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British Poultry Science Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/cbps20
An allometric‐autoregressive approach to poultry development M. J. Belt
a b
a
, N. H. Casey & G. A. Smith
a
a
Department of Livestock Science , University of Pretoria , Pretoria, 0002, Republic of South Africa b
Animal and Dairy Science Research Institute , Private Bag X2, Irene, 1675, Republic of South Africa Published online: 08 Nov 2007.
To cite this article: M. J. Belt , N. H. Casey & G. A. Smith (1992) An allometric‐autoregressive approach to poultry development, British Poultry Science, 33:2, 279-288, DOI: 10.1080/00071669208417466 To link to this article: http://dx.doi.org/10.1080/00071669208417466
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/ terms-and-conditions
British Poultry Science (1992) 33: 279-288
AN ALLOMETRIC-AUTOREGRESSIVE APPROACH TO POULTRY DEVELOPMENT M. J. BELT1, N. H. CASEY AND G. A. SMITH
Downloaded by [McGill University Library] at 21:15 01 February 2015
Department of Livestock Science, University of Pretoria, Pretoria 0002, Republic of South Africa Received for publication 28th February 1991
Abstract 1. The relative rates of development in a commercial layer and a broiler strain of chicken fed 180 or 230 g crude protein/kg were investigated by the use of the allometric-autoregressive model. Development was divided into pre-pubertal (0 to 8 weeks) and pubertal phases (8 to 22 weeks). 2. Significant strain effects were observed, at all ages, in rates of gain of live (L) body mass, carcase (C) mass, non-carcase (N) mass and empty-body (EB) mass as well as C, N and EB moisture, protein and fat content. 3. Significant dietary effects were observed in C and EB fat in the pre-pubertal phase and L mass, N protein and C fat in the subsequent pubertal period.
INTRODUCTION
Roux (1974) demonstrated that, because both live body mass and cumulative food intake for immature animals are described by Gompertz curves, an allometric relationship exists between these variables. He further advocated that food intake may be more accurately measured than body mass and so that this leads to a reduction of error. Roux (1976) subsequently related cumulative heat production and the primary chemical components of body composition (protein, fat) to cumulative metabolisable energy intake with considerable success. According to von Bertalanffy (1960) many studies of the rat show discontinuity in the allometric regression line so that up to a certain body mass the metabolic rate increases more, and after this point, less, than expected from the 'surface rule' of Racine (1953). Von Bertalanffy (1960) continued by stating that, because interruptions are frequently found in allometric plots, not all the data can be fitted by a single regression line. Scrutiny usually reveals that 1 Present address: Animal and Dairy Science Research Institute, Private Bag X2, Irene 1675, Republic of South Africa.
279
Downloaded by [McGill University Library] at 21:15 01 February 2015
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M. J. BELT, N. H. CASEY AND G. A. SMITH
these breaks are not incidental but are associated with definable alterations in biological processes. It is possible that one of these breaks corresponds with the onset of puberty. This is denoted in may physiological changes related to a shift in hormonal balance. Roux (1976, 1981) called attention to the unsatisfactory non-random distribution of observed points around fitted conventional growth curves. He concluded that it was necessary to make use of more than one regression line to describe the mass-food relationship of an animal, because of sudden changes in gradient at various biologically important ages. The theory described by Roux (1974, 1976, 1981) has been successfully applied in the description of different growth responses in nutrition and genetic investigations using domestic ruminants (Meissner, 1977; Meissner and Roux, 1982; Meissner et ah, 1982; Roux et al., 1982), pigs (Roux and Kemm, 1981) and rats (Scholtz and Roux, 1981). For a detailed description of this model, Roux (1976) should be consulted. In essence, it makes use of an autoregression of cumulative metabolisable energy (CME) intake to identify the various physiological phases of growth. Allometric relationships are consequently calculated using separate regression analyses for each growth phase. The conventional allometric function for the description of growth is Y=aXb or ln(y)=ln(o)+6 1n(X) where y=live body mass; X=CME intake; ln(«)=intercept; and 6=gradient. The autoregression for X may be expressed as [X(0-aJ =p[X(t- l)-cQ+e(t) or = [ax-X(0)]p'+ !>£(«-/) i-o
where X(0=ln[CME intake] at time V, X(0)=ln[CME intake] at time 0; ax=ln[CME intake] at time oo; /?=gradient of autoregression; and e=developmental error term. It follows that as t—»oo then X—>ax for \p\ < 1 . The function is similar for Y. Because ln(0)= — oo, a value for CME intake at birth is necessary in the calculation of the autoregressive equation. The energetic efficiency from conception to birth has been estimated as 0-67 (Scholtz et ah, 1981); cumulative energy intake at birth is, therefore 1*5 X amount of energy in the body at birth, or the amount of energy in the egg before incubation in the case of avian species.
