A simplified method to estimate body growth parameters of the European eel Anguilla anguilla

A simple approach is proposed to fit a body growth model for the European eel Anguilla anguilla to data‐poor case studies. The model is a modified von Bertalanffy curve allowing for delayed sex determination and sexual dimorphism. The proposed procedure provides preliminary estimates of model parameters on the basis of average age and body length of silver eels.     

Growth of the African elephant (Loxodonta africana)

The three-stage desk calculation of the von Bertalanffy equation to describe growth in height and weight with age in the elephant is compared with a new approach to calculating the three coefficients in the function by a computer. The two methods give different results with respect to the weight/age calculations. Theoretical von Bertalanffy equations calculated by both methods to describe growth in height and weight with age in the African elephant in Zambia are compared with previously published equations for the elephant in East Africa. Details are given of growth in height in two known-age African elephants, a female ‘Diksie’ and a male ‘Kartoum’. Theoretical growth in height curves for the female African and Asiatic elephant are compared. The coefficients K and / for growth in height are not transferable to the growth in weight equations. Inherent inaccuracies in the calculation of the coefficients in the von Bertalanffy equation are discussed, and it is concluded that in animals which have a long life-span such as the elephant, the equation serves as a purely empirical representation of weight-at-age data and that there is little biological significance in the parameters it contains. The computer-calculated curves give the best fit to the data. The regression of log age on log shoulder height from 2–20 years of age provides a more realistic approach to comparative growth studies. The increase in adrenal weight with age is linear. Tusk growth in relation to age and sex in Zambia is compared with East Africa. It is concluded that the tusks in Zambia are smaller and are more difficult to sex correctly than their East African counterparts, possibly a consequence of the Zambian elephant having a greater degree of tusk wear. Allometric growth is described with emphasis on the estimation of body weight from shoulder height. The most reliable estimates are obtained from a purely empirical representation of the data, a semilog plot of log body weight on shoulder height.     

Growth characteristics of freshwater pearl mussels,Margaritifera margaritifera (L.)

• 1 Shell growth in the freshwater pearl mussel, Margaritifera margaritifera, was investigated. Three non‐linear growth models (i.e. power, logistic and von Bertalanffy) were fitted to Scottish length‐at‐age data sets and compared.
• 2 Overall, the von Bertalanffy model outperformed the other two approaches, generating the smallest residuals in eight out of 11 samples (the logistic model provided slightly better fits to the other three). It was concluded that individual M. margaritifera appear to grow in an approximately asymptotic fashion and that the von Bertalanffy equation is an appropriate growth model to fit to freshwater pearl mussel length‐at‐age data.
• 3 The ranges in von Bertalanffy parameter estimates observed (k = 0.023–0.075 year^‐1, L_∞ = 77–158 mm, t_o = ‐3.93–4.33 years) are typical of those reported in northern European populations.
• 4 Most of the populations investigated had relatively low k‐values and high maximum age (A_max) estimates. This feature, which suggests high long‐term productivity and less vulnerability to decline (i.e. larger, longer‐living mussels produce more offspring), may be a reason why these populations have survived until now. The population which appears to be the most vulnerable (i.e. which has the highest k and lowest A_max) is probably not recruiting adequately at present.
• 5 An index of absolute growth (mean shell length‐at‐age) was also used for comparing different populations. Observed between‐ and within‐river differences in mussel growth patterns may be associated with a number of environmental factors, particularly water temperature and productivity.
• 6 A significant positive relationship between river length and mean mussel length‐at‐age was observed. In general, mussels grow large in large, cold rivers and vice versa, although there are exceptions which suggest that additional factors may be involved.

