Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-05T08:02:26.728Z Has data issue: false hasContentIssue false

A review of mathematical functions for the analysis of growth in poultry

Published online by Cambridge University Press:  12 July 2010

H. DARMANI KUHI
Affiliation:
Animal Sciences Group, Faculty of Agriculture, University of Ilam, Ilam 69315/516, Iran
T. PORTER
Affiliation:
Centre for Nutrition Modelling, Department of Animal and Poultry Science, University of Guelph, Guelph ON, N1G 2W1, Canada
S. LÓPEZ
Affiliation:
Instituto de Ganadería de Montaña (Universidad de León – CSIC), Departamento de Producción Animal, Universidad de León, E-24007 León, Spain
E. KEBREAB
Affiliation:
Department of Animal Science, University of California, Davis, CA 95616, USA
A.B. STRATHE
Affiliation:
Department of Animal Science, University of California, Davis, CA 95616, USA
A. DUMAS
Affiliation:
Centre for Nutrition Modelling, Department of Animal and Poultry Science, University of Guelph, Guelph ON, N1G 2W1, Canada
J. DIJKSTRA
Affiliation:
Animal Nutrition Group, Wageningen University, PO Box 338, 6700 AH Wageningen, The Netherlands
J. FRANCE*
Affiliation:
Centre for Nutrition Modelling, Department of Animal and Poultry Science, University of Guelph, Guelph ON, N1G 2W1, Canada
*
Corresponding author: [email protected]
Get access

Abstract

Poultry industries face various decisions in the production cycle that affect the profitability of an operation. Predictions of growth when the birds are ready for sale are important factors that contribute to the economy of poultry operations. Mathematical functions called ‘growth functions’ have been used to relate body weight (W) to age or cumulative feed intake. These can also be used as response functions to predict daily energy and protein dietary requirements for maintenance and growth (France et al., 1989). When describing growth versus age in poultry, a fixed point of inflexion can be a limitation with equations such as the Gompertz and logistic. Inflexion points vary depending on age, sex, breed and type of animal, so equations such as the Richards and López are generally recommended. For describing retention rate against daily intake, which generally does not exhibit an inflexion point, the monomolecular would appear the function of choice.

Type
Review Article
Copyright
World's Poultry Science Association 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BLAXTER, K.L. and BOYNE, A.W. (1978) The estimation of nutritive value of feeds as energy sources for ruminants and the derivation of feeding systems. Journal of Agricultural Science 90: 47-68.CrossRefGoogle Scholar
BLAXTER, K.L. and WAINMAN, F.W. (1961) The utilization of food by sheep and cattle. Journal of Agricultural Science 57: 419-425.CrossRefGoogle Scholar
BRIDGES, T.C., TURNER, L.W., STAHLY, T.S., USRY, J.L. and LOEWER O.J., (1992) Modeling the physiological growth of swine part I: Model logic and growth concepts. Transactions of ASAE 35: 1019-1028.CrossRefGoogle Scholar
BRODY, S. (1945) Bioenergetics and Growth with Special Reference to the Efficiency Complex in Domestic Animals. New York, USA: Hafner Publishing Company Inc.Google Scholar
BURNHAM, K.P. and ANDERSON, D.R. (2002) Model Selection and Multimodel Inference – A Practical Information-Theoretic Approach. New York, USA: Springer.Google Scholar
BUYSE, J., GEYPENS, B., MALHEIROS, R.D., MORAES, V.M., SWENNEN, Q. and DECUYPERE, E. (2004) Assessment of age-related glucose oxidation rates of broiler chickens by using stable isotopes. Life Sciences 75: 2245-2255.CrossRefGoogle ScholarPubMed
CRAIG, B.A. and SCHINCKEL, A.P. (2001) Nonlinear mixed effects model for swine growth. Professional Animal Scientist 17: 256-260.CrossRefGoogle Scholar
DARMANI KUHI, H., KEBREAB, E., LOPEZ, S. and FRANCE, J. (2003a) A comparative evaluation of functions for the analysis of growth in male broilers. Journal of Agricultural Science 140: 451-459.CrossRefGoogle Scholar
