evaluation.py

#   The energetic value of feeds is described using four different country-specific systems of feed evaluation, the
#   German, Finnish, British and French system.
#
#   Energy is the first limiting factor for the performance of a dairy cow, apart from feed intake capacity, therefore
#   the accuracy of the energetic evaluation of the feeds is of great importance for the accuracy of SOLID-DSS as a whole.
#   Offering several different systems of energy evaluation also improves the usability of SOLID-DSS. This first version
#   of SOLID-DSS includes the above mentioned four systems of energy evaluation, but adding further systems is desirable.
#
#   For the protein evaluation of feeds, only the German uCP system is used.
#
#   Generally speaking, the protein value of a feed is related to the degradability of the protein in the rumen, the
#   content of amino acids in the undegraded crude protein and the digestibility of the amino acids in the undegraded
#   dietary protein. Internationally, there is a trend towards sophisticated systems of protein evaluation that take the
#   dynamics of feed digestion into account and describe the nitrogen metabolism in the gastro-intestinal tract of
#   ruminants.
#
#   The British system of protein evaluation, for example, is one of those sophisticated systems, requring digestibility
#   parameters analysed with in vitro and NIRS methods.
#
#   The diet model of SOLID-DSS is used in conjunction with the plant growth models. Unfortunately none of the plant
#   growth models available today can supply the data needed to characterize feeds according to the British system of
#   protein evaluation.
#
#   That is why the German uCP system, which is the simplest out of the four above-mentioned country-specific systems of
#   feed evaluation, is used for all countries in SOLID-DSS. Even though the amount of utilizable protein at the
#   duodenum is defined as the sum of ruminally undegraded protein and microbial protein, the uCP content of a feed is
#   calculated with simple empirical equations.
#
#   In a comparison between the German uCP system with the Finnish system and the NRC (2001), using data from US
#   production experiments, Schwab et al. (2005) found that the German uCP system predicted milk protein yield as well or
#   even better than the NRC and Finnish system, despite being much simpler. The fact that the German uCP system performed
#   well in comparison with more sophisticated systems, despite its simplicity, encourages its use for SOLID-DSS.
#
#   Feed intake is predicted according to GrazeIn, a system based on the fill value system of INRA (Agabriel 2010). In
#   order to calculate the fill values of the forages, the parameters QIL (for dairy cows) and QIB (for dairy heifers)
#   are calculated, see below.
#
#   REFERENCES
#
#   Agabriel, J. 2010. Alimentation des bovins, ovins et caprins. Besoins des animaux - Valeurs des aliments. Tables INRA
#   2010. Editions Quae, France.
#
#   Feed into Milk Consortium. 2004. Feed into Milk. A new applied feeding system for dairy cows. An advisory manual.
#   Ed. Thomas, C. Nottingham University Press, UK.
#
#   GfE [Society of Nutrition Physiology] 2001. Empfehlungen zur Energie- und Nährstoffversorgung der Milchkühe und
#   Aufzuchtrinder [Recommendations on the energy and nutrient supply for dairy cows and heifers]. DLG-Verlag, Frankfurt/
