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Journal articles on the topic 'Modèle de von Bertalanffy'

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Published: 4 June 2021
Last updated: 6 February 2022

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1

Balafrej, Mohammed, Abdelatif Sahnoun, and Mohamed Sadik. "Comparaison des modèles mathématiques non linéaires et détermination du modèle qui décrit au mieux la croissance de la race Sardi." Revue d’élevage et de médecine vétérinaire des pays tropicaux 73, no. 4 (2020): 255–61. http://dx.doi.org/10.19182/remvt.31945.

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L’objectif de cette étude a été d’identifier le modèle mathématique non linéaire le plus approprié pour décrire la courbe de croissance de la race Sardi. Cette étude a été menée sur un troupeau d’ovins élevé dans la station de sélection de Krakra située à El Borouj au Maroc. Les effectifs comprenaient 763 mâles et 649 femelles correspondant respectivement à 3814 et 3240 observations pour les âges types : naissance, 10 jours, 30 jours, 90 jours et poids adulte. Pour modéliser la relation entre le poids et l’âge, cinq modèles ont été ajustés aux données de croissance, à savoir Brody, Logistic, Gompertz, Von Bertalanffy et Richards. Les modèles de croissance ont été ajustés aux données par la méthode du maximum de vraisemblance. Le critère d’information d’Akaike (AIC), le critère d’information bayésien (BIC) et la déviance ont été utilisés pour comparer la pertinence statistique des différents modèles de croissance. Parmi ces modèles, celui de von Bertalanffy a eu les plus petites valeurs d’AIC, du BIC et de la déviance, indiquant que ce modèle permettait la représentation des données la meilleure pour les deux sexes de cette race. Les paramètres de cette fonction peuvent être utilisés pour définir de nouveaux critères de sélection et améliorer les prévisionsde production par une meilleure gestion de l’alimentation.
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2

Omotosho, B. O., M. N. Bemji, K. Bamisile, et al. "Comparative study of growth patterns of Kalahari Red goats and West African dwarf goats reared in Southwest Nigeria." Nigerian Journal of Animal Production 47, no. 5 (2020): 213–26. http://dx.doi.org/10.51791/njap.v47i5.1334.

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This study focused on comparing growth traits (body weights at birth, 3-month weaning and 6-month post-weaning) as well as growth curves of Kalahari Red (KR), a newly introduced goat breed in Nigeria and West African Dwarf (WAD) goat semi-intensively managed. Data on growth traits and weekly live weights were collected from 124 kids consisting of 61 KR and 63 WAD goats. The data were subjected to least squares analysis of variance to evaluate the effects of breed, sex, season, birth type and parity. The results showed that KR kids exceeded WAD kids in body weights at birth (2.30±0.06 kg vs 1.56±0.06 kg), 3-month weaning (8.88±0.57 kg vs 3.88±0.20 kg) and 6-month post-weaning (13.97±0.86 kg vs 5.05±0.37 kg). Corresponding pre-weaning average daily gain (ADG) estimates were 84.44±2.44 g and 31.73±1.16 g and post-weaning ADG were 61.88±1.81g and 24.84±1.21 g. Growth patterns of the two breeds were described using four different non-linear models: Brody, Gompertz, Logistic and Von Bertalanffy. Models were compared using parameter estimates (asymptotic weight 'A', integration constant 'B' and rate of maturity 'k'). Model with good fit was adjudged using coefficient of determination (R2) and residual mean squares (RMS). The KR goats had higher parameter estimates than WAD goats. Von Bertalanffy model had the highest 'A' estimates (24.24±0.94 kg vs 11.99±0.54 kg for KR and WAD goats). Gompertz had highest 'B' and 'k' estimates (5.37±0.20 vs 3.38±0.09) and (0.19±0.01 vs 0.13±0.01) for KR and WAD goats. All four growth models generally had R2 exceeding 99% and low RMS, hence giving good fit to the observed growth data. They can be used to implement feeding and management decisions that will optimize productivity. Information on superior growth performance of the Kalahari Red goat can be utilized to further investigate genetic improvement of the indigenous West African Dwarf population through crossbreeding. Cette étude s'est concentrée sur la comparaison des traits de croissance (poids corporel à la naissance, sevrage à 3 mois et 6 mois après le sevrage) ainsi que les courbes de croissance du Kalahari Red (KR), une race de chèvre nouvellement introduite au Nigéria et West AfricanDwarf (WAD) chèvre gérée de manière semi-intensive. Des données sur les traits de croissance et le poids vif hebdomadaire ont été collectées auprès de 124 chevreaux comprenant 61 chèvres KR et 63 chèvres WAD. Les données ont été soumises à une analyse des moindres carrés de la variance pour évaluer les effets de la race, du sexe, de la saison, du type de naissance et de la parité. Les résultats ont montré que les enfants KR dépassaient les enfants WAD en poids corporel à la naissance (2.30 ± 0.06 kg vs 1.56 ± 0.06 kg), au sevrage de 3 mois (8.88 ± 0.57 kg vs 3.88 ± 0.20 kg) et 6 mois après le sevrage (13.97 ± 0.86 kg contre 5.05 ± 0.37 kg). Les estimations correspondantes du gain quotidien moyen (ADG) présevrage étaient de 84.44 ± 2.44 g et 31.73 ± 1.16 g et l'ADG post-sevrage était de 61.88 ± 1.81 g et 24.84 ± 1.21 g. Les modèles de croissance des deux races ont été décrits à l'aide de quatre modèles non linéaires différents :Brody, Gompertz, Logistic et Von Bertalanffy. Les modèles ont été comparés à l'aide d'estimations de paramètres (poids asymptotique « A », constante d'intégration « B » et taux de maturité « k »). Le modèle avec un bon ajustement a été évalué en utilisant le coefficient de détermination (R2) et les carrés moyens résiduels (RMS). Les chèvres KR avaient des estimations de paramètres plus élevées que les chèvres WAD. Le modèle de Von Bertalanffy présentait les estimations « A » les plus élevées (24.24 ± 0.94 kg contre 11.99 ± 0.54 kg pour les chèvres KR et WAD). Gompertz avait les estimations « B » et « k » les plus élevées (5.37 ± 0.20 vs 3.38 ± 0.09) et (0.19 ± 0.01 vs 0.13 ± 0.01) pour les chèvres KR et WAD. Les quatre modèles de croissance avaient généralement un R2 supérieur à 99% et un RMS faible, ce qui correspondait bien aux données de croissance observées. Ils peuvent être utilisés pour mettre en œuvre des décisions d'alimentation et de gestion qui optimiseront la productivité. Les informations sur la performance de croissance supérieure de la chèvre rouge du Kalahari peuvent être utilisées pour étudier plus avant l'amélioration génétique de la population indigène de nains d'Afrique de l'Ouest par croisement.
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3

Claudia Cristina Paro de, Paz, Venturini Guilherme Costa, Contini Enio, Costa Ricardo Lopes Dias da, Lameirinha Luara Paula, and Quirino Celia Raquel. "Nonlinear models of Brazilian sheep in adjustment of growth curves." Czech Journal of Animal Science 63, No. 8 (2018): 331–38. http://dx.doi.org/10.17221/87/2017-cjas.

