Journal of Fish Biology (1999) 54, 18–32 Article No. jfbi.1998.0840, available online at http://www.idealibrary.com on Growth and production of the dominant pelagic fish, Acanthobrama terraesanctae, in subtropical Lake Kinneret, Israel I. O*  P. W Israel Oceanographic and Limnological Research, Yigal Allon Kinneret Limnological Laboratory, POB 345, Tiberias, 14102, Israel (Received 30 January 1998, Accepted 10 August 1998) Acanthobrama terraesanctae (local name lavnun), an endemic planktivorous cyprinid, dominates total fish numbers (>80%) in Lake Kinneret, and may have a significant top–down impact on the lake ecosystem. The length of young-of-the-year fish calculated from the von Bertalanffy equation agreed with field observations of juvenile growth. An unusual bi-modal length– frequency distribution observed in May 1993 provided additional help in age identification. Males grew more slowly than females and reached a lower maximum length. Total mortality coefficients (exponents) of males and females >12 cm (minimal legal size of fish in the catch) were similar (c. 1·52). An average cohort reaches maximum biomass during its second year. Maximum production is created at the end of the second year. The production : biomass ratio of the population was 1·16, and 36% of total lavnun standing stock was taken by fishing. From the late 1980s to early 1990s, when standing stock and population structure were stable, the average harvest of 1000 t was consistent with a total lavnun biomass of 2800 t, which constitutes 50–70% of the total fish stock measured acoustically in the lake. Such a biomass could be sustained by the known production of zooplankton. Absence of verified growth data for lavnun contributed to the collapse of the fishery in 1993, because it hampered timely revision of fishery policy in response to the drastic changes in the lavnun stock in 1992. ? 1999 The Fisheries Society of the British Isles Key words: size-specific growth; production; population structure. INTRODUCTION Growth is one of the important variables in studies of life cycles, population dynamics, production, and the ecological significance of species in an ecosystem. Estimation of fish growth parameters depends on correct identification of growth structures, determination of age classes from the size–frequency distributions, and assumptions underlying the growth models employed. Temporal peculiarities of fish growth, changes in trophic relationships and spatial heterogeneity of populations makes investigation of fish growth complex. In order to assess fish ages reliably, several independent methods should be applied. Good results are achieved when a target age can be identified. Acanthobrama terraesanctae (Steinitz), known locally as lavnun, or the Kinneret sardine, is the key pelagic fish in subtropical Lake Kinneret, Israel. This endemic cyprinid dominates the pelagic fish stocks of the lake and comprises >50% of the total fish stock and >80% of total fish numbers (Walline *Author to whom correspondence should be addressed. Tel.: 972 6 6721444; fax: 972 6 6724627; email: ostrovsky@ocean.org.il 18 0022–1112/99/010018+15 $30.00/0 ? 1999 The Fisheries Society of the British Isles        19 et al., 1992, 1993). Consistent with its pelagic habitat, lavnun consume zooplankton almost exclusively in all life stages (Gophen et al., 1990). Although during the period 1976–1993, lavnun made up about half the annual fishery catch of 2000 t, because of its low market value, lavnun made up <10% of the total value (about US$4·3 million in 1993) of the fishery (Shapiro & Znovsky, 1996). Nevertheless, the lavnun population has been of increasing interest because it is thought to affect water quality through top–down or consumer-controlled effects on the ecosystem. Analysis of the effect of the lavnun stock on water quality has been hampered by the lack of reliable basic data, including that for age and growth. Published values for the age of the fish in the lavnun fishery are irreconcilable. In particular, Landau (1991) estimated the maximal age of this fish at c. 20 years based on inspection of opercular structure (the exact method was not described). This estimation of the age of the largest lavnun was four to five times higher than that found by other authors (e.g. Davidoff, 1986). Based on estimated age composition and catch, Landau assessed lavnun standing stock as of the order of 15 000–20 000 t for the 1980s. Such a biomass exceeds three to five times the total fish stock as measured acoustically (Walline et al., 1993). Thus, it is of immediate practical importance to obtain verified age estimates for lavnun, as an aid in estimating population size. The aim of this paper is to evaluate length and weight growth, using an approach combining several methods, including analysis of scales, analysis of population