Von Bertalanffy Equation Research Articles

한국 서해안 갈색띠매물고둥, Neptunea (Barbitonia) arthritica cumingii의 연령과 성장

The age and growth of Neptunea (Barbitonia) arthritica cumingii sampled from the West Sea of Korea were determined from 1,062 operculums from October 2007 to September 2008. Age of Neptunea (Barbitonia) arthritica cumingii was determined from the rings on the operculum. The relationship between shell height (SH; mm) and shell width (SW; mm) was expressed by the following equation : SW = 0.5757 SH + 0.222 (R = 0.8723), and shell height (SH; mm) and total weight (TW; g) was highly correlated by the equation : TW = 0.0002 SH (R = 0.9121). The main spawning periods was estimated June to July through fatness index analysis. The relationship between shell height and ring radius of operculum in each ring group was expressed as a regression line. Therefore, there is a correspondence in each ring formation. Based on the monthly variations in the marginal index (MI) of the operculum, it is assumed that the ring of this species was formed once a year during the period of July to August. Growth curves for shell height (SH) and total weight (TW) fitted to the von Bertalanffy's equation were expressed as follows :        

동해 원산 연안 대복, Gomphina (Macridiscus) veneriformis (LAMARCK, 1818) 의 연령과 성장

본 조사는 2006년 2월부터 2007년 1월까지 12개월에 걸쳐 북한 원산 연안에서 형망에 의해 어획되어 주문진 검역소로 수입되어지는 대복을 실험에 사용하였다. 총 표본수는 3,899개체였고, 비만도를 통하여 추정한 대복의 산란기는 7-8월이며, 주산란기는 8월로 조사되었다. 대복의 패각에 나타난 윤문은 연 1회 형성되는 주기성 윤문으로, 주 윤문형성시기는 7월로 조사되어, 산란 후 초륜이 형성되기까지의 기간은 약 11개월 (0.92년) 로 나타났다. 대복의 상대성장식은 다음과 같다. SH = 0.7405 SL + 0.2227 (<TEX>$R^2$</TEX> = 0.9671) SW = 0.3657 SL + 0.4253 (<TEX>$R^2$</TEX> = 0.922) <TEX>$$TW=0.4274{\times}10^{-3}{\times}SL^{2.7876}$$</TEX> (<TEX>$R^2$</TEX> = 0.9591) 대복의 von Bertalanffy 성장식은 다음 식을 통해 나타낼 수 있었다. <TEX>$$SL_t=70.80(1-e^{-0.217(t+0.367)})$$</TEX> <TEX>$$TW_t=(1-e^{-0.217(t+0.367)})^{2.7876}$$</TEX> The age and growth of Gomphina (Macridiscus) veneriformis sampled from February 2006 to January 2007 on the Wonsan coast of East Sea were determined from 3,899 shell. Age of Gomphina (Macridiscus) veneriformis was estimated from the ring on the surface of shell. The relationship between shell length (SL) and shell height (SH) was expressed by the following equation : SH = 0.7405 SL + 0.2227 (<TEX>$R^2$</TEX> = 0.9671), and shell length (SL) and shell width (SW) was highly correlated by the equation : SW = 0.3657 SL + 0.4253 (<TEX>$R^2$</TEX> = 0.922). The relationship between shell length (SL) and total weight (TW) was also expressed by the following equation : <TEX>$TW=0.4274{\times}10^{-3}{\times}SL^{2.7876}$</TEX> (<TEX>$R^2$</TEX> = 0.9591). The main spawning periods was estimated August through fatness index analysis. Based on the monthly variations in the marginal index (MI) of the shell, it is assumed that the ring of this species was formed once a year during the period of July. Growth curves for shell length (SL) and total weight (TW) fitted to the von Bertalanffy's equation were expressed as follows : <TEX>$$SL_t=70.80(1-e^{-0.217(t+0.367)})$$</TEX> <TEX>$$TW_t=(1-e^{-0.217(t+0.367)})^{2.7876}$$</TEX>

On the Characterization of Intermediates in the Isodesmic Aggregation Pathway of Hen Lysozyme at Alkaline pH

