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1.
Growth data of two different commercial turbot (Scophthalmus maximus) strains reared in recirculating aquaculture systems were analysed with the aim to determine the most suitable model for turbot. To assess the model performance three different criteria were used: (1) The mean percentage deviation between the estimated length and actual length; (2) the residual standard error with corresponding degrees of freedom and (3) the Akaike information criterion. The analyses were carried out for each strain separately, for sexes within strains and for a pooled data set containing both strains and sexes. We tested a pre‐selection of six models, containing three to four parameters. Models were of monomolecular shape or sigmoid shape with a flexible point of inflection including the special case of monomolecular shape in defined cases of their parameters. The 4‐parametric Schnute model achieved best fit in 62% of all cases and criteria tested, followed by the also 4‐parametric generalized Michaelis–Menten equation in 48% and the 4‐parametric Janoschek model (38%). The von Bertalanffy growth function achieved only 29%, Brody 24% and a new flexible function 19% best fit. In a 1–1000 day growth‐simulation sigmoid shaped curves were produced by the Schnute model in 71% of cases. The Janoschek and the Michaelis–Menten model each produced sigmoid curves in 57% of all cases. This indicates that a flexible 4‐parametric function reflects the growth curve of turbot the best and that this curve is rather sigmoid than monomolecular shaped.  相似文献   

2.
Seeking the most suitable model to describe the growth of turbot, we analysed growth data of two different turbot (Scophthalmus maximus) strains reared communally in a recirculating aquaculture system. We fitted 10 different nonlinear growth models to individual weight gain data (n = 2,010) during the grow‐out phase. Analyses were carried out for each strain, for sexes within strains and for a pooled data set containing both strains and sexes. To assess the model performance, three different criteria are used. Further, a growth‐simulation was performed to evaluate the shape of the generated curve. This way we could assess the capability of the models to predict future growth. The 3‐parametric Gompertz model achieved the best fit in 42.9% of all cases tested and the lowest Bayesian information criterion in 100% of cases. The model produced realistically shaped curves and asymptotic values matching the biological attributes of the species. In contrast, 5‐parametric functions projected unrealistically shaped curves and predicted improbable mature sizes. Our results show that increasing number of parameters do not lead to increasing goodness of fit, but tend to result in overfitting, and demonstrate the advantages of the 3‐parametric Gompertz model for describing the growth of turbot.  相似文献   

3.
ABSTRACT:   Age and growth of the yellowstriped butterfish, Labracoglossa argentiventris , around Izu Oshima Island were studied using a total of 1450 fish. Age was determined by counting the edge of the opaque zones as a ring mark on sectioned sagittal otoliths. Formation of the first ring was observed during spring or summer, corresponding to 1.5 years after hatching. Thereafter, one ring was formed each year in the same season as the previous year. The growth of the butterfish was rapid until 2 years of age. The maximum likelihood method was applied to the age and length data for estimating parameters in von Bertalanffy, Gompertz, and Logistic growth models. The selected model, based on the Akaike Information Criterion, was the von Bertalanffy growth model, which indicated differential asymptotic length and variance by sex.  相似文献   

4.
The common practice among researchers who study fish growth is to a priori adopt the von Bertalanffy growth model (VBGM), which is the most used and ubiquitous equation in the fisheries literature. However, in many cases VBGM is not supported by the data and many species seem to follow different growth trajectories. The information theory approach frees the researcher from the limiting concept that a ‘true’ growth model exists. Multi‐model inference (MMI) based on information theory is proposed as a more robust alternative to study fish growth. The proposed methodology was applied to 133 sets of length‐at‐age data. Four candidate models were fitted to each data set: von Bertalanffy growth model (VBGM), Gompertz model, Logistic and the Power model; the three former assume asymptotic and the latter non‐asymptotic growth. In each case, the ‘best’ model was selected by minimizing the small‐sample, bias‐corrected form of the Akaike information criterion (AICc). To quantify the plausibility of each model, the ‘Akaike weight’wi of each model was calculated. Following a MMI approach, the model averaged asymptotic length for each case was estimated, by model averaging estimations of interpreting Akaike weights as a posterior probability distribution over the set of candidate models. The VBGM was not selected as the best model in 65.4% of the cases. Most often VBGM was either strongly supported by the data (with no other substantially supported model) or had very low or no support by the data. The estimation of asymptotic length was greatly model dependent; as estimated by VBGM was in every case greater than that estimated by the Gompertz model, which in turn was always greater than that estimated by the Logistic model. The percentage underestimation of the standard error of , when ignoring model selection uncertainty, was on average 18% with values as high as 91%. Ignoring model selection uncertainty may have serious implications, e.g. when comparing the growth parameters of different fish populations. Multi‐model inference by model averaging, based on Akaike weights, is recommended as a simple and easy to implement method to model fish growth, for making robust parameter estimations and dealing with model selection uncertainty.  相似文献   