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Growth curves of the Morada Nova sheep males and females were described using nonlinear models and the relationships between body weight and thoracic circumference were evaluated. Altogether 1516 repeated measures of body weight and thoracic circumference of the Morada Nova sheep (668 males and 848 females) taken since birth till 730 days of age were used. The Brody, Richards, von Bertalanffy, Gompertz, and Logistic models have been tested. The Fisher’s test (F) was used to verify the differences (P &lt; 0.05) in growth curves between males and females. The Gompertz model presented a significant difference (P &lt; 0.001) for growth curve parameters between males (asymptotic weight (A) = 40.5 kg and maturing rate (k) = 0.0043 kg/day) and females (A = 36.44 kg and k = 0.0028 kg/day). The relationships between body weight and thoracic circumference presented R<sup>2</sup> above 0.7 and a high significance (P &lt; 0.0001) for all categories, showing that the thoracic circumference may be a good indicator of body weight. In addition, a significant effect (P &lt; 0.05) of the relationship between thoracic circumference and prediction of animal’s body weight was verified using the models of linear, quadratic, and cubic regression. Among the models studied, the Gompertz model presented the best fit and biological interpretation. Furthermore, the Gompertz model indicated the need to separate animals by sex in order to properly meet nutritional requirements and determine adequate slaughter age. Thoracic circumference can be used to predict animal body weight with a high accuracy.
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4

Cházaro-Olvera, Sergio, Manuel Ortiz, Ignacio Winfield, and Brizeida Viveros-Villaseñor. "Parámetros poblacionales de Nototropis minikoi y Ampithoe longimana (Crustacea: Amphipoda) en dos Islas del Mar Caribe mexicano." Revista de Biología Marina y Oceanografía 56, no. 1 (2021): 1. http://dx.doi.org/10.22370/rbmo.2021.56.1.2794.

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Se analizó la estructura de la población, el crecimiento, la fecundidad y la supervivencia de Nototropis minikoi y Ampithoe longimana en Isla Contoy e Isla Mujeres del caribe mexicano. Se midieron la temperatura, salinidad y oxígeno disuelto in situ. Se recolectaron un total de 2.815 anfípodos de ambas especies: 1.407 de Nototropis minikoi y 1.408 de Ampithoe longimana. La temperatura presentó valores de 26 a 27 °C, salinidad de 35 a 36 unidades y oxígeno disuelto de 6 a 9 mg L-1. Los juveniles representaron el mayor porcentaje con 55 a 73% en N. minikoi y del 57 a 67% en A. longimana. Con el método de Bhattacharya se encontraron de 4 a 5 clases modales. Con el modelo de von Bertalanffy se encontró que las hembras presentaron la mayor longitud máxima con 10,88 mm (k= 0,35) y 14,54 mm (k= 0,24) en N. minikoi y A. longimana, respectivamente. El promedio de huevos fue de 6,83 ± 4,50 a 8,55 ± 5,22 en N. minikoi y 7,55 ± 4,82 a 8,33 ± 3,79 en A. longimana. La supervivencia fue de 13,70 y 36,63% para N. minikoi y de 13,31 y 28,11% para A. longimana, lo cual corresponde a especies con estrategia “r”. Los resultados evidenciaron una relación costo-beneficio entre los parámetros poblacionales, dado que a una tasa de crecimiento lenta y un mayor número de clases modales se alcanzan tamaños máximos mayores.
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5

Tirtadanu, Tirtadanu, and Umi Chodrijah. "PARAMETER POPULASI DAN TINGKAT PEMANFAATAN KEPITING BAKAU (Scylla serrata Forsskal, 1775) DI PERAIRAN SEBATIK, KALIMANTAN UTARA." Jurnal Penelitian Perikanan Indonesia 24, no. 3 (2018): 187. http://dx.doi.org/10.15578/jppi.24.3.2018.187-196.

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Salah satu informasi yang diperlukan untuk merumuskan pengelolaan kepiting bakau (Scylla serrata Forsskal, 1775) yang berkelanjutan adalah parameter populasi dan tingkat pemanfaatannya. Penelitian ini bertujuan untuk mengkaji parameter populasi dan tingkat pemanfaatan kepiting bakau di perairan Sebatik. Penelitian dilakukan pada Maret-Desember 2017. Sampel kepiting bakau di peroleh dari hasil tangkapan nelayan dengan alat tangkap bubu di perairan Sebatik. Pertumbuhan dianalisis berdasarkan persamaan Von Bertalanffy dengan mengamati pergeseran struktur ukuran kepiting tiap bulan dan tingkat pemanfaatan diperoleh dari metode kurva konversi panjang dengan hasil tangkapan. Hasil penelitian menunjukkan kepiting bakau yang tertangkap bubu di perairan Sebatik berukuran lebar karapas (carapace width) antara 84-144 mmCW dengan rata-rata ukuran yang tertangkap adalah 107,05±12,3 mmCW pada kepiting jantan dan 110,2±8,86 mmCW pada kepiting betina. Pertumbuhan berat kepiting bakau jantan lebih cepat dibandingkan ukurannya (b=3,6) sebaliknya pertumbuhan berat kepiting bakau betina lebih lambat dibandingkan ukurannya (b=2,5). Nisbah kelamin kepiting bakau menunjukkan kondisi tidak seimbang (5,5 : 1) dengan proporsi jantan lebih dominan dibandingkan betina. Lebar karapas asimptotik (CW) kepiting bakau jantan adalah 151,2 mmCW dan betina adalah 140,5 mmCW. Laju pertumbuhan (K) kepiting bakau adalah 0,75 tahun-1 pada kepiting jantan dan 0,79 tahun-1 pada kepiting betina. Status pemanfaatan kepiting bakau telah berada dalam tahapan mendekati lebih tangkap (E=0,5-0,55) sehingga disarankan tidak melakukan penambahan upaya penangkapan kepiting bakau di perairan Sebatik. One of the information needed for formulating the sustainable management of mud crab is the availability of information on the population parameters and its exploitation rate. The current research aimed to study the population parameters and the exploitation rate of mud crab in Sebatik Waters. Field research was conducted in March – December 2017. Samples of mud crab were obtained from the catch of fisherman by trap in Sebatik Waters. The Von Bertalanffy growth parameters were constructed through monthly modals progression analysis of the size of carapace width frequencies distributions and the exploitation rate was estimated through the method of length converted catch curve. The results showed that the carapace width of mud crabs caught by trap in Sebatik Waters ranged between 84 to 144 mmCW with the mean size of 107.05±12.3 mmCW for male and 110.2±8.86 mmCW for female. The growth of weights of male crab (b=3.6) is faster than its size, while the growth of weight of female crab was slower than its size (b=2,5). The sex ratio of mud crab was unbalanced (5.5 : 1) that the proportion of male was more dominant than female. Asymptotic carapace width (CW) of mud crab was 151.2 mmCW for male and 140.5 mmCW for female. The growth rate (K) of mud crab was 0.75 year-1 for male and 0.79 year-1 for female. The exploitation status of mud crab was starting to overfishing (E=0,5-0,55) so it suggest to not increase the fishing effort of mud crab fishery in Sebatik Waters.
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6

