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.

     

Stock identification of Raja clavata L. (Chondrichthyes, Rajidae) in two contiguous areas of the Mediterranean

The abundance, occurrence, biological features, growth and mortality parameters of the thornback ray, Raja clavata L. 1758 (Rajformes, Rajidae), coming from two contiguous areas of the Strait of Sicily (Central Mediterranean Sea) were analysed in order to discriminate the stocks. The two investigated areas include bottoms off southern Sicily (I-G16) and bottoms further at large (O-G16). The density indexes, biomass indexes and occurrences were substantially lower in I-G16 than O-G16. On the contrary, the biological traits were more similar, although significant differences were detected in the sex ratio, in the median total length of all specimens, in the length frequency distribution, in the estimated maximum length and in the female length-weight slope parameter. The median length of fully mature specimens did not significantly differ between the two areas. The von Bertalanffy’s asymptotic length and the ratio of total mortality/von Bertalanffy’s curvature parameter suggest a total mortality higher in the I-G16 than the O-G16 populations. This article supports the hypothesis that the investigated populations, in spite of a similar original life cycle, have evolved in two distinct unit stocks as a consequence of the different fishing efforts and the low-intermingling rate between the two areas.     

Growth and annual survival estimates to examine the ecology of larval lamprey and the implications of ageing error in fitting models

This study used existing western brook lamprey Lampetra richardsoni age information to fit three different growth models (i.e. von Bertalanffy, Gompertz and logistic) with and without error in age estimates. Among these growth models, there was greater support for the logistic and Gompertz models than the von Bertalanffy model, regardless of ageing error assumptions. The von Bertalanffy model, however, appeared to fit the data well enough to permit survival estimates; using length‐based estimators, annual survival varied between 0·64 (95% credibility interval: 0·44–0·79) and 0·81 (0·79–0·83) depending on ageing and growth process error structure. These estimates are applicable to conservation and management of L. richardsoni and other western lampreys (e.g. Pacific lamprey Entosphenus tridentatus) and can potentially be used in the development of life‐cycle models for these species. These results also suggest that estimators derived from von Bertalanffy growth models should be interpreted with caution if there is high uncertainty in age estimates.     

Estimation of growth parameters from published data for several Mediterranean fishes

Two sets of von Bertalanffy growth parameter (VBGP) estimates are provided for several Mediterranean fish stocks. All estimates are based on the non‐linear least square regression and accompanied by uncertainty measures (i.e. standard errors). The first set consists of growth parameters estimated from 73 published length‐at‐age data with no previous VBGP estimations; in this case, fitting was possible for 30 length‐at‐age sets, corresponding to 22 species, two estimates of which (Mycteroperca rubra and Myctophum punctatum) are the first for the Mediterranean. The second set refers to the re‐estimation of VBGPs from 69 published length‐at‐age data with available original VBGP estimates derived from linear methods (i.e. Ford‐Walford, von Bertalanffy and Gulland‐Holt plots); in this case, fitting was possible for 50 sets. Overall VBGP estimation was not possible for 43 and 19 cases for the first and second sets, respectively. This was because either (a) <4 mean length‐at‐age data were available, or (b) fitting was not possible because of an exponential or a very slow linear increase of length with age, or (c) estimates were unrealistic (i.e. L_max/L_∞ < 0.7) mainly because of unrealistic length‐at‐ages and/or insufficient sampling of older individuals. These estimations and re‐estimations enrich the available data on growth parameters of Mediterranean fishes, both in terms of quantity and quality of information.     

Age and growth of longnose trevally (Carangoides chrysophrys) in the Arabian Sea

The ages and growth of longnose trevally (Carangoides chrysophrys), caught in the northwest Arabian Sea between April 2005 and September 2006, were investigated. Age and growth of 336 fish specimens were determined using sectioned sagittae otoliths. Annual opaque growth rings were formed between December and March, with the majority being laid down in February and March, coinciding with the spawning period and high water temperatures. Marginal zone or edge analysis was used to validate the annual deposition of the opaque zone in the otoliths. This species showed large variations in length‐at‐age, suggesting large growth variations among individuals of the same cohort. The estimated von Bertalanffy growth model differed significantly between the sexes, with males having larger mean lengths at age and reaching a larger asymptotic size. The von Bertalanffy growth models were TL (cm) = 73.34[1‐exp (?0.25 (t + 1.21))] and TL(cm) = 73.26[1‐exp (?0.24 (t + 1.20))] for males and females, respectively.     