Protein aggregation leading to formation of amyloid fibrils is a symptom of several diseases like Alzheimer’s, type 2 diabetes and so on. Elucidating the poorly understood mechanism of such phenomena entails the difficult task of characterizing the species involved at each of the multiple steps in the aggregation pathway. It was previously shown by us that spontaneous aggregation of hen-eggwhite lysozyme (HEWL) at room temperature in pH 12.2 is a good model to study aggregation. Here in this paper we investigate the growth kinetics, structure, function and dynamics of multiple intermediate species populating the aggregation pathway of HEWL at pH 12.2. The different intermediates were isolated by varying the HEWL monomer concentration in the 300 nM—0.12 mM range. The intermediates were characterized using techniques like steady-state and nanosecond time-resolved fluorescence, atomic force microscopy and dynamic light scattering. Growth kinetics of non-fibrillar HEWL aggregates were fitted to the von Bertalanffy equation to yield a HEWL concentration independent rate constant (k = (6.6±0.6)×10−5 s−1). Our results reveal stepwise changes in size, molecular packing and enzymatic activity among growing HEWL aggregates consistent with an isodesmic aggregation model. Formation of disulphide bonds that crosslink the monomers in the aggregate appear as a unique feature of this aggregation. AFM images of multiple amyloid fibrils emanating radially from amorphous aggregates directly confirmed that on-pathway fibril formation was feasible under isodesmic polymerization. The isolated HEWL aggregates are revealed as polycationic protein nanoparticles that are robust at neutral pH with ability to take up non-polar molecules like ANS.

On the 3/4-exponent von Bertalanffy equation for ontogenetic growth

The von Bertalanffy equation has been widely used to describe the ontogenetic growth of animals. Recently a new ontogenetic growth model (OGM) was proposed based on allometric scaling and has gained very good attention from the readers. Mathematically speaking, this model is a special case of von Bertalanffy equation with a scaling exponent (α) being 3/4. This new OGM has been criticized on several grounds, such as contradicting the law of energy conservation. Its generality has also been questioned as it fits poorly to the growth of many crop species. Moreover, fish growth fits the von Bertalanffy equation better when α=2/3 rather than when α=3/4. Here, we fit the von Bertalanffy equation with α=2/3 or 3/4 or unknown, and also the logistic equation, to the body length data of three freshwater fish species. This allows us to test: (i) how the choice of the scaling exponent α in the von Bertalanffy equation affects its performance, and (ii) whether the logistic equation provides a better fit than the von Bertalanffy equation for fish growth, as already demonstrated for crop growth. Results showed that the OGM (α=3/4) fitted better than unknown α or α=2/3 in the von Bertalanffy equation but worse than the logistic equation. When choosing α values between 1/2 and 1, we found that increasing the value of α could improve the goodness-of-fit but potentially lead to overfitting and unreliable estimates of model parameters. This suggests that there is no universal value of α for different species or taxa. Use of 2/3 or 3/4 value for the scaling exponent α in the von Bertalanffy equation should be carefully decided based on observed relationships between metabolic rate and body weight, and not merely based on the goodness-of-fit. As a rule of thumb, the logistic equation is still the best model for describing the ontogenetic growth of animals and plants. Future research should be aimed at clarifying the potential linkages between the logistic equation and the metabolic theories.

Parámetros de crecimiento y variaciones de densidad de una población de Strombus gigas (Neotaenioglossa: Strombidae), del parque Xel-Ha área natural protegida