DARMANI KUHI, H., KEBREAB, E. LÓPEZ, S., and FRANCE, J. (2003b) An evaluation of different growth functions for describing the profile of live weight with time (age) in meat and egg strains of chicken. Poultry Science 82: 1536-1543.CrossRefGoogle ScholarPubMed
DARMANI KUHI, H., KEBREAB, E., LÓPEZ, S. and FRANCE, J. (2004) A comparative evaluation of functions for describing the relationship between live-weight gain and metabolizable energy intake in turkeys. Journal of Agricultural Science 142: 691-695.CrossRefGoogle Scholar
DARMANI KUHI, H., KEBREAB, E., LÓPEZ, S. and FRANCE, J. (2009) Application of the law of diminishing returns to estimate maintenance requirement for amino acids and their efficiency of utilization for accretion in young chicks. Journal of Agricultural Science 147: 383-390.CrossRefGoogle Scholar
DARMANI KUHI, H., KEBREAB, E., OWEN, E. and FRANCE, J. (2001) Application of the law of diminishing return to describing the relationship between metabolizable energy intake and growth rate in broilers. Journal of Animal and Feed Sciences 10: 661-670.CrossRefGoogle Scholar
DAVIDSON, F.A. (1928) Growth and senescence in purebred Jersey cows. University of Illinois Agriculture Experimental Station Bulletin 302: 182-235.Google Scholar
DUMAS, A., DIJKSTRA, J. and FRANCE, J. (2008) Mathematical modelling in animal nutrition: a centenary review. Journal of Agricultural Science 146: 123-142.CrossRefGoogle Scholar
FITZHUGH, H.A. JR (1976) Analysis of growth curves and strategies for altering their shape. Journal of Animal Science 42: 1036-1051.CrossRefGoogle ScholarPubMed
FRANCE, J., DHANOA, M.S., CAMMELL, S.B., GILL, M., BEEVER, D.E. and THORNLEY, J.H.M. (1989) On the use of response functions in energy balance analysis. Journal of Theoretical Biology 140: 83-99.CrossRefGoogle Scholar
FRANCE, J., DIJKSTRA, J. and DHANOA, M.S. (1996a) Growth functions and their application in animal science. Annales de Zootechnie 45: 165-174.CrossRefGoogle Scholar
FRANCE, J., DIJKSTRA, J., THORNLEY, J.H.M. and DHANOA, M.S. (1996b) A simple but flexible growth function. Growth, Development and Aging 60: 71-83.Google ScholarPubMed
FRÉCHET, M. (1927) Sur la loi de probabilité de l'écart maximum. Annales de la Société Polonaise de Mathematique 6: 93-116.Google Scholar
GAHL, M.J., FINKE, M.D., CRENSHAW, T.D. and BENEVENGA, N.J. (1991) Use of a four parameter logistic equation to evaluate the response of growing rats to ten levels of each indispensable amino acid. Journal of Nutrition 121: 1720-1729.CrossRefGoogle ScholarPubMed
GOMPERTZ, B. (1825) On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London 115: 513-583.Google Scholar
GOUS, R.M., MORAN, E.T. JR, STILBORN, H.R., BRADFORD, G.D. and EMMANS, G.C. (1999) Evaluation of the parameters needed to describe the overall growth, the chemical growth, and the growth of feathers and breast muscles of broilers. Poultry Science 78: 812-821.CrossRefGoogle ScholarPubMed
HENDRICKS, W.A. (1931) Fitting the curve of the diminishing increment to feed consumption-live weight growth curves. Science 74: 290-291.CrossRefGoogle ScholarPubMed
HILL, A.V. (1910) The combinations of haemoglobin with oxygen and with carbon monoxide I. Journal of Physiology 40: 471-480.Google Scholar
HURWITZ, S., FRISCH, A., BAR, U., EISNER, I., BENGAL, I. and PINES, M. (1983) The amino acid requirements of growing turkeys. 1. Model construction and parameter estimation. Poultry Science 62: 197-205.CrossRefGoogle ScholarPubMed
JULL, M.A. and TITUS, H.W. (1928) Growth of chickens in relation to feed consumption. Journal of Agricultural Research 36: 541-550.Google Scholar
KEBREAB, E., FRANCE, J., DARMANI KUHI, H. and LOPEZ, S. (2008) A comparative evaluation of functions for partitioning nitrogen and amino acid intake between maintenance and growth in broilers. Journal of Agricultural Science 146: 163-167.CrossRefGoogle Scholar
KEBREAB, E., SCHULIN-ZEUTHEN, M., LÓPEZ, S., DIAS, R.S., DE LANGE, C.F.M. and FRANCE, J. (2007) Comparative evaluation of mathematical functions to describe growth and efficiency of phosphorus utilization in growing pigs. Journal of Animal Science 85: 2498-2507.CrossRefGoogle ScholarPubMed