     

The growth and age structure of Chilean jack mackerel (Trachurus murphyi) following its influx to New Zealand waters

The Chilean jack mackerel (Trachurus murphyi) is a predominantly Southeast Pacific Ocean species. It is relatively difficult to determine its age, and multiple studies of its growth off South America have produced markedly different sets of von Bertalanffy parameters. T. murphyi was first identified from New Zealand waters in the mid-1980s and has comprised part of the commercial landings of Trachurus species (along with Trachurus declivis and Trachurus novaezelandiae) since then. Results from 13 years of age determination of New Zealand samples using sectioned otoliths indicate that a partially validated age determination method has been developed, with a precision level (average percentage error) of 4.6%. The best available von Bertalanffy growth parameters for the New Zealand population (sexes combined) are as follows: L_∞, 51.9 cm fork length; K, 0.223 per year; t₀, −0.5 year. Analyses by sex showed that males have a significantly larger L_∞ than females. Estimated annual catch-at-length and catch-at-age distributions from the fishery are presented for 2007–2019. There have been at least two episodes of immigration of T. murphyi from international waters, but little evidence of spawning success to maintain the New Zealand population.     

Modelling the growth of Japanese eel Anguilla japonica in the lower reach of the Kao-Ping River, southern Taiwan: an information theory approach

Information theory was applied to select the best model fitting total length ( L _T)-at-age data and calculate the averaged model for Japanese eel Anguilla japonica compiled from published literature and the differences in growth between sexes were examined. Five candidate growth models were the von Bertalanffy, generalized von Bertalanffy, Gompertz, logistic and power models. The von Bertalanffy growth model with sex-specific coefficients was best supported by the data and nearly overlapped the averaged growth model based on Akaike weights, indicating a similar fit to the data. The Gompertz, generalized von Bertalanffy and power growth models were also substantially supported by the data. The L _T at age of A. japonica were larger in females than in males according to the averaged growth mode, suggesting a sexual dimorphism in growth. Model inferences based on information theory, which deal with uncertainty in model selection and robust parameter estimates, are recommended for modelling the growth of A. japonica .     

Grooming and resting of otters Lutra lutra in a marine habitat

The weight gain in lactating harbour seal pups and sex-specific growth curves are described. The relationship between body length, body weight and age were derived by regression analysis based on length and age data from 365 seals, and weight values from 136 seals. The asymptotic values of the curves describing body length were 148.0 cm and 147.2 cm in females and 153.9 cm and 155.5 cm in males using Gompertz and von Bertalanffy, respectively. The corresponding body weight values were 72.8 kg and 76.7 kg in females and 90.7 kg and 88.4 kg in males.     

Simple methods to obtain preliminary growth estimates for fishes

Explored were methods to derive preliminary information on growth from other known life history parameters such as maximum size and size and age at first maturity. Use was made of the fact that with asymptotic length known, only one point is needed to determine the general shape of a von Bertalanffy growth curve. An empirical relationship was used to predict asymptotic length from maximum observed length. We used mean size reached at age 1 or 2 or mean age and size at first maturity, as is often provided in the literature, to derive preliminary von Bertalanffy growth curves. Results of this approach were then compared with published growth estimates. We used an empirical relationship to predict length at first maturity from asymptotic length when only the age at first maturity was given in the literature. Temperate fishes usually have restricted spawning periods lasting a few months per year and maturity is typically reached in the first, second, third, or later year, i.e. in steps of 12 months, with larger species maturing later. We used data in FishBase ( http://www.fishbase.org ) to establish typical ranges for age at first maturity and growth performance of temperate fishes as a function of maximum size. We present an approach that uses this framework to derive preliminary growth estimates for species of which only the maximum size is known.     

Growth with seasonally varying temperatures: an expansion of the von Bertalanffy growth model

The von Bertalanffy growth function has limitations for describing the growth of fishes in seasonal climates. In the present work, a new equation is proposed where the growth parameter k is substituted by a function related to monthly water temperatures. The computer program GROWTHS was developed to fit and simulate the growth for seasonally varying temperatures. Examples for natural populations of Barbatula barbatula and Cottus gobio are presented.     