structure, and observations of the size of the smallest lavnun at different times of year. We make special use of an unusual event (cold winter in 1991–1992) to help us identify a year class in the population as an aid in verifying the ages obtained by other methods. Such a combined approach is necessary to avoid problems that can arise in studies of this type, and which are illustrated by the failure of previous studies to reach a consensus on the growth rate of lavnun. We also apply the results of the age analysis to estimate the age structure of the lavnun population, to evaluate the relationship between biomass, production and catch, and to assess the total stock size in the lake. MATERIALS AND METHODS Most of the fish in our analysis were obtained on a survey on the night of 12–13 May 1993, but fish from other seasons in 1996–1997 were examined to elucidate formation of wide and narrow rings on scales. Samples of fish were obtained from purse seine hauls at six representative stations around the lake (Fig. 1) chosen on the basis of several years of acoustic surveys (Walline et al., 1992). It was necessary to sample at several different sites in order to obtain a representative length–frequency (L–F) distribution, because our experience has shown that L–F distributions differ noticeably (and statistically significantly) between locations. At each station a single purse seine set was made from a commercial fishing boat. The net used was a commercial purse seine (20-mm stretch with 28-mm stretch bunt), but with an added 10-mm stretch liner outside the bunt to retain fish smaller than commercial size. Fish samples were frozen after the cruise for later analysis. In the laboratory the total length of all the fish from each sample was measured to the nearest 0·25 cm. The weight of each fish in a random subsample was recorded. The sex of fish was determined by direct examination of gonads, as Yaron’s (1968) method based on the relative length of pelvic fins did not give reliable results. In this study we used the scale structure, a helpful tool in age analysis (Chugunova, 1963; Bagenal & Tesch, 1978; Jearld, 1985). Closely spaced circuli on lavnun scales were 20 .   .  Jordan River 1 km 2 1 3 6 4 5 N F. 1. Locations in Lake Kinneret, Israel where purse seine samples were taken in May 1993. 4 3 2 1 2 1 F. 2. Scales illustrating the pattern of circuli with location of annuli indicated. The scale on the left is from a 19-cm female, and the scale on the right is from an 11-cm male. Numbers indicate the age of formation of closely spaced circuli (see text). distinguished easily from zones of wide circuli (Fig. 2), as has been noted by Davidoff (1986). For more details about scale analysis see Results. The von Bertalanffy growth equations were computed by Walford’s (1946) method for males and females. The lengths of fish in two consecutive years, Lt and Lt+1, were estimated as the medians of successive peaks on length–frequency histograms and as the average lengths of fish with the appropriate number of dark bands on their scales. The transformation of the length growth equation to weight growth was made using a power length–weight relationship. Coefficients calculated from Walford plots and for length– weight relationships are reported with associated standard errors (..). The growth rate        21 (dW/dt) of fish of specific size was calculated using the differential form of the von Bertalanffy equation as follows (Ostrovsky et al., 1993): dW/dt=W b k (L£ "L) L "1, (1) where L and W are the length and weight of the fish, b is exponent in the weight–length relationship, and k and L£ are parameters of von Bertalanffy’s equation (the growth constant and asymptotic length of fish, respectively). The weight growth data were used for assessment of the age-specific biomass (B), production (P), eliminated biomass (E), and catch (C) of an average cohort as follows (Winberg, 1971; Ostrovsky, 1984): Bi =NiWi, (2) Pi =Ni(dW/dt)i, (3) Ei =(dN/dt)iWi =NiWiZ, (4) Ci =NiWi(Z"M), (5) where Ni is number of fish in the ith age group, (dW/dt)i is age-specific growth rate [equation (1)], Wi is the mean weight of fish in the ith age group, Z is total specific mortality rate, (dN/dt)i =ZNi is absolute mortality rate, and M is natural specific mortality rate. Z was evaluated as a slope of catch curve for commercial size fish (>12 cm). M was calculated from Pauly’s (1980, 1983) formula. For fish less than commercial size (<12 cm), Z was taken equal to M. The catch (C) refers only to commercial size fish. Changes in the average cohort parameters with fish age were used to evaluate the relationship between P, C, and B for a hypothetical steady state lavnun population (see Discussion). RESULTS SIZE–FREQUENCY DISTRIBUTION OF FISH The smallest fish (3 cm) found in the May 1993 sample was much smaller than those from the