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

World's Poultry Science Journal

Volumn 66, Issue 2, 2010, Pages 227-239

  Darmani Kuhi, H ^a   Porter, T ^b   Lopez S ^c   Kebreab, E ^d   Strathe, A B ^d   Dumas, A ^b   Dijkstra, J ^e   France, J ^b  

^a ILAM UNIVERSITY   (Iran)

^b UNIVERSITY OF GUELPH   (Canada)

^c UNIVERSITY OF LEÓN   (Spain)

^d UNIVERSITY OF CALIFORNIA   (United States)

^e WAGENINGEN UNIVERSITY   (Netherlands)

Author keywords

age; growth; growth functions; intake; poultry

Indexed keywords

ANIMALIA; AVES;

EID: 77958614348     PISSN: 00439339     EISSN: 17434777     Source Type: Journal    
DOI: 10.1017/S0043933910000280     Document Type: Review

References (74)

1. 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.
2. BLAXTER, K.L. and WAINMAN, F.W. (1961) The utilization of food by sheep and cattle. Journal of Agricultural Science 57: 419-425.
3. 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.
4. BRODY, S. (1945) Bioenergetics and Growth with Special Reference to the Efficiency Complex in Domestic Animals. New York, USA: Hafner Publishing Company Inc.
5. BURNHAM, K.P. and ANDERSON, D.R. (2002) Model Selection and Multimodel Inference - A Practical Information-Theoretic Approach. New York, USA: Springer.
6. 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.
7. CRAIG, B.A. and SCHINCKEL, A.P. (2001) Nonlinear mixed effects model for swine growth. Professional Animal Scientist 17: 256-260.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
13. DAVIDSON, F.A. (1928) Growth and senescence in purebred Jersey cows. University of Illinois Agriculture Experimental Station Bulletin 302: 182-235.
14. DUMAS, A., DIJKSTRA, J. and FRANCE, J. (2008) Mathematical modelling in animal nutrition: a centenary review. Journal of Agricultural Science 146: 123-142.
15. FITZHUGH, H.A. JR. (1976) Analysis of growth curves and strategies for altering their shape. Journal of Animal Science 42: 1036-1051.
16. 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.
17. FRANCE, J., DIJKSTRA, J. and DHANOA, M.S. (1996a) Growth functions and their application in animal science. Annales de Zootechnie 45: 165-174.
18. 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.
19. FRÉCHET, M. (1927) Sur la loi de probabilité de l'écart maximum. Annales de la Société Polonaise de Mathematique 6: 93-116.
20. 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.
21. 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.
22. GOUS, R.M., MORAN JR., E.T., 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.
23. HENDRICKS, W.A. (1931) Fitting the curve of the diminishing increment to feed consumption-live weight growth curves. Science 74: 290-291.
24. HILL, A.V. (1910) The combinations of haemoglobin with oxygen and with carbon monoxide I. Journal of Physiology 40: 471-480.
25. 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.
26. JULL, M.A. and TITUS, H.W. (1928) Growth of chickens in relation to feed consumption. Journal of Agricultural Research 36: 541-550.
27. 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.
28. 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.
29. 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.
30. 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.
31. LEONARD, T. and HSU, J.S.J. (2001) Bayesian Methods. Cambridge, UK: Cambridge Univ. Press.
32. LISTER, D., COWEN, T. and McCANCE, R.A. (1966) Severe under-nutrition in growing and adult animals. British Journal of Nutrition 20: 633-639.
33. 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.
34. 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).
35. LOTKA, A.J. (1925) Elements of Physical Biology. Baltimore: Williams and Wilkins Company.
36. McCANCE, R.A. (1960) Severe under-nutrition in growing and adult animals. 1. Production and general effects. British Journal of Nutrition 14: 59-73.
37. MICHAELIS, L. and MENTEN, M.L. (1913) Die Kinetik der Invertinwirkung. Biochemische Zeitschrift 49: 333-369.
38. MITSCHERLICH-KÖNIGSBERG, E.I. (1909) Das Gesetz des Minimums und das Gesetz des abnehmenden Bodenertrages. Landwirtschaftliche Jahrbücher 38: 537-552.
39. MONOD, J. (1942) Recherches sur la Croissance des Cultures Bactériennes, 2me Édn. Paris: Hermann.
40. 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.
41. 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.
42. MURRAY, J.A. (1921) Normal growth in animals. Journal of Agricultural Science 11: 258-274.
43. NATIONAL RESEARCH COUNCIL (1994) Nutrient Requirements of Poultry, ninth revised edition. Washington DC, USA: National Academy Press.
44. PEARL, R. (1925) The Biology of Population Growth. New York, USA: Alfred A. Knopf Inc.
45. 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.
46. 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.
47. PÜTTER, A. (1920) Studien über Physiologischeähnlichkeit. VI. Wachstumsähnlichkeiten. Pflügers Archiv fur die Gesamte Physiologie des Menschen und der Tiere 180: 298-340.
48. RICHARDS, F.J. (1959) A flexible growth function for empirical use. Journal of Experimental Botany 10: 290-300.
49. 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).
50. RITZMAN, E.G. (1917) Nature and rate of growth in lambs during the first year. Journal of Agricultural Research 11: 607-623.
51. 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.
52. ROBERTSON, T.B. (1916) Experimental studies on growth II. The normal growth of the white mouse. Journal of Biological Chemistry 24: 363-383.
53. ROBERTSON, T.B. (1923) The Chemical Basis of Growth and Senescence. Philadelphia: J. B. Lippincott Company.
54. ROSIN, P. and RAMMLER, E. (1933) The laws governing the fineness of powdered coal. Journal of the Institute of Fuel 7: 29-36.
55. 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.
56. SAS (2000) SAS/STAT User's Guide, Version 8 Edition. Cary, NC, USA: SAS Inst. Inc.
57. 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 lownutrient excretion diets. Professional Animal Scientist 22: 401-408.
58. 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.
59. 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.
60. SCHUMACHER, F.X. (1939) A new growth curve and its applicability to timber yield studies. Journal of Forestry Research 37: 819-820.
61. 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.
62. 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.
63. 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.
64. 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.
65. 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.
66. VERHULST, P.-F. (1838) Notice sur la loi que la population suit dans sa croissance. Correspondance, Mathématiques et Physique 10: 113-121.
67. VON BERTALANFFY, L. (1950) An outline of general system theory. British Journal for the Philosophy of Science 1: 134-165.
68. VON BERTALANFFY, L. (1957) Quantitative laws in metabolism and growth. Quarterly Review of Biology 32: 217-231.
69. 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.
70. 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.
71. WEIBULL, W. (1951) A statistical distribution function of wide applicability. Journal Applied Mechanics -Transactions ASME 18: 293-297.
72. WINSOR, C.P. (1932) The Gompertz curve as a growth curve. Proceedings of the National Academy of Sciences 18: 1-8.
73. 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.
74. WRIGHT, S. (1926) The biology of population growth; the natural increase of mankind - reviews. Journal of the American Statistical Association 21: 493-497.