A Formulation of the von Bertalanffy Growth Curve when the Growth Rate is Roughly Constant

1969 ◽  
Vol 26 (11) ◽  
pp. 3069-3072 ◽  
Author(s):  
William Knight
Keyword(s):  
Growth Rate ◽  
Growth Curve ◽  
Von Bertalanffy ◽  
Alternate Form ◽  
Usual Form

The author contends that the parameters of any growth curve should be a direct description of the graphical appearance of the data. For growth that is even approximately linear this is not true of the von Bertalanffy curve in its usual form (von Bertalanffy, Human Biol. 10: 181–213, 1938). On the above grounds, an alternate form of the von Bertalanffy curve for use in such instances is proposed.

Additive and non-additive genetic effects of growth-curve parameters of Holstein, Ayrshire and crossbred females

1994 ◽  
Vol 74 (3) ◽  
pp. 401-409 ◽  
Author(s):  
D. Perotto ◽  
R. I. Cue ◽  
A. J. Lee ◽  
A. J. McAllister ◽  
J. R. Batra ◽  
...  
Keyword(s):  
Growth Rate ◽  
Dairy Cattle ◽  
Growth Curve ◽  
Growth Traits ◽  
Individual Performance ◽  
Breeding Value ◽  
Average Lifetime ◽  
Additive Effects ◽  
Positive Effects ◽  
Maternal Performance

Crossbreeding parameters (line additive, dominance and additive × additive epistatic effects for individual and for maternal performance) on growth traits of females from a crossbreeding experiment between Holstein-based (HS) and Ayrshire-based (AS) lines were estimated by individual animal models, incorporating all known additive genetic relationships among animals, through restricted maximum likelihood and mixed-model methodologies. The growth traits [asymptotic weight (A), rate parameter (k), inflection parameter (m), average lifetime absolute growth rate (AGR), average lifetime absolute maturing rate (AMR) and average lifetime relative growth rate (RGR)] were estimated by fitting the Richards function to the observed growth curve of 3076 individuals. The statistical model included the random effect of the animal breeding value and the fixed effects of genetic group and station–year–season of birth. Results indicated that the HS exceeded (P < 0.001) the AS in additive effects for individual performance for both A and AGR. The HS exceeded (P < 0.05) the AS in additive effects for maternal performance for A. Individual heterosis was positive for A (P < 0.001) and for AGR (P < 0.01). Maternal heterosis was negative for A (P < 0.05) and positive for AMR (P < 0.05). Total heterosis (TH) had positive effects on both AGR and AMR (P < 0.05). Heterosis retained in advanced crossbred generations was not significant (P > 0.05) for any of the studied traits. The results suggest that crossbreeding designed to exploit TH can alter the shape of the growth curve of dairy cattle. Key words: Crossbreeding, dairy cattle, growth curve

scholarly journals Growth curve of Atlantoscia floridana (van Name) (Crustacea, Isopoda, Philosciidae) from a Brazilian Restinga Forest

2004 ◽  
Vol 21 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Paula Beatriz Araujo ◽  
Georgina Bond-Buckup
Keyword(s):  
Growth Rate ◽  
Growth Curve ◽  
Urban Areas ◽  
Field Data ◽  
Growth Curves ◽  
Rio Grande ◽  
Rio Grande Do Sul ◽  
Differential Growth ◽  
Estimate Life Expectancy ◽  
Males And Females

The terrestrial isopod Atlantoscia floridana (van Name, 1940) occurs from the U.S.A. (Florida) to Brazil and Argentina. In the southernmost Brazilian State, Rio Grande do Sul, the species is recorded in many localities, in urban and in non-urban areas. The growth curve of Atlantoscia floridana based on field data is presented. The specimens were sampled from April, 2000 to October, 2001 at the Reserva Biológica do Lami (RBL), Rio Grande do Sul. Captured individuals were sexed and had their cephalothorax width measured, with the data analyzed with von Bertalanffy's model. The growth curves for males and females are described, respectively, by the equations: Wt = 1.303 [1 - e-0.00941 (t + 50.37)] and Wt = 1.682 [1 - e-0.00575 (t + 59.13)]. The curves showed differential growth between sexes, where females reach a higher Wµ with a slower growth rate. Based on the growth curves it was also possible to estimate life expectancy for males and females.