Chroust, Gerhard, and Wolfgang Hofkirchner. "Ludwig von Bertalanffy returns home." Systems Research and Behavioral Science 23, no. 5 (2006): 701–3. http://dx.doi.org/10.1002/sres.794.

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7

Martyushev, L. M. "Ontogenetic growth: Schmalhausen or von Bertalanffy?" Physics of Life Reviews 10, no. 3 (2013): 389–90. http://dx.doi.org/10.1016/j.plrev.2013.06.001.

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8

Diniz, Carlos Alberto Ribeiro, Francisco Louzada-Neto, and Lia Hanna Martins Morita. "The multiplicative heteroscedastic Von Bertalanffy model." Brazilian Journal of Probability and Statistics 26, no. 1 (2012): 71–81. http://dx.doi.org/10.1214/10-bjps120.

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9

Kimura, Daniel K. "Extending the von Bertalanffy growth model using explanatory variables." Canadian Journal of Fisheries and Aquatic Sciences 65, no. 9 (2008): 1879–91. http://dx.doi.org/10.1139/f08-091.

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von Bertalanffy parameters are usually estimated for a species, perhaps by sex, in some well-defined geographical area. An alternative way to estimate von Bertalanffy parameters is to model them in a general fixed-effects nonlinear model. For this model, the length of the ith individual is modeled as yi = f(φ, ti, xi) + εi, where yi is the length and ti is the age of the ith specimen at the time of sampling, φ are the unknown parameters required to model von Bertalanffy growth, and xi are covariates associated with the ith specimen that minimally contain sex information (xi1), but may also contain additional covariates. Standard nonlinear least squares and associated likelihood methods can be used to estimate parameters for this model. For Pacific ocean perch ( Sebastes alutus ), we model the effect that depth of collection has on estimated von Bertalanffy growth parameters; for sablefish ( Anoplopoma fimbria ), we model the effects due to latitude of collection; and for walleye pollock ( Theragra chalcogramma ) in the eastern Bering Sea, we model the effects due to variations in year classes. Results illustrate how modeling von Bertalanffy growth parameters directly using explanatory variables can be used to describe how growth relates to geographic, environmental, or biological factors.
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10

Hearn, William S., and George M. Leigh. "Comparing Polynomial and von Bertalanffy Growth Functions for Fitting Tag–Recapture Data." Canadian Journal of Fisheries and Aquatic Sciences 51, no. 8 (1994): 1689–91. http://dx.doi.org/10.1139/f94-169.

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The properties of polynomial and von Bertalanffy growth functions are compared for analysing data from tag–recapture experiments in which fish are recaptured once. For the quadratic and von Bertalanffy growth functions, explicit formulae are obtained for the expected growth increment in terms of length-at-release, time-at-liberty, and the function parameters. If the least-squares fitting technique is used the von Bertalanffy function fits tag–recapture data with no more bias (probably less) than any other growth function, including polynomial growth functions. A bias-reduction technique for fitting the von Bertalanffy growth function to tag–recapture data is not applicable to other growth functions. We conclude that, apart from the straight line, the von Bertalanffy growth function is the one with the most desirable mathematical and statistical properties for fitting to tag–recapture data. The matter of the function that best characterises the way a specific fish species grows can be adequately addressed only by analyses of multiple measurements of individual fish.
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11

Hofkirchner, Wolfgang. "Social relations: Building on Ludwig von Bertalanffy." Systems Research and Behavioral Science 36, no. 3 (2019): 263–73. http://dx.doi.org/10.1002/sres.2594.

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12

Rodriguez, Jorge, Luis H. Romero N, and Ana María Sanabria R. "Solución Numérica de la Ecuación Diferencial de Von Bertalanffy." Revista de Ciencias 10 (November 8, 2011): 91–96. http://dx.doi.org/10.25100/rc.v10i0.599.

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13

Maino, James L., and Michael R. Kearney. "The universality of the von Bertalanffy growth curve." Physics of Life Reviews 20 (March 2017): 63–65. http://dx.doi.org/10.1016/j.plrev.2017.01.010.

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14

Prajneshu and R. Venugopalan. "von Bertalanffy growth model in a random environment." Canadian Journal of Fisheries and Aquatic Sciences 56, no. 6 (1999): 1026–30. http://dx.doi.org/10.1139/f99-035.

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The well-known von Bertalanffy growth model for describing age-length relationship is formulated in a randomly fluctuating environment. The fluctuations in the system are assumed to be described by a Gaussian white noise stochastic process. The resulting model, in terms of a stochastic differential equation, is solved analytically. It is shown that the probability density function of length of a fish is a Gaussian stochastic process. Finally, as an illustration, the methodology is applied to a set of pearl oyster (Pinctada fucata (Gould)) data.
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15

Chambers, Mark S., Leesa A. Sidhu, Ben O’Neill, and Nokuthaba Sibanda. "Flexible von Bertalanffy growth models incorporating Bayesian splines." Ecological Modelling 355 (July 2017): 1–11. http://dx.doi.org/10.1016/j.ecolmodel.2017.03.026.

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16

Lipinski, M. R., and M. A. Roeleveld. "Minor extension of the von Bertalanffy growth theory." Fisheries Research 9, no. 4 (1990): 367–71. http://dx.doi.org/10.1016/0165-7836(90)90054-y.

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17

Wang, You-Gan, Mervyn R. Thomas, and Ian F. Somers. "A maximum likelihood approach for estimating growth from tag–recapture data." Canadian Journal of Fisheries and Aquatic Sciences 52, no. 2 (1995): 252–59. http://dx.doi.org/10.1139/f95-025.