The queen conch, Strombus gigas, is a gastropod of commercial importance in the Caribbean. Population studies are based on size frequency analysis, using either length or weight parameters for the whole live organism. This contribution used mark-recapture data to estimate the Von Bertalanffy equation parameters and population number variation within a non harvest population from a protected area, to clarify the biometric parameters that better suit for the whole population, or for the juvenile and adult fractions. Conchs from Xel-Ha Park were monthly sampled from November 2001 to August 2005. Every conch found was measured and marked with a numbered tag that identified month and locality; and monthly abundance was estimated with Jolly's method. Length, lip thickness and weight increments were used to estimate the Von Bertalanffy growth equation parameters with Appeldoorn's subroutine of FISAT program. The population number varied through the study, with a minimum of 49 in April 2003 and maximum of 9 848 during June 2005. Conchs make only temporary use of Xel-Ha cove. Shell length gave the best fit for the juvenile fraction: L(infinity)=251, K=0.3, C=0.8 Wp=0.3; and lip thickness for adults: L(infinity)=47.78, K=0.17, C=0.1, Wp=0.86, while, the whole population was better represented by weight: L(infinity)=3850, K=0.36, C=0.8, Wp=0.3. A maximum age of 19 years was estimated from the population. Natural mortality was 0.49/year for juveniles and 0.29/year for adults. There were two pulses of recruitment: fall-winter and summer. It is concluded that population studies from length frequency data, should be analyzed independently in two groups, shell for the juvenile fraction and lip thickness for the adult fraction, or if it is not possible to analyze the population fractions separately, weight should be used to avoid miss calculation of the age structure.

Ruffe (Gymnocephalus Cernuus L.) Growth and Diet in Lake Dusia (Southern Lithuania)

Abstract The ruffe, Gymnocephalus cernuus (L.), is considered to be a food competitor with many commercially valuable fishes such as bream, Abramis brama (L.), roach, Rutilus rutilus (L.), pikeperch, Sander lucioperca (L.), and perch, Perca fluviatilis L. This paper presents the results of an investigation into the fish community structure of Lake Dusia and the population parameters (morphometry, age, growth, diet) of ruffe as one of the prevailing fish species in the lake. The fish community of Lake Dusia was dominated by ruffe, perch, and roach. The ruffe population constituted 64.1% of the fish community of the lake in relative abundance and 36.8% in biomass. An analysis of the ruffe diet revealed that Gammaridae and Chironomidae were the principal components in all age-classes. The ruffe population was comprised mainly of individuals 3+ and 4+ years of age. The mean total length (TL) of ruffe was 13.39 ± 1.79 cm (minimum-maximum: 6.12-19.93 cm). The growth in length calculated using the von Bertalanffy equation was Lt = 21.3[1-e-a161(t-0,335)]. Ruffe growth rates were found to slow as the fish aged. Ruffe growth variations were linked to population density, fish community structure in the water body, abundance of invertebrates (zooplankton and zoobenthos), and type of water body.

Patterns of the growth of soft-shell clam Mya arenaria L. (Bivalvia) in shallow water estuaries of the southern Baltic Sea

We explored the shell shape and growth performance of the soft-shell clam Mya arenaria L. in two shallow brackish water estuaries of the southern Baltic Sea – Darss-Zingst and Ruegen lagoons. Observed clams ranged from 2 to 50.1mm in length with detected age up to 6 years old. The growth patterns of the clams were analyzed using the von Bertalanffy growth function (VBGF). An isometric relationship was found between shell length and shell height or shell thickness. Asymptotic length and weight were predicted according to von Bertalanffy equation as L∞=82.75mm and W∞=10.9g. The relationship of wet weight to length was allometric, with exponent b=3.09. Observed shell lengths were close to values predicted by the model. Our study distinguished patterns of the molluscan growth in estuarine transitional environment of the southern Baltic Sea in comparison with other coastal habitats with pronounced spatial environmental heterogeneity.

Age structure and growth of the Gurra rufa (Cyprinidae), in southern Iran

The age structure and growth of Gurra rufa (Heckel, 1843), in the Dalaki river (Boushehr province in southern Iran) were studied in samples caught from May 2007 to September 2007. The maximum total lengths were 171 mm in females (168) and 188 mm in males (156). Age determination based on the scale and opercle readings shows that the population has 4 age classes. The growth of both sexes was isometric (b=2.89 males, b=2.93 females). The highest growth rate was observed between age 1 and 2 in both sexes. Growth parameters were computed by the von Bertalanffy equation for females and males as: L∞ = 164.14, W∞ =117.11¸ t0 = -1.16, K= 0.189 and L∞=168.16, W∞=116.28, t0=-1.14, K= 0.213 respectively.