A Novel Unification Method to Characterize a Broad Class of Growth Curve Models Using Relative Growth Rate

2019 ◽  
Vol 81 (7) ◽  
pp. 2529-2552
Author(s):  
Biman Chakraborty ◽  
Amiya Ranjan Bhowmick ◽  
Joydev Chattopadhyay ◽  
Sabyasachi Bhattacharya
Keyword(s):  
Growth Rate ◽  
Relative Growth Rate ◽  
Growth Curve ◽  
Broad Class ◽  
Relative Growth ◽  
Growth Curve Models

GROWTH OF THE SALMON EMBRYO

1943 ◽  
Vol 21d (2) ◽  
pp. 19-33 ◽  
Author(s):  
F. R. Hayes ◽  
F. H. Armstrong
Keyword(s):  
Growth Rate ◽  
Atlantic Salmon ◽  
Growth Curve ◽  
Growth Rates ◽  
Growth Cycle ◽  
Quantitative Relation ◽  
Random Errors ◽  
Relative Growth ◽  
Cycle Growth ◽  
Zero Time

Wet and dry weights of Atlantic salmon are given up to the end of yolk sac absorption, and from them the growth rates are determined. Attempts are made to smooth the growth curve by the methods of Brody, Murray-Schmalhausen, and MacDowell et al. Of these the last is best taking zero time as nine days after fertilization. It is concluded that, as to weight, the interval considered ends before the point of inflection of a Sachs growth cycle. Growth in length, however, represents a complete cycle, hence there can be no simple quantitative relation between length and weight. Deviations from the smoothly descending relative growth rate (RGR or Minot) curve are considered, with the conclusion that all such irregularities so far presented can be attributed to random errors (except possibly the posthatching rise in RGR of the trout at 12° reported by Wood). In general weighing is not sufficiently sensitive as a method, to permit a detailed description of the RGR.

Growth modelling in accordance with daily water temperature in European grayling (Thymallus thymallusL.)

1999 ◽  
Vol 56 (6) ◽  
pp. 994-1000 ◽  
Author(s):  
J P Mallet ◽  
S Charles ◽  
H Persat ◽  
P Auger
Keyword(s):  
Growth Rate ◽  
Water Temperature ◽  
Good Description ◽  
Biological Significance ◽  
Temperature Fluctuations ◽  
Fish Growth ◽  
Von Bertalanffy ◽  
European Grayling ◽  
Daily Water Temperature ◽  
Daily Water

The model of von Bertalanffy has been and is still widely used to model fish growth, mainly because of its good description of annual growth over the whole life span. However, it does not take into account a seasonal variability in growth rate, an important phenomenon that appears quite well correlated with water temperature fluctuations in temperate climates. In the present study, we demonstrated that it was possible to model such variations by including daily water temperature in the von Bertalanffy growth formula owing to the correlation between the growth coefficient k and water temperature. The model we chose to describe such a correlation includes parameters with obvious biological significance and is mathematically well structured, which allowed an extensive use of our growth model. Hence, we use our new model to describe annual variability in the growth of European grayling (Thymallus thymallus L.) in a river section where water temperature could rise up to the thermal tolerance limit for this species, inducing reduced growth rates and severe mortality events. Finally, we were able to explain the growth rate variability from one year to the next by interannual water temperature fluctuations.

scholarly journals Growth curve of Repartida goats reared in the Caatinga region, Brazil

2017 ◽  
Vol 38 (2) ◽  
pp. 1041 ◽  
Author(s):  
Luanna Chácara Pires ◽  
Théa Mírian Medeiros Machado ◽  
Paulo Luiz Souza Carneiro ◽  
João Batista Lopes da Silva ◽  
Andréa Duarte de Holanda Barbosa ◽  
...  
Keyword(s):  
Growth Rate ◽  
Body Weight ◽  
Growth Curve ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Lower Probability ◽  
High Birth Weight ◽  
Average Growth ◽  
Nutritional Deficit ◽  
Weight Data