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The Fabens method is commonly used to estimate growth parameters k and l∞ in the von Bertalanffy model from tag–recapture data. However, the Fabens method of estimation has an inherent bias when individual growth is variable. This paper presents an asymptotically unbiassed method using a maximum likelihood approach that takes account of individual variability in both maximum length and age-at-tagging. It is assumed that each individual's growth follows a von Bertalanffy curve with its own maximum length and age-at-tagging. The parameter k is assumed to be a constant to ensure that the mean growth follows a von Bertalanffy curve and to avoid overparameterization. Our method also makes more efficient use of the measurements at tag and recapture and includes diagnostic techniques for checking distributional assumptions. The method is reasonably robust and performs better than the Fabens method when individual growth differs from the von Bertalanffy relationship. When measurement error is negligible, the estimation involves maximizing the profile likelihood of one parameter only. The method is applied to tag–recapture data for the grooved tiger prawn (Penaeus semisulcatus) from the Gulf of Carpentaria, Australia.
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18

Cerrato, Robert M. "Interpretable Statistical Tests for Growth Comparisons using Parameters in the von Bertalanffy Equation." Canadian Journal of Fisheries and Aquatic Sciences 47, no. 7 (1990): 1416–26. http://dx.doi.org/10.1139/f90-160.

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Likelihood ratio, t-, univariate χ2-, and T2-tests have been proposed to compare von Bertalanffy parameters among stocks. As commonly applied, all of these tests are approximate, with the accuracy of each dependent on the nonlinearity of the von Bertalanffy equation, sample size, and if present, the degree of heterogeneity in the error variances. An empirical comparison of these procedures shows that the likelihood ratio test often differs in outcome from the others. Analysis of the conflicting cases by confidence region comparisons and Monte Carlo simulations almost always resolved the outcome in favor of the likelihood ratio test. The parameter effects component of nonlinearity was found to be the principal factor biasing the t-, univariate χ2-, and T2-tests. Reparameterizations of the von Bertalanffy equation substantially reduced, but did not completely eliminate, conflicting outcomes. It is concluded that the likelihood ratio test is the most accurate of the procedures considered in this study, and whenever possible, it should be the approach of choice.
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Garnero, A. Del V., C. R. Marcondes, L. A. F. Bezerra, H. N. Oliveira, and R. B. Lôbo. "Parâmetros genéticos da taxa de maturação e do peso assintótico de fêmeas da raça Nelore." Arquivo Brasileiro de Medicina Veterinária e Zootecnia 57, no. 5 (2005): 652–62. http://dx.doi.org/10.1590/s0102-09352005000500011.

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Utilizaram-se 14.563 pesagens de 1158 fêmeas da raça Nelore, nascidas entre 1984 e 1995, pertencentes a 10 fazendas, distribuídas em sete estados do Brasil. Com o objetivo de estabelecer um padrão médio de crescimento, obter parâmetros individuais das curvas e estimar os componentes de variância, herdabilidade e correlações genéticas dos parâmetros das curvas, foram comparados os modelos de Von Bertalanffy, Brody, logístico e Gompertz. Foram utilizados o procedimento NLIN e o programa MTDFREML sob modelo animal em análise unicaráter e bicaráter. Os parâmetros médios dos pesos assintóticos (A) e das taxas de maturidade (K) foram: 515,06 e 0,071 para Von Bertalanffy; 552,77 e 0,045 para Brody; 501,11 e 0,097 para logístico, e 507,00 e 0,083 para Gompertz, respectivamente. As estimativas de herdabilidade para A e K foram de alta magnitude: 0,39 e 0,42 para Von Bertalanffy, 0,42 e 0,44 para Brody, 0,40 e 0,41 para logístico e 0,39 e 0,39 para Gompertz, respectivamente. As correlações genéticas variaram entre -0,69 e -0,49. Todos os modelos foram adequados para descrever o crescimento. A ordem de escolha do melhor modelo para descrever a curva de crescimento foi: Brody, Von Bertalanffy, logístico e Gompertz. Essas características seriam passíveis de inclusão em índice de seleção para seleção de fêmeas Nelore.
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Renner-Martin, Katharina, Norbert Brunner, Manfred Kühleitner, Werner Georg Nowak, and Klaus Scheicher. "On the exponent in the Von Bertalanffy growth model." PeerJ 6 (January 4, 2018): e4205. http://dx.doi.org/10.7717/peerj.4205.

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Von Bertalanffy proposed the differential equation m′(t) = p × m(t)a − q × m(t) for the description of the mass growth of animals as a function m(t) of time t. He suggested that the solution using the metabolic scaling exponent a = 2/3 (Von Bertalanffy growth function VBGF) would be universal for vertebrates. Several authors questioned universality, as for certain species other models would provide a better fit. This paper reconsiders this question. Based on 60 data sets from literature (37 about fish and 23 about non-fish species) it optimizes the model parameters, in particular the exponent 0 ≤ a < 1, so that the model curve achieves the best fit to the data. The main observation of the paper is the large variability in the exponent, which can vary over a very large range without affecting the fit to the data significantly, when the other parameters are also optimized. The paper explains this by differences in the data quality: variability is low for data from highly controlled experiments and high for natural data. Other deficiencies were biologically meaningless optimal parameter values or optimal parameter values attained on the boundary of the parameter region (indicating the possible need for a different model). Only 11 of the 60 data sets were free of such deficiencies and for them no universal exponent could be discerned.
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Lv, Qiming, and Jonathan W. Pitchford. "Stochastic von Bertalanffy models, with applications to fish recruitment." Journal of Theoretical Biology 244, no. 4 (2007): 640–55. http://dx.doi.org/10.1016/j.jtbi.2006.09.009.

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22

Varona, L., C. Moreno, L. A. Garcia Cortes, G. Yague, and J. Altarriba. "Two-step versus joint analysis of Von Bertalanffy function." Journal of Animal Breeding and Genetics 116, no. 5 (1999): 331–38. http://dx.doi.org/10.1046/j.1439-0388.1999.00220.x.

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23

Bello, Rafael E. "The systems approach ? A. Bogdanov and L. von Bertalanffy." Studies in Soviet Thought 30, no. 2 (1985): 131–47. http://dx.doi.org/10.1007/bf01043756.

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24

Rodríguez B., Carlos Julio, and Jorge Rodríguez B. "A Growth Functional Equation." Revista de Ciencias 8 (November 8, 2011): 111–14. http://dx.doi.org/10.25100/rc.v8i0.617.

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25

Lumingas, L. J. L., and M. Guillou. "Growth zones and back-calculation for the sea urchin, Sphaerechinus granularis, from the Bay of Brest, France." Journal of the Marine Biological Association of the United Kingdom 74, no. 3 (1994): 671–86. http://dx.doi.org/10.1017/s0025315400047731.