KEBREAB, E., STRATHE, A.B., YITBAREK, A., NYACHOTI, C.M., DIJKSTRA, J., LÓPEZ, S. and FRANCE, J. (2010) Modelling the efficiency of phosphorus utilization in growing pigs. Journal of Animal Science, in press.Google Scholar
KOEHLER, R., PAHLE, T., GRUHN, K., ZANDER, R., JEROCH, H. and GEBHARDT, G. (1988) Estimation of the rates of protein synthesis for the whole body of growing broilers. Archives of Animal Nutrition 38: 565-572.Google Scholar
LEONARD, T. and HSU, J.S.J. (2001) Bayesian Methods. Cambridge, UK: Cambridge Univ. Press.Google Scholar
LISTER, D., COWEN, T. and McCANCE, R.A. (1966) Severe under-nutrition in growing and adult animals. British Journal of Nutrition 20: 633-639.CrossRefGoogle Scholar
LÓPEZ, S., FRANCE, J., GERRITS, W.J.J., DHANOA, M.S., HUMPHRIES, D.J. and DIJKSTRA, J. (2000) A generalized Michaelis-Menten equation for the analysis of growth. Journal of Animal Science 78: 1816-1828.CrossRefGoogle ScholarPubMed
LÓPEZ, S. (2008) Non-linear functions in animal nutrition, in: FRANCE, J. & KEBREAB, E. (Eds.) Mathematical Modelling in Animal Nutrition, pp. 47-88 (Wallingford, UK: CAB International).Google Scholar
LOTKA, A.J. (1925) Elements of Physical Biology. Baltimore: Williams and Wilkins Company.Google Scholar
McCANCE, R.A. (1960) Severe under-nutrition in growing and adult animals. 1. Production and general effects. British Journal of Nutrition 14: 59-73.CrossRefGoogle Scholar
MICHAELIS, L. and MENTEN, M.L. (1913) Die Kinetik der Invertinwirkung. Biochemische Zeitschrift 49: 333-369.Google Scholar
MITSCHERLICH-KÖNIGSBERG, E.I. (1909) Das Gesetz des Minimums und das Gesetz des abnehmenden Bodenertrages. Landwirtschaftliche Jahrbücher 38: 537-552.Google Scholar
MONOD, J. (1942) Recherches sur la Croissance des Cultures Bactériennes, 2me Édn. Paris: Hermann.Google Scholar
MORAN, E.T., POSTE, L.M., FERKET, P.R. and AGAR, V. (1984) Response of large tom turkeys differing in growth characteristics to divergent feeding systems: performance, carcass quality, and sensory evaluation. Poultry Science 63: 1778-1792.CrossRefGoogle Scholar
MORGAN, P.H., MERCER, L.P. and FLODIN, N.W. (1975) General model for nutritional responses of higher organisms. Proceedings of the US National Academy of Science 72: 4327-4331.CrossRefGoogle ScholarPubMed
MURRAY, J.A. (1921) Normal growth in animals. Journal of Agricultural Science 11: 258-274.CrossRefGoogle Scholar
NATIONAL RESEARCH COUNCIL, (1994) Nutrient Requirements of Poultry, ninth revised edition. Washington DC, USA: National Academy Press.Google Scholar
PEARL, R. (1925) The Biology of Population Growth. New York, USA: Alfred A. Knopf Inc.Google Scholar
PESTI, G.M., VEDENOV, D., CASON, J.A. and ILLARD, L. (2009) A comparison of methods to estimate nutritional requirements from experimental data. British Poultry Science 50: 16-32.CrossRefGoogle ScholarPubMed
PORTER, T., KEBREAB, E. DARMANI KUHI, H., , LÓPEZ, S., STRATHE, A.B. and FRANCE, J. (2010) Flexible alternatives to the Gompertz equation for describing growth with age in turkey hens. Poultry Science 89: 371-378.CrossRefGoogle Scholar
PÜTTER, A. (1920) Studien über Physiologische Ähnlichkeit. VI. Wachstumsähnlichkeiten. Pflügers Archiv fur die Gesamte Physiologie des Menschen und der Tiere 180: 298-340.CrossRefGoogle Scholar
RICHARDS, F.J. (1959) A flexible growth function for empirical use. Journal of Experimental Botany 10: 290-300.CrossRefGoogle Scholar
RICKER, W.E. (1979) Growth rates and models, in: HOAR, W.S., RANDALL, D.J. & BRETT, J.R. (eds.) Fish Physiology, Volume VIII, pp. 677-743 (New York, USA: Academic Press).Google Scholar
RITZMAN, E.G. (1917) Nature and rate of growth in lambs during the first year. Journal of Agricultural Research 11: 607-623.Google Scholar
ROBERTSON, T.B. (1908) On the normal rate of growth of an individual and its biochemical significance. Archiv fur Entwicklungsmechanik der Organismen 25: 581-614.CrossRefGoogle Scholar
ROBERTSON, T.B. (1916) Experimental studies on growth II. The normal growth of the white mouse. Journal of Biological Chemistry 24: 363-383.CrossRefGoogle Scholar