ALLOMETRIC-AUTOREGRESSIVE MODEL
281
Downloaded by [McGill University Library] at 21:15 01 February 2015
MATERIALS AND METHODS
Two domestic fowl strains, one selected for reproductive performance (layer) and the other for productive performance (broiler), were fed one of two isoenergetic (13-4 MJ ME/kg) diets containing 180 or 230 g crude protein/kg formulated according to National Research Council (1984) recommendations. The 4 treatment groups were denoted LI 80, L230, B180 abnd B230. The 960 birds were reared under conventional broiler management procedures. Twenty four birds per pen were housed in floor pens in a controlled environment, at a density of 6-4 birds/m2, and given free access to food and water. At 14-d intervals from hatch to 22 weeks of age, mean live body mass and cumulative food consumption per treatment were recorded. No birds were slaughtered at week 20, the birds being weighed and allowed to grow through to week 22. In addition, 6 birds with live mass closest to the mean for each treatment were killed by exsanguination, plucked by hand and had their digestive tracts emptied, The empty-body was separated into standard carcase and non-carcase fractions, weighed and stored in polyethylene bags at — 20°C. The body components are defined below; body: the whole plucked bird; empty-body: the body after removal of the contents of the alimentary tract; carcase: the standard 'oven-ready' bird excluding giblets, lungs and kidneys (i.e. dressed carcase); non-carcase: head, neck, feet and all viscera, organs, glands, adipose tissue and connective tissue not included with the carcase. Carcase and non-carcase components were ground in a frozen state in a mincer fitted with a 4-mm sieve, mixed thoroughly and ground twice again. Representative samples of approximately 100 g were subsequently drawn from each component and freeze-dried for 30 h at 30 millitorr and — 60°C. A further 10 g sample was drawn from the ground components before freeze drying, for moisture determination. Freeze-dried samples were then homogenised in a blender, bottled and stored at — 15°C. Samples were analysed in duplicate for moisture, protein, fat (ether extract) and ash content using standard (AOAC, 1980) methods. An analysis of deviations from the conventional allometric function showed an increasing trend up to an age of approximately 8 weeks, followed by a decreasing trend, for moisture, protein and ash content. The converse was true for fat content. The non-random distribution of observed points indicated that the accuracy of the linear fit would be enhanced by partitioning the data into two phases. In doing this, the smoothing effect that a single fitted function exerts on the observed variation is eliminated. The autoregressive function was fitted to CME (MJ) intake values using ln[CME intake] with time (t) as dependent variate and In [CME intake] with time (t— 1) as independent variate, where t=age in 14-day intervals from birth. For this procedure, the figures for CME intake at birth were assumed to be equivalent to the amount of energy in the eggs before incubation. The resulting phases of development, indicated by changes in p, were noted.
282
M. J. BELT, N. H. CASEY AND G. A. SMITH
The log-transformed composite and proximate data were subsequently related allometrically to CME intake by separate phases according to the model published by Roux et al. (1982). The results were then subjected to pooled regression analysis and least-squares analysis of covariance.