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A procedure for accurately determining age and growth of the sea urchin Sphaerechinus granularis (Lamarck) (Echinodermata: Echinoidea) in the Bay of Brest (France) is described. Readings of growth lines were made from the longitudinal cross-section of interambulacral oral plates of sea urchins collected in February 1993. These results agree with age estimates calculated using the ELEFAN I programme based on diameter-frequency distributions of sea urchins collected from February 1992 to March 1993. A non-linear regression (monomolecular equation) best describes the relationship between test diameter and plate thickness. The diameter-at-age data can be increased by back-calculation, assuming a constant proportional deviation from the mean size of the test. Although von Bertalanffy growth curves fitted to actual observations were similar to those fitted to back-calculated diameter-at-age data, the latter produced a more adequate curve and increased the quality of the growth parameter estimators. The von Bertalanffy growth curve estimated by ELEFAN I shows a pattern similar to the back-calculated von Bertalanffy growth curve.
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26

Araújo, Ronyere Olegário de, Cintia Righetti Marcondes, Maria Cecília Florisbal Damé, et al. "Classical nonlinear models to describe the growth curve for Murrah buffalo breed." Ciência Rural 42, no. 3 (2012): 520–25. http://dx.doi.org/10.1590/s0103-84782012000300022.

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With the objective of to adjust nonlinear models for the growth curves for a buffaloes herd raised in floodable lands in Rio Grande do Sul state, monthly records measured from birth to two years-old of 64 males and 63 females born between 1982 and 1989 were used. The models used were: Von Bertalanffy, Brody, Gompertz and Logistic. The parameters were estimated by NLIN procedure and the criteria used to evaluate the adjustment given by the models were: asymptotic standard deviation; coefficient of determination; average absolute deviation of residues and asymptotic index. Von Bertalanffy and Brody models overestimated the male asymptotic weight (A) in 15.9 and 171.3kg, respectively, and the Gompertz and Logistic models underestimated it in 4.5 and 13.4kg, respectively. For females, the Logistic model underestimated the asymptotic weight (-2.09kg), and Gompertz, Von Bertalanffy and Brody overestimated this parameter in 8.04, 17.7, and 280.33kg, respectively. The biggest average deviation was estimated by Brody model for both sexes, characterizing the biggest index. Considering the criteria, it is recommended the Gompertz and Logistic models for adjust females and males Murrah buffaloes breed growth curves.
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27

James, Ian R. "Estimation of von Bertalanffy Growth Curve Parameters from Recapture Data." Biometrics 47, no. 4 (1991): 1519. http://dx.doi.org/10.2307/2532403.

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28

Wang, Yoy-Gan, and Mervyn R. Thomas. "Accounting for individual variability in the von Bertalanffy growth model." Canadian Journal of Fisheries and Aquatic Sciences 52, no. 7 (1995): 1368–75. http://dx.doi.org/10.1139/f95-132.

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Estimation of von Bertalanffy growth parameters has received considerable attention in fisheries research. Since Sainsbury (1980, Can. J. Fish. Aquat. Sci. 37: 241–247) much of this research effort has centered on accounting for individual variability in the growth parameters. In this paper we demonstrate that, in analysis of tagging data, Sainsbury's method and its derivatives do not, in general, satisfactorily account for individual variability in growth, leading to inconsistent parameter estimates (the bias does not tend to zero as sample size increases to infinity). The bias arises because these methods do not use appropriate conditional expectations as a basis for estimation. This bias is found to be similar to that of the Fabens method. Such methods would be appropriate only under the assumption that the individual growth parameters that generate the growth increment were independent of the growth parameters that generated the initial length. However, such an assumption would be unrealistic. The results are derived analytically, and illustrated with a simulation study. Until techniques that take full account of the appropriate conditioning have been developed, the effect of individual variability on growth has yet to be fully understood.
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29

Tibaldeo, Roberto Franzini. "Hans Jonas’ ‘Gnosticism and Modern Nihilism’, and Ludwig von Bertalanffy." Philosophy & Social Criticism 38, no. 3 (2012): 289–311. http://dx.doi.org/10.1177/0191453710389451.

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‘Gnosticism and Modern Nihilism’ (published in Social Research, 1952) is indeed one of Hans Jonas’ most famous essays, to which its author reserved very deep attention during his philosophical career. As a former pupil of Martin Heidegger and Rudolf Bultmann, Jonas started to deal with religious topics, and specifically with Gnosticism, from the very outset of his philosophical career in the 1920s. After gaining recognition thanks to his remarkable philosophical-existential interpretation of Gnosticism, he returned to the modern age and its philosophical characters. Principally, Jonas discovered that modern philosophy up to Heidegger and Sartre suffered from a peculiar spiritual disease – namely, nihilism – that he had already traced in ancient Gnosticism and that he intended to reject. Therefore, Jonas’ acquaintance with ancient religion and thinking gave him a deep insight into the modern age and provided him with a first glimpse of what was later to become his biological philosophy. However, whoever could imagine that the idea of tracing similarities between Gnosticism and modern thinking came to Jonas at the beginning of 1950 from the famous philosopher and biologist Ludwig von Bertalanffy? In this article, I shall endeavour to demonstrate this thesis by quoting from unpublished documents. However, I shall also try to prove that Jonas did not follow von Bertalanffy’s advice completely. The overall aim is, therefore, both to highlight the origins of an essential turning point in the thinking of Hans Jonas, and, on such a basis, to outline the innovation and originality of his philosophical contribution.
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Ghosh, Himadri, and Prajneshu. "von Bertalanffy stochastic differential equation growth model with multiplicative noise." Journal of Statistics and Management Systems 21, no. 8 (2018): 1407–17. http://dx.doi.org/10.1080/09720510.2018.1467644.

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31

Pouvreau, David. "The project of “general systemology” instigated by Ludwig von Bertalanffy." Kybernetes 42, no. 6 (2013): 851–68. http://dx.doi.org/10.1108/k-05-2013-0090.

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De Oliveira, Márcia Ferreira Cardoso, and Maria Hermínia De Paula Leite Mello. "EQUAÇÃO DE VON BERTALANFFY APLICADA AO CRESCIMENTO DE FRANGO COLONIAL." Cadernos do IME - Série Matemática, no. 13 (December 16, 2019): 107–19. http://dx.doi.org/10.12957/cadmat.2019.47283.

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A equação diferencial chamada de Equação de Von Bertalanffy é utilizada como modelo matemático para descrever o crescimento do frango colonial. A partir de dados estatísticos, verificar-se a adequação do modelo matemático para obtenção de dados relativos ao crescimento do frango colonial, visando a determinação da melhor época para o abate da ave.
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33

Kühleitner, Manfred, Norbert Brunner, Werner-Georg Nowak, Katharina Renner-Martin, and Klaus Scheicher. "Best-fitting growth curves of the von Bertalanffy-Pütter type." Poultry Science 98, no. 9 (2019): 3587–92. http://dx.doi.org/10.3382/ps/pez122.

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34

Edwards, Maureen P., and Robert S. Anderssen. "Symmetries and solutions of the non-autonomous von Bertalanffy equation." Communications in Nonlinear Science and Numerical Simulation 22, no. 1-3 (2015): 1062–67. http://dx.doi.org/10.1016/j.cnsns.2014.08.033.