first (mostly juvenile) abundant size group, which were dominant in the samples (Fig. 3). Fingerlings collected with a cast net in May 1979, had average lengths of 2·3–3·2 cm (Gophen & Scharf, 1981). A similar average length (3·1 cm) was observed on 20 May 1984 as well (Landau et al., 1988). Between April and June 1980 lavnun were from 2 to 3·5 cm in size (Davidoff, 1986). Thus, the 3-cm fish found in our samples was close to the typical fingerling size for this time of year (0+ age class), i.e. it was born in winter 1992–1993, as spawning takes place between December and March (Steinitz, 1959). In our samples from May 1993, the size of fish in the smallest clear-cut size group was much greater than the fingerling size and ranged from about 5 to 10 cm (Fig. 3). In April 1988 in a catch made using an identical net with the small mesh bunt (10 mm stretch), the standard length of the first age group varied between 6 and 11 cm (Walline et al., 1992). In winter 1980–1981, the modal size of the first size group was larger [10·5 cm, Davidoff (1986)], almost certainly because the smaller fish were not caught, as the sampling was done using a commercial net (the minimum legal commercial size of lavnun was 12 cm). 22 .   .  8 (a) 6 4 2 0 2 6 10 14 18 (b) 6 Abundance (%) 22 4 2 0 2 6 10 14 18 22 (c) 6 4 2 0 2 6 10 14 Length (cm) 18 22 F. 3. Length–frequency distribution for juveniles, males, and females taken in purse seine samples collected in May 1993. (a) Juveniles (n=3222); (b) males (n=770); (c) females (n=1102). The smallest dominant size group was isolated clearly from the larger size group by a distinct minimum in the L–F plot (Fig. 3). The position of the minimum was about the same as that observed on the L–F histograms in spring in previous years (Walline et al., 1992). The fixed position of the maxima and minima on the L–F histogram in different years indicates that this size group consists of a specific age class. An unusual bimodality was observed in the May 1993 L–F distribution in this smallest size group/year class, a pattern which can be seen clearly on the histogram for all the catches combined (Fig. 3). This bimodal pattern was never observed before [see L–F distributions in Walline et al. (1992), for example]. The difference in modal sizes of these two peaks was much less than the difference in size between the bimodal size group and the next larger size group/peak. This suggests that the fish in the bimodal group constituted a single age class rather 23        T I. The correspondence between the number of dark rings observed on the scales, estimated age (years) and size (cm) for male and female lavnun collected in May 1993 Dark rings No rings 1 2 3 4 6 Age 1+ 2+ 3+ 4+ 5+ 6+ or 7+ Male size range L–F 5·0–10·0* 11·0–13·0 13·0–15·75 15·5–17·0 — — 3328 427 209 — — — Scales Female size range L–F Scales 23 31 25 16 — — 5·0–10·0* 11·75–14·0 15·0–18·5 18·0–20·25 20·0–21·5 22·5 3328 394 332 — — — 23 16 28 37 10 1 N N N, the number of fish from the L–F histogram or for which scales were examined. *Most of the fish were juveniles, so no sex could be determined. than two different age classes. The L–F distributions of the 5–10 cm group taken from individual hauls were bimodal in the middle part of the lake, while in the south and north of the lake they were unimodal. In the southern part of the lake, the mean size (&..) of this group (8·23&0·69 cm) was larger than the mean size in the northern part of the lake (6·53&0·67 cm). At least two or three peaks on the left-hand of the L–F distributions and minima between them were observed consistently in our study (Fig. 3) and in other years (Davidoff, 1986; Walline et al., 1992). In the same season, the position of these extremes is always about the same, provided that selectivity of the net used permits their observation. Thus, the occurrence of these peaks should be related to age classes, but not attributed to differing year class success, as suggested by Landau (1991). This is confirmed by the observation that no peaks on L–F histograms were observed when several samples collected in different seasons were mixed together as in Steinitz (1959) and Landau (1991). CORRESPONDENCE OF SCALE BANDS AND SIZE GROUPS We found wide circuli only on scales of fish >9·5–10·5 cm. These wide bands were detected close to the scale edge during the spring–summer months. Davidoff (1986) also noted formation of a wide ring structure in late spring, when water temperature is rising. Wide bands form characteristically during periods of fast fish growth (Jearld, 1985). The season during which lavnun form wide bands coincides with higher abundance of cladocera (the preferred prey of lavnun) during the first half of the year (Gophen & Landau, 1977). The formation of wide bands in spring is also consistent with data showing that food abundance is an important factor affecting lavnun growth (Gophen et al., 1990). Our observations showed that for fish >11–12 cm, narrow circuli were detected near the scale edge in the autumn–winter. During this period, the most intensive formation of lavnun gonads occurs: from October till February gonads increase in weight from 0·6% of body weight to 9% (Sivan, 1967). Expenditure of a significant part of assimilated energy for gonad growth suggests that somatic growth of fish would be expected to decrease, provided that food consumption 24 .   .  20 25 (a) (b) 20 Lt + 1 (cm) 15 15 10 10 5 0 5 5 10 15 20 0 5 10 15 20 Lt (cm) F. 4. Walford plots for male (a) and female (b) lavnun (see text). Each point is plotted with associated standard error. does not increase. Such a change in growth pattern could account for the formation of narrow rings on the scales by mature fish. Since nearly all lavnun were fully mature by the time they reach a size of 11–13 cm, it is likely that fish this size or larger would have clear annuli. On scales of juveniles (<10 cm length) collected from autumn to spring, no narrow circuli band was observed, consistent with our observation that formation of narrow annuli is coupled to gametogenesis apparently and can be detected clearly only for mature fish. In May 1993 purse seine samples, fish forming the smallest size group (5–10 cm) on the L–F histograms had scales without a clearly detectable dark band of closely spaced circuli. Fish from larger size classes (11–17 cm for males and 12–22·5 cm for females) always had scales with closely spaced circuli positioned close to the scale edge (Fig. 2). Both males and females with the same number of dark bands varied by size slightly, and at the same time their average size was significantly different from that of fish with a different number of dark bands (Table I). Males were smaller than females with the same numbers of dark bands. The ring patterns detected on scales from males and females were consistent with major peaks on the L–F histograms, indicating that fish with different number of circuli (different size classes) correspond to various age classes. GROWTH EQUATIONS Growth equations were derived by plotting the mean lengths of fish in two consecutive age classes (Fig. 4) detected by number of circuli and/or by position of peaks on L–F histograms. We used the medians of successive peaks on L–F histograms (a few hundred fish in each age class) where they were clearly observed. Where the peaks were not clearly detected (for fish older than 3+), we used the average length of fish with the appropriate number of dark bands on their scales. Length growth of lavnun is described by the following equations: male: (r2 =0·9955) Lt+1 =(6·72&0·51)+(0·662&0·043) Lt, (6) female: (r2 =0·9995) Lt+1 =(7·03&0·16)+(0·716&0·011) Lt. (7)        25 Both regressions calculated using the average fish length were significant (P<0·001). The difference in the coefficients in the equations describing Walford’s plots for males and females were statistically significant (P<0·001). The related integral form of the von Bertalanffy equations are: male: Lt =19·89(1"e "0·412t), (8) female: Lt =24·78(1"e "0·334t), (9) where Lt is the fish length (cm) at age t (year). To simplify the growth expressions, we used fish age counted from the moment of time when L=0, as in equations (8) and (9). The age of fish, taken from the moment of hatching, is (t+to), where to (=0·08 year=28 days) is a constant calculated from equations (8) and (9) as the time required for fish development from L=0 to L=0·65 cm, the minimum length of fingerlings found in the plankton. To assess the weight growth curve, the weight–length relationship was calculated as follows (n=57, r2 =0·992): logW=(3·430&0·042)logL"(2·551&0·050), (10) W=0·00281 L3·430. (11) or The exponent (b=3·43) is significantly (P<0·001, t-test) higher than 3, that is lavnun growth is positively allometric. This equation is slightly different than that of Landau (1991), W=0·00504 L3·24, implying that in May 1993, small fish (6–12 cm) were slightly lighter (10–20%) than those measured by Landau, while the weight of large fish (21–22 cm) was about the same. The equations of weight growth were obtained by substituting (8) or (9) into equation (11): male: Wt =80·2(1"e "0·412t)3·43, (12) female: Wt =168(1"e "0·334t)3·43. (13) Difference in growth rates of males and females is responsible for the shift in the position of their size classes on the L–F histograms, and is partially responsible for the observed changes in the sex ratio with size (Fig. 5). That males are dominant in smaller size classes, while only females were present in the largest size classes, was noted by Steinitz (1959). Differing growth rates for male and female lavnun and change in the length-specific sex ratio with growth can result in errors when a Walford plot is constructed for both sexes combined. Slower growing males, which dominate in smaller size classes, ensure low values for length increment of small fish, while fast-growing females, which dominate in large classes, ensure a high length increment for large fish. Thus, the slope of Walford’s plot will be steeper than for males or females separately. The slope change will lead to overestimation of L£ and affect estimates of the size-specific growth rate of fish. 26 .   .  % Mature females 100 80 60 40 20 0 2 6 10 14 Length (cm) 18 22 F. 5. Per cent of mature females in the population as a function of length. DISCUSSION Observation of fingerling growth made in 1979 by Gophen & Scharf (1981) showed that the average total length of lavnun fingerlings increased from 1·30 to 4·06 cm between 18 March and 10 August, i.e. about 0·58 cm month"1. A similar growth rate (0·53 cm month"1) was obtained from the samples taken with cast net between 26 March and 20 May 1984 (Landau et al., 1988). The latter was very close to the growth rate (0·50 cm month"1) estimated by otolith increment analysis (Landau et al., 1988). Thus, if young-of-the-year (YOY) grow at similar rates throughout the year, they should reach 6·7–6·9 cm length by the end of December and 9·0–9·3 cm length in mid-May of their second year. Because the length increment decreases generally with fish size and growth also decreases in the autumn–winter season as available food declines, one can expect that these assessments are slight overestimates. This estimate of one-year-old fish size (c. 7 cm) at the end of December (December–January is the midpoint of the spawning season; Steinitz, 1959; Gafny et al., 1992) is close to lavnun age estimates made by Lissner from scale analysis (5–8 cm, Steinitz, 1959). These assessments coincide with the average lengths of 1-year-old fish (1+to) calculated by equations (7) and (8) (7·1 and 7·5, respectively), suggesting that the growth equations obtained by examination of L–F histograms and scales of fish older than 1+ also describe correctly the growth rate of YOY. According to our analyses, the age of the fish in the 5–10-cm group in the May 1993 samples was 1+, i.e. they should have been born during the winter of 1991–1992. The variation in lengths within this cohort is consistent with the duration of the spawning season and a growth rate of 0·5–0·6 cm month"1. In the winter of 1991–1992, water temperature dropped a few degrees Celsius below the normal winter temperature in Lake Kinneret (14–16) C) following an enormous discharge of cold Jordan River water. In the middle of the spawning season, the surface water temperature in the northern part of the lake, where the Jordan River enters, was lower by 2–3) C relative to that in the central and southern parts of the lake. The observed lower mean size of the 1+ fish in the north relative to those in the southern part of the lake suggests that reduced water temperature could affect fish hatching and/or depress fingerling growth        27 Length (cm) 20 15 10 5 0 1 2 3 4 Age (years) 5 6 7 F. 6. Length at age for male (– – –) and female (——) lavnun according to this study and compared to curves obtained in other studies. +, Steinitz (1959); 0, Yashouv & Berner (1960); ,, Davidoff (1986). rate. The bimodal distribution of the 1+ fish caught in the middle of the lake could be the result of mixture of northern and southern sub-schools. An alternative explanation is that the bimodal distribution at central stations was the result of the formation of a sub-school under the unusual temperature regime. The effect of extremely low temperature on fish hatching can be demonstrated using data of Gafny et al. (1992) on lavnun egg development at different temperatures (T, ) C). Using their measurements of egg development time (D, days) at two temperatures typical for the spawning season (16 and 20–21) C), we calculated the relationship between egg development rate (1/D day "1) and T following Ostrovsky (1995): 1/D=0·0518 (T"14·1), (14) where (T"14·1) is the effective temperature for egg development, and To =14·1) C is a constant. To is customarily close to the lower limit of the thermo-tolerant zone of development. Temperatures below this disturb the normal physiology of organisms and eggs and result in increased mortality (Winberg, 1987). In the case of lavnun, this constant was close to the observed threshold for egg development [c. 13) C, Gafny et al. (1992)]. In January– February 1992, water temperature on the spawning grounds dropped to as low as 10–12) C. Such an extreme reduction in temperature could have caused reduced hatching during this period, and certainly would have caused slower development rates. Since record low temperatures occurred in the middle of the spawning season, the two modal groups in the 1991–1992 year class observed in catches from the middle part of the lake could also have formed as a result of two maxima in fish hatching (one prior to and one after the period of extremely low temperature). In either case, the unique L–F distribution of the 5–10-cm fish group in the May 1993 samples suggest that these fish hatched in the unusually cold winter of 1991–1992. The age estimations made by Davidoff (1986) were close to our results (Fig. 6). However, complications in determination of the first age class (see above) should 28 .   .  Number of fish 10 000 1000 100 10 1 0 1 2 3 4 5 Age group (years) 6 7 F. 7. Number of fish in each age class in the catch plotted against age for male and female lavnun (see text). #, Males; 0, females; ,, juveniles. have caused underestimation of subsequent age classes. Missing the first age class was apparently compensated for in age estimates of older fish because some annual rings were assumed to be cutting-over rings (Davidoff, 1986). Data of Yashouv & Berner (1960), who investigated the growth of unusually large lavnun (definitely females), are fitted well by our female growth curve (Fig. 6). Lissner’s scale readings [reported by Steinitz (1959)] suggest that fish of smaller sizes were about a year older than found by Davidoff (1986). Landau (1991), examining opercula with a polarizing filter for determination of lavnun age and without using any means to verify ages, found very low growth rates, such that 8–10-cm fish were about 3–4 years old and 15–16-cm fish were more than 9–10 years old. Fish can reach such sizes in an aquarium (probably under favourable food and temperature conditions) in 1 and 2 years, respectively [Fishelson, cited by Davidoff (1986)]. This suggests that the lavnun growth rate reported by Landau (1991) was incorrect. Using the growth equations (8) and (9), we calculated the relative number of males and females at different ages from the L–F data of May 1993. Plots of the numbers of males and females versus age show that fish >3 years decreased exponentially with age (Fig. 7). We suggest that the observed proportion between age classes corresponds to changes in an average cohort abundance, because the L–F lavnun distributions and total lavnun catch in the late 1980s and early 1990s were rather similar (see above). This allows an estimate of specific mortality rate for large fish (>3 years) in an average cohort. Z was about constant and similar for males (1·49&0·28) and females (1·55&0·06), resulting in an average of 1·52. Expressed on an annual basis, relative mortality for these males and females was about 100(1"e "1·52)=78% per year. Calculation of the natural mortality for lavnun, using Pauly’s (1980) formula with a 20% reduction because lavnun school (Pauly, 1983), resulted in an M=0·70. From these values for M and Z, the exploitation rate, E=100(Z"M)(Z) "1, was calculated for the older part of the lavnun population as c. 54% during the end of 1980s and beginning of the 1990s, when these fish (>3 year old) were born. Analysis of the composition of lavnun commercial catches indicated that at the end of the 1980s,        29 –1 E, P (kg year ), B (kg) 5 4 3 2 1 0 1 2 3 Age (year) 4 5 F. 8. Dynamics of an average cohort. The calculations of P, E, B were made using equations (2)–(4) for a hypothetical cohort (as sum of males and females), which decreases in number exponentially (Z=M=0·7 for the first two years, Z=1·52 for older fish). The initial number of fish was taken as 1000. 0, E; /, P; -, B. fish <12 cm were absent in the purse seine catches, while fish >14 cm were taken with the highest efficiency (Hambright & Shapiro, 1997). This information together with the age structure data suggests that exploitation of the lavnun population began with the 2–2+ year class. The application of the coefficients of total and natural mortality and the growth equations allowed us to calculate age-related changes in an average cohort (Fig. 8). Maximum production of an average cohort is generated during its second year, prior to full maturation. During the third year maximal fish biomass is eliminated as the result of fishing effort and natural mortality. The cohort reaches maximum biomass at the beginning of its third year. This description of changes with age for a single cohort would apply also to a steady state population of multiple age classes, i.e. when recruitment and mortality are unchanging from year to year. For such a population production, catch and biomass can be estimated as the sum of those parameters over the existing year classes. Thus, total P=ÓPj, total C=ÓCj, and average biomass Bavg =ÓBjavg, where Bjavg is annual average biomass of the j-th year class (=average cohort biomass for year j of its life). These simple calculations show that for a steady state population annual production exceeds the average biomass by 1·16 times (P/B ratio). The ratio