Individual growth of Drepanotrema cimex (Pulmonata: Planorbidae) from Arenalcito pond, natural reserve multiple uses Martin García Island, Buenos Aires, Argentina.

The species of the genus Drepanotrema, most of them endemic to the Neotropical region, belong to the Planorbidae. Of the nine species of this genus, six are found in Argentina. The present investigation analysed the individual growth of Drepanotrema cimex in Arenalcito pond (34°11' S, 58°15' W), Martín García Island Natural Reserve of Multiple Uses, Buenos Aires Province, Argentina. A total of 14 samples were collected (n = 1931) from February 2006 to June 2007. Five environmental variables were measured: water temperature, dissolved oxygen (mg L-1), electrical conductivity (µS cm-1), total dissolved solids, and pH. The individual growth of the species was analysed mathematically by means of the von Bertalanffy equation, where: Lt = 5,6(1-e-2,0592 (t-0,293)). The parameter L∞ was estimated by the Ford-Walford Method. The population of D. cimex was characterised by a complex and dynamic size structure throughout the annual cycle. The analysis of the curves revealed unimodal (2006) and polymodal (April to June 2007) distributions, which pattern served to identify the existence of cohorts within the population studied.

Life-History Traits of the Invasive Population of Prussian Carp, &lt;I&gt;Carassius Gibelio&lt;/I&gt; (Actinopterigi: Cypriniformes: Cyprinidae), from Gelingüllü Reservoir, Yozgat, Turkey

Background. Prussian carp, Carassius gibelio (Bloch, 1782), is one of the successful invaders of freshwater systems of Turkey. Although, Prussian carp has rapidly expanded its area of distribution in Anatolia during the last two decades, there is limited information about its biological features in new environments. In order to determine the impact of invasive species on ecosystem, the life history characteristics of an exotic fish species in different locations should be monitored. The presently reported study provides information about the growth and reproduction of Prussian carp introduced into a reservoir in Central Anatolia. Materials and methods. Age, growth, and reproduction of Prussian carp were studied during a 3-year period in Geling&#252;ll&#252; Reservoir, K&#305;z&#305;l&#305;rmak River Basin. A total of 344 specimens were caught by gill nets. Age was determined from scales. Length&#8211;weight relation, von Bertalanffy equation, and specific growth rate were used to evaluate the fish growth. In order to assess growth and reproduction patterns, fecundity, GSI, and variations in oocyte size were determined. Results. Both males and females reached a maximum age of 5+ years. Fork length was 6&#8211;27 cm in males and 5.6&#8211;26.8 cm in females. Both sexes matured during their second year of life (1+ year). In the Geling&#252;ll&#252; Reservoir population the males were predominant&#190;the overall sex ratio was 1.39 : 1 (193 males to 139 females) and differed significantly from unity. The von Bertalanffy growth equation was Lt = 32.17 (1 &#8211; e&#8211;0.232(t &#8211; 0.094)) cm for males and Lt = 36.03 (1 &#8211; e&#8211;0.212(t &#8211; 0.205)) cm for females. Growth in length was approximately 70% in males and 85% in females during the first year of life. The somatic condition of the fish increased markedly during late spring and summer. A prolonged spawning period was observed from April to August. Maximum egg diameter was 1.51 mm and maximum absolute fecundity was 174 000 oocytes. Conclusion. Compared to previously published data, the studied Prussian carp population was characterized by more rapid growth during the first year of life, earlier maturity, higher fecundity, and a shorter life span. These life history characteristics are typical of invasive species.

Ichthyofauna Composition and Population Parameters of Fish Species from the Special Nature Reserve "Koviljsko-Petrovaradinski Rit" (Vojvodina, Serbia)