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35

Temming, Axel, and Jens P. Herrmann. "A generic model to estimate food consumption: linking von Bertalanffy’s growth model with Beverton and Holt’s and Ivlev’s concepts of net conversion efficiency." Canadian Journal of Fisheries and Aquatic Sciences 66, no. 4 (2009): 683–700. http://dx.doi.org/10.1139/f09-028.

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In this paper, a mathematical derivation is presented that links von Bertalanffy’s growth model with the concept of net conversion efficiency of Beverton and Holt, aiming at the development of an equation that can calculate food consumption rates of wild populations from parameters of the von Bertalanffy growth equation and an estimate of the net food conversion efficiency of Beverton and Holt. The derivation is based on Pauly’s version of the generalized von Bertalanffy equation, which allows the allometric exponent of the anabolism term to differ from 2/3, as in the standard von Bertalanffy equation. As a side product, a general model is formulated that describes the gross growth conversion efficiency (K1 of Ivlev) as a function of weight of the organism. The new equations for the estimation of food consumption are applied in two case studies, North Sea cod ( Gadus morhua ) and whiting ( Merlangius merlangus ), for which a variety of consumption estimates is available from conventional gastric evacuation-based methods. The new method produces results that show a similar degree of variability as was observed in various applications of the gastric evacuation method.
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36

Romuald Sonan Assi, Awa Traoré, Martin Kouamé Kouamé, Innocent Allepo Abe, and Mathurin Koffi. "Growth parameters of Brycinus longipinnis (Günther, 1864) from the Aghien Lagoon (South East of Côte D’ivoire)." World Journal of Advanced Research and Reviews 11, no. 1 (2021): 113–19. http://dx.doi.org/10.30574/wjarr.2021.11.1.0324.

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The growth of Brycinus longipinnis caught at Aghien Lagoon was studied between June 2014 and May 2015 through growth type, condition factor and growth parameters according to the Von Bertalanffy model. Sampling was conducted using experimental fisheries. Growth type was determined from the length-weight relationship and growth parameters according to the Von Bertalanffy model from the FiSAT software. The growth was of negative allometric type (b = 2.59). The Brycinus longipinnis population grows faster towards the asymptotic length ((L∞ = 92.40 mm SL) with a growth coefficient K of 0.36 year-1. It is also a long-lived fish species with maximum longevity (tmax) of 8.32 years.
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FERNANDES, Felipe Augusto, Édipo Menezes SILVA, Kelly Pereira LIMA, Sérgio Alberto JANE, Tales Jesus FERNANDES, and Joel Augusto MUNIZ. "PARAMETERIZATIONS OF THE VON BERTALANFFY MODEL FOR DESCRIPTION OF GROWTH CURVES." REVISTA BRASILEIRA DE BIOMETRIA 38, no. 3 (2020): 369. http://dx.doi.org/10.28951/rbb.v38i3.457.

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The growth curves of animals, in general, have an “S” shape, also known as sigmoidal curves. This type of curve is well fitted by nonlinear regression models, including von Bertalanffy’s model, which has been widely applied in several areas, being presented in literature through different parameterizations, which in practice, can complicate its understanding, affect nonlinearity measures and inferences about parameters. To quantify the nonlinearity present in a Bates and Watts model, a geometric concept of curvature has been used. The aim of this work was to analytically develop three parameterizations of the von Bertalanffy’s nonlinear model referring to its nonlinearity, implications for inferences and to establish relationships between parameters in the different ways of expressing the models. These parameterizations were adjusted to the growth data of sheep. For each parameterization, the intrinsic and parametric curvature measurements described by Bates and Watts were calculated. The parameterization choice affects nonlinearity measures, consequently, influences the reliability and inferences about estimated parameters. The forms most used in literature showed the greatest deviations from linearity, showing the importance of analyzing these measures in any growth curve study. Parameterization should be used in which the b estimate represents the abscissa of the inflection point, as it presents minor linearity deviations and direct biological interpretation for all parameters.
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38

Shelton, Andrew O., and Marc Mangel. "Estimating von Bertalanffy parameters with individual and environmental variations in growth." Journal of Biological Dynamics 6, sup2 (2012): 3–30. http://dx.doi.org/10.1080/17513758.2012.697195.

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39

Shi, Pei-Jian, Tetsuroh Ishikawa, Hardev S. Sandhu, et al. "On the 3/4-exponent von Bertalanffy equation for ontogenetic growth." Ecological Modelling 276 (March 2014): 23–28. http://dx.doi.org/10.1016/j.ecolmodel.2013.12.020.

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40

Ratkowsky, D. A. "Statistical Properties of Alternative Parameterizations of the von Bertalanffy Growth Curve." Canadian Journal of Fisheries and Aquatic Sciences 43, no. 4 (1986): 742–47. http://dx.doi.org/10.1139/f86-091.

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The von Bertalanffy growth curve is often used in fisheries research to describe the relationship between the weight or length of a fish and its age. The equation is also encountered in various other branches of science and applied science in a variety of different parameterizations and names; for example, it is also known as the asymptotic regression equation or the three-parameter exponential equation. Since these equations are all nonlinear regression models, the properties of the least squares estimators of the parameters of these models may be very different from their large-sample properties, where the estimators are unbiased, have the minimum attainable variance, and are normally distributed, the conditions that pertain in a linear model. Different parameterizations will have estimators which approximate the asymptotic properties to varying degrees of closeness. My study of eight parameterizations shows that one of them, a generalization which allows unequal age increments of a parameterization proposed by Schnute and Fournier, is far superior to any of the other models, which include the most commonly used parameterization, in that it exhibits close-to-linear behavior. Two of the three parameters in this model represent the expected mean lengths corresponding to the youngest and oldest ages, respectively, in the sample, and thus have a ready biological interpretation. I discuss why it is important to have a close-to-linear model when one wishes to make comparisons between two or more data sets. Methodology is briefly described for carrying out such comparisons, and some further remarks are made about why biologists should be concerned about the statistical properties of the models that they use. Although most data sets I used for illustration are obtained from marine animals, the conclusions are general and apply to all disciplines which make use of the von Bertalanffy model in whichever guise or form it appears.
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41

Oyamakin, S. O., and A. U. Chukwu. "Statistical analysis of an alternative von Bertalanffy model for tree growth." Journal of Coupled Systems and Multiscale Dynamics 2, no. 3 (2014): 157–63. http://dx.doi.org/10.1166/jcsmd.2014.1049.

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42

Stamatopoulos, C., and J. F. Caddy. "Estimation of von Bertalanffy growth parameters: A versatile linear regression approach." ICES Journal of Marine Science 45, no. 2 (1989): 200–208. http://dx.doi.org/10.1093/icesjms/45.2.200.

