Lactation Curve Parameter Estimation
AllCurves() runs multiple lactation curve models and extracts selection criteria for each model.
This package summarises the most common lactation curve models from the last century and provides a tool
for researchers to quickly decide on which model fits their data best to proceed with their analysis.
Start parameters were optimized based on a dataset with 1.7 million Holstein-Friesian cows. If convergence fails,
the start parameters need to be manually adjusted.
The models included in the package are taken from:
(1) Michaelis-Menten: Michaelis, L. and M.L. Menten (1913).
(1a) Michaelis-Menten (Rook): Rook, A.J., J. France, and M.S. Dhanoa (1993).
(1b) Michaelis-Menten + exponential (Rook): Rook, A.J., J. France, and M.S. Dhanoa (1993).
(2) Brody (1923): Brody, S., A.C. Ragsdale, and C.W. Turner (1923).
(3) Brody (1924): Brody, S., C.W. Tuner, and A.C. Ragsdale (1924).
< https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2140670/>
(4) Schumacher: Schumacher, F.X. (1939) in Thornley, J.H.M. and J. France (2007).
< https://books.google.com.au/books/about/Mathematical_Models_in_Agriculture.html?id=rlwBCRSHobcC&redir_esc=y>
(4a) Schumacher (Lopez et al. 2015): Lopez, S. J. France, N.E. Odongo, R.A. McBride, E. Kebreab, O. AlZahal, B.W. McBride, and J. Dijkstra (2015).
(5) Parabolic exponential (Adediran): Adediran, S.A., D.A. Ratkowsky, D.J. Donaghy, and A.E.O. Malau-Aduli (2012).
(6) Wood: Wood, P.D.P. (1967).
(6a) Wood reparameterized (Dhanoa): Dhanoa, M.S. (1981).
(6b) Wood non-linear (Cappio-Borlino): Cappio-Borlino, A., G. Pulina, and G. Rossi (1995).
(7) Quadratic Polynomial (Dave): Dave, B.K. (1971) in Adediran, S.A., D.A. Ratkowsky, D.J. Donaghy, and A.E.O. Malau-Aduli (2012).
(8) Cobby and Le Du (Vargas): Vargas, B., W.J. Koops, M. Herrero, and J.A.M Van Arendonk (2000).
(9) Papajcsik and Bodero 1: Papajcsik, I.A. and J. Bodero (1988).
(10) Papajcsik and Bodero 2: Papajcsik, I.A. and J. Bodero (1988).
(11) Papajcsik and Bodero 3: Papajcsik, I.A. and J. Bodero (1988).
(12) Papajcsik and Bodero 4: Papajcsik, I.A. and J. Bodero (1988).
(13) Papajcsik and Bodero 6: Papajcsik, I.A. and J. Bodero (1988).
(14) Mixed log model 1 (Guo and Swalve): Guo, Z. and H.H. Swalve (1995).
< https://journal.interbull.org/index.php/ib/issue/view/11>
(15) Mixed log model 3 (Guo and Swalve): Guo, Z. and H.H. Swalve (1995).
< https://journal.interbull.org/index.php/ib/issue/view/11>
(16) Log-quadratic (Adediran et al. 2012): Adediran, S.A., D.A. Ratkowsky, D.J. Donaghy, and A.E.O. Malau-Aduli (2012).
(17) Wilmink: J.B.M. Wilmink (1987).
(17a) modified Wilmink (Jakobsen): Jakobsen J.H., P. Madsen, J. Jensen, J. Pedersen, L.G. Christensen, and D.A. Sorensen (2002).
(17b) modified Wilmink (Laurenson & Strucken): Strucken E.M., Brockmann G.A., and Y.C.S.M. Laurenson (2019).
< http://www.aaabg.org/aaabghome/AAABG23papers/35Strucken23139.pdf>
(18) Bicompartemental (Ferguson and Boston 1993): Ferguson, J.D., and R. Boston (1993) in Adediran, S.A., D.A. Ratkowsky, D.J. Donaghy, and A.E.O. Malau-Aduli (2012).
(19) Dijkstra: Dijkstra, J., J. France, M.S. Dhanoa, J.A. Maas, M.D. Hanigan, A.J. Rook, and D.E. Beever (1997).
(20) Morant and Gnanasakthy (Pollott et al 2000): Pollott, G.E. and E. Gootwine (2000).
(21) Morant and Gnanasakthy (Vargas et al 2000): Vargas, B., W.J. Koops, M. Herrero, and J.A.M Van Arendonk (2000).
(22) Morant and Gnanasakthy (Adediran et al. 2012): Adediran, S.A., D.A. Ratkowsky, D.J. Donaghy, and A.E.O. Malau-Aduli (2012).
(23) Khandekar (Guo and Swalve): Guo, Z. and H.H. Swalve (1995).
< https://journal.interbull.org/index.php/ib/issue/view/11>
(24) Ali and Schaeffer: Ali, T.E. and L.R. Schaeffer (1987).
< https://cdnsciencepub.com/doi/pdf/10.4141/cjas87-067>
(25) Fractional Polynomial (Elvira et al. 2013): Elvira, L., F. Hernandez, P. Cuesta, S. Cano, J.-V. Gonzalez-Martin, and S. Astiz (2012).
(26) Pollott multiplicative (Elvira): Elvira, L., F. Hernandez, P. Cuesta, S. Cano, J.-V. Gonzalez-Martin, and S. Astiz (2012).
(27) Pollott modified: Adediran, S.A., D.A. Ratkowsky, D.J. Donaghy, and A.E.O. Malau-Aduli (2012).
(28) Monophasic Grossman: Grossman, M. and W.J. Koops (1988).
(29) Monophasic Power Transformed (Grossman 1999): Grossman, M., S.M. Hartz, and W.J. Koops (1999).
(30) Diphasic (Grossman 1999): Grossman, M., S.M. Hartz, and W.J. Koops (1999).
(31) Diphasic Power Transformed (Grossman 1999): Grossman, M., S.M. Hartz, and W.J. Koops (1999).
(32) Legendre Polynomial (3th order): Jakobsen J.H., P. Madsen, J. Jensen, J. Pedersen, L.G. Christensen, and D.A. Sorensen (2002).
(33) Legendre Polynomial (4th order): Jakobsen J.H., P. Madsen, J. Jensen, J. Pedersen, L.G. Christensen, and D.A. Sorensen (2002).
(34) Legendre + Wilmink (Lidauer): Lidauer, M. and E.A. Mantysaari (1999).
< https://journal.interbull.org/index.php/ib/article/view/417>
(35) Natural Cubic Spline (3 percentiles): White, I.M.S., R. Thompson, and S. Brotherstone (1999).
(36) Natural Cubic Spline (4 percentiles): White, I.M.S., R. Thompson, and S. Brotherstone (1999).
(37) Natural Cubic Spline (5 percentiles): White, I.M.S., R. Thompson, and S. Brotherstone (1999)
(38) Natural Cubic Spline (defined knots according to Harrell 2001): Jr. Harrell, F.E. (2001).
< https://link.springer.com/book/10.1007/978-3-319-19425-7>
The selection criteria measure the goodness of fit of the model and include:
Residual standard error (RSE),
R-square (R2),
log likelihood,
Akaike information criterion (AIC),
Akaike information criterion corrected (AICC),
Bayesian Information Criterion (BIC),
Durbin Watson coefficient (DW).
The following model parameters are included:
Residual sum of squares (RSS),
Residual standard deviation (RSD),
F-value (F) based on F-ratio test.