Making the most of survey data: Incorporating age uncertainty when fitting growth parameters

Individual growth is an important parameter and is linked to a number of other biological processes. It is commonly modeled using the von Bertalanffy growth function (VBGF), which is regularly fitted to age data where the ages of the animals are not known exactly but are binned into yearly age groups, such as fish survey data. Current methods of fitting the VBGF to these data treat all the binned ages as the actual ages. We present a new VBGF model that combines data from multiple surveys and allows the actual age of an animal to be inferred. By fitting to survey data for Atlantic herring (Clupea harengus) and Atlantic cod (Gadus morhua), we compare our model with two other ways of combining data from multiple surveys but where the ages are as reported in the survey data. We use the fitted parameters as inputs into a yield‐per‐recruit model to see what would happen to advice given to management. We found that each of the ways of combining the data leads to different parameter estimates for the VBGF and advice for policymakers. Our model fitted to the data better than either of the other models and also reduced the uncertainty in the parameter estimates and models used to inform management. Our model is a robust way of fitting the VBGF and can be used to combine data from multiple sources. The model is general enough to fit other growth curves for any taxon when the age of individuals is binned into groups.     

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.     

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 .     

The growth of the common two-banded seabream, Diplodus vulgaris (Teleostei, Sparidae), in Canarian waters, estimated by reading otoliths and by back-calculation

The yearly nature of increment formation in the otoliths of 1–9‐year‐old seabream, Diplodus vulgaris (E. Geoffrey Saint‐Hilaire 1817), from the Canary Islands was validated. The marginal increment method showed that the opaque rings were formed in summer, and the translucent rings in winter. The Brody Proportional Hypothesis and the power length–radius relationship used to back‐calculate the growth trajectories of D. vulgaris showed that this growth model could provide reasonable growth estimates in this species. Growth back‐calculation and growth estimates obtained by direct otolith readings were similar. Data on age and size used to estimate the parameters of the von Bertalanffy growth model for D. vulagris from the Canary Islands showed that males and females had similar growth rates.     

Vital population statistics based on length frequency analysis of the exploited Japanese eel (Anguilla japonica) stock in the Kao‐Ping River,southern Taiwan

Vital statistics such as growth, mortality, and maturity parameters are crucial in understanding the population dynamics of a species. A total of 7 074 Japanese eels (Anguilla japonica) in the lower reach of the Kao‐Ping River, southern Taiwan, were collected with eel tubes in 1998 ～ 2004 and shrimp nets in 2004 ～ 2007. Data from 2004 were excluded due to mixed gear information and escapement of cultured eels; in subsequent years escaped cultured eels were identified and excluded from analyses. The estimated asymptotic length in the von Bertalanffy growth function (84.5–110 cm) was smaller, while the Brody growth parameter (0.30–0.44 year^?1) was higher using electronic length frequency analysis (ELEFAN) than when using Shepherd’s length composition analysis (SLCA). The total instantaneous mortality rate (Z) was around 1 for periods 1998–2003 and 2 year^?1 for 2005–2007 using length‐converted catch curves. The 95% confidence intervals of Z did not overlap for two of the periods, suggesting that the mortality rates were significantly higher during 2005–2007, possibly due to the introduction of shrimp nets. The maturity function differed significantly between sexes, indicating that females become silver eels at a larger size. The Japanese eels in the lower reach of the Kao‐Ping River were likely heavily exploited, thus management and conservation actions are strongly recommended.     

The importance of incorporating age and sex when backcalculating length in bullhead Cottus gobio

The present study backcalculated body length for a data set of a bullhead Cottus gobio population located at different sampling sites in a river network. Model comparison between various growth models, which included successively new parameters, showed the effect and importance of taking sex, age and the location in the river network into account. The data sets obtained by backcalculation were fitted by the von Bertalanffy growth function, which revealed the effect of the backcalculation formula on the estimation of the von Bertalanffy growth parameters. Fitting results and parameter estimates showed again the importance of incorporating age and sex when backcalculating body length in the C. gobio population studied.     