Downloaded by [McGill University Library] at 21:15 01 February 2015
RESULTS
It was observed that, in all groups, a break occurred in the linear plot at approximately 8 weeks of age. This was assumed to be a physiological 'break', at which the course of metabolic events of the birds in the specified treatment was modified and a new developmental state initiated. This was assumed to be a point of physiological age equivalance in all treatment birds. This point will be defined as the onset of puberty for the purposes of this study and the phases of development described as being pre-pubertal and pubertal. The autoregression relationships are presented in Table 1. The gradient (p) between strains and phases of development differ considerably while the coefficients of determination (r2) indicate highly significant (P
Phase 1 (pre-pubertal) B180 0-81 ±0-07 0-90±0-06 L180 0-91 ±0-06 L230 B230 0-77±0-02 1 0-84 ±0-03 PME
0-985 0-992 0-992 0-988
0-89 + 0-10 0-98 + 0-07 1-00 + 0-09 0-89 + 0-01 0-92 + 0-04
0-974 0-991 0-984 0-999
0-67±0-04 0-73 + 0-10 0-74±0-12 0-64 ±0-06 0-69 ±0-04
0-991 0-996 0-953 0-982
Phase 2 (pubertal) B180 0-54±0-03 0-58±0-02 L180 0-58±0-03 L230 0-60 + 0-04 B230 PME 0-58±0-01
0-980 0-990 0-989 0-978
0-56 + 0-03 0-63 + 0-03 0-62±0-03 0-66±0-03 0-62 + 0-02
0-980 0-987 0-985 0-989
0-62 ±0-04 0-54±0-03 0-60 + 0-05 0-64±0-06 0-60±0-03
0-976 0-983 0-963 0-951
' PME = pooled mean estimate (ft).
relationships. Layers had steeper gradients than broilers in the first phase, but this strain effect was absent in the second phase of development. No significant correlation was detected between phases for live mass or carcase mass. A significant (P
British Poultry Science Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/cbps20
An allometric‐autoregressive approach to poultry development M. J. Belt
a b
a
, N. H. Casey & G. A. Smith
a
a
Department of Livestock Science , University of Pretoria , Pretoria, 0002, Republic of South Africa b
Animal and Dairy Science Research Institute , Private Bag X2, Irene, 1675, Republic of South Africa Published online: 08 Nov 2007.
To cite this article: M. J. Belt , N. H. Casey & G. A. Smith (1992) An allometric‐autoregressive approach to poultry development, British Poultry Science, 33:2, 279-288, DOI: 10.1080/00071669208417466 To link to this article: http://dx.doi.org/10.1080/00071669208417466
PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/ terms-and-conditions
British Poultry Science (1992) 33: 279-288
AN ALLOMETRIC-AUTOREGRESSIVE APPROACH TO POULTRY DEVELOPMENT M. J. BELT1, N. H. CASEY AND G. A. SMITH
Downloaded by [McGill University Library] at 21:15 01 February 2015
Department of Livestock Science, University of Pretoria, Pretoria 0002, Republic of South Africa Received for publication 28th February 1991
Abstract 1. The relative rates of development in a commercial layer and a broiler strain of chicken fed 180 or 230 g crude protein/kg were investigated by the use of the allometric-autoregressive model. Development was divided into pre-pubertal (0 to 8 weeks) and pubertal phases (8 to 22 weeks). 2. Significant strain effects were observed, at all ages, in rates of gain of live (L) body mass, carcase (C) mass, non-carcase (N) mass and empty-body (EB) mass as well as C, N and EB moisture, protein and fat content. 3. Significant dietary effects were observed in C and EB fat in the pre-pubertal phase and L mass, N protein and C fat in the subsequent pubertal period.
