DOI: 10.2478/v10043-011-0006-2 Acta Zoologica Lituanica, 2011, Volumen 21, Numerus 1 ISSN 1648-6919 Growth, mortality, recruitment and yield of Parailia Pellucida BoulenGer, 1901 (osteichthyes: schilBeidae) in a tropical flood river system, southeastern niGeria Bilikis iyabo uneKe, christopher didiugwu nwani, okechukwu oKoGwu, florence oKoh Department of Applied Biology, Faculty of Biological Sciences, Ebonyi State University Abakaliki, Nigeria. E-mail: unekebi@yahoo.com abstract. The growth parameters, mortality rates, exploitation rate, recruitment pattern, yield/biomass per recruit and the corresponding ishing mortality at this level of Parailia pellucida (Boulenger) in the Anambra lood river system, southeastern Nigeria, was studied using the length-frequency based analysis of FiSAT II software. Growth parameters were as follows: asymptotic length (L∞) = 11.03 cm TL, growth curvature (K) = 0.63 yr-¹. The total mortality (Z) = 2.42 yr-¹, natural mortality (M) = 1.68 yr-¹, and ishing mortality (F) was 0.74 yr-¹. Exploitation rate (E) was 0.31. P. pellucida exhibited the bimodal continuous recruitment pattern. The Selection Ogive procedures for relative yield/biomass per recruit showed that Emax was 0.70. The stock was not overexploited (E < Emax); the ishing pressure should be maintained and monitored to guide against possible overexploitation since the lood river system operates unrestricted and unregulated isheries activities. Key words: growth, mortality, recruitment, yield, Parailia pellucida IntroductIon Although Parailia pellucida Boulenger, 1901 is not the only schilbeid species present in the Anambra lood river system, its abundance by number and weight in lift-net ishery is notable and signiicant. The target schilbeids constituted 55% by number and weight, respectively, of the overall catch (Ezenwaji 2004). According to Ezenwaji and Ofiah (2003) this abundance may be attributed to a number of factors such as early sexual maturity, all-year-round breeding, food availability, high growth rate, short life span, high natural mortality and environment. The river system is characterised by many tributaries and loodplain water bodies, mainly small-sized (<500 m²) and medium-sized (<5000 m²) ponds and lakes (Welcomme 1985) which are fringed by riparian shrubs and forests. The vegetation in the river system is the rainforest Guinea mosaic and it is typical of this area and areas north of it (Ezenwaji 1998). The dry season occurs from October and November to March, while the rainy season is from April to September and October. The present study was undertaken to evaluate the status of the ishery of P. pellucida using length-based stock assessment procedures. This information is necessary in formulating management and conservation policies as well as in the further development of ishery for this species in Nigeria. Furthermore, with regard to the information gap about small ish, the population parameters estimated for P. pellucida forms a comparison base for other population studies of small-sized ish species of tropical environments. The results also provide baseline information (as well as reference points) that can be incorporated into wider reference systems relevant to current isheries assessment and management in the tropical region. MaterIal and Methods The sampling of P. pellucida was made at the Otuocha River port from artisanal ishers. Fig. 1 shows the sampling location (Otuocha) in the Anambra lood river system, southeastern Nigeria. Samples were collected monthly for 13 consecutive months. Random sampling was done from the catches of every other artisanal isher landed at the river port. P. pellucida were mainly caught by ishers using lift nets. Samples were preserved in 10% formalin until further analysis. Total length (TL) was measured to the nearest 0.1 cm with a meter rule measuring board. Weight measurement was made with a Mettler PC 2000 electronic weighing balance to the nearest 0.1 g. The data were pooled monthly and subsequently grouped into 1 cm class intervals. The data were analysed using the FiSAT (FAO-ICLARM Stock Assessment Tools) as