Qualitative and quantitative ichthyofauna composition, morphometric characteristics, sex ratio, age and growth for fish species from Koviljsko-Petrovaradinski Rit were examined. A total of 1715 individuals which were classified into 18 species, from 7 families, were caught between August 2006 and October 2008. The greatest proportional contribution in total number of fish had Rutilus rutilus, while the greatest mass contribution had Carassius gibelio. Diversity and richness indices showed the highest values in the Dunavac locality. Female:male sex ratio varied from 1:0.33 in Sander lucioperca to 1:3.67 in Leuciscus idus and could not be observed in Aspius aspius, Neogobius fluviatilis and Cobitis taenia due to presence of only juvenile individuals. According to the scale readings, age distribution varied from I to VII year. The von Bertalanffy equation and growth performance index were determined by FiSAT II software in Esox lucius, Perca fluviatilis, Lepomis gibbosus, R. rutilus, L. idus, C. gibelio and Alburnus alburnus. Finally, distribution and population parameters of an invasive C. gibelio were discussed. Slightly poorer ichthyofauna diversity, low presence of economically significant species and reduced presence of individuals from higher age categories can point to irrational fishing, degradation of habitat, destruction of spawning areas and pronounced anthropogenic influence.

Age and Growth of Barbel Steed Hemibarbus labeo in Goe-san Lake in Korea

Age and growth of Hemibarbus labeo caught from Goe-san Lake in South Korea from March to November, 2011, were studied. A total of 201 specimens was collected, ranging from 110 to 580 mm in total length (TL). Males and females made up 47.9% and 52.1% of the sample, respectively. Marginal increment analyses showed that vertebral increments, each composed of one opaque and one hyaline zone, were deposited annually. Opaque edges were prevalent from June to July. The relationship between TL and vertebral radius was linear, with equations of R = 0.008TL - 0.208 (male) and R = 0.009TL - 0.272 (female). Regression equations between TL and total weight (TW) were <TEX>$TW=9{\times}10^{-6}TL^{2.987}$</TEX> (male), <TEX>$TW=8{\times}10^{-6}TL^{3.014}$</TEX> (female), and <TEX>$TW=9{\times}10^{-6}TL^{2.988}$</TEX> (combined sexes), according to the von Bertalanffy growth equation. Back-calculated TL was expressed using the von Bertalanffy equation as follows: <TEX>$L_t=438.25(1-e^{-0.175(t+0.164)})$</TEX> for males, <TEX>$L_t=483.36(1-e^{-0.147(t+0.115)})$</TEX> for females, and <TEX>$L_t=464.86(1-e^{-0.162(t+0.176)})$</TEX> for the sexes combined. The growth performances were 4.526, 4.536, and 4.544, respectively.

Age, growth, reproduction and feeding of John Dory, Zeus faber (Pisces: Zeidae), in the Saros Bay (North Aegean Sea)

Summary The age, growth, reproduction, sexual maturity and stomach content of John Dory (Zeus faber), caught in the Bay of Saros (North Aegean Sea) between September 2006 and September 2008, were investigated. The female-male ratio was 1.6 : 1. The total length of females ranged from 13.8 cm to 52.8 cm, and of males from 12.2 cm to 42.9 cm. The length-weight relationship was W = 0.0174*L2.936. Age data derived from vertebral centra readings were used to estimate the growth parameters of the von Bertalanffy equation. Growth parameters for females were L∞ = 58.50 cm K = 0.11 year−1, t0 = −0.99 year and for males L∞ = 45.01 cm, K = 0.13 year−1, t0 = −1.17 year. Maximum age was 18 years for females and 17 years for males. Length at first maturity for both females and males was 25.4 cm. Monthly values of the gonadosomatic index indicated that spawning occurred mainly in two peaks: one between January and June, and the other from August to September. Stomach content analysis showed the most-preferred prey to be Pisces (IRI% 97.3).

The Variation of Several Biological Characteristics of the Chub, Squalius cephalus (L., 1758), in the Orenler Dam Lake, Northwest Anatolia, Turkey

