age or length group whose ages were determined or whose lengths were measured. The variance component caused by the among-load variation is given by (2)

s:

=

5

i= B

('Li..

-

l2

' L ...

where P,.. is the estimated mean proportion at age or length L in the catch and P L j . is the mean proportion at age or length L in sample i. The variance component caused by among-fish variation is

The total cost (C) of the sampling program is given by for thee-stage sampling and by for two-stage sampling where c, is the cost of detemining the age or length of a fish. Because the financial costs of taking a sample, determining ages of fish, etc., are dependent on the time used, we used time instead of money to describe the cost structure of the study. It was approximated that it takes 5 h to sample a load (c,), 6 min to obtain a subsample from a load (e2),and 3 min to detemine the age of a fish (c,). The value of c, is low because the a g e length key was used to detemine ages. Total sampling time was constrained to 305 h, the time used to sample in 1990, to facilitate comparisons between the 1990 smpling and the optimal scheme.

n - l

where P L i . . is the mean proprtion of fish at age or length group & in load i and P,..~is the mean proportion of fish at age or length group & in the catch. -The variance component due to among-sample variation is given by

where PLU,is the mean proportion of fish at age or length group L in samplej of load i. The variance component caused by among-fish variation is given by

If the cost of a survey is considered, the equation

Results The values of m' (optimal number of subsamples) indicate whether three-stage smpling was worthwhile. It seems clear that two-stage smpling is appropriate for the age structure of the catch (average rn4 = 1.1). Ody age group 3 would require three-stage sampling (m' = 2.0). Length intervals of 4 ern (Brabrand 1985) and 5 cm (Bask 1989) have been found appropriate when studying the diet of roaches. Consequently, we decided to apply the 4-cm intewds, and two-stage sampling turned out to be appropriate (average "m lea). Only the smallest (