explained in details by Gayanilo et al. (1996). First the Powell-Wetherall method as modiied by Pauly (1986) 11 Growth, mortality, recruitment and yield of Parailia pellucida iver ue R Ri ve r Ben pk O While the potential longevity of the ish was estimated according to Taylor (1958) and Pauly (1980): Is Ad ad a Ri ve r Anambra Rive N R he Ogurugu Ezech River Niger River Anambra basin φ¹ = 2 log L∞ + log K r ive o r ive rR ge Ni Here, T was 25.7°C (the mean annual surface water temperature in the river). The overall growth performance index φ¹ was quantiied using the model of Pauly and Munro (1984): Nigeria Enguwu-Otu Ponds Sampling locations Rivers and lakes Rive Roads Oroma Etiti Anambra Some towns Ez u Otuocha Ri ve r Ugwuoba Nsugbe Awka 10 km Onitsha Figure 1. Map of the Anambra lood river system showing the sampling location (Otuocha) (Ezenwaji 1998). was employed in the estimation of the asymptotic length (L∞) of the von Bertalanffy Growth function (VBGF) and the ratio of the total mortality to growth coeficient (Z/K) from the linear relationship: L – L¹ = a + bL where L¹ is the cut-off length of the smallest fully recruited ish for each size class, L = (L∞ + L¹) / [1 + (Z/K)], which is the mean length of all ishes ≥Lt. Thus, plotting L – L¹ against L¹ gives a linear regression from which a and b could be estimated and hence L∞ and (Z/K) (Powell 1979; Wetherall 1986). A preliminary L∞ was calculated as a/b and Z/K as – (1 + b) /b. The ELEFAN procedure in FISAT was then used to sequentially arrange and restructure the monthly lengthfrequency data set. The K-scan routine from the FISAT program provided estimates of L∞ and K. Taylor (1958) suggested the rule of thumb, Lmax/0.95 ≈ L∞. Total mortality (Z) was estimated following the lengthconverted catch curve method (Pauly 1983; Gayanilo & Pauly 1997) from the pooled length frequency data for the study period. The empirical model of Pauly (1980) was used to estimate the instantaneous natural mortality coeficient M: Log M = -0.0066 – 0.279log L∞ + 0.6543log K + + 0.4634log T tmax ≈ 3 / K. The ascending left arm of the non-seasonalized lengthconverted catch curve was used to compute the probability of capture (P) of each size class i. This involves dividing the number of ishes actually sampled by the expected numbers (obtained by backward extrapolation of the straight portion, i.e. the descending part of the catch curve) in each length class of the ascending part of the catch curve. By plotting the cumulative probability of capture against class mid-length, a resultant curve was obtained from which the length at irst capture Lc was taken as corresponding to the cumulative probability at 50%. The recruitment pattern of the ish was constructed using the entire length frequency data set. This involved projecting backward, along a trajectory described by the computed VBGF, all length frequency data onto a 1-year time scale (Pauly & Morgan 1987). Then, employing the maximum likelihood method, the distribution was resolved into its Gaussian components using the NORMSEP (normal separation) procedure of Hasselblad (1966). The model of Beverton and Holt (1966) as modiied by Pauly and Soriano (1986) was used to predict the relative yield per recruit (Y¹/R) of the species to the isheries: (Y¹/R) = EUM/K [1- (3U) / (1 + m) + (3U²) / (1 + 2 m) – – (U³) / (1 + 3 m)] where E = F /Z is the current exploitation rate, i.e. the fraction of death caused by ishing activity, F is the instantaneous ishing mortality coeficient, U = 1 – (Lc / L∞) = the fraction of growth to be completed by ish after entry into the exploitation phase, m = (1 - E) / (M/K) = K/Z. The relative biomass per recruit (B¹/ R) was estimated as: B¹/ R = (Y¹/ R) /F Then, Emax (exploitation rate producing maximum yield), E0.1 (exploitation rate at which the marginal increase of Y¹/R is 10% of its virgin stock) and E0.5 (exploitation rate under which the stock is reduced to half its virgin biomass) were computed through the irst derivative of the Beverton and Holt (1966) function. Yield contours were plotted to assess the impact on yield of changes in exploitation rate E and critical length ratio Lc/L∞. 