Bertalanffy Growth Research Articles

청평 내수면에 서식하는 엷은재첩, Corbicula (Corbiculina) papyracea Heude의 성장모수 추정

This study was to estimate population growth parameters of the freshwater bivalve, Corbicula (Corbiculina) papyacca (Heude) in Korea. Samples were collected from Jojong stream in Chungpyeong from September 1999 to August 2000. Ages were determined from the ring of shell, The shell length of the samples ranged from 4,2 mm to 28.1 mm, The ring on the surface of shell was formed once a year from January to March, Marginal increment analysis of shell rings indicated that annuli were formed in June. Spawning period was estimated to be May to August with a peak between June and July through fatness analysis, and thus rings were considered to be true annual marks. Von Bertalanffy's growth parameter were estimated from a nonlinear method with the value of logical maximum shell length (<TEX>$L_{propto}$</TEX>) was 34,36 mm, K was 0.1531/year, logical age of shell length 0 (<TEX>$t_{0}$</TEX>) was -0,5246 year, and logical maximum total weight (<TEX>$W_{propto}$</TEX>) was 11.42 g.

Sensitivity of the BEAM4 fisheries bioeconomic model to the main biological input parameters

Several runs of the BEAM4 model were carried out, combining several sets of input parameters from von Bertalanffy's growth curve ( Lt= L ∞[1− e - k( t- to) ]) and the natural mortality ( M), with sets of parameters from the length–weight relationship ( W= aL b ). Further simulations were made with variations of ±20% in the input parameters: recruitment ( R), catchability coefficient ( q), and the lengths at which 50 and 75% of the fishes are retained by the net ( L 50% and L 75%,). The data used were those of the pair trawl fisheries for “corvina” Micropogonias furnieri, off southeastern Brazil. Results showed variations in the output (landed weight) ranging from −62 to 147% associated with the diverse sets of VBGF and LWR parameters, and lower variations associated with the other input parameters tested.

Do Bertalanffy's growth curves result from optimal resource allocation?

Bertalanffy's equation is commonly used to model indeterminate growth. Bertalanffy claimed that this growth pattern results from growth potential decreasing with age. An alternative approach provided by life history theory predicts that indeterminate growth is optimal for organisms in a seasonal environment and results not from decreasing growth potential but from allocating increasingly less energy with age into growth, and more into reproduction. Bertalanffy's curves are the result of evolutionary optimization and should not be used in optimization models as an assumption, but they can be used as a tool to describe the indeterminate growth pattern phenomenologically.

Population dynamics of Corbicula fluminea (Bivalvia) in the Paraná River Delta (Argentina)

Benthic individuals and drifting planktonic juveniles of Corbicula fluminea were sampled in the Lower Delta of the Parana River (Argentina) at monthly intervals between October 1995 and October 1996. Densities of settled clams above 1 mm, around 300–1000 ind. m-2, varied little throughout the year. Below 1 mm benthic juveniles, on the other hand, showed a single conspicuous abundance peak in October-November (up to 1722 ind. m-2), and were practically absent during the rest of the year (overall annual mean: 1070 ± 797 ind. m-2). Drifting juveniles showed one major peak in December 1995 (160 ind. m-3), and a minor one at the end of March (24 ind. m-3). Length-frequency analyses of the monthly field data clearly indicate a highly structured population with a single well defined reproduction period centered on October–November. Population parameters derived from the seasonally oscillating version of von Bertalanffy's growth formula were as follows: maximum shell length: 32 mm (maximum observed shell length: 33 mm); growth constant: 0.65; growth seasonality (i.e., span of summer-to-winter growth-rate difference): 0.7; winter point (i.e., time of the year when growth is minimum): 0.5 (June–July); estimated size range for one year-old individuals: 15.3–22.4 mm; for two years: 23.5–27 mm, and three years: 27.5–29.3 mm. Comparison with previous data confirm the influence of water temperature on the clam's reproduction and growth and furnish additional evidence suggesting that food availability may be as important for recruitment as thermic regimes. Contrasts between traits of the population analyzed herein with those described previously from a nearby (ca. 10 km) site more influenced by industrial pollution point at the influence of water quality on Corbicula's recruitment and growth.