5.
ABSTRACT:   A new practical growth model through the partial reconstruction for the von Bertalanffy function (VBF) has been proposed. In numerous studies on various species, VBF has been recognized as an appropriate function to describe growth. Here the difference in growth dynamics between soft and hard tissues is considered using VBF. A differential equation in which the growth rates of these two tissue types are described, gives a four parameter model. This advanced model showed characteristics such as: (i) S-shape curve similar to the Gompertz model; (ii) unfixed point of inflection; and (iii) definition as an implicit function. The characteristic indicated in (iii) makes it impossible to apply the method of least squares to data analysis. Therefore, a solution was introduced combining Lagrange's method of indeterminate coefficients and the Newton method. Data analysis for verifying the performance of the advanced model was conducted on published data on growth of the bivalve Spisula sachalinensis . As a result of the comparison among the existing growth models, the advanced model produced the minimum value of Akaike information criterion (AIC).  相似文献   

6.
Several methods were used in an attempt to develop an age and growth model for the Atlantic angel shark (Squatina dumeril). Band counts from vertebral sections, which were fit to the traditional von Bertalanffy growth equation, the Gompertz growth equation, and the two-parameter von Bertalanffy growth equation, did not produce realistic parameter estimates. Additionally, a length-based Bayesian model was applied to fishery-independent length–frequency data, and a full Bayesian model was fitted to length-at-age data to estimate parameters for von Bertalanffy growth equation. Both the length-based and full Bayesian models failed to converge; the length–frequency data showed high bimodality unrelated to season, year, or other factors, and band counts were not predictable by length. Vertebral band counts were not valid for ageing Atlantic angel sharks, and length-based methods, which require normally distributed length–frequencies, were not appropriate for this data set. This study represents the first attempt at modeling age and growth for this species and provides research guidelines for future research initiatives.  相似文献   

7.
《Fisheries Research》2006,82(2-3):229-235
Model selection based on information theory is a relatively new paradigm in biological sciences with several advantages over the classical approaches. The aim of the present study was to apply information theory in the area of modelling fish growth and to show how model selection uncertainty may be taken into account when estimating growth parameters. The methodology was applied for length–age data of four species of fish, taken from the literature. Five-candidate models were fitted to each dataset: von Bertalanffy growth model (VBGM), generalized VBGM, Gompertz growth model, Schnute–Richards growth model, and logistic. In each case, the ‘best’ model was selected by minimizing the small-sample, bias-corrected form of the Akaike information criterion (AIC). To quantify the plausibility of each model, given the data and the set of five models, the ‘Akaike weight’ wi of each model was calculated. The average model was estimated for each case based on wi. Following a multi-model inference (MMI) approach, the model-averaged asymptotic length L¯∞ for each species was estimated, using all five models, by model-averaging estimations of L∞ and weighting the prediction of each model by wi. In the examples of this study, model selection uncertainty caused a magnification of the standard error of the asymptotic length of the best model (up to 3.9 times) and thus in all four cases estimating L∞ from just the best model would have caused overestimation of precision of the asymptotic length. The VBGM, when used for inference, without being the best model, could cause biased point estimation and false evaluation of precision. Model selection uncertainty should not be ignored even if VBGM is the best model. Multi-model inference by model-averaging, based on Akaike weights, is recommended for making robust parameter estimations and for dealing with uncertainty in model selection.  相似文献   

8.
A new concept related to growth coefficient   总被引：1，自引：0，他引：1  
SAKUTARO  YAMADA 《Fisheries Science》2002,68(6):1250-1253
ABSTRACT: Although the notion of growth coefficient is important in growth analysis, its meaning is not necessarily pointed out clearly, at least analytically. The present paper, based on the von Bertalanffy model, gives an extended quantity of it and investigates its properties for logistic and Gompertz models. It is age dependent and converges to the coefficient of age in the models, growth coefficient in the traditional sense. The graphs of the quantity and the length show similarity for the logistic model, but not for the Gompertz model, although they show the same type of fluctuation. Moreover, the analysis indicates that the newly defined quantity has a property suitable to be called a growth density of the growth of length. Our discussion also shows the importance of the notion of growth remainder.  相似文献   