12 Uneke B. I., Nwani Chr. D., Okogwu O., Okoh F. seasonalized length-converted catch curve (Fig. 5) was 2.42 yr-¹. Estimations of M at 25.7°C and F for P. pellucida were as follows: 1.68 yr-¹ and 0.74 yr-¹. The rate of exploitation (E) was estimated as 0.31 and that of the Emax value recorded as 0.70. The lower value of E indicated that there was no overishing during that period. This assumption is based on Gulland (1971). He stated that suitable yield is optimized when F = M, i.e. when E is more than 0.50, the stock is generally considered to be overished. The probability of capture for each length group had the estimation of L25, L50 and L75 as 4.09, 4.84, and 5.61 cm TL respectively (Fig. 6). The population of P. pellucida displayed the continuous and bimodal recruitment (Fig. 7): the irst peak between June–July with 15.77 and 18.93% recruitment respectively, and August–September for the second peak with 19.39 and 13.85% recruitment respectively. Selection Ogive procedure (Fig. 8) of P. pellucida gave Emax = 0.70, E0.1 = 0. 56 and E0.5 = 0.34. results Powell-Wetherall’s method (Fig. 2) computed L ∞ =11.39 cm TL and Z/K = 2.602. K value according to Ursin (1984) was 0.72 yr-¹. Using the ELEFAN 1 analysis, the optimized and seasonalized VBG curves yielded the following growth estimates with the K-scan (Fig. 3): L∞ = 11.03 cm TL, K = 0.63 yr-¹ and φ¹ = 1.88. These curves superimposed over the length-frequency histograms represent the restructured length-frequency histogram (Fig. 4). t0, and tmax were estimated as -0.34 yr, and 4.76 years respectively. Lmax encountered was 11.0 cm TL. The von Bertalanffy length (Lt) growth function was Lt = 11.03 [1- exp-0.63 (t + 0.34)] and the von Bertalanffy weight (Wt) growth function was Wt = 8.81 [1- exp-0.63 (t + 0.29)] 3.442. The smallest sampled unit of P. pellucida was 3.80 cm TL. The smallest mature male and female P. pellucida sampled were 4.8 and 5.2 cm TL respectively. The computed Z value for P. pellucida using the non4 1.0 0.9 0.8 0.7 Score function Mean L–L' 3 2 0.6 0.5 0.4 0.3 0.2 1 0.1 0 0 7 Cut-off length (L', cm) 3 0.1 0.5 1 Growth constant K (/year) 5 10 1 1.7 2 Growth performance index (') 2.7 3 11 Figure 2. Powell-Wetherall plot of P. pellucida. Figure 3. K-Scan graph of P. pellucida. 12 Length (cm) 10 8 6 4 2 0 J F 2004 M A M J J A S O N D J F 2005 M A M J J A Figure 4. VBG curve of P. pellucida with restructured length-frequency histograms using ELEFAN 1. S O N D 13 Growth, mortality, recruitment and yield of Parailia pellucida 1.00 11 8 ln (N/dt) ln (N/dt) 0.75 0.50 5 0.25 2 0 0 0 1 5 2 3 4 Relative age (years-t0) 0 Figure 5. Length-converted catch curve of P. pellucida. 0.02 Relative biomass / Recruit (B’/R) 0.75 0.50 0.25 J F M A M J J A Months S O N D 0.01 0.01 0.01 0.01 0.00 0.00 0 Relative yield / Recruit (Y/R) 1.00 10 5.5 3.5 4.5 Length classes (cm) Figure 6. Probability of capture analysis of P. pellucida. 20 Recruitment (%) 2.5 0.00 0.0 0.2 0.4 0.6 Exploitation ratio (E) 0.8 1.0 Figure 7. Continuous bimodal recruitment pattern of P. pellucida. Figure 8. Relative yield and biomass per recruit of P. pellucida using Selection Ogive procedure. dIscussIon k = 0.85 yr-¹, indicating a fast growing ish; this is in agreement with the values of K and φ¹ of this study (0.63 yr-¹ and 1.88 respectively), which is high and showed that the growth of small ish is fast. Growth performance index Ø compares the growth performance of different populations of ish species. Faster growth rates are a defensive mechanism against predators. This is in line with the values of the growth performance index (1.87 and 4.48) of P. pellucida from the Fresh Water Reaches of Lower Nun River, Niger Delta, Nigeria (Abowei 2009) and in the upper portion of Jebba reservoir, Nigeria (Olaosebikan et al. 2006) respectively. A characid Brycinus lateralis of the Okavango Delta of Botswana showed L∞ and K values of 17.00 cm TL and 2.80 yr-¹ respectively, also a mormyrid Petrocephalus catastoma of the same locality had values of L∞ and K as 20.00 cm TL and 0.78 yr-¹ (Mosepele & Nengu 