INTRODUCTION
Roux (1974) demonstrated that, because both live body mass and cumulative food intake for immature animals are described by Gompertz curves, an allometric relationship exists between these variables. He further advocated that food intake may be more accurately measured than body mass and so that this leads to a reduction of error. Roux (1976) subsequently related cumulative heat production and the primary chemical components of body composition (protein, fat) to cumulative metabolisable energy intake with considerable success. According to von Bertalanffy (1960) many studies of the rat show discontinuity in the allometric regression line so that up to a certain body mass the metabolic rate increases more, and after this point, less, than expected from the 'surface rule' of Racine (1953). Von Bertalanffy (1960) continued by stating that, because interruptions are frequently found in allometric plots, not all the data can be fitted by a single regression line. Scrutiny usually reveals that 1 Present address: Animal and Dairy Science Research Institute, Private Bag X2, Irene 1675, Republic of South Africa.
279
Downloaded by [McGill University Library] at 21:15 01 February 2015
280
M. J. BELT, N. H. CASEY AND G. A. SMITH
these breaks are not incidental but are associated with definable alterations in biological processes. It is possible that one of these breaks corresponds with the onset of puberty. This is denoted in may physiological changes related to a shift in hormonal balance. Roux (1976, 1981) called attention to the unsatisfactory non-random distribution of observed points around fitted conventional growth curves. He concluded that it was necessary to make use of more than one regression line to describe the mass-food relationship of an animal, because of sudden changes in gradient at various biologically important ages. The theory described by Roux (1974, 1976, 1981) has been successfully applied in the description of different growth responses in nutrition and genetic investigations using domestic ruminants (Meissner, 1977; Meissner and Roux, 1982; Meissner et ah, 1982; Roux et al., 1982), pigs (Roux and Kemm, 1981) and rats (Scholtz and Roux, 1981). For a detailed description of this model, Roux (1976) should be consulted. In essence, it makes use of an autoregression of cumulative metabolisable energy (CME) intake to identify the various physiological phases of growth. Allometric relationships are consequently calculated using separate regression analyses for each growth phase. The conventional allometric function for the description of growth is Y=aXb or ln(y)=ln(o)+6 1n(X) where y=live body mass; X=CME intake; ln(«)=intercept; and 6=gradient. The autoregression for X may be expressed as [X(0-aJ =p[X(t- l)-cQ+e(t) or = [ax-X(0)]p'+ !>£(«-/) i-o
where X(0=ln[CME intake] at time V, X(0)=ln[CME intake] at time 0; ax=ln[CME intake] at time oo; /?=gradient of autoregression; and e=developmental error term. It follows that as t—»oo then X—>ax for \p\ < 1 . The function is similar for Y. Because ln(0)= — oo, a value for CME intake at birth is necessary in the calculation of the autoregressive equation. The energetic efficiency from conception to birth has been estimated as 0-67 (Scholtz et ah, 1981); cumulative energy intake at birth is, therefore 1*5 X amount of energy in the body at birth, or the amount of energy in the egg before incubation in the case of avian species.