9.
以1~6月龄三疣梭子蟹"中宁1号"为材料,采用Logistic、Gompertz和von Bertalanffy3种模型分别拟合了体质量、体长、全甲宽、甲宽、体高、大螯长节长、大螯不动指长及第一步足长节长共8个形态性状的生长特征,旨在寻找各性状的最佳生长模型,并对其增长规律进行研究。结果表明:三疣梭子蟹体质量性状生长过程以Logistic生长模型(R2=0.999)的拟合效果最佳;除体质量外的其它7个性状则均以von Bertalanffy生长模型(R2为0.990~0.994)拟合效果最好;各性状模型经ANOVA检验后均具有统计学意义(P0.01)。根据各性状的最佳生长模型得出各性状的极限值分别为体质量231.44 g、体长84.45 mm、全甲宽164.44 mm、甲宽128.47 mm、体高43.69 mm、大螯长节长59.96 mm、大螯不动指长90.89 mm、第一步足长节长37.20 mm。体质量的快速生长区间及拐点分别为2.14~3.91月龄及3.02月龄;其它7个性状快速生长区间的始速点为0月龄,终速点为2.05~2.35月龄,拐点在1月龄左右。各性状间的生长速率、生长加速率、相对增长率与绝对增长率存在一定差异。总之,体质量性状生长过程符合"慢-快-慢"的特征,其它性状则表现为"快-慢"的特征。以上结果可为三疣梭子蟹"中宁1号"选择育种及养殖生产提供参考依据。  相似文献   

10.
Sexual dimorphism in growth and maturation of individually tagged turbot (n= 421), Scophthalmus maximus Rafinesque, was studied in a long-lasting (20 months) growth experiment with four temperature regimes. The influence of onset of puberty and subsequent maturation on growth was evaluated. There were no initial size differences, but the final weight of females was larger than that of males at all temperature regimes, except at the lowest temperature. Surplus energy (sum of increase in somatic weight and gonad weight) in females was on average greater than in males from 8 months prior to first spawning. Significant growth (as specific growth rate, SGR) differences between maturing and immature fish were detected from the age of 9 months post hatch. Maturing females had the highest growth rate and reached the largest size (1.8 kg in 20 months), whereas male body weights reached a plateau and levelled off around 1.0 kg. To optimize production characteristics in turbot aquaculture and achieve more homogeneous growth, methods should be developed to produce all-female broods.  相似文献   

11.
鱼类生长的幂指数生长方程   总被引：12，自引：0，他引：12  
陆小萏 《水产学报》2002,26(3):281-284
研究鱼类生长往往需要选择适当的数学模型来处理实际数据以表征生长的某些特点 ,或用于比较生长速度 ,或用于消除随机因素的影响 ,使生长曲线圆润化 ,以显示生长的趋势。其中受到高度重视并被广泛应用的是贝特朗菲方程 (ｖｏｎＢｅｒｔａｌａｎｆｆｙｅｑｕａｔｉｏｎ)。然而该模型在理论上有不足之处 ,适用范围也不够理想。为此 ,取陆文杰[1] 对林木生长研究中提出并命名的数学模型———幂指数生长方程 ,用大量的鱼类生长数据[2 -6] 验证结果 ,证实该方程比贝氏方程更适于研究鱼类生长规律。1　材料与方法1 .1　数据及其来源共 12 4份 ,75…  相似文献   

12.
东海北部小黄鱼异方差生长模型   总被引：1，自引：0，他引：1  
为揭示同方差和异方差结构对鱼类生长模型估计精度的影响,本研究以东海小黄鱼(Larimichthys polyactis)为案例,选用2007 2009年东海北部近海常规监测的小黄鱼基础生物学测定资料,采用对数正态函数型、幂函数型和指数函数型方差结构,分别对Schnute生长模型3种基本形式的von Bertalanffy(LVB)、Gompertz和Schnute模型进行了拟合分析,并采用似然比检验和AIC准则,选择确定最优拟合模型。结果表明,在渔获群体低龄化的条件下,其生长模型的参数估计值对方差结构较为敏感;对数正态函数型、幂函数型和指数函数型方差结构函数对3种生长模型的参数估计值较为接近,参数标准误和变异系数相对较小,小黄鱼生长模型以异方差结构函数拟合的效果较同方差结构更为精确和稳健;采用幂函数型和指数函数型方差结构拟合生长模型,其AIC值较同方差条件大幅降低,生长模型拟合的各月龄组置信区间范围差距缩小,明显提高了生长模型拟合度。  相似文献   