2003) revealing small ishes’ fast growth. Various authors, As there is apparently no previous study on growth parameters of P. pellucida, presented data cannot be accurately contrasted. L∞ of 11.03 and 11.39 cm TL of ELEFAN and Powell-Wetherall analysis for P. pellucida differs from maximum size of 15.0 cm TL recorded by De Vos (1995) but is in agreement with maximum size of 12.0 cm TL as reported by Olaosebikan and Raji (1998). Furthermore, considering the information gap about small ish, the parameters estimated for P. pellucida constitute a comparison base for other growth studies of small-sized ish species of tropical environments. According to Cunha et al. (2007) the estimated growth parameters for Moenkhausia dichroura (Kner 1858) (Characiformes, Characidae), a small-sized and very abundant ish of the Pantanal lentic habitats commonly known as pequira, were L∞ = 81 mm (standard length), 14 notably Beverton (1963) and Taylor (1958), have noted that there is generally a good agreement in various ish stocks between Lmax, the largest length recorded from a given stock, and L∞, the asymptotic length estimated for that stock. Taylor (1958) suggested the rule of thumb, Lmax/0.95 ≈ L∞. This is consistent with Lmax (11.0 cm) and L∞ (11.39 cm) values of P. pellucida in this study. The need to conserve biodiversity and reduce pressure on capture isheries in order to ensure sustainability, provide alternate means of employment, income, food and nutritional security brings to light the important role of aquacultural practices (Francis & Sikoki 2007). The approach of L∞ at a fast growth rate around and above 0.50 yr-¹ indicates species suitability for aquaculture, thus K value of 0.61 yr-¹ reveals that P. pellucida is suitable for aquaculture. As stated by Abowei (2009), mortality rates of P. pellucida (Boulenger, 1901) from the Fresh Water Reaches of Lower Nun River, Niger Delta, Nigeria were high, with total mortality (Z) value as 1.4yr-¹, natural mortality (M) value as 0.55, ishing mortality (F) value as 0.87. Value for the rate of exploitation was 0.67 with corresponding percentage value of 67%. This is in agreement with the values (Z = 2.42 yr-¹, M = 1.68 yr-¹ and F = 0.74 yr-¹) recorded for P. pellucida in this study; this also may not be unconnected with deaths due to diseases and old age leading to natural mortality. Small-sized ishes have high turnover rates (P/B ratio; Allen 1971). P/B is equal to Z so that high Z in small-sized ish species relects their high turnover rates. They can therefore withstand high ishing mortalities. Therefore, P. pellucida, which is a fast growing ish with short life span, had high ishing mortality. This is consistent with studies on blueish (Pomatomus saltatrix) caught by artisanal ishery which showed high Z and F values, 0.96 yr-¹ and 0.60 yr-¹ respectively (Akyol & Ceyhan 2007). Also, according to Olaosebikan et al. (2006) P. pellucida in the upper portion of Jebba reservoir, Nigeria, had high ishing mortality (F) of 4.8396 yr-¹, M of 1.7196yr-¹, Z of 6.5496 yr-¹ and E of 0.74. As stated by Barry and Tegner (1989), as a general rule, if Z/K ratio is <1, the population is growth-dominated; if it is >1, then it is mortality-dominated; if it is equal to 1, then the population is in an equilibrium state where mortality balances growth. A growth-dominated population indicates that smaller (younger) ish were in better condition than bigger (older) ones, the younger ish should be used for species conservation. In a mortality-dominated population, if Z/K ratio = 2, then it is a lightly exploited population. Z/K ratio for P. pellucida was 2.60, thus the level of exploitation was light. In the upper portion of Jebba reservoir, Nigeria, P. pellucida recruits into ishery throughout the year with Uneke B. I., Nwani Chr. D., Okogwu O., Okoh F. an extended pulse from September to March, corresponding to the period of two lood regimes of the lake (Olaosebikan et al. 2006). P. pellucida in this study exhibited the continuous year-round bimodal recruitment. P. pellucida had high ishing mortality. Thus, recruits are released into ishery throughout