The Gompertz curve or Gompertz function is a type of mathematical model for a time series , named after Benjamin Gompertz — It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-hand or future value asymptote of the function is approached much more gradually by the curve than the left-hand or lower valued asymptote. This is in contrast to the simple logistic function in which both asymptotes are approached by the curve symmetrically. It is a special case of the generalised logistic function. The function was originally designed to describe human mortality, but since has been modified to be applied in biology, with regard to detailing populations.

Author:Gashura Yokora
Country:South Africa
Language:English (Spanish)
Published (Last):3 July 2018
PDF File Size:19.25 Mb
ePub File Size:7.9 Mb
Price:Free* [*Free Regsitration Required]

Growth curve by Gompertz nonlinear regression model in female and males in tambaqui Colossoma macropomum. POVH 4. Was evaluated the pattern of growth among females and males of tambaqui by Gompertz nonlinear regression model. Five traits of economic importance were measured on animals during the three years, totaling morphometric data analyzed.

Different curves were adjusted between males and females for body weight, height and head length and only one curve was adjusted to the width and body length. In general, males had lower maximum growth rate 8. Multiple factors affect the efficiency of the animal growth in fish farm, such as genetics, sex, nutrition and environment Oliva-Teles The knowledge on body growth has strategic importance for genetic improvement; besides providing information to animal selection based in important economic traits can be used to predict or fit the optimal slaughter age Knizetova et al.

A form to predict and evaluate the animal body growth is by growth curves study from individual growth curves. The usual models applied to describe growth are based on differential equations that seek a biological interpretation Arango and Van Vleck Different non-linear equations are used in animal production to describe the animal growth over time with different biological interpretation meaning related to initial conditions, growth rate, or adult body weight, all linked to economic aspects of production.

In order to estimate body growth of the tambaqui and evaluate differences between males and females was used the Gompertz nonlinear regression model. This model is an most appropriate nonlinear equation to describe the tambaqui growth, together with the Logistic model Costa et al. However, Gompertz model has desirable properties in a growth curve, which unlike other functions, initial and always greater than zero body mass, which reflects the fact that the animal already born with some mass Fialho Gompertz model has only three parameters, equivalent in number to a quadratic function.

However, it fits better and the growth curve can be used in a time interval that covers the entire life of animal. Were analyzed biometric data from animals measured for three years - for economic important traits. All procedures were carried out according to the international practices for animal use and care under the control of an internal committee of the Universidade Federal do Rio Grande do Sul, Brazil. The offspring of each family remained in the same environment until it reached a body weight of 20 g more or less 1 month when it was possible to mark the animals by Passive Integrated Transponder Tags PIT in the dorsal muscle.

After, the animals were transferred to earth ponds tank m 2 remained during the whole period with alimentation two-fold per day up to apparent satiation. Were measured body weight BW grams , length of head LH cm from anterior end of the head and caudal operculum , body width BWi cm from 1 st dorsal fin ray , body height BH cm from 1 st dorsal fin ray and body length BL cm by pachymeter, ictiometer and measuring tape graduated mm.

Gompertz nonlinear regression model was used to describe growth curves in tambaqui sorted by sex. This can be described as, , where, y represents the interest trait, a is the maximum value of y asymptotic values , b is a constant rate of exponential growth, e is the base of natural logarithms, t is the age in days and k is the age at inflection point. Were tested the curve adequacy for each trait using eight equations to obtain the best fit for Gompertz model parameters in population, i.

The adequacy test was performed using an adaptation of likelihood ratio test proposed by Regazzi Regazzi and Silva A simple equation, called M8, considered the Gompertz parameters were the same at males and females; and a complete equation, called M1, considered a specific parameter for each sex; other models tested were simplifications of M1 equation Table I.

This is the first study where were estimated the body growth pattern of tambaqui C. Length and body height were the first traits achieved the maximum growth rate, followed by head length, weight and body width Fig.

Thereby, we can determine that the bone tissue was deposited first followed muscle tissue Table II , indicated by the order in days to reach the inflection point for head length days , length days , width days , height days and body weight days. Data females are represented by gray color and males are represented by black color.

The triangles represent the data for males and females together. The curves study showed growth patterns similar between males and females for length and body width Fig.

Width and body length were better fitted at one only growth curve for males and females. Although the maximum growth rate of 0. Inversely, head length, weight and body height showed different estimation for males and females Fig 1 c; 1d; 1e. Were observed differences of the female's asymptotic values a and age at inflection point k in comparison to males; fitting curves with different estimates for the parameters at each sex M3 equation.