13.
A growth model for the endangered cyprinid fish Tribolodon nakamurai was derived following otolith analyses of 16 wild and 53 reared specimens. The asteriscus was the most appropriate to measure size among three otolith elements, and its height OH  mm was used as size index of otolith. Standard length L  cm was best back-calculated using the Gompertz model, L  = 70.0·exp[–exp{−0.553 (OH   –  2.73)}]. Translucent zones on the lapilli, analyzed from 5-year-old-reared fish, were regarded as winter slow-growing zones. The ages of 10 wild specimens of 37.0–48.1 cm standard length were calculated as 7–10 years by counting the translucent zones on the lapilli. Age t was best back-calculated using the allometry model, t  = 1.33· OH 1.37. The growth trajectory of T.   nakamurai followed a slender S curve, three typical growth models, von Bertalanffy, Logistic and Gompertz, and Richards' model, which is a general formula of the above three, being fitted using the maximum likelihood method. The Gompertz model, Lt  = 60.2·exp[–exp{−0.258( t  − 4.68)}], was found by Akaike's information criterion (AIC) to be the statistically most acceptable growth model.  相似文献   

14.
Commercial abalone growers and aquaculture researchers need to monitor and compare the growth rate of their stocks. Growth rates based on both length and weights are often calculated, but the process of disturbance for measurement will affect the results of most studies. In natural populations, constant (linear) growth in length has been supported, while logarithmic transformations for growth rates (length and weight) have been used for aquaculture studies. This study of growth of greenlip abalone (Haliotis laevigata, Leach) over a prolonged period (3 years) indicates that both data treatments are suitable. If weights are being used, then a growth model that allows for exponential growth, such as specific growth rate (SGR), must be used. If lengths are measured, then the calculation of simple differences in the lengths over time is sufficient. The apparent paradox in use of two forms of measure is comfortably rationalized as a result of the weight–length relationship and the von Bertalanffy relationship for this species. Thus, methods of minimal disturbance and stress, such as photographic estimation of length, could be used to accurately monitor growth trends in aquacultural studies as well as in industry.  相似文献   

15.
Multimodel frameworks are common in contemporary elasmobranch growth literature. These techniques offer a proposed improvement over individual growth functions by incorporating additional candidate models with alternative characteristics. Sigmoid functions (e.g. Gompertz and logistic) are a popular alternative to the commonly used von Bertalanffy growth function (VBGF) as they are hypothesized to better suit certain taxa based on body shape (such as batoids) or reproductive mode (such as egg‐layers). However, this hypothesis has never been tested. This study examined 74 elasmobranch multimodel growth studies by comparing the growth curves of their respective candidate models. Hypotheses regarding model performances were rejected as the VBGF was equally likely to fit best for all taxa and reproductive modes. Subsequently, no individual model was suited to be used a priori. Differences between candidate model fits were greatest at age zero with Gompertz and logistic functions providing estimates that were 15% and 23% larger on average than the VBGF, respectively. However, length‐at‐age estimates of the different models became negligible at older ages. Differences between candidate models were mostly small (≤5%), and the multimodel framework only marginally affected length‐at‐age estimates. However, there were cases where some candidate models provided inappropriate fits that contrasted considerably to the best fitting model. In some of these instances, a single‐model framework could have yielded biologically unrealistic growth estimates. Therefore, no study could pre‐empt whether or not it required a multimodel framework. A framework was subsequently recommended to maximize the accuracy of model fits for elasmobranch length‐at‐age estimates using multimodel approaches.  相似文献   

16.
This article models the growth of a population in aquaculture, including the phenomenon of size heterogeneity. Experimental observations of six initial densities (90, 130, 180, 230, 280 and 330 shrimps m−2) in an intensive culture of Penaeus vannamei in freshwater were used to fit a growth model. For this, three mathematical functions were analysed (Gompertz, von Bertalanffy and Pütter), which were modified in order to include the effect of initial density. Two models were constructed, one assuming the hypothesis of homogeneous individual growth and the other including size-heterogeneity throughout the culture cycle. For the second case, a stabilisation time was evaluated which defines the future heterogeneity of the cohort. In each initial density, the stabilisation phase was reached at approximately 2 g. However, the time taken for this phase to start increased with increasing initial culture density. The modified von Bertalannfy function was the most effective of the three equations in predicting growth. The weight predictions, assuming homogeneity and variability of sizes, presented low Percentage Root Mean Square Errors (PRMSE). However, the inclusion of size variability in the fit produced better statistical results than when they were not included (PRMSE decreased from 16% to 12%). This confirms the importance of taking into account size heterogeneity at an intensive level. Particularly at the technical level when the aquaculture producer is required to make stocking and harvest plans.  相似文献   