In the present study, several growth parameters of 338 Squalius cephalus (L., 1758) specimens collected from the Orenler dam lake (Turkey) between July 2005 and June 2006 were studied. The population comprised 50.74% males, 46.29% females, and 2.97% males+females. In the examined samples, the age of females and males ranged from I to VII and I to VI, respectively. The fork length and weight of females were 14.7-38.0 cm and 40.68-27.0 g, respectively; these values were 16.3-33.7 cm and 57.7-560.0 g, respectively, for males. The age-length and age-weight relationships at time t were calculated by the von Bertalanffy equation for females, and the following results were obtained: Lt = 37.12[1–e–0.36(t–(–0.96))], Wt = 775.6[1–e–0.36(t–(–0.96))]3.27, Lt = 43.59[1–e–0.3356(t–(–0.719))], and Wt = 1123.2[1–e–0.3356(t–(–0.719))]3.08. The calculated length-weight relationship was W = 0.36L3.27 for females and W = 0.03356L3.08 for males. The average condition factor was 1.412 for females and 1.284 for males. Consequently, in the Orenler dam lake, S. cephalus grows very well according to the study’s results.

The Variation of Several Biological Characteristics of the Chub, Squalius cephalus (L., 1758), in the Orenler Dam Lake, Northwest Anatolia, Turkey

In the present study, several growth parameters of 338 Squalius cephalus (L., 1758) specimens collected from the Orenler dam lake (Turkey) between July 2005 and June 2006 were studied. The population comprised 50.74% males, 46.29% females, and 2.97% males+females. In the examined samples, the age of females and males ranged from I to VII and I to VI, respectively. The fork length and weight of females were 14.7-38.0 cm and 40.68-27.0 g, respectively; these values were 16.3-33.7 cm and 57.7-560.0 g, respectively, for males. The age-length and age-weight relationships at time t were calculated by the von Bertalanffy equation for females, and the following results were obtained: L t = 37.12[1–e –0.36( t –(–0.96)) ], W t = 775.6[1–e –0.36( t –(–0.96)) ] 3.27 , L t = 43.59[1–e –0.3356( t –(–0.719)) ], and W t = 1123.2[1–e –0.3356( t –(–0.719)) ] 3.08 . The calculated length-weight relationship was W = 0.36 L 3.27 for females and W = 0.03356 L 3.08 for males. The average condition factor was 1.412 for females and 1.284 for males. Consequently, in the Orenler dam lake, S. cephalus grows very well according to the study’s results.

Stock Assessment and Potential management of Sardinella aurita Fisheries in the East Mediterranean sea (North Sinai coast).

Age, growth and population biology of Sardinella aurita were studies from a small fishery of East Mediterranean Sea (North Sina i coast). 4450 specimens ranged between 6 and 22.9 cm total length and varied from 3 to 77.1 g total weight, were collected from January to December, 2010. The relat ionship between length and weight was estimated as W=0.016 L 2.611 . Age was determined using scales reading technique and the longevity of this species was fou nd to be 4 years. Growth in length and in weight at the end of each year were calculat ed. The growth parameters of the Von-Bertalanffy equation were calculated as L �= 28.37cm, K= 0.2336 Yr -1 and t 0= 0.9808 Yr. Growth performance index O was estimated as 2.2742. Total, natural and fishing mortality rates were 0.99.7 Yr -1 , 0.3507 Yr -1 and 0.53 Yr -1 respectively. The currently exploitation rate (E=0.6) indicate that t he stock of S. aurita in North Sinai fishery is not overexploitation. The mean index of growth performance is lower than that for the another regions this may be related to unsuitable environment.

The growth and reproduction of white bream (Blicca bjoerkna L. 1758) in an oligo-mesotrophic lake in northwest Anatolia (Sapanca, Turkey)

Growth parameters and the reproduction period of white bream (Blicca bjoerkna L. 1758) sampled from Sapanca Lake were determined monthly between November 2000 and October 2001. Three hundred and fifty white bream specimens caught ranged in age from 1^+ to 9^+ years, and the majority of the samples consisted of individuals of the 5^+-year-old age group. The von Bertalanffy equation was determined as Lt = 22.169 (1 - exp {-0.215[t + 0.986]}), Ø': 2.02 for males and Lt = 31.917 (1 - exp {-0.122[t + 1.087]}), Ø': 2.10 for females. The length-weight relationship was estimated as W = 0.0046 TL exp. 3.315 ± 0.002 for males (r^2 = 0.9653, P < 0.05), and W = 0.0036 TL exp. 3.417 ± 0.002 for females (r^2 = 0.9671, P < 0.05). Regression coefficients for sex were significant (t-test, P < 0.05). The slope (b) significantly differed (ANCOVA, P < 0.05) between months. The fact that the b values for male and female white breams differed from 3.0 indicates that there was positive allometric growth. Sex ratio was 1:1.36 (X^2; P < 0.05). Spawning period of white breams began at the end of April and continued until the beginning of July; water temperature during this period ranged between 13.7 and 28.5 °C.