The state of the walleye pollock in the northern part of the Okhotsk Sea, North Pacific

Aspects of pollock biology, including growth and mortality rates are presented, based on 4 years (1991–1994) sampling of Polish commercial catches in the international waters of the Okhotsk Sea. To estimate stock dynamics, production models were fitted using Russian CPUE data, 1985–1993. The length of fish in the catches ranged from 23 to 65 cm, with a dominant mode of 35–45 cm. Fish aged 2–22 years were recorded, with fish 4–8 years old dominating the catch. The mean age and length of the exploited fish were stable in the period analyzed. The von Bertalanffy's growth curves fitted to males and females separately showed a significantly higher asymptotic length for females. Specimens with gonads at the spawning stage were found in the catches, suggesting that the spawning ground is nearby. Biomass estimates for the most recent years were about 10 million tons, and mean fishing mortality was 0.19. The natural mortality value obtained by the Pauly (1980) formula was 0.2. The optimum catch levels, resulting from production models, slightly exceed 2 million tons, and the optimum fishing mortalities are in the range 0.27–0.30. This is consistent with the F − 0.1 value from the yield per recruit analysis.

Von Bertalanffy's Growth Equation Should Not Be Used to Model Age and Size at Maturity

Von Bertalanffy's Growth Equation Should Not Be Used to Model Age and Size at Maturity

Population Size and Growth in the Turtle Graptemys oculifera

Population sizes of Graptemys oculifera were estimated using two mark-recapture proce- dures at five sites on the Pearl River in Mississippi. These were compared with density estimates from basking counts at the same sites to determine if the latter could be used as indices of population size. Density estimates from the mark-recapture studies ranged from 85 to 341 G. oculifera per river km. Jolly- Seber and Schnabel population estimates were similar at three sites, but low numbers of recaptures resulted in inflated Jolly-Seber estimates at the two remaining sites. The Schnabel mark-recapture model appeared to be better suited for estimating population sizes of G. oculifera. Basking surveys provided a rough index to population sizes, but comparisons between sites were potentially complicated by differential wariness of basking turtles. Growth curves were constructed for each sex by fitting data from recaptured turtles to the von Bertalanffy and logistic growth models. The former model provided a better fit to the data than did the latter. Juveniles of both sexes grew at approximately the same rate. Males matured at 3.5 yr of age and females between 10 and 16 yr. Sex ratios were biased toward males at all sites. The ringed map turtle (Graptemys oculifera) is endemic to the Pearl River of Mississippi and Louisiana where it is restricted primarily to the main channel of the river and to the lower

Sexual maturation, age and growth of striped sea bream, Lithognathus mormyrus L., on the eastern coast of the Adriatic sea

Striped sea bream, Lithognathus mormyrus L., are hermaphoroditic protandrous fish. Sex ratios are given for length and age classes, indicating the males change sex mainly at lengths between 25.0 and 32.5 cm, in age classes 4 to 7, with more than 30% of the population changing sex in age class 6 to 7. Males were also observed up to a length of 34.5 cm. Length-weight relationship showed no significant difference from isometric growth in winter (b = 3.05) and a negative allometric growth in summer (b = 2.69). The age composition was established using the Bhattacharya method and additional observations of annual rings on scales. Six age classes were obtained from Kaštela Bay (age 3: 21.7 cm, age 4: 26.5 cm, age 5: 28.4 cm, age 6: 30.3 cm, age 7: 31.6 cm, age 8: 33.4 cm) and from Mirna Bay (age 2.5: 19.4 cm, age 3.5: 24.1 cm, age 4.5: 26.9, age 5.5: 29.4 cm, age 6.5: 31.3 cm, age 7.5: 32.8 cm). Von Bertalanffy's growth equation was fitted to these mean length-at-age data resulting in parameter values of L∞= 36.2 cm, K = 0.297, t0=−0.08 for Kašela Bay and L∞= 37.3 cm, K = 0.262, t0=−0.39 for Mirna Bay.