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43

McGarvey, Richard, and John E. Feenstra. "Estimating length-transition probabilities as polynomial functions of premoult length." Marine and Freshwater Research 52, no. 8 (2001): 1517. http://dx.doi.org/10.1071/mf01172.

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In length-based lobster stock-assessment models where the population is subdivided into discrete length classes, growth is represented as a matrix of length-transition probabilities. At specific times during the model year, the length-transition probabilities specify the proportions growing into larger length classes. These probabilities are calculated by integration of gamma or normal distributions over the length intervals of each larger length class. The mean growth from any given length category is commonly modelled by a von Bertalanffy or other continuous growth curve. The coefficients of variation, describing variance among individuals, are modelled by functions constant or linear with length. These approaches have yielded good descriptions of growth for males and juveniles, but the von Bertalanffy curve does not capture the rapid decrease in mean growth rate after maturity for females. We generalized this length-transition model by writing the parameters of the growth distributions as polynomial functions of carapace length. This generalization procedure increases the number of parameters depending on the degree of polynomial employed. In fits to South Australian rock lobster (Jasus edwardsii) tagrecovery data, each increase in polynomial degree yielded a significantly better fit for females and successfully represented the decrease in growth at maturity. For males, the von Bertalanffy description was little improved by higher polynomials.
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He, Ji X., and Donald J. Stewart. "A stage-explicit expression of the von Bertalanffy growth model for understanding age at first reproduction of Great Lakes fishes." Canadian Journal of Fisheries and Aquatic Sciences 59, no. 2 (2002): 250–61. http://dx.doi.org/10.1139/f02-008.

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An initial annual growth rate of body length and its regular decrease with increasing age has general linkages with age at first reproduction (tR). We clarify their combinations and develop predictive functions. We use a complete Ford–Walford plot with yearling size (L1) on the y axis and show a slope transition between the relative yearling growth rate (ρy) and the Ford–Walford slope (ρ). The three stage-specific variables define a complete body-length trajectory over ages, including all von Bertalanffy growth parameters and the Ford–Walford intercept (Lint). The difference between asymptotic length (Linf) and yearling length is growth potential after the first annulus. Yearling growth is a transition period, so growth potential can be adjusted as ρLinf or Linf – Lint. Changes in the three life-stage variables have contrasting effects on growth potential and von Bertalanffy growth parameters, so they have contrasting relations with tR. For most invertebrate-eating fishes in the Laurentian Great Lakes, dominant changes in growth trajectories were reflected in ρ, so tR was predicted by the von Bertalanffy growth coefficient, K. For walleye (Stizostedion vitreum) populations around the Great Lakes, dominant changes in growth trajectories were from yearling size or yearling growth, so tR was predicted using Lint. Our results have clear implications for understanding fish population dynamics.
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45

Farrell, Edward D., Stefano Mariani, and Maurice W. Clarke. "Age and growth estimates for the starry smoothhound (Mustelus asterias) in the Northeast Atlantic Ocean." ICES Journal of Marine Science 67, no. 5 (2010): 931–39. http://dx.doi.org/10.1093/icesjms/fsp295.

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Abstract Farrell, E. D., Mariani, S., and Clarke, M. W. 2010. Age and growth estimates for the starry smoothhound (Mustelus asterias) in the Northeast Atlantic Ocean. – ICES Journal of Marine Science, 67: 931–939. Age, growth, and longevity were estimated for the starry smoothhound (Mustelus asterias), based on the interpretation of sectioned vertebrae of 106 males (35–104 cm stretch total length, STL) and 114 females (44–112 cm STL). Growth curves were fitted to length-at-age data using von Bertalanffy and Gompertz models. The three-parameter von Bertalanffy growth function (VBGF) provided the best statistical fit to the male data (L∞ = 103.7 cm STL, L0 = 38.1 cm STL, k = 0.195 year−1). The Gompertz growth function provided the best statistical fit to the female data, although the estimated parameters were biologically unreasonable. Therefore, the three-parameter VBGF was also accepted for females (L∞ = 123.5 cm STL, L0 = 34.9 cm STL, k = 0.146 year−1). Longevity was estimated to be 13 and 18.3 years for males and females, respectively. The length–weight relationship is also presented for 304 male and 424 female M. asterias. The von Bertalanffy model was fitted to the weight-at-age data. These estimates can form the basis of future work on the assessment and management of this species.
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Renner-Martin, Katharina, Norbert Brunner, Manfred Kühleitner, Werner-Georg Nowak, and Klaus Scheicher. "Optimal and near-optimal exponent-pairs for the Bertalanffy-Pütter growth model." PeerJ 6 (November 23, 2018): e5973. http://dx.doi.org/10.7717/peerj.5973.

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The Bertalanffy–Pütter growth model describes mass m at age t by means of the differential equation dm/dt = p * ma − q * mb. The special case using the von Bertalanffy exponent-pair a = 2/3 and b = 1 is most common (it corresponds to the von Bertalanffy growth function VBGF for length in fishery literature). Fitting VBGF to size-at-age data requires the optimization of three model parameters (the constants p, q, and an initial value for the differential equation). For the general Bertalanffy–Pütter model, two more model parameters are optimized (the pair a < b of non-negative exponents). While this reduces bias in growth estimates, it increases model complexity and more advanced optimization methods are needed, such as the Nelder–Mead amoeba method, interior point methods, or simulated annealing. Is the improved performance worth these efforts? For the case, where the exponent b = 1 remains fixed, it is known that for most fish data any exponent a < 1 could be used to model growth without affecting the fit to the data significantly (when the other parameters were optimized). We hypothesized that the optimization of both exponents would result in a significantly better fit of the optimal growth function to the data and we tested this conjecture for a data set (20,166 fish) about the mass-growth of Walleye (Sander vitreus), a fish from Lake Erie, USA. To this end, we assessed the fit on a grid of 14,281 exponent-pairs (a, b) and identified the best fitting model curve on the boundary a = b of the grid (a = b = 0.686); it corresponds to the generalized Gompertz equation dm/dt = p * ma − q * ln(m) * ma. Using the Akaike information criterion for model selection, the answer to the conjecture was no: The von Bertalanffy exponent-pair model (but not the logistic model) remained parsimonious. However, the bias reduction attained by the optimal exponent-pair may be worth the tradeoff with complexity in some situations where predictive power is solely preferred. Therefore, we recommend the use of the Bertalanffy–Pütter model (and of its limit case, the generalized Gompertz model) in natural resources management (such as in fishery stock assessments), as it relies on careful quantitative assessments to recommend policies for sustainable resource usage.
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Salim, Gazali, and Pius Bae Kelen. "El Von Bertalanffy and Mortality from Fish Kurau (Polynemustaenitatus) of The Catch Fisherman in Waters Bunyu." INSIST 3, no. 2 (2018): 165. http://dx.doi.org/10.23960/ins.v3i2.165.