between catch and the total lavnun standing stock (C/B ratio) was 0·36, indicating that about one third of the available standing stock was fished to sustain the observed population structure steady state. At the end of the 1980s, the average harvest was about 1000 t year"1 (Ben-Tuvia et al., 1992). Assuming that no drastic changes occurred in the lavnun population structure, which seems to have been the case, the average biomass of lavnun in Lake Kinneret can be estimated to be about 1000/0·36= 2800 t. Walline et al. (1992) estimated the total pelagic fish stock in Lake Kinneret, based mainly on acoustic surveys, to be around 4000–6000 t, consistent with suggestions that lavnun dominate the pelagic fish community of Lake Kinneret. Thus, the lavnun stock size estimated primarily using information 30 .   .  about fish growth rate, population structure and multi-annual harvest, is close to independent acoustic assessments of the fish population. Another independent estimate of the maximum possible standing stock of lavnun can be made using information on production of zooplankton in the lake and basic allometric bioenergetic relationships for fish. The minimal amount of zooplankton required to sustain a unit of fish biomass could be calculated using Winberg’s (1956) equation for standard metabolic rate with correction for active metabolism (#1·7). Fish with weights of 6–30 g (dominant weights of fish in the population) expend about 18 times their body weight per year on active metabolism at an average lake temperature of 23) C. Thus, fish require an amount of food equivalent to 23 times their biomass (food utilization coefficient was taken as 0·8). Because the caloric equivalent of lavnun wet weight is three times higher than that of Kinneret zooplankton (Ostrovsky, unpublished), a unit of fish biomass requires about 70 units of wet weight of zooplankton per year to satisfy their metabolic expenses. Thus, the total annual production of about 200 000 t of zooplankton (Gophen, personal communication) can maintain about 2900 t of planktivorous fish. This approximate measure is close to our assessment of lavnun stock in the lake. In contrast, Landau’s evaluation of the lavnun stock size (15 000–20 000 t), obtained from a much lower growth rate estimate and supposed long life span (maximum age was assessed to be 20 years), is not consistent with data available on zooplankton production in the lake. High fishing pressure on the lavnun population and apparent dependence of lavnun recruitment and stock on ambient conditions [e.g. water level fluctuation, Gafny et al. (1992)] emphasize the importance of proper fishery management in Lake Kinneret. Specifics of lavnun growth, mortality, and secondary production must not be ignored when fishery policy is elaborated, as is illustrated by recent events in the Lake Kinneret lavnun fishery. An unusually successful recruitment of lavnun during the flood winter 1991–1992 led to a sharp two- to three-fold increase in the abundance of sub-commercial-sized fish. This increase in fish numbers was detected acoustically as early as summer 1992 (Walline & Kalikhman, unpublished). As noted above, a cohort reaches its maximum production rate during the second year of its development. High fish production is attended normally by augmented food consumption. Therefore, it was to be expected that the large lavnun year class would upset the existing balance between fish and their food (zooplankton) in 1993, the second year of this large year-class’s development. Significant deterioration in lavnun body condition factor was found at the end of 1993 (Ostrovsky & Walline, unpublished). Adults, which spend much of their energy on gonad production, were affected most strongly by the lack of food, and disappeared by the end of 1993. Their disappearance was followed by the collapse of the fishery (Hambright & Shapiro, 1997). Thus, the sharp rise in fish numbers detected acoustically was followed by unfavourable changes in the fish stock and the Kinneret ecosystem one year later. Immediate response by fishery managers (e.g. enhanced fishing pressure on sub-commercial-sized fish) could have prevented or reduced some of the undesirable changes, if the data (specifically the growth data reported here) necessary for adjusting fishery policy and suitable monitoring of biological and fishery parameters had been available.        