Growth and survival response of Penaeus stylirostris (Stimpson) to fertilization, pelleted feed and stocking density in earthen ponds

Abstract. Growth and survival response of Penaeus stylirostris (Stimpson) to fertilization, pelleted feeding and stocking density were analysed for the conditions prevailing on the Baja California peninsula (Mexico). Three 0·25-ha earthen ponds were longitudinally divided in half with mesh structures. One half received inorganic fertilization (trial F) and the other supplementary feeding using a pelletized ration (trial PF). The initial stocking rates were approximately 5, 10 and 15 PL5/m2 in both trials. After 210 days, final mean weights ranged from 15·0 to 5·3g and survival from 48·6 to 17·8%. Growth and survival were analysed by means of a reparameterization of the von Bertalanffy's growth model and the exponential mortality equation. Results indicated that: (1) final mean weight was dependent on density in both trials (P < 0·01) although growth rate was only affected in trial PF (P < 0·01); (2) pelleted feeding produced both greater final mean weight and increased growth rate at densities higher than 5 PL/m2 (P < 0·005); (3) the ratio tail weight/total weight was influenced by density in trial F (P < 0·015); (4) the mortality equation served to explain differences in survival to a limited extent. An increase in growth rate after 170 days occurring at the intermediate density in trial PF was attributed to an increase in mortality, which allowed the remaining individuals to attain larger sizes. Further research to increase biomass yields should focus on the optimization of pond depth, the supply of vigorous post-larvae and on the possible influences of seasonal variations of planktonic communities of the lagoons on the productivity of ponds.

Age and Growth of Nibea albiflora(Sciaenidae) Distributed in Ariake Sound.

The age and growth of Nibea albiflora in Ariake Sound were studied by measuring the radii of otolith annulus. A difference was found in the relationship between male and female otolith size and fish length, and the regression for each sex is shown. The annulus is formed once a year near the intensive spawning period. A bimodal frequency distribution of the Ist annulus size shows that the fish consist of two groups which grow differently. They seem to grow from two groups of the young of the year born at different times in the spawning season. An inverse relationship was recognized between growth in the Ist and 2nd years. With this mechanism, the fish of the group which are born late in a spawning season and have delayed growth almost overtake in size the ones born earlier 2 years after birth. Von Bertalanffy's growth equations were derived from back-calculated lengths of fish with a larger 1st annulus.Male: Lt=307.2(1-e-(0.3436+0.3579t))Female: Lt=357.1(1-e-(0.2459+0.3105t))Adult females had a higher growth rate than males. N. albiflora in Ariake Sound have significantly different growth rates from the Seto Inland Sea population.

北海道苫小牧におけるバカガイの年齢と成長

The age and growth of the sunray surf clam Mactra chinensis in Tomakomai were studied by measuring shell rings. Monthly measurement of shell increment from the last ring indicated ring formation to occur annually from November to January when seawater temperature dropped below about 10°C, and thus to be regardable as an age indicator. Age at the first ring formation was estimated at 0 by observing the shell rings of newly settled clams. Age was determined by counting the number of rings, and the relationship between age and shell length was expressed using von Bertalanffy's growth equation: Lt=78.31 [1-exp{-0.67(t-0.34)}], Lt being shell length (mm) at age t (years).

Estimates of some biological parameters for the Cape hakes off the South African west coast

Maturation and growth data for Cape hakes Merluccius capensis and M. paradoxus collected during direct research surveys over the period 1986 – 1990 are analysed. A logistic model is fitted to the fraction of mature fish by length. Males mature earlier than females, but there is little difference in length at different levels of sexual maturity for the two species. The Schnute, Von Bertalanffy and linear growth equations are fitted to the age-length data by maximizing the likelihood function. The Schnute growth equation occasionally provides a statistically superior fit to the data than the Von Bertalanffy equation. However, both these equations provide a reasonable fit over the age ranges considered. The growth curve is near linear for females, but less so for males. It appears that females grow slightly faster than males. However, the difference in growth rate is less than that suggested by some previous age-and-growth analyses. It is not possible to determine whether or not the values of the growth and ...

