A description of the growth of sheep

The idea that an animal of a given kind has, and grows to, a final or mature size is a useful one and several equations have been proposed that describe such growth to maturity (Winsor, 1932; Parks, 1982; Taylor, 1982). The Gompertz is one of these growth functions and describes in a comparatively simple, single equation the sigmoidal pattern of growth. It has 3 parameters, only 2 of which are important - mature size A and the rate parameter B. Estimates of A and B, however, are highly correlated. Considering A and B as a lumped parameter (AB) may overcome this problem. A Gompertz, or any other, growth function is not expected to describe all growth curves. When the environment (e.g., feed, housing) is non-limiting, it may provide a useful and succinct description of growth. The objectives of this study were to examine: (i) if the Gompertz equation adequately describes the growth of two genotypes of sheep under conditions designed to be non-limiting; and, (ii) if the lumped parameter AB has more desirable properties for estimation than A and B separately.

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A description of the growth of sheep and its genetic analysis

Animal Science ◽

10.1017/s1357729800052176 ◽

2002 ◽

Vol 74 (1) ◽

pp. 51-62 ◽

Cited By ~ 39

Author(s):

R.M. Lewis ◽

G.C. Emmans ◽

W.S. Dingwall ◽

G. Simm

Keyword(s):

Growth Rate ◽

Growth Parameters ◽

Live Weight ◽

Great Majority ◽

Maximum Growth ◽

Rate Parameter ◽

Daily Growth ◽

Lean Growth ◽

Lumped Parameter ◽

Mature Size

AbstractThe Gompertz is one of a family of growth functions that, when the environment (e.g. food, housing) is non-limiting, provides a useful description of growth as a comparatively simple, single equation. It has three parameters of which the important ones are mature size, A, and the rate parameter, B. Estimates of A and B, however, are highly correlated and defining their separate values for individual animals is problematic. This problem was explored using five methods for estimating the parameters, or transformations of them, to describe the growth of two genotypes of Suffolk sheep kept under non-limiting conditions. One genotype was under selection for high lean growth rate and the other was its control. Live weights that were collected at least fortnightly from near birth to 150 days of age over a 9-year period on 1934 lambs were used. The Gompertz form adequately described the growth of the great majority of the lambs evaluated. When considering A and B as a lumped parameter, Z = A·B, and fitting Z, B and an initial condition (a transformed birth weight) as the parameters, the problems in estimation were substantially overcome as shown by a low correlation of Z with estimates of B both within and across animals. Usefully Z has a biological interpretation in that Z/e is the maximum daily growth rate. Since the Gompertz form adequately described growth in these sheep, the extent of genetic co-variation for the growth parameters values (A, B, Z) was estimated to determine if they were amenable to selection. A weighted univariate animal model was fitted. Mature size, A, and the rate parameter, B, were moderately heritable (0·37 (s.e. 0·04) and 0·38 (s.e. 0·05), respectively) as was live weight at 150 days of age (0·31 (s.e. 0·06)). However there was a substantial negative genetic relationship between A and B (–0·48). Z was highly heritable (0·72 (s.e.0·05)). After 9 years of selection, the genotype selected for high lean growth rate was heavier (P < 0·001) at 150 days of age (5·2 kg) and at maturity (6·6 kg), with a maximum growth rate (Z/e) that was 1·12 times that of the control. Our lumped parameter Z, in effect a rate parameter scaled for mature size, avoided problems in estimating A and B and, in so doing, offers a general and robust description of lamb growth amenable to selection.

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WAVE GROWTH UNDER VARIABLE WIND CONDITIONS

Coastal Engineering Proceedings ◽

10.9753/icce.v32.waves.40 ◽

2011 ◽

Vol 1 (32) ◽

pp. 40 ◽

Cited By ~ 3

Author(s):

Marta Alomar ◽

Rodolfo Bolaños- Sánchez ◽

Agustín Sanchez-Arcilla ◽

Abdel Sairouni

Keyword(s):

Growth Rates ◽

Scaling Law ◽

Growth Curves ◽

Wave Model ◽

Growth Function ◽

Western Mediterranean ◽

Entire Area ◽

Wave Growth ◽

Growth Functions ◽

Variable Wind

Parametric wave growth curves are commonly used to empirically calculate wave height under fetch limited conditions and to tune the source functions of spectral wave models. There is not a unique wave growth function and many deviations from the first similarity laws have been reported. The applicability of the commonly used functions in variable wind conditions is expected to be limited. In this study we calculated wave growth curves with data from an instrumental set-up in the north-western Mediterranean. This region is characterized by non-homogeneous wind conditions (both in time and space). The first growth functions we calculated from the observations suggested higher wave growth rates than previously described by other authors. A close look to the sources of discrepancy in the calculations under such wind conditions revealed the importance to accurately separate sea from swell and to use only locally generated sea. The source of the wind data used for the scaling law is thought to be responsible for the remaining discrepancies from the commonly used growth functions. Wind and wave data from a high resolution simulation were used to calculate the growth functions from a spectral wave model, and to explore the importance of using in-situ wind measures to scale the variables. Simulated wave growth rates are lower than observed and lower than previously reported by other authors. Wind measurements from the most offshore buoy seem to be representative enough of the winds over the entire area. The results support the applicability of the well-known functions in the region of interest when certain conditions are met; i.e. pure wind sea conditions, and choosing a representative wind speed to scale the variables.