17.
The growth of 1-month-old juvenile sole, Solea senegalensis (Kaup, 1858), was monitored for 6 months in earthen ponds of commercial fish farms located at the Tagus and Sado Estuaries. The postlarvae were introduced into net cages at a density of 50 m−2. Data obtained from different growth experiments carried out under similar environmental conditions were analysed. To describe the growth of juvenile sole, the comprehensive model proposed by Schnute was fitted to the data. This model provides a better fit than, for instance, the Gompertz model, to the length at age of S. senegalensis juveniles. Seven-month-old sole juveniles have 80% probability of attaining a length of 10.9–11.7 cm and a weight between 11.0 and 13.7 g. The growth equation can be used to predict fish growth under these environmental conditions and thus identify appropriate farm management options.  相似文献   

18.
The life history of North American Atlantic salmon (Salmo salar) is characterized by extensive round‐trip migrations between freshwater rearing habitats and marine feeding grounds off the coasts of Canada and Greenland. Growth is rapid during the marine migration, and growth rate and condition factor may be indicators of salmon health during this period. Growth data were evaluated from a tag‐recovery program conducted from 1969 to 1991 using hatchery‐reared Atlantic salmon smolts released in the Penobscot River, Maine, U.S.A. Information from recaptures of 3167 salmon that were at large in the marine environment for 1 month to 3 yr was analyzed. Length–weight measurements coupled with time‐at‐large data were used to estimate von Bertalanffy and allometric growth parameters specific to the marine phase. Variations in growth and condition factor in relation to smolt age, release date, and temperature conditions in the northwest Atlantic were also examined. The von Bertalanffy k parameter declined with ordinal release date, indicating faster growth rates during the first year of smolts released earlier in the spring. The 2‐yr‐old smolts had a larger k than 1‐yr‐old smolts, although 1‐yr‐old smolts grew to a larger asymptotic size. Sea surface temperature had variable effects on growth parameters and condition factor, with temperature at the beginning of the migration and in overwintering habitat during the first year at sea having the greatest influence on length–weight relationships. Determining the mechanisms that influence growth of individuals during the marine phase will help elucidate the factors responsible for historic growth trends, establishing a baseline for current research.  相似文献   

19.
Biological and life-cycle information is essential to any fisheries management program. We have investigated temporal changes in growth parameters in the von Bertalanffy growth curve for green turtles, Chelonia mydas, in waters around the Ogasawara Islands. The variance model of individual variability of growth used in our study was one derived from the stochastic differential equation with the white noise of constant intensity. Maximum likelihood estimates of the parameters were made using the data of 102 recovery records of tagging experiments from 1974 to 1995. The estimations were carried out for each of two models of linear and sudden changes in the parameters, and the best model was selected using Akaike's information criterion. The selected model was that all of the parameters excepting asymptotic straight carapace length were linear functions of year and that the asymptotic length was constant over the years. The estimated values of the growth coefficient in 1974 and 1995 were 0.0317 and 0.192 per year, respectively, and the estimated value of the asymptotic straight carapace length was 97.2 cm. Implications of the results and future issues to be resolved in near future are discussed.  相似文献   

20.
A model for fish growth simulation based on the bioenergetic factorial approach is presented. This work presents a novel approach that extends the traditional bioenergetic model by explicitly including the Energy and Protein fluxes (EP model). This is a valuable feature that allows the dynamic simulation of fish proximate composition. For the aquaculture industry it represents a trade-off between detailed process simulation and feasibility of model implementation, namely regarding data gathering on an operational setting. The EP model is targeted to simulate fish production in commercial farms. Farm data for feed intake, feed composition (energy and protein content), temperature over time and the initial fish body weight are the only required data to run the model. Furthermore, apparent digestibility coefficient (ADC) values of the feed used in the farm must be known or else ADC values of feeds with similar composition can be used. The EP model implementation is illustrated for the gilthead seabream (Sparus aurata) based on published experimental data. The model was validated (r = 0.997, p < 0.05, n = 12) using a published experimental data set for gilthead seabream reared in a range of temperatures that reproduce the conditions in most countries producing this species. For the entire growth period (488 days) the estimated mean absolute error (MAE) is 8.8 g.fish−1 and the mean absolute percentage error (MAPE) is 8.3%. Simulation of fish growth in real operational conditions is evaluated with three datasets from a commercial farm that operates in earthen ponds with temperatures ranging between 12.6 °C and 24.8 °C. Overall the model outputs match well with the production data in the 3 batches. Initial weight ranged between 2.8 g and 3.7 g. The deviation between the data and simulated final weights is below 15 g, for a final weight around 435 g. The maximum absolute error is 21.1 g per fish (MAE) and in percentage 8.3% (MAPE).  相似文献   

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