the year although with two modes. It is also important to note that P. pellucida grows fast, reaching maturity early as indicated by the length of the smallest mature male and female (4.8 and 5.2 cm TL respectively). High mortality recorded in this study is also responsible for the continuous year-round recruitment pattern. This agrees with Sparre and Venema (1998) who report that when a population is being ished, it has an effect on other factors, e.g. there will be a greater rate of recruitment, a faster growth. This is because ishing creates ‘room’ for more new recruits; it removes slow-growing ish, which are replaced by smaller fast-growing ish. The smallest sampled unit of P. pellucida, 3.80 cm TL, is in line with the computed value L25 = 4.09 cm TL. The Selection Ogive procedure (which used the computed probability of capture of each size class) assumes that the chance of capturing any ish is a function of its length. P. pellucida’ computed exploitation rate E of 0.31 is less than the predicted Emax of the Selection Ogive (0.70) procedures. This indicates that P. pellucida stock is not overexploited, which agrees with the deductions earlier made from the Z/K ratio. conclusIon The present situation of the P. pellucida stocks does not call for management intervention. However, considering that open-access isheries are prone to overcapitalization (or overexploitation) in the absence of proper management, then mesh size should be increased in the event of any increase in effort. P. pellucida in the lood river system has a rapid growth rate (K =0.63 yr-¹), small maximum size (L∞ =11.03 cm TL), short life span (tmax ≈ 5 years), early sexual maturity (lm/L∞ = 0.57) and high natural mortality (M = 1.68 yr-¹). These are all r-selected traits. Thus, ecologically P. pellucida could be regarded as a r-selected species. references Abowei, J. F. N. 2009. Morphometric Parameters of Parailia pellucida (Boulenger, 1901) from the Fresh Water Reaches of Lower Nun River, Niger Delta, Nigeria. Advanced Journal of Food and Science Technology 1 (1): 43–50. Growth, mortality, recruitment and yield of Parailia pellucida Akyol, O. and Ceyhan, T. 2007. Exploitation and mortalities of blueish (Pomatomus saltatrix L.) in the sea of Marmana. Turkey. Journal of Applied Biological sciences 1: 25–27. Allen, K. R. 1971. Relation between production and biomass. Journal of the Fisheries Research Board of Canada 28: 1573–1581. Barry, J. P. and Tegner, M. J. 1989. Inferring demographic processes from size-frequency distributions: simple models indicate speciic patterns of growth and mortality. US Fishery Bulletin 88: 13–19. Beverton, R. J. H. 1963. Maturation, growth and mortality of clupeid and engraulid stocks in relation to ishing. Rapport Process-Verb Conseil International pour l’ Exploration de la Mer 154: 44–67. Beverton, R. J. H. and Holt, S. J. 1966. Manual of methods for ish stock assessment. Part II. Tables of yield function. FAO Fisheries Biology Technical Papers (38) 10: 1–67. Cunha, N. L., Catella, A. C. and Kinas, M. A. 2007. Growth parameters estimate for a small ish of the Pantanal, Brazil: Moenkhausia dichroura (Characiformes; Characidae). Brazillian Journal of Biology 67: 293–297. De Vos, L. 1995. Results of a systematic revision of African Schilbeids at the species level. In: L. De Vos (ed.) A systematic revision of the African Schilbeidae (Teleostei, Siluriformes) with an annoted bibliography. Annals of Museum of Royal Africa Central Zoology 3: 271. Ezenwaji, H. M. G. 1998. The breeding biology of Clarias albopuractus in semi-intensively managed ponds in the lood plain the River Anambra, Nigeria. Ecology of Freshwater Fish 7: 101–107. Ezenwaji, H. M. G. 2004. Studies on the atalla ishery of the lower Anambra River, Nigeria. Bio-Research 2: 82–90. Ezenwaji, H. M. G. and Ofiah, F. N. 2003. The biology of Pellonula leonensis Boulenger 1916 (Osteichthyes: Clupeidae) in Anambra River, Nigeria. Journal of Biological Research and Biotechnology 1: 33–50. Francis, A. and Sikoki, F. D. 2007. Growth coeficient of ish species within the Andoni River, Niger Delta, Nigeria and their