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On the mathematical description of lactation curves

  • A. J. Rook (a1), J. France (a1) and M. S. Dhanoa (a2)

Summary

The lactation curve may be represented mathematically by the general equation Y = Aϕ1(t)ϕ2(t), where A is a positive scalar, ϕ1,(t) is a positive monotonically increasing function with an asymptote at ϕ1 = 1, and ϕ2 is a monotonically decreasing function with an initial value of unity and an asymptote at ϕ2 = 0. Functions considered as candidates for ϕ1 were: (Mitscherlich), (Michaelis-Menten), (generalized saturation kinetic), 1/(1 + b0 (logistic), b0 exp (Gompertz) and [1+ tanh(b0 + b1t)]/2 (hyperbolic tangent). Candidates for ϕ2 were e–ct (exponential) and 1/(1 + ct) (inverse straight line). The 12 models thus obtained and Y = Atb e–ct (Wood's model) were fitted to whole-lactation data from 23 animals. Mitscherlich x exponential, Michaelis-Menten x exponential, logistic x exponential, logistic × inverse straight line and Wood's model all fitted well. For these models, expressions for time to peak, maximum yield, total yield over a finite lactation and relative decline at the midway point of the declining phase were obtained. The Mitscherlich x exponential model generally fitted better than Wood's model and, unlike Wood's model, gives simple algebraic formulae for all these summary statistics.

Copyright

COPYRIGHT: © Cambridge University Press 1993

References

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Beale, E. M. L. (1960). Confidence regions in non linear estimation. Journal of the Royal Statistical Society 22, 41–88.
Dhanoa, M. S. (1981). A note on an alternative form of the lactation model of Wood. Animal Production 32, 349–351.
Elston, D. A., Glasbey, C. A. & Neilson, D. R. (1989). Non-parametric lactation curves. Animal Production 48, 331–339.
Emmans, G. C., Neilson, D. R. & Gibson, A. (1983). A general description of dairy cow potential. Animal Production 36, 546 (Abstract).
Grossman, M. & Koops, W. J. (1988). Multiphasic analysis of lactation curves in dairy cattle. Journal of Dairy Science 71, 1598–1608.
Morant, S. V. & Gnanasakthy, A. (1989). A new approach to the mathematical formulation of lactation curves. Animal Production 49, 151–162.
Neal, H. D. St. C. & Thornley, J. H. M. (1983). The lactation curve in cattle: a mathematical model of the mammary gland. Journal of Agricultural Science, Cambridge 101, 389–400.
Oldham, J. D. & Emmans, G. C. (1989). Prediction of responses to required nutrients in dairy cows. Journal of Dairy Science 72, 3212–3229.
Papajcsik, I. A. & Bodero, J. (1988). Modelling lactation curves of Friesian cows in a subtropical climate. Animal Production 47, 201–207.
Ross, G. J. S. (1987). MLP Maximum Likelihood Program. Oxford: Numerical Algorithms Group.
Wood, P. D. P. (1967). Algebraic model of the lactation curve in cattle. Nature, London 216, 164–165.
Wood, P. D. P. (1977). The biometry of lactation. Journal of Agricultural Science, Cambridge 88, 333–339.

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  • Cited by 61

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On the mathematical description of lactation curves

  • A. J. Rook (a1), J. France (a1) and M. S. Dhanoa (a2)

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