KEBAN VE KARAKAYA BARAJ GÖLLERİNDE YAŞAYAN Capoeta trutta (Heckel, 1843)’NIN BÜYÜME PARAMETRELERİNİN KARŞILAŞTIRILMASI

In this study; the growth characteristics of 1843 population of Capoeta trutta Heckel, 1843 living in the Keban and Karakaya Dam Lake has been studied and the results have been com-pared statistically. 259 fish out of Keban Dam Lake and 281 fish out of Karakaya Dam Lake; at total 540 fish have been analysed for the study. The age of the fish has been determined by looking at their otolith and the ages range from 1 to 8. Von Bertalanffy equation of the popula-tion in Keban Dam Lake has been determined as Lt= 91.79 [1-e–0.0600(t+2.2866)] in the females, as Lt= 95.30[1-e–0.0541(t+2.4362)] in males, and as Lt= 92.57[1-e–0.0577(t+2.3032)] in all individuals. The height- weight relation of the Keban Dam Lake population has been determined as W=0.0151 L 2.9274 in females, as W=0.0170 L 2.9019 in males as W=0.0168 L 2.9032 in all individuals; in Karakaya Dam Lake the relation is respectively as the following W=0.0210 L 2.8400; W=0.0237 L 2.8078; W=0.0211 L 2.8271

Selection of growth functions for describing length-at-age relationships in fish species displaying different life history traits: unexpected alternatives to the von Bertalanffy equation and advantages of a pluralistic statistical approach.

Abstract Simple growth models have proven helpful to study and predict growth trajectories of fish with different life histories and from various environments, and have found numerous applications in ecology, fisheries and aquaculture worldwide. The most applied simple models (e.g. von Bertalanffy) convey little information about life history traits, are facing criticism, and their goodness of fit is assessed using a limited number of statistical outputs. This review challenges the von Bertalanffy and certain statistical outputs using real-life data, and proposes more explanatory alternatives. The length-at-age relationship from three different wild populations of four fish species (lake herring, lake whitefish, northern pike and walleye) is described using the monomolecular, Schumacher, Gompertz, logistic, von Bertalanffy and Richards equations. Comparison between models was based on least squares and likelihood theories involving several statistical outputs currently encountered in model comparison and selection studies. The analysis demonstrates that the monomolecular, Schumacher and Richards equations often stood as alternatives to the von Bertalanffy and highlighted residual sum of squares, standard error (SE) of parameter estimates and, to a lesser extent, Akaike weight as statistical outputs facilitating discrimination between candidate models. Based on visual appraisal, different equations fitted similar trajectories across the 12 growth profiles. However, the assumptions and statistical performance served to select the most appropriate models and discern life history traits of the species under study. Results indicate that comparison and selection of models should consider not only the statistical performance of equations but also the purpose of the study along with the biological/physical interpretation of parameters.

Growth and production of the bivalve Macoma balthica (Linnaeus, 1758) (Cardiida: Tellinidae) in the southeastern part of the Baltic Sea

The growth and production of the Baltic clam Macoma balthica in the southeastern part of the Baltic Sea were studied. The shell length of M. balthica reached 23.5 mm, the maximum age was 13+ years. The linear growth was described by the von Bertalanffy equation for shallow-water area (depths 9–40 m): L τ = 23.99(1 − e −0.1293(τ − (−0.9578))), and for the deep-water area (41–81 m): L τ = 20.61(1 − e −0.1813(τ − (−0.5608))). The annual production was lower (25.35 ± 1.72 kJ/m2) in the shallow-water area than in the deep-water area (71.23 ± 4.48 kJ/m2), with values of P s /B ratio 0.44 and 0.38, respectively.