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Growth and spatiotemporal distribution of juvenile shortfin mako (Isurus oxyrinchus) in the western and central North Pacific

Marine and Freshwater Research ◽

10.1071/mf14316 ◽

2015 ◽

Vol 66 (12) ◽

pp. 1176 ◽

Cited By ~ 14

Author(s):

M. Kai ◽

K. Shiozaki ◽

S. Ohshimo ◽

K. Yokawa

Keyword(s):

North Pacific ◽

Linear Models ◽

North Pacific Ocean ◽

Age Groups ◽

Growth Curves ◽

Growth Function ◽

Gaussian Mixture ◽

Isurus Oxyrinchus ◽

Shortfin Mako ◽

Central North Pacific

This paper presents an estimation of growth curves and spatiotemporal distributions of juvenile shortfin mako shark (Isurus oxyrinchus) in the western and central North Pacific Ocean using port sampling data collected from 2005 to 2013. The monthly length compositions show a clear transition of three modes in the size range of smaller than 150-cm precaudal length (PCL), which were believed to represent the growth of age-0 to age-2 classes, and they were then decomposed into age groups by fitting a Gaussian mixture distribution. Simulation data of lengths at monthly ages were generated from the mean and standard deviation of each distribution, and fit with a von Bertalanffy growth function. Parameters of the estimated growth curves for males and females were 274.4 and 239.4cm PCL for the asymptotic length and 0.19 and 0.25 year–1 for the growth coefficient indicating apparently faster growth than previously reported. Generalised linear models were applied to age-0 to explore the seasonal changes of PCL by area. They were born during late autumn and winter off the coast of north-eastern Japan, an area known to have relatively high productivity compared with other pelagic areas, and gradually expanded their habitat eastward and northward with the seasons as they grew.

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PATTERNS OF GROWTH IN HEIGHT AND WEIGHT FROM BIRTH TO EIGHTEEN YEARS OF AGE

PEDIATRICS ◽

10.1542/peds.24.5.904 ◽

1959 ◽

Vol 24 (5) ◽

pp. 904-921

Author(s):

Robert B. Reed ◽

Harold C. Stuart

Keyword(s):

Growth Curves ◽

Growth Patterns ◽

Individual Growth ◽

Growth Spurt ◽

Adolescent Growth Spurt ◽

Wide Range ◽

Basic Facts ◽

The Individual ◽

Rates Of Growth ◽

Mature Size

In this report is displayed the range of variation observed in the growth curves of height and weight in a series of 134 children observed from birth to 18 years. For purposes of simplification the individuals have been classified on the basis of their rates of growth during three successive 6-year intervals. Even in terms of this crude classification several basic facts about individual growth patterns of height and weight are apparent. The wide range of differences between individuals applies not only to facts about size at specific ages but also to the pattern of change followed from age period to age period. The rate of growth during early childhood, i.e. before 6 years of age, is associated with, but not specifically predictive of, size at maturity and timing of the adolescent growth spurt. Individuals with rapid growth before 6 years of age tend to have large mature size and early adolescent growth spurt. It will be the objective of future reports from this research project to determine the manner in which the individual differences in growth demonstrated and classified here are related to aspects of physical development, to environmental influences such as dietary intake and to the level of health of the child.

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One-dimensional game of life and its growth functions

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171292000656 ◽

1992 ◽

Vol 15 (3) ◽

pp. 499-508

Author(s):

Mohammad H. Ahmadi

Keyword(s):

Power Series ◽

Rational Function ◽

Formal Power Series ◽

Infinite Product ◽

Growth Function ◽

The Other ◽

Arbitrary Integer ◽

One Dimensional ◽

Growth Functions ◽

Formal Power

We start with finitely many1's and possibly some0's in between. Then each entry in the other rows is obtained from the Base2sum of the two numbers diagonally above it in the preceding row. We may formulate the game as follows: Defined1,jrecursively for1, a non-negative integer, andjan arbitrary integer by the rules:d0,j={1 for j=0,k (I)0 or 1 for 0<j<kd0,j=0 for j<0 or j>k (II)di+1,j=di,j+1(mod2) for i≥0. (III)Now, if we interpret the number of1's in rowias the coefficientaiof a formal power series, then we obtain a growth function,f(x)=∑i=0∞aixi. It is interesting that there are cases for which this growth function factors into an infinite product of polynomials. Furthermore, we shall show that this power series never represents a rational function.