This work aimed to determine which non-linear model (Brody, Gompertz, logistic, von Bertalanffy or Richards) best represents the average growth curve of goats, in addition to evaluating the effect of the environment. The weight data of 40 Repartida goats reared in the Brazil Caatinga were included in this study. Weight data was collected every 30 days from birth until 270 days of age. The parameters of the models (A, mature body weight; B, constant of integration; k, maturation rate; m, inflection point) were estimated using the NLIN procedure of SAS. The logistic model showed a slightly higher average fit in comparison to the other models. The absolute growth rate suggests that the maximum growth rate was reached early. The effect of the contemporary groups was significant (P < 0.05), but only for the estimated k parameter. The estimated correlation between the A and k parameters was significant and negative, indicating a lower probability of a high body weight in adulthood. Goats of the Repartida ecotype are characterized by their high birth weight and low weight at maturity, which combined with the nutritional deficit, suggests that these animals have adapted to the adverse conditions of the Brazilian Caatinga region.

scholarly journals Modeling Math Growth Trajectory—An Application of Conventional Growth Curve Model and Growth Mixture Model to ECLS K-5 Data

2016 ◽  
Vol 2 (1) ◽  
pp. 166 ◽  
Author(s):  
Yi Lu
Keyword(s):  
Gender Differences ◽  
Growth Rate ◽  
Growth Curve ◽  
Growth Mixture Modeling ◽  
Mixture Modeling ◽  
Growth Curve Model ◽  
Growth Mixture ◽  
Curve Model ◽  
The Mean ◽  
Math Growth

<p>To model students’ math growth trajectory, three conventional growth curve models and three growth mixture models are applied to the Early Childhood Longitudinal Study Kindergarten-Fifth grade (ECLS K-5) dataset in this study. The results of conventional growth curve model show gender differences on math IRT scores. When holding socio-economic status (SES) constant, gender differences reduced on the mean start IRT scores, growth rate, and acceleration rate. Growth mixture modeling applied to ECLS K-5 children reliably identified three classes of children based on their math growth trajectories. Growth mixture modeling results indicate that gender differences are different depending on different math development classes. After controlling for SES, growth mixture modeling results show that gender differences on the mean start IRT scores, linear growth rate, and quadratic growth rate reduced in all subpopulations. Growth mixture modeling result also show that after controlling for gender, the effects of SES on math development are different in different subpopulations.</p>

Growth ecology of the tree lizard Urosaurus bicarinatus (Squamata: Phrynosomatidae), in a tropical dry forest of the Chamela Region, Mexico

2016 ◽  
Vol 66 (2) ◽  
pp. 189-199 ◽  
Author(s):  
Aurelio Ramírez-Bautista ◽  
Uriel Hernández-Salinas ◽  
J. Gastón Zamora-Abrego
Keyword(s):  
Growth Rate ◽  
Life History ◽  
Growth Rates ◽  
Average Rate ◽  
Growth Patterns ◽  
Dry Forest ◽  
Von Bertalanffy ◽  
Mexican Pacific ◽  
Males And Females ◽  
Tree Lizard

Determination of growth rate provides an important component of an organism’s life history, making estimations of size at maturity, survival rate, and longevity possible. Here, we report on growth rate of males and females of the tropical tree lizard Urosaurus bicarinatus, in a seasonal environment in the state of Jalisco on the Mexican Pacific Coast. We calculated body growth rates and fitted these to the Von Bertalanffy, the logistic-by-length, and the logistic-by-weight growth models. The Von Bertalanffy model provided the best fit, and we used it to analyze the growth pattern. Males and females did not differ in estimated asymptotic size and other characteristic growth parameters. Estimated growth curve predicted an age at maturity of 38 mm SVL on 120 days for males, and 40 mm SVL on 170 days for females. On the basis of the similarities in the growth rates between the sexes, comparisons were made between seasons, and we found that the average rate of growth was slightly, albeit insignificantly, higher in the rainy season than in the dry season. The similarities in the growth patterns for the sexes of this species might be indicative of variance in its life history traits (e.g., fecundity, egg size) compared to those of other populations of this species and other species of this genus; therefore, it is important to document interpopulation differences to understand the evolutionary changes that have led to optimal adaptation in a particular environment more accurately.

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