Effect of spatial differences in growth on distribution of seasonally co‐occurring herring Clupea harengus stocks

The mechanisms most likely to determine the distribution of the two major herring Clupea harengus stocks in their common early summer feeding ground in the eastern North Sea, Skagerrak and Kattegat were investigated through analysis of acoustic survey data from six consecutive years. No change was detected in biomass of North Sea autumn spawning C. harengus (NSAS) over time, whereas the biomass of western Baltic spring spawning C. harengus (WBSS) declined severely. Analyses of centre of abundance by stock showed no change in NSAS distribution, whereas the WBSS changed to a more western distribution over time. Contrary to previous perception of the juvenile migration, NSAS were found to leave the study area at the age between 1 and 2 years and WBSS 1 year olds were encountered in the Skagerrak. The estimated parameters of von Bertalanffy growth equations showed marked differences between areas with fish in the eastern part of the area having the lowest size at age at all ages. Further, their growth conditions appeared to deteriorate progressively over the period studied. Both NSAS and WBSS showed the highest condition in the North Sea and Skagerrak while condition was substantially lower in age Kattegat. The westward movement of spring spawners over time suggests that growth rate and possibly density of conspecifics influence the migration pattern and distribution of C. harengus in the area. In contrast, there was no evidence to suggest that distribution was constant over time within stocks or that distribution reflected size‐dependent limitations on migration distance.     

Validated age,growth and maturity of the bonnethead Sphyrna tiburo in the western North Atlantic Ocean

The age, growth and maturity of bonnetheads Sphyrna tiburo inhabiting the estuarine and coastal waters of the western North Atlantic Ocean (WNA) from Onslow Bay, North Carolina, south to West Palm Beach, Florida, were examined. Vertebrae were collected and aged from 329 females and 217 males ranging in size from 262 to 1043 mm and 245 to 825 mm fork length, L_F, respectively. Sex‐specific von Bertalanffy growth curves were fitted to length‐at‐age data. Female von Bertalanffy parameters were L_∞ = 1036 mm L_F, k = 0·18, t₀ = ?1·64 and L₀ = 272 mm L_F. Males reached a smaller theoretical asymptotic length and had a higher growth coefficient (L_∞ = 782 mm L_F, k = 0·29, t₀ = ?1·43 and L₀ = 266 mm L_F). Maximum observed age was 17·9 years for females and 16·0 years for males. Annual deposition of growth increments was verified by marginal increment analysis and validated for age classes 2·5+ to 10·5+ years through recapture of 13 oxytetracycline‐injected specimens at liberty in the wild for 1–4 years. Length (L_F50) and age (A₅₀) at 50% maturity were 819 mm and 6·7 years for females, and 618 mm and 3·9 years for males. Both female and male S. tiburo in the WNA had a significantly higher maximum observed age, L_F50, A₅₀ and L_∞, and a significantly lower k and estimated L₀ than evident in the Gulf of Mexico (GOM). These significant differences in life‐history parameters, as well as evidence from tagging and genetic studies, suggest that S. tiburo in the WNA and GOM should be considered separate stocks.     

Determination of the unknown age at first capture of western rock lobsters (Panulirus cygnus) by random effects model

We propose a method for fitting growth curves to multiple recapture data of lobsters when the age at first capture is unknown. The von Bertalanffy growth curve is used to model the growth. To account for individual variability, the unknown age in logarithmic scale of a lobster at first capture, the individual asymptotic size, and the individual growth coefficient of its carapace length are modeled as random effects with a trivariate normal distribution. Unlike previously suggested models, the present model permits correlation between the growth coefficient and the age at first capture and can be fitted readily using existing software. The error structures between consecutive recaptures of a lobster are assumed to be a first-order autoregressive process with unequally spaced time points. A comparison between this model and the Fabens growth equation is given. The proposed method is a flexible method and can be applied to fit different growth equations when the age at first capture is unknown.     

Temperature and salinity effects on post-marsupial growth of Neomysis integer (Crustacea: Mysidacea)

There has been an increasing interest in using the brackish water mysid Neomysis integer as a toxicological test species for Western European estuarine systems. In this respect, more data on growth, moulting and development in this species is needed. The influence of prevailing environmental variables (e.g. temperature, salinity) and age on these processes as well as their optimal range have to be known in order to develop optimal laboratory cultures and to differentiate between chemically induced variability and natural variability in toxicity testing. Individual post-marsupial growth (size, intermoult period, growth factor) was studied from first day neonates until adulthood at eight environmentally relevant temperature-salinity conditions. Three salinities (5, 15 and 30 psu) were tested at 15 and 20 °C, and two more extreme temperatures (8 and 25 °C) were tested at a salinity of 5 psu.Survival and growth of N. integer were detected within the whole range tested, but sexual maturation was only possible in the narrower range of 15-25 °C and 5-15 psu. The size at maturity of N. integer increased with decreasing temperature and increasing salinity. Salinity seems to have a stronger effect than temperature on the duration of maturation. The sigmoid von Bertalanffy growth model was fitted to the individual and pooled data, except for the 8 °C experiment where growth was linear. Estimates from pooled data were comparable with individually based estimates, but generally underestimated the asymptotic length. Temperature was negatively correlated with the asymptotic length and positively correlated with the growth constant K. Higher temperatures caused smaller intermoult periods but had no effect on the growth increment, while salinity effects were less straightforward and dependent on the water temperature. A tool is provided to estimate the age, moult number, intermoult period, growth factor and growth rate from the body standard length of N. integer. Experimentally derived von Bertalanffy parameter estimates resulted in a higher growth performance index compared with field-based estimates for the Schelde estuary and Galgenweel populations of N. integer.     