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MONOID GROWTH FUNCTIONS FOR BRAID GROUPS

International Journal of Algebra and Computation ◽

10.1142/s0218196791000122 ◽

1991 ◽

Vol 01 (02) ◽

pp. 201-205 ◽

Cited By ~ 5

Author(s):

MARCUS BRAZIL

Keyword(s):

Braid Group ◽

Growth Function ◽

Braid Groups ◽

Growth Functions

It is shown that for all n, the braid group on n strings, Bn, has rational growth with respect to a certain set of elements of the group which generate it as a monoid. In particular, the precise growth function for B4 is calculated.

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Comparing Polynomial and von Bertalanffy Growth Functions for Fitting Tag–Recapture Data

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/f94-169 ◽

1994 ◽

Vol 51 (8) ◽

pp. 1689-1691 ◽

Cited By ~ 2

Author(s):

William S. Hearn ◽

George M. Leigh

Keyword(s):

Growth Function ◽

Growth Increment ◽

Bias Reduction ◽

Release Time ◽

Von Bertalanffy ◽

Growth Functions ◽

Straight Line ◽

Von Bertalanffy Growth Function ◽

Multiple Measurements ◽

The One

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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Model for Aerobic Growth of Shigella flexneri Under Various Conditions of Temperature, pH, Sodium Chloride and Sodium Nitrite Concentrations

Journal of Food Protection ◽

10.4315/0362-028x-55.7.509 ◽

1992 ◽

Vol 55 (7) ◽

pp. 509-513 ◽

Cited By ~ 26

Author(s):

LAURA L. ZAIKA ◽

JOHN G. PHILLIPS ◽

ROBERT L. BUCHANAN

Keyword(s):

Sodium Chloride ◽

Growth Kinetics ◽

Sodium Nitrite ◽

Shigella Flexneri ◽

Brain Heart Infusion ◽

Growth Curves ◽

Quadratic Model ◽

Aerobic Growth ◽

Gompertz Equation ◽

Kinetics Of

A modified factorial design was used to measure the effects and interactions of temperature (10 to 37°C), pH (5.5 to 7.5), sodium chloride (0.5 to 5.0%), and sodium nitrite (0 to 1000 ppm) on the aerobic growth kinetics of Shigella flexneri in brain heart infusion broth. A total of 592 cultures were analyzed, with growth curves being generated using the Gompertz equation. A quadratic model for growth of S. flexneri in terms of temperature, pH, sodium chloride, and sodium nitrite concentrations was obtained by response surface analysis. This model provides an estimate of bacterial growth in response to any combination of the variables studied within the specified ranges. Estimates obtained with the model compared favorably with growth of S. flexneri in milk.

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Comparison of Growth Kinetics for Healthy and Heat-Injured Listeria monocytogenes in Eight Enrichment Broths

Journal of Food Protection ◽

10.4315/0362-028x-65.8.1333 ◽

2002 ◽

Vol 65 (8) ◽

pp. 1333-1337 ◽

Cited By ~ 22

Author(s):

TODD M. SILK ◽

TATIANA M. T. ROTH ◽

C. W. DONNELLY

Keyword(s):

Listeria Monocytogenes ◽

Growth Curves ◽

Lag Phase ◽

Phase Duration ◽

Enrichment Broth ◽

Selective Enrichment ◽

Gompertz Equation ◽

Selective Agents ◽

Time Required ◽

Maximum Population Density

Detection of Listeria in food products is often limited by performance of enrichment media used to support growth of Listeria to detectable levels. In this study, growth curves were generated using healthy and heat-injured Listeria monocytogenes strain F5069 in three nonselective and five selective enrichment broths. Nonselective enrichment media included the current Food and Drug Administration Bacteriological Analytical Manual Listeria enrichment broth base (BAM), Listeria repair broth (LRB), and Trypticase soy broth. Selective enrichment media included BAM with selective agents and LRB with selective agents, BCM L. monocytogenes preenrichment broth, Fraser broth, and UVM-modified Listeria enrichment broth. The Gompertz equation was used to model the growth of L. monocytogenes. Gompertz parameters were used to calculate exponential growth rate, lag-phase duration (LPD), generation time, maximum population density (MPD), and time required for repair of injured cells. Statistical differences (P < 0.05) in broth performance were noted for LPD and MPD when healthy and injured cells were inoculated into the broths. With the exception of Fraser broth, there were no significant differences in the time required for the repair of injured cells. Results indicate that the distinction between selective and nonselective broths in their ability to grow healthy Listeria and to repair sublethally injured cells is not solely an elementary issue of presence or absence of selective agents.

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