ROBERTSON, T.B. (1923) The Chemical Basis of Growth and Senescence. Philadelphia: J. B. Lippincott Company.Google Scholar
ROSIN, P. and RAMMLER, E. (1933) The laws governing the fineness of powdered coal. Journal of the Institute of Fuel 7: 29-36.Google Scholar
SAKOMURA, N.K., LONGO, F.A., OVIEDO-RONDON, E.O., BOA-VIAGEM, C. and FERRAUDO, A. (2005) Modelling energy utilization and growth parameter description for broiler chickens. Poultry Science 84: 1363-1369.CrossRefGoogle ScholarPubMed
SAS, (2000) SAS/STAT User's Guide, Version 8 Edition. Cary, NC, USA: SAS Inst. Inc.Google Scholar
SCHINCKEL, A.P., PENCE, S., EINSTEIN, M.E., HINSON, R., PRECKEL, P.V., RADCLIFFE, J.S. and RICHERT B.T., (2006) Evaluation of different mixed model nonlinear functions on pigs fed low-nutrient excretion diets. Professional Animal Scientist 22: 401-408.CrossRefGoogle Scholar
SCHULIN-ZEUTHEN, M., KEBREAB, E., DIJKSTRA, J., LÓPEZ, S., BANNINK, A., DARMANI KUHI, H., THORNLEY, J.H.M. and FRANCE, J. (2008) A comparison of the Schumacher with other functions for describing growth in pigs. Animal Feed Science and Technology 143: 314-327.CrossRefGoogle Scholar
SCHULIN-ZEUTHEN, M. KEBREAB, E., , GERRITS, W.J.J., LÓPEZ, S., FAN, M.Z., DIAS, R.S. and FRANCE, J. (2007) Meta-analysis of phosphorus balance data from growing pigs. Journal of Animal Science 85: 1953-1961.CrossRefGoogle ScholarPubMed
SCHUMACHER, F.X. (1939) A new growth curve and its applicability to timber yield studies. Journal of Forestry Research 37: 819-820.Google Scholar
STRATHE, A.B., DANFÆR, A., CHWALIBOG, A., SØRENSEN, H. and KEBREAB, E. (2010a) A multivariate nonlinear mixed-effect method for analyzing energy partition in growing pigs. Journal of Animal Science, in press.CrossRefGoogle Scholar
STRATHE, A. B., DANFÆR, A., SØRENSEN, H. and KEBREAB, E. (2010b) A multilevel nonlinear mixed-effects approach to model growth in pigs. Journal of Animal Science 88: 638-649.CrossRefGoogle ScholarPubMed
SUMMERS, J.D., JACKSON, S. and SPRATT, D. (1989) Weight gain and breast yield of large white male turkeys fed diets varying in protein content. Poultry Science 68: 1547-1552.CrossRefGoogle ScholarPubMed
THORNLEY, J.H.M. and FRANCE, J. (2007) Mathematical Models in Agriculture: Quantitative Methods for the Plant, Animal and Ecological Sciences. Second Edition. Wallingford, UK: CABI Publishing, 923 pp.Google Scholar
VEDENOV, D. and PESTI, G.M. (2008) A comparison of methods of fitting several models to nutritional response data. Journal of Animal Science 86: 500-507.CrossRefGoogle ScholarPubMed
VERHULST, P.-F. (1838) Notice sur la loi que la population suit dans sa croissance. Correspondance, Mathématiques et Physique 10: 113-121.Google Scholar
VON BERTALANFFY, L. (1950) An outline of general system theory. British Journal for the Philosophy of Science 1: 134-165.CrossRefGoogle Scholar
VON BERTALANFFY, L. (1957) Quantitative laws in metabolism and growth. Quarterly Review of Biology 32: 217-231.CrossRefGoogle ScholarPubMed
WALDROUP, P.W., ADAMS, M.H. and WALDROUP, A.L. (1997) Evaluation of National Research Council amino acid recommendations for large white turkeys. Poultry Science 76: 711-720.CrossRefGoogle ScholarPubMed
WALDROUP, P.W., ANTHONY, N.B. and WALDROUP, A.L. (1998) Effects of amino acid restriction during starter and grower periods on subsequent performance and incidence of leg disorders in two strains of male large white turkeys. Poultry Science 77: 702-713.CrossRefGoogle ScholarPubMed
WEIBULL, W. (1951) A statistical distribution function of wide applicability. Journal Applied Mechanics - Transactions ASME 18: 293-297.CrossRefGoogle Scholar
WINSOR, C.P. (1932) The Gompertz curve as a growth curve. Proceedings of the National Academy of Sciences 18: 1-8.CrossRefGoogle ScholarPubMed
WOOD, T.B. and YULE, G.U. (1914) Statistics of British feeding trials and the starch equivalent theory. Journal of Agricultural Science: 6: 233-251.CrossRefGoogle Scholar
WRIGHT, S. (1926) The biology of population growth; the natural increase of mankind – reviews. Journal of the American Statistical Association 21: 493-497.CrossRefGoogle Scholar