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The aim of the research are analyzing the growth model using Von Bertalanffy and mortality in Polynemus taeniatus. Research methods a descriptive kuantitatif by using the case study. Determining the location of sampling are purposive sampling, by following fishing boats Drift Gill Net. Sampling funded every two weeks once upon a huge tide. Data collection techniques using survey. Data retrieval in the form of total length and total weight. The samples from 4 (times) for 3 months. Each sample taking having vulnerable time between 2-5 day in bunyu waters. Research results use the model von bertalanffy obtained maximum length fish kurau (p.taeniatus) is 156,794 cm in 349 days. Value K of 0.0364 cm. Value To of -1,2819 cm. The results of data processing of fish catch kurau (P.taeniatus) obtained by mortalitas natural 0,435; mortalitas total of 1.121; mortalitas arrest of 0,6859; the exploitation of fish kurau 0,61.
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48

Ó, Alan Oliveira do, Aurino de Araújo Rêgo Neto, Gleyson Vieira dos Santos, José Lindenberg Rocha Sarmento, Daniel Biagiotti, and José Ernandes Rufino de Sousa. "Curva de crescimento de ovinos Santa Inês no Vale do Gurgueia." Revista Brasileira de Saúde e Produção Animal 13, no. 4 (2012): 912–22. http://dx.doi.org/10.1590/s1519-99402012000400019.

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Objetivou-se descrever o crescimento de ovinos Santa Inês no Vale do Gurgueia a partir da análise de modelos não lineares: Brody,Von Bertalanffy, Richards, Logístico e Gompertz. Após a definição do modelo de melhor ajuste, avaliou-se a influência de fatores ambientais (estação de nascimento, sexo, tipo de parto e idade da mãe ao parto) sobre os parâmetros da curva. Foram utilizados dados do desenvolvimento ponderal de 61 ovinos, do nascimento aos 350 dias de idade, no período de janeiro de 2009 a dezembro de 2010. Os parâmetros foram estimados por meio do NLIN do SAS. Os modelos de Von Bertalanffy, Richards, Logístico e Gompertz ajustaram bem os dados de crescimento, entretanto, os modelos de Brody e Richards apresentaram maior variação no Quadrado Médio dos Resíduos. Com base no gráfico de dispersão dos resíduos, constatou-se que o modelo de Gompertz apresentou ajuste ligeiramente superior ao modelo de Von Bertalanffy. A taxa de crescimento absoluto estimada demonstrou crescente até os 28 dias de idade. O efeito de sexo foi importante fonte de variação para o parâmetro A, bem como os efeitos de idade da mãe ao parto aos parâmetros B e K. As correlações estimadas entre os parâmetros A e K, B e K foram negativas. Efeitos ambientais mostraram-se importantes fatores que influenciam os parâmetros da curva de crescimento de ovinos Santa Inês no estado do Gurgueia.
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FALCÃO, Paula Fernanda, Victor Breno PEDROSA, Raphael Patrick MOREIRA, et al. "Curvas de crescimento de cordeiros da raça Ile de France criados em confinamento." Revista Brasileira de Saúde e Produção Animal 16, no. 2 (2015): 377–86. http://dx.doi.org/10.1590/s1519-99402015000200012.

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O objetivo com este trabalho foi avaliar os modelos não lineares que melhor descrevem a curva de crescimento de ovinos machos da raça Ile de France criados em confinamento no estado do Paraná. Para tanto, foram realizadas pesagens quinzenais no período de fevereiro de 2013 a junho de 2013, desde o nascimento até o abate (120 dias) de 31 machos da raça Ile de France. As curvas de crescimento foram obtidas pelos modelos não lineares de Brody, Von Bertalanffy, Gompertz e Logístico em que foram considerados os parâmetros da taxa de maturação (K), peso assintótico (A), idade do animal (t), constante de integração que determina a proporção de crescimento após nascimento (B) e proporção do valor assintótico em que ocorre o ponto de inflexão da curva (m), de acordo com o modelo adotado. Os parâmetros foram estimados pelo método Marquardt aplicado ao procedimento NLIN do programa estatístico SAS e os critérios utilizados para verificar a precisão do ajuste das curvas foram o quadrado médio do resíduo e o coeficiente de determinação. Os modelos Brody, Von Bertalanffy, Gompertz e Logístico resultaram respectivamente em 26,4579; 26,1668; 26,1360 e 26,1582 para o quadrado médio do resíduo e 0,8130; 0,9580; 0,9587 e 0,9580 para o coeficiente de determinação. Considerando os critérios adotados, o modelo Gompertz, seguidopor Logístico e Von Bertalanffy, apresentaram o melhor ajuste para descrever o crescimento dos machos da raça Ile de France.
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Gomiero, Juliana Sampaio Guedes, Rilke Tadeu Fonseca de Freitas, Vander Bruno dos Santos, Fabyano Fonseca da Silva, Paulo Borges Rodrigues, and Priscila Vieira Rosa Logato. "Curvas de crescimento morfométrico de piracanjuba (Brycon orbignyanus)." Ciência e Agrotecnologia 33, no. 3 (2009): 882–89. http://dx.doi.org/10.1590/s1413-70542009000300031.

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Abstract:
Conduziu-se um experimento no setor de piscicultura da Universidade Federal de Lavras M.G., com o objetivo de estabelecer curvas de crescimento morfométrico em função do peso corporal para a piracanjuba (Brycon orbignyanus). Alevinos de piracanjuba foram cultivados em viveiros de terra e alimentados com ração comercial até atingirem peso aproximado de 1 kg. Durante o período experimental realizaram-se amostragens aleatórias, onde foram avaliadas as medidas morfométricas comprimento da cabeça (CCAB), comprimento padrão (CP), altura (AND) e largura (LND) tomada no 1ºraio da nadadeira dorsal e as razões morfométricas (CCAB/CP, AND/CP, LND/CP, AND/LND) utilizando-se as funções de Brody, von Bertalanffy, Gompertz e Logística. As funções estudadas apresentaram bom ajuste para todas as medidas morfométricas e para a razão CCAB/CP. As funções de Brody, von Bertalanffy e Gompertz apresentaram qualidades de ajuste semelhantes e superiores à função Logística para as medidas morfométricas. Para a razão CCAB/CP a função Logística apresentou-se superior às demais. A taxa de crescimento da CCAB e LND foi superior às do CP e AND, indicando um crescimento mais rápido da cabeça e largura do que do comprimento padrão e altura. Conclui-se que todos os modelos estudados apresentaram bom ajuste, sendo o de Brody e o de von Bertalanffy os que descrevem melhor o crescimento morfométrico da piracanjuba.
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