Determinate growth in a paternal mouthbrooding fish whose reproductive success is limited by buccal capacity

The life history of the paternal mouthbrooding cardinal fish Apogon doederleini was investigated in the temperate waters of Japan, with particular reference to its growth and reproductive rate. Both males and females almost ceased to grow at age 3 years, although living to 7 years of age. Their growth pattern, represented by the relative size at sexual maturity to the asymptotic size and the von Bertalanffy growth coefficient, was among the most determinate in ectothermic vertebrates. Brood size just before hatching increased in proportion to the second power of the body size of the brooding male, and correlated more positively with the male's than the female's body size, suggesting that it was limited by the male's buccal capacity. The estimated total number of broods hatched in a breeding season showed a weak or no correlation with the body size or age in either sex. Using life-history parameters based on data of A. doederleini, a simulation model of energy allocation without considering sexual interaction revealed that the optimal growth pattern shows an indeterminate growth that differs greatly from the actual growth pattern of A. doederleini. This suggests that there are some brooding constraints to size-advantage of reproductive success in this species. The possible mechanism of such reproductive constraint is discussed.     

Implications of a warming North Sea for the growth of haddock Melanogrammus aeglefinus

The present study aimed firstly, to test for a temperature effect on North Sea haddock Melanogrammus aeglefinus growth and secondly, to develop a model that could be used to assess total length (L(T)) and mass (M)-at-age response to different temperature scenarios. The von Bertalanffy growth model was fitted on a cohort-by-cohort basis from 1970 to 2006. The asymptotic L(T) (L(∞)) was negatively correlated with temperature while the rate at which L(∞) is reached (K) was positively correlated with temperature. K was negatively correlated with density, whereas no effect on L(∞) was observed. These effects were incorporated into a von Bertalanffy model which was extended to include temperature and density as explanatory variables. Only the temperature variable was significant. Fitting the extended von Bertalanffy model revealed that L(∞) decreased while K increased with increasing temperature, resulting in up to a 40% loss of individual yield at older ages. The dramatic decline observed in the mean age at which 50% of the population becomes mature suggests that higher temperatures resulted in larger young M. aeglefinus that matured earlier and therefore reached a smaller maximum size. In a global warming context, the loss of individual yield observed at old ages is likely to reduce the fisheries yield for M. aeglefinus in the North Sea.     

Age and growth of eels Anguilla japonica in a Chinese river

Age and growth of Anguilla japonica sampled from the Qiulu River in southern China were studied. Mean body lengths and weights of the eels at each age were back-calculated from their otoliths. The growth parameters for the von Bertalanffy function gave L _∞= 98–2cm, K =0·07 and t ₀=− 1·94. Scales were observed to form firstly at the middle part of the lateral line, at a minimum body length of 160 mm and were inappropriate for ageing.     

Age, growth and reproduction of Sarcocheilichthys nigripinnis from the Qingyi Stream in the Huangshan Mountains

Identifying the life-history strategies of fish and their associations with the surrounding environment is the basic foundation in the conservation and sustainable utilization of fish species.We examined the age,growth,and reproduction of Sarcocheilichthys nigripinnis using 352 specimens collected monthly from May 2009 to April 2010 in the Qingyi Stream.We found the sex ratio of this study population was 0.58:1(female:male),significantly different from expected 1:1.Females and males both comprised four age groups.The annuli on the scales were formed during February and March.No obvious between-sex difference was observed in length-weight and length-scale-radius relationships.The total length in back-calculation significantly increased with age for both sexes,but did not differ significantly at each age between the two sexes.An inflection point was observed in the growth curves given by the von Bertalanffy growth function for total weight.At this inflection point,fish were 3.95 years.Both sexes reach their 50% sex maturity at age 2,when females and males were 94.7 mm and 103.0 mm total length.The temporal pattern of the gonado-somatic index corresponded to a spawning period that occurred from April through July.The non-synchronicity of egg diameter in each mature ovary during the breeding period suggested these fish may be batch spawners.The absolute fecundity increased significantly with total length and weight,whereas no significant correlation was observed between the relative fecundity and body size.     