淀山湖翘嘴鲌的年龄结构与生长特性

研究翘嘴鲌的年龄结构与生长特征可为探其繁殖、性成熟年龄、存活率等习性积累有效数据, 并可为优化鱼类种群结构、科学利用其种质资源提供参考依据。以2016年5月至2017年4月逐月于淀山湖采集到的452尾翘嘴鲌(Culter alburnus)为研究材料, 研究其年龄结构与生长特征间的紧密联系。结果表明: 翘嘴鲌体长15.32—77.91 cm; 体重范围43—5567 g。雌雄群体间的体长和体重的差异不显著(P>0.05), 体长和体重拟合关系式为W=0.00002L2.9211 (R2=0.9143, n=452), 符合匀速生长特性; 选用鳞片鉴定年龄、测量鳞径, 并建立von Berta-lanffy生长方程, L_t=99.65[1–e–0.1357(t+0.6287)]; W_t=11874.27[1–e–0.1357(t+0.6287)]2.9211。采集的翘嘴鲌样本由1—6龄组成, 优势年龄组3龄, 占样本总数的55.71%, 表明生长趋于低龄化、小型化; 生长拐点年龄为7.2711龄时对应的体长和体重分别为65.54 cm和3471.79 g。     

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.     

Reproductive biology of squaretail coralgrouper Plectropomus areolatus using age‐based techniques

The squaretail coralgrouper Plectropomus areolatus was identified as a fast‐growing, early maturing and relatively short‐lived aggregation‐spawning epinephelid. Examinations of sectioned otoliths found females and males first maturing at 2 and 3 years, respectively, suggesting protogynous hermaphroditism; however, no transitionals were observed in samples. Age distribution for the two sexes was similar and both were represented in the oldest age class; however, significant sex‐specific differences in size‐at‐age were identified. Both sexes fully recruit into the fishery at age 4 years and reach 90% of asymptotic length by age 3 years. Underwater visual assessments, combined with the gonado‐somatic indices, revealed a 5 month reproductive season, with interannual variability observed in the month of highest density within the spawning aggregation. Catch restrictions on adults during spawning times and at reproductive sites, combined with gear‐based management and enhanced enforcement, are recommended to maintain spawning stocks. Based on the available evidence, the sexual pattern for this species is unresolved.     

Choosing the right sigmoid growth function using the unified‐models approach

Growth of the young is an important part of the life history in birds. However, modelling methods have paid little attention to the choice of regression model used to describe its pattern. The aim of this study was to evaluate whether a single sigmoid model with an upper asymptote could describe avian growth adequately. We compared unified versions of five growth models of the Richards family (the four‐parameter U‐Richards and the three‐parameter U‐logistic, U‐Gompertz, U‐Bertalanffy and U4‐models) for three traits (body mass, tarsus‐length and wing‐length) for 50 passerine species, including species with varied morphologies and life histories. The U‐family models exhibit a unified set of parameters for all models. The four‐parameter U‐Richards model proved a good choice for fitting growth curves to various traits – its extra d‐parameter allows for a flexible placement of the inflection point. Which of the three‐parameter U‐models was the best performing varied greatly between species and between traits, as each three‐parameter model had a different fixed relative inflection value (fraction of the upper asymptote), implying a different growth pattern. Fixing the asymptotes to averages for adult trait value generally shifted the model preference towards one with lower relative inflection values. Our results illustrate an overlooked difficulty in the analysis of organismal growth, namely, that a single traditional three‐parameter model does not suit all growth data. This is mostly due to differences in inflection placement. Moreover, some biometric traits require more attention when estimating growth rates and other growth‐curve characteristics. We recommend fitting either several three‐parameter models from the U‐family, where the parameters are comparable between models, or only the U‐Richards model.