Comparative growth studies on Lethrinus lentjan, Lacépède 1802 and Lethrinus mahsena, Forsskål 1775 (Pisces, Lethrinidae) in the Red Sea

Growth characteristics for two lethrinids, Lethrinus lentjan Lacépède 1802 and Lethrinus mahsena, Forsskål 1775 in the Red Sea off Jeddah were studied. With ages determined by scale readings, back-calculated lengths up to the seventh year of life were obtained for each species. Regressions of fish length on scale radius were also computed. Growth in weight was highest during the third and fourth years of life for L. lentjan and L. mahsena, respectively. Within each species, males and females gave virtually identical growth rates. Three exponential equations were derived for each species, representing the weight/length relationship separately for males, females and the sexes combined. Condition factor ( K) values were also determined and variations of these values with fish size and month of capture were studied. The parameters of von Bertalanffy's growth equation were estimated for the two studies. Sex ratio at age suggests sex reversal from female to male during the fifth and seventh year of life for L. lentjan and L. mahsena, respectively.

Growth, biomass, mortality, production and potential yield of the West African clam, Egeria radiata (Lamarck) (Lamellibranchia, Donacidae) in the Cross River system, Nigeria

An important fishery for the West African hemi-estuarine clam, Egeria radiata exists in the lower reaches of the Cross River (CR) system. The stock is heavily exploited but its productivity and potential yield have not been studied. This paper discusses the distribution and ecology of, and presents data on growth, abundance, mortality, biological production and potential yield of the CR stock of E. radiata based principally on length structured relative age. Growth was exponential and conformed to the von Bertalanffy's growth model (VBGM), with the parameters L∞ = 9.3 cm, K = 0.36 and To = −0.10 year. The instantaneous total mortality coefficient (Z) by the catch curve method was 0.82 yr−1; natural mortality coefficient (M) was estimated at 0.32 yr−1. Total mean biomass computed from data obtained in two month's grab sample surveys in the area of occurrence of E. radiata was 1923 kg ha−1 for total (i.e. flesh + shell) and 628 kg ha−1 for flesh (i.e. shell-free) production units. The production-to-mean-biomass (or P/B ratio, R′) were 0.31 and 0.52 for total and shell-free production units respectively. The maximum sustainable yield (Ymax) was estimated at 398.4 kg ha−1 for total and 112.2 kg ha−1 for shell-free production units. With an exploitation ratio (E) of 0.61 and an estimated present catch rate of 1970 tonnes(t) yr−1 total weight (or about 82% of Ymax) the Egeria stock of the CR is currently being fished above the level of its optimum yield. Much of the fishing pressure is on the very young clams, thus lowering the age at first capture (Tc) to 1 year. This is an unhealthy situation for a species with limited area of distribution and low (< 1.0) P/B ratio; it can lead to rapid extinction of the stock if for some reason there is a substantial reduction in annual recruitment. It is recommended that in order to conserve this valuable resource and keep it at a level of sustained optimum yield, there should be a regulation prohibiting the landing of young clams (< 6.0 cm shell length). Furthermore the fishermen should learn to cultivate the animal by transplanting the young clams to new beds upstream to give them time to grow larger before harvesting. This type of management has been practised in Ghana for a long time and has helped to conserve the Egeria stock of the Volta River. The need for a continuous monitoring of the effluents from the Nigerian Newsprint Manufacturing Company's factory located at the bank of the CR in the centre of the clam industry is stressed; such monitoring would ensure that dangerous toxic chemicals are not discharged into the river to damage the Egeria industry.

Age dependence of natural mortality coefficient in fish population dynamics.

From a viewpoint of life history of fish, the natural mortality can be divided into three phases: initial, stable death, and death by senescence, and the respective phases correspond to the three growth phases: early, stable growth, and senescence. According to the relation between natural motality and the growth, a functional formula of the natural mortality coefficient is given in this study. When the von Bertalanffy's growth parameters are known, the natural mortality coefficient can be calculated for each age. As a function of age, the natural mortality coefficient has some general characters throughout the life.