aquaculture implications. Journal of Fisheries International 2 (1): 22–27. Gayanilo, F. C. Jr. and Pauly, D. (eds) 1997. FAO-ICLARM stock assessment tools (FiSAT). Reference manual. FAO Computerized Information Series (Fisheries) 8: 262. Gayanilo, F. C. Jr., Sparre, P. and Pauly, D. 1996. FAOICLARM Stock Assessment Tools (FiSAT) User’s Guide. FAO Computerized Information Series (Fisheries) 8: 126. Gulland, J. A. 1971. The ish resources of the ocean. Farnham, Surrey: Fishing News Books Ltd. Hasselblad, V. 1966. Estimation of parameters for a mixture 15 of normal distributions. Technometrics 8: 431–444. Mosepele, K. and Nengu, S. 2003. Growth, mortality, maturity and length-weight parameters of selected ishes of the Okavango Delta, Botswana. ACP-EU Fishery Research Representation 14: 281. Olaosebikan, B. D. and Raji, A. 1998. Field guide to Nigerian freshwater ishes. Nigeria: Federal College of Freshwater Fisheries Technology. Olaosebikan, B. D., Muschoot, T. and Umar, Y. 2006. Growth, mortality and yield of P. pellucida (Siluriformes: Schilbeidae) in the upper portion of Jebba reservoir, Nigeria. Nigerian Journal of Fisheries 2/3 (2): 343–357. Pauly, D. 1980. On the inter-relationships between natural mortality, growth performance and mean environmental temperature in 175 ish stock. Journal of conservation (Conseil International pour l’ Exploration de la Mer) 39 (3): 175–192. Pauly, D. 1983. Some simple methods for the assessment of tropical ish stocks. FAO Fisheries Technical Paper 234: 52. Pauly, D. 1986. On improving operation and use of the ELEFAN programs; Improving the estimation of L∞. Fishbyte 4: 18–20. Pauly, D. and Munro, J. L. 1984. Once more, on the composition of growth in ish and invertebrates. Fishbyte 2: 21. Pauly, D. and Soriano, M. L. 1986. Some practical extensions to Beverton and Holt’s relative yield-per-recruit model. In: J. L. Maclean, L. B. Dizon and L. V. Hosillos (eds) First Asian Fisheries Forum, pp. 149–495. Philippines: Asian Fisheries Society. Pauly, D. and Morgan G. R. (eds) 1987. Length-based methods in isheries research. ICLARM Conference Proceedings 13: 468. Pauly, D., Moreau, J. and Abad, N. 1995. Comparison of a restructured and length-structured catch curves of brown trout Salmo trutta in two french rivers. Fisheries Research 24: 103–204. Powell, D. G. 1979. Estimation of mortality and growth parameter from the length-frequency in the catch. Rapport Conseil International pour l’ Exploration de la Mer 175: 167–169. Sparre, P. and Venema, S. C. 1998. Introduction to tropical ish stock assessment, Part 1 manual. FAO Fisheries Technical Paper 306: 1–376. Taylor, C. C. 1958. Cod growth and temperature. Journal of conservation (Conseil International pour l’ Exploration de la Mer) 23: 366–370. Ursin, E. 1984. The tropical, the temperate and the artic sea as media for ish production. Dana 3: 43–60. Welcomme, R. L. 1985. River Fisheries. FAO Fisheries Technical Paper 262: 1–330. 16 Wetherall, J. A. 1986. A new method for estimating growth and mortality parameters from length-frequency data. Fishbyte 4: 12–14. Parailia Pellucida Boulenger, 1901 (osteIchthyes: schIlBeIdae) augIMo teMpaI, MIrtIngumas, prieaugis ir gausumas pietryčių Nigerijoje B. I. Uneke, Chr. D. Nwani, O. Okogwu, F. Okoh santrauka Parailia pellucida (Boulenger) augimo tempai, mirtingumas, išteklių eksploatavimas, prieaugis, gausumas/ biomasė ir mirtingumas dėl žvejybos patvindomos Uneke B. I., Nwani Chr. D., Okogwu O., Okoh F. Anambra upės baseine pietryčių Nigerijoje buvo tirti atliekant ilgio-dažnumo analizę FISAT II programa. Nustatyti šie augimo parametrai: asimptotinis ilgis (L∞) = 11,03 cm, augimo koeicientas (K) = 0,63 yr-¹. Kiti parametrai: bendras mirtingumas (Z) = 2,42 yr-¹, natūralus mirtingumas (M) = 1,68 yr-¹, mirtingumas dėl žvejybos (F) = 0,74 yr-¹, eksploatavimo koeicientas (E) = 0,31. Nustatyti du P. pellucida prieaugio pikai. Pagal Selection Ogive metodiką, skirtą nustatyti santykinį žuvų kiekį/biomasę prieaugio metu, Emax = 0,70. Žuvų išteklių eksploatavimas neviršija maksimalios normos (E < Emax). Received: 3 January 2011 Accepted: 14 March 2011