31 We thank S. Pisanty and J. Shapiro for their contribution of fish samples from purse seine catches; I. Kalikhman for productive discussions; and two anonymous reviewers for helpful comments. This study was supported by grants from the Israeli Ministry of Science No. 3730292, the Rich Foundation, and the US–Israel Binational Science Foundation. References Bagenal, T. B. & Tesch, F. W. (1978). Age and growth. In Methods for Assessment of Fish Production in Freshwater, 3rd edn (Bagenal, T. B., ed.), pp. 101–136. Oxford: Blackwell. Ben-Tuvia, A., Davidoff, E. B., Shapiro, J. & Shefler, D. (1992). Biology and management of Lake Kinneret fisheries. Israeli Journal of Aquaculture—Bamidgeh 44, 48–65. Chugunova, N. I. (1963). Age and growth studies in fish. Office of Technical Services, Washington, D.C., 132 (translated from the Russian) (1959). Handbook for the Study of Age and Growth of Fishes, 164 pp. Moscow: Academia Nauk. Davidoff, E. B. (1986). Verification of the scale method for aging the cyprinid, Mirogrex terraesanctae terraesanctae (Steinitz, 1952) in Lake Kinneret (Israel). Israeli Journal of Aquaculture—Bamidgeh 38, 108–125. Gafny, S., Gasith, A. & Goren, M. (1992). Effect of water level fluctuation on shore spawning of Mirogrex terraesanctae (Steinitz), (Cyprinidae) in Lake Kinneret, Israel. Journal of Fish Biology 41, 863–971. Gophen, M. & Landau, R. (1977). Trophic interactions between zooplankton and sardine Mirogrex terraesanctae populations in Lake Kinneret, Israel. Oikos 29, 166–174. Gophen, M. & Scharf, A. (1981). Food and feeding habits of Microgrex fingerlings in Lake Kinneret (Israel). Hydrobiologia 78, 3–9. Gophen, M., Serruya, S. & Threlkeld, S. T. (1990). Long term patterns in nutrients, phytoplankton and zooplankton of Lake Kinneret and future predictions for ecosystem structure. Archiv für Hydrobiologie 118, 449–460. Hambright, K. D. & Shapiro, J. (1997). The 1993 collapse of the Lake Kinneret bleak fishery. Fisheries Management and Ecology 4, 275–283. Jearld, A. (1985). Age determination. In Fisheries Techniques (Nielsen, L. A. & Johnson, D. L., eds), pp. 301–324. Bethesda: American Fisheries Society. Landau, R. (1991). Mirogrex terraesanctae (Cyprinidae) of Lake Kinneret: biomass changes in relation to inflow; growth rate in relation to fish/zooplankton interaction. Hydrobiologia 218, 1–14. Landau, R., Gophen, M. & Walline, P. (1988). Larval Mirogrex terraesanctae (Cyprinidae) of Lake Kinneret (Israel): growth rate, plankton selectivities, consumption rates and interaction with rotifers. Hydrobiologia 169, 91–106. Ostrovsky, I. (1984). Analysis of production in cohort of organisms with parabolic type of growth. Journal of General Biology 45, 246–254 (in Russian). Ostrovsky, I. (1995). The parabolic pattern of animal growth: determination of equation parameters and their temperature dependencies. Freshwater Biology 33, 357–371. Ostrovsky, I., Gophen, M. & Kalikhman, I. (1993). Distribution, growth, production, and ecological significance of the clam Unio terminalis in Lake Kinneret, Israel. Hydrobiologia 271, 49–63. Pauly, D. (1980). On the interrelationship between natural mortality, growth parameters and mean environmental temperature in 175 fish stocks. Journal du Conseil International pour l’Exploration de la Mer 39, 175–192. Pauly, D. (1983). Some simple methods for the assessment of tropical fish stocks. FAO Fisheries Technical Paper 234, 52 p. Shapiro, J. & Znovsky, G. (eds) (1996). The Fisheries and Aquaculture of Israel, 1994, in Figures. Jerusalem: Israel Ministry of Agriculture, Dept. of Fisheries. 53 p. 32 .   .  Sivan, P. (1967). Seasonal changes in the gonads of Acanthobrama terraesanctae H. Steinitz from Lake Tiberias. Sea Fisheries Research Station Haifa, Bulletin 44, 22–41. Steinitz, H. (1959). Dr Lissner’s study of biology of Acanthobrama terraesanctae in Lake Tiberias. Bulletin of the Research Council of Israel 8B, 43–64. Walford, L. A. (1946). A new graphic method of describing the growth of animals. Biological Bulletin of the Woods Hole Marine Biological Laboratory 90, 141–147. Walline, P., Pisanty, S. & Lindem, T. (1992). Acoustic assessment of number of pelagic fish in Lake Kinneret. Hydrobiologia 231, 153–163. Walline, P. D., Pisanty, S., Gophen, M. & Berman, T. (1993). The ecosystem of Lake Kinneret, Israel. In Trophic Models of Aquatic Ecosystems (Christensen, V. & Pauly, D., eds), pp. 103–109. ICLARM Conference Proceedings 26. Winberg, G. G. (1956). Rate of Metabolism and Food Requirements of Fish. Minsk: Beloruss State Unversity. [Fishery Research Board of Canada Translation, Ser. No. 194 (1960)]. Winberg, G. G. (1971). Methods for Estimation of Production of Aquatic Animals. New York: Academic Press. Winberg, G. G. (1987). Dependence of development rate on temperature. In Production– Hydrobiological Research of Water Ecosystem (Alimov, A. F., ed.), pp. 5–34. Leningrad: Nauka (in Russian). Yashouv, A. & Berner, E. (1960). The growth rate of several unusually large specimens of Acanthobrama terraesanctae (Steinitz) in Lake Tiberias. The Fisherman’s Bulletin 3, 20–22 (in Hebrew). Yaron, Z. (1968). The Endocrine System and the Gonadal Cycle of Acanthobrama terraesanctae (Cyprinidae, Teleosti). Ph.D. thesis, The Hebrew University of Jerusalem (in Hebrew with English summary).