ALLOMETRIC-AUTOREGRESSIVE MODEL
281
Downloaded by [McGill University Library] at 21:15 01 February 2015
MATERIALS AND METHODS
Two domestic fowl strains, one selected for reproductive performance (layer) and the other for productive performance (broiler), were fed one of two isoenergetic (13-4 MJ ME/kg) diets containing 180 or 230 g crude protein/kg formulated according to National Research Council (1984) recommendations. The 4 treatment groups were denoted LI 80, L230, B180 abnd B230. The 960 birds were reared under conventional broiler management procedures. Twenty four birds per pen were housed in floor pens in a controlled environment, at a density of 6-4 birds/m2, and given free access to food and water. At 14-d intervals from hatch to 22 weeks of age, mean live body mass and cumulative food consumption per treatment were recorded. No birds were slaughtered at week 20, the birds being weighed and allowed to grow through to week 22. In addition, 6 birds with live mass closest to the mean for each treatment were killed by exsanguination, plucked by hand and had their digestive tracts emptied, The empty-body was separated into standard carcase and non-carcase fractions, weighed and stored in polyethylene bags at — 20°C. The body components are defined below; body: the whole plucked bird; empty-body: the body after removal of the contents of the alimentary tract; carcase: the standard 'oven-ready' bird excluding giblets, lungs and kidneys (i.e. dressed carcase); non-carcase: head, neck, feet and all viscera, organs, glands, adipose tissue and connective tissue not included with the carcase. Carcase and non-carcase components were ground in a frozen state in a mincer fitted with a 4-mm sieve, mixed thoroughly and ground twice again. Representative samples of approximately 100 g were subsequently drawn from each component and freeze-dried for 30 h at 30 millitorr and — 60°C. A further 10 g sample was drawn from the ground components before freeze drying, for moisture determination. Freeze-dried samples were then homogenised in a blender, bottled and stored at — 15°C. Samples were analysed in duplicate for moisture, protein, fat (ether extract) and ash content using standard (AOAC, 1980) methods. An analysis of deviations from the conventional allometric function showed an increasing trend up to an age of approximately 8 weeks, followed by a decreasing trend, for moisture, protein and ash content. The converse was true for fat content. The non-random distribution of observed points indicated that the accuracy of the linear fit would be enhanced by partitioning the data into two phases. In doing this, the smoothing effect that a single fitted function exerts on the observed variation is eliminated. The autoregressive function was fitted to CME (MJ) intake values using ln[CME intake] with time (t) as dependent variate and In [CME intake] with time (t— 1) as independent variate, where t=age in 14-day intervals from birth. For this procedure, the figures for CME intake at birth were assumed to be equivalent to the amount of energy in the eggs before incubation. The resulting phases of development, indicated by changes in p, were noted.
282
M. J. BELT, N. H. CASEY AND G. A. SMITH
The log-transformed composite and proximate data were subsequently related allometrically to CME intake by separate phases according to the model published by Roux et al. (1982). The results were then subjected to pooled regression analysis and least-squares analysis of covariance.
Downloaded by [McGill University Library] at 21:15 01 February 2015
RESULTS
It was observed that, in all groups, a break occurred in the linear plot at approximately 8 weeks of age. This was assumed to be a physiological 'break', at which the course of metabolic events of the birds in the specified treatment was modified and a new developmental state initiated. This was assumed to be a point of physiological age equivalance in all treatment birds. This point will be defined as the onset of puberty for the purposes of this study and the phases of development described as being pre-pubertal and pubertal. The autoregression relationships are presented in Table 1. The gradient (p) between strains and phases of development differ considerably while the coefficients of determination (r2) indicate highly significant (P
Phase 1 (pre-pubertal) B180 0-81 ±0-07 0-90±0-06 L180 0-91 ±0-06 L230 B230 0-77±0-02 1 0-84 ±0-03 PME
0-985 0-992 0-992 0-988
0-89 + 0-10 0-98 + 0-07 1-00 + 0-09 0-89 + 0-01 0-92 + 0-04
0-974 0-991 0-984 0-999
0-67±0-04 0-73 + 0-10 0-74±0-12 0-64 ±0-06 0-69 ±0-04
0-991 0-996 0-953 0-982
Phase 2 (pubertal) B180 0-54±0-03 0-58±0-02 L180 0-58±0-03 L230 0-60 + 0-04 B230 PME 0-58±0-01
0-980 0-990 0-989 0-978
0-56 + 0-03 0-63 + 0-03 0-62±0-03 0-66±0-03 0-62 + 0-02
0-980 0-987 0-985 0-989
0-62 ±0-04 0-54±0-03 0-60 + 0-05 0-64±0-06 0-60±0-03
0-976 0-983 0-963 0-951
' PME = pooled mean estimate (ft).
relationships. Layers had steeper gradients than broilers in the first phase, but this strain effect was absent in the second phase of development. No significant correlation was detected between phases for live mass or carcase mass. A significant (P