Life-history variations of killifish (Aphanius sophiae) populations in two environmentally different habitats in central Iran

Two populations of Aphanius sophiae from two different habitats (one in a spring with stable environmental conditions and the other in a river with variable conditions) were examined to determine whether these conditions elicit differences in life history traits. Age composition revealed that females from the spring live longer. Von Bertalanffy growth parameters showed that L(∞) in the river population was higher than in the spring population. GSI showed a shorter reproduction period in A. sophiae from the river system. Egg diameter was significantly larger in the spring population. These results confirm the hypothesis of the response of killifish to local selective pressures in different habitats through adaptations via changes in the duration of the reproductive period, egg diameter, size changes, age composition and growth rate.     

Age and growth of the European catfish (Silurus glanis) in a Turkish Reservoir and comparison with introduced populations

The European catfish, Silurus glanis, is native to eastern Europe and western Asia and is among the largest freshwater fish in the world. Despite its increasing economic importance and its frequent introductions, the ecology and life-history of this species is poorly known due to the difficulty of sampling such a large species in large rivers and standing waters. Our study provides the first data on age and growth of this species in Turkish waters, where it is native. We report the length-weight relationships and age and size structure of this population, which were significantly different between females and males. A marginal increment analysis indicated that annulus formation occurred between May and June. The estimates of three growth functions (von Bertalanffy, logistic and Gompertz) are reported, with the von Bertalanffy growth providing a better fit and more realistic parameter estimates. Growth rates were significantly higher in males than in females and were overall higher compared to other native populations but similar to introduced populations of similar latitude.     

Population structure and growth of the Japanese littleneck clam <Emphasis Type="Italic">Ruditapes philippinarum</Emphasis> in Amursky Bay,Sea of Japan

This paper deals with the size, age, and sex structure of population and growth of the Japanese littleneck clam Ruditapes philippinarum in Amursky Bay (Peter the Great Bay, Sea of Japan). One-year-olds and individuals with a shell length less than 19.8 mm were not found in the population under study. The population consisted mostly of 3-4-year-old clams (72.4%) with a shell length of 35–45 mm (67.8%). The maximum recorded age of R. philippinarum was 7 years, and maximum shell length was 52.7 mm. The male to female ratio was approximately 2: 1. Hermaphroditism (2.1%) and parasitic castration (1.4%) were observed. Linear growth rates of clams were found to increase until the age of three years old (11.6 ± 0.6 mm/year). Mollusks reach a commercial size of over 35 mm in shell length in the fourth year of life. The parameters of the von Bertalanffy equation describing group linear growth were L _∞ = 56.6 mm, k = 0.302 year^?1, and t ₀ = 0.468 year. The relationship between the shell length and the wet body weight is described by the equation W = 0.000253L^2.954.     

Age and growth of the Black Sea turbot, Psetta maxima (Linneaus, 1758) (Pisces: Scophthalmidae), estimated by reading otoliths and by back-calculation

Age and growth of the Black Sea turbot, Psetta maxima, were determined from a total of 1445 individuals collected along the eastern Black Sea coast between 1990 and 1996. Age was estimated by interpreting growth rings in whole and broken sagittal otoliths. The former method underestimated the age over 5 years, and a maximum age of 11 years was observed by the latter. Marginal increment analysis clearly showed that a single annulus is formed in early summer each year. Growth in length differed between sexes, and females attained a larger size than males at the same age. No significant difference was found between the mean observed total length (TL), the back‐calculated TL derived from radius measurements and the TL estimated from otolith size–fish size relationship. The von Bertalanffy growth parameters estimated by the length‐at‐age data were: L_∞ = 96.24 cm; K = 0.119 year^?1; t₀ = ?0.01 year for the entire population.     