Growth, mortality and potential yield of bonga, Ethmalosa fimbriata (Bowdich 1825) of Nigerian inshore waters

The distribution of and fisheries for bonga, Ethmalosa fimbriata (Clupeidae), in Nigerian inshore waters east of the Niger delta are discussed. Data on length frequency collected between 1973 and 1982 are analysed to obtain the von Bertalanffy's growth parameters ( L ∞=30 cm, K=0.43 and T 0=−0.20) which are then used to estimate the instantaneous total ( Z), natural ( M) and fishing ( F) mortality coefficients. Catch-per-effort statistics (1973–1982) allow for a simple graphical treatment of Schaefer's logistic model from which the maximum sustainable yield ( Y max=30 075 t year −1) is derived for the stock of bonga in this part of the Nigerian coast. Considering the level of mean catch (25 030 t year −1), which is very close to the optimum level of yield ( Y ec) and the mean value of the exploitation ratio ( F Z =0.57 ), it is concluded that the stock of E. fimbriata of the inshore waters east of the Niger delta is being fished at about its Y ec. Although this is the desirable level of exploitation if profit is to be maximized, this fishery might be allowed to expand beyond Y ec to contribute to the solution of an important socio-economic problem, namely, reduction of unemployment, but fishing at Y max should be avoided to prevent the collapse of the stock.

Growth and life span of short-finned squid Illex argentinus in the waters off Argentina.

The data on size composition and some biological charactors of Illex argentinus in the waters off Argentina were collected by R/V SHINKAI MARU from April 1978 to April 1979. Based on the mean lengths of monthly size compositions, the von Bertalanffy's growth equations were estimated. The equations were ML=26.48 (1-e-0.28(t-0.44)) for males and ML=34.13(1-e-0.18(t-0.27)) for females where ML and t were mantle length in cm and age in month, respectively. It was indicated that this species had a one-year life span, viz. they were born in austral winter to early spring, attained at maturity at the same season of the next year and died after spawning.

Equations for Describing Growth of the Schistosome Host Snail Biomphalaria glabrata

Biomphalaria glabrata and Stagnicola palustris were raised in aquaria under crowded and uncrowded conditions. Measurements of greatest shell diameter were taken at regular intervals. Von Bertalanffy and logistic growth curves were fitted by least squares and maximum likelihood methods. The resulting parameter estimates produced better fits for the logistic equation than for the von Bertalanffy equation.

Comparison of age and growth of two types of Hilsa ilisha in Bangladesh waters.

The age and growth of two types of Hilsa ilisha from the rivers Padma and Meghna were examined by means of otolith readings. The relationship between body length and otolith size was found to be linear for both the types A and B, and significantly different between types. In the case of type A hyaline zones appeared during June and July while in type B it was in January and February, i. e., during their respective spawning season. Back-calculated mean lengths ranged from 158.8 to 417.5mm and 142.8 to 398.3mm at the age of 1 to 5 years of types A and B, respectively. A marked difference in the growth by weight was also observed in the two types. Bertalanffy's growth equation fitted well to length at age and were; Lt=642(1-exp(-0.1907(t+0.4929))) for type A and Lt=680(1-exp(-0.1608(t+0.4689))) for type B.

Time of ring formation of otolith and growth curve of hoki Macruronus novaezelandidae (HECTOR) in waters around New Zealand.

As there only otolith samples for six month period, the time of the ring formation was estimated by comparing the back-calculated length with the growth curve for younger age groups obtained from fhe movement of the mode of fhe length composition. The rings were estimated to be formed from February to May, one ring in a year. The largest number of rings counted was 12. VON BERTALANFFY's growth curve was fitted to the back-calculated total length. Almost no appreciable difference was observed between sexes, but some differemce was shown between regions. Growth equation in cm and year for each region is EAST region Lt=124[1-e-0.124(t+0.30)] Lt=132[1-e-0.122(t+0.39)] Lt=133[1331-e-0.121(t+0.21)] East region showed the smaillest growty among three. These growth curves were compared with those of other authors and some discussions were presented.