The body length showed a slow growth, going from 46 to 55 cm at 2 kg and 4 kg, respectively Fig. The maximum growth rate of 0. The body weight showed a growth faster than morphometric traits. Muscle deposition was different to males and females Fig. The males weighted on average The difference between males e females is evidenced through of growth maximum rate, 8. Differentially, the difference between males and females for body height was small, lower than 1 cm in both 2 kg and 4 kg Table III.

The maximum growth rate reached was 0. The growth curve for the head length showed a slow growth Fig.

Although measures very similar growth, different curves were adjusted for each sex. There were differences at the estimates of b parameter for body height and head length M6 equation indicating a constant exponential growth different between males and females Fig.

The PCA showed that animals with greater body length and length head showed lower body height. Data of females are represented at black and males are represented at grey. From these results is possible to corroborate the observations reported by fish farmers, that the females grow faster than males after reproductive maturation Vieira et al. However, from this date is possible to estimate the maximum growth rate and, thus, fit the better slaughter age for each sex.

The shape of body, sex and body weight are very important in choosing the processing performed by the industry, as it influences the operations of beheading, gutting and cleaning, besides influencing the final yield of the processing Carneiro et al.

According the processing industry the slaughter weight of this species current is 2 kg, which was achieved at days of cultivation. In this point, is possible to observe at both sexes the same body growth pattern Fig. On the other hand, the females showed a maximum growth rate for body weight higher than males, 9. To meet the demand of this niche market for large animals, the cultivation of female's tambaqui is the most indicated due to its capacity growth faster than males.

Currently, the market for larger animals is stocked mainly with extractive fishing at the Amazon Basin Rivers. However, overexploitation generates a decrease of the natural stocks of animals this size in the rivers of region, indicating the depletion of natural stocks of these species Da Silva Batista and Petrere Junior In Brazil, the Environment Ministry classified the species as overexploited or threatened by overexploitation statute no.

In this context, cultivation of tambaqui is of utmost importance in the conservation this species and supplying the consumer market. Thus, the understanding of animal growth has strategic importance for obtaining maximum growth of animals, optimizing the slaughter age for each sex.

There differences in growth patterns between adult male and female evidenced by the different curves fitted, indicating the existence of sexual dimorphism of this specie. The understanding of differences observed on body growth and growth rates between the sexes is important for more success in the cultivation strategy employed.

Were showed differences at the maximum growth rate between the sexes suggesting the need to adapt the actual production system to use the maximum growth potential of each sex. Size of beef cows: early ideas, new developments. Gen Mol Res 1: Cryopreservation of tambaqui Colossoma macropomum semen: extenders, cryoprotectants, dilution ratios and freezing methods.

Cryo Letters Responses of digestive enzymes of tambaqui Colossoma macropomum to dietary cornstarch changes and metabolic inferences. Modelling the growth of tambaqui, Colossoma macropomum Cuvier, in floodplain lakes: model selection and multimodel inference. Braz J Biol Characterization of the commercial fish production landed at Manaus, Amazonas State, Brazil. Acta Amaz Acta Sci Fialho FB. Innovative molecular approach to the identification of Colossoma macropomum and its hybrids.

An Acad Bras Cienc Hamoy IG and Santos S. Multiplex PCR panel of microsatellite markers for the tambaqui, Colossoma macropomum , developed as a tool for use in conservation and broodstock management.

Genet Mol Res Modifying growth curve parameters by multitrait genomic selection. J Anim Sci Analysis os growth-curves of fowl. Br Poult Sci Purification, characterization and substrate specificity of a trypsin from the Amazonian fish tambaqui Colossoma macropomum.

Biochem Biophys Red Commun Hormonal induction and semen characteristics of tambaqui Colossoma macropomum.

Zygote Oliva-Teles A. Nutrition and health of aquaculture fish. J Fish Dis Growth of the tambaqui Colossoma macropomum Cuvier Characiformes: Characidae : which is the best model? Dados no delineamento inteiramente casualizado. Rev Mat Estat Biologia reprodutiva de Tambaqui. Correspondence to: Fernanda de Mello E-mail: Fernandade. This is an open-access article distributed under the terms of the Creative Commons Attribution License.

Services on Demand Journal. Agrarian Sciences Growth curve by Gompertz nonlinear regression model in female and males in tambaqui Colossoma macropomum.


Gompertz function



The Gompertz Curve as a Growth Curve


Related Articles