徐家河水库陆封近太湖新银鱼生物学研究

1992年5月至1996年8月对徐家河水库近太湖新银鱼的形态学,繁殖特性,生长以及食性进行了研究。结果表明,徐家河水库近太湖新银鱼主要以枝角类和桡足类为食,繁殖季节为3-6月,其中4月中旬为繁殖高峰期,与太湖新银鱼不同只有春季产卵群体,生命周期为一年。体重与体长关系为:W=2.014×10-6L3.170(r=0.999)。其von Benrtalanffy生长方程为Lt=65.071-e-0.2394(t+0.5066)forbody length and Wt=1.1281-e-0.2394(t+0.5066)3.170。       

The life history of rock gurnard (Trigloporus lastoviza, Brünn. 1768) in the Saronikos Gulf

Age, growth and reproduction of rock gurnard in the Saronikos Gulf (Greece) were studied. Otoliths from 638 specimens (sex combined) were read for age determination. The body length-otolith radius relationship was found linear (L = -18.0 + 4.99 _xR; where L = fish length in mm, R = otolith radius 20 X). The life span of females seemed to be longer than that of males, indicating a differential mortality with sex. The growth was lower than that in the Catalane Sea. The maximum age of fish collected was VIII and the maximum fork length estimated by von Bertalanffy equation was 356 mm. Weight increased as the 3.054252 power or the length. Reproduction was observed to take place between winter and early spring and occasionally in early winter. Males began to mature after completion of the second year and the females after the third. The exploitation rate was rather high, which suggests that the rock gurnard stock was overfished in Saronikos Gulf. The male to female ratio was usually 1:1.     

Description of growth by simple versus complex models for Baltic Sea spring spawning herring

The objective was to find a length–growth model to help differentiate between herring stocks (Clupea harengus l.) when their length–growth shows systematically different patterns. The most essential model restriction was that it should react robustly against variations in the underlying age range which varies not only over time but also between the different herring stocks. Because of the limited age range, significance tests as well as confidence intervals of the model parameters should allow a small sample restriction. Thus, parameter estimation should be of an analytical rather than asymptotic nature and the model should contain a minimum set of parameters. The article studies the comparative characteristics of a simple non‐asymptotic two‐parameter growth model (allometric length–growth function, abbreviated as ALG model) in contrast to higher parametric and more complex growth models (logistic and von‐Bertalanffy growth functions, abbreviated as LGF and VBG models). An advantage of the ALG model is that it can be easily linearized and the growth coefficients can be directly derived as regression parameters. The intrinsic ALG model linearity makes it easy to test restrictions (normality, homoscedasticity and serial uncorrelation of the error term) and to formulate analytic confidence intervals. The ALG model features were exemplified and validated by a 1995 Baltic spring spawning herring (BSSH) data set that included a 12‐year age range. The model performance was compared with that of the logistic and the von‐Bertalanffy length–growth curves for different age ranges and by means of various parameter estimation techniques. In all cases the ALG model performed better and all ALG model restrictions (no autocorrelation, homoscedasticity, and normality of the error term) were fulfilled. Furthermore, all findings seemed to indicate a pseudo‐asymptotic growth for BSSH. The proposed model was explicitly derived for of herring length‐growth; the results thus should not be generalized interspecifically without additional proof.     

南渡江上游海南半鲿生物学参数估算

为研究海南半鲿(Hemibagrus hainanensis Tchang 1935)种群生物学及资源动态特征, 2019年1—12月于南渡江上游采集358尾海南半鲿,其体长范围为42—289 mm,体质量范围为1.14—282.79 g。利用FiSATⅡ软件中ELEFAN I法估算南渡江上游海南半鲿种群参数,其资源变动趋势则通过Beverton-Holt动态综合模型进行评估。结果显示:von Bertalanffy生长方程所描述的各参数值分别为L∞=304.5 mm、K=0.49、t0=–0.29,体质量的生长拐点为t=1.95,即TL=202.9 mm。利用Pauly经验公式和长度变换渔获曲线法分别估算出:自然死亡系数(M)为1.05,总死亡系数(Z)为1.22,捕捞死亡系数(F)为0.17及资源开发率(E)为0.14,表明其资源未处在过度捕捞状态。研究结果填补了南渡江上游海南半鲿的种群生长特性及动态特征基础资料的空白,为其种群资源恢复和保护策略的制定提供理论依据。