#   Main, Germany.
#
#   Lebzien, P., Voigt, J., Gabel, M. und Gädeken, D. 1996. Zur Schätzung der Menge an nutzbarem Rohprotein am Duodenum
#   von Milchkühen. [On the estimation of utilizable crude protein at the duodenum of dairy cows] Journal of Animal
#   Physiology and Animal Nutrition 76:218-223.
#
#   MTT. 2006. Rehutaulukot ja ruokintasuositukset [Feed tables and feeding recommendations]. Agrifood Research Finland,
#   Jokioninen, Finland.
#
#   MTT 2014. Rehutaulukot ja ruokintasuositukset [Feed tables and feeding recommendations] [online]. Agrifood
#   Research Finland, Jokioinen. Accessed last on November 20, 2014, available at:
#   https://portal.mtt.fi/portal/page/portal/Rehutaulukot/feed_tables_english
#
#   Schwab, G.C., Huhtanen, P., Hunt, C.W. and Hvelplund, T. 2005. Nitrogen requirements of cattle. In: Pfeffer, E. and
#   Hristov, A.N. (ed.). Nitrogen and Phosphorus Nutrition of Cattle. CABI Publishing, Wallingford, UK. p. 13-70.
#
#   Tran, G. et Sauvant, D. 2002. In: Sauvant D., Perez J.-M. et Tran G. (eds.) Tables de composition et de valeur
#   nutritive des matières premières destinées aux animaux d´élevage: porcs, volailles, bovins, ovins, caprins, lapins,
#   chevaux, poissons. Paris, Inra-AFZ, France. p. 22.
#
#   LICENSE
#
#   Copyright 2014 Jan Vaillant   <jan.vaillant@zalf.de>
#   Copyright 2014 Lisa Baldinger <lisa.baldinger@boku.ac.at>
#
#   Distributed under the MIT License. See accompanying file LICENSE or copy at http://opensource.org/licenses/MIT
#
#   Any publication for which this file or a derived work is used must include an a reference to:
#
#   Vaillant, J. and Baldinger, L. 2016.
#   Application note: An open-source JavaScript library to simulate dairy cows and young stock,
#   their growth, requirements and diets.
#   Computers and Electronics in Agriculture, Volume 120, January 2016, Pages 7–9
# */
#
# dairy.feed = dairy.feed ||:}
#
# dairy.feed.evaluation = (function ():
#
# #
#   The German system of feed evaluation is described in GfE (2001)
#
#   Energy is expressed in MJ net energy lactation (NEL)
#
#   Protein is expressed in g utilizable crude protein at the duodenum (uCP)
# */
#
# de = (function ():
#
#   #
#     Equation for calculating gross energy (GE) taken from GfE (2001) equation 1.1.1
#
#     GE  [MJ kg-1 (DM)]  gross energy
#     CP  [g kg-1 (DM)]   crude protein, e.g. 235
#     EE  [g kg-1 (DM)]   ether extracts, e.g. 43
#     CF  [g kg-1 (DM)]   crude fibre, e.g. 172
#     OM  [g kg-1 (DM)]   organic matter, e.g. 905
#   */
#
#   GE = function (CP, EE, CF, OM):
#
#     return 0.0239 * CP + 0.0398 * EE + 0.0201 * CF + 0.0175 * (OM - EE - CP - CF)
#
#   }
#
#   #
#     Equation for calculating metabolizable energy (ME) taken from GfE (2001) equation 1.1.2
#
#     ME  [MJ kg-1 (DM)]  metabolizable energy
#     CP  [g kg-1 (DM)]   crude protein, e.g. 235
#     EE  [g kg-1 (DM)]   ether extracts, e.g. 43
#     EED [kg kg-1]       digestibility of ether extracts, e.g. 0.61
#     CF  [g kg-1 (DM)]   crude fibre, e.g. 172
#     CFD [kg kg-1]       digestibility of crude fiber, e.g. 0.81
#     OM  [g kg-1 (DM)]   organic matter, e.g. 905
#     OMD [kg kg-1]       digestibility of organic matter, e.g. 0.84
#   */
#
#   ME = function (CP, EE, EED, CF, CFD, OM, OMD):
#
#     ME = 0
#
#     #contents of digestible ether extracts, digestible crude fiber and digestible organic matter [g kg-1 (DM)]*/
#     dEE = EE * EED
#     dCF = CF * CFD
#     dOM = OM * OMD
#
#     # metabolizable energy [MJ kg-1 (DM)], e.g. 12.0 */
#     ME = 0.0312 * dEE + 0.0136 * dCF + 0.0147 * (dOM - dEE - dCF) + 0.00234 * CP
#
#     return ME
#
#   }
#
#   #
#     Equation for calculating the metabolizability (q) taken from  GfE (2001) page 17
#
#     Equation for calculating net energy for lactation (NEL) taken from GfE (2001) equation 1.3.1
#
#     NEL [MJ kg-1 (DM)]  net energy for lactation, e.g. 7.04
#     ME  [MJ kg-1 (DM)]  metabolizable energy
#     GE  [MJ kg-1 (DM)]  gross energy
#   */
#
#   NEL = function (ME, GE):
#
#     NEL = 0
#
#     #the metabolizability is the factor between GE and ME, e.g. 64*/
#     q = ME / GE * 100
#
#     # net energy for lactation [MJ kg-1 (DM)]*/
#     NEL = 0.6 * (1 + 0.004 * (q - 57)) * ME
#
#     return NEL
#
#   }
#
#   #
#     Equation for calculating utilizable crude protein at the duodenum (uCP) taken from GfE (2001) Table 2.1.1, equation
#     1a, originally published by Lebzien et al. (1996). (In the above mentioned comparison between different systems of
#     protein evaluation done by Schwab et al. (2005), equation 1a was used as well.)
#
#     uCP [g kg-1 (DM)]   utilizable crude protein
#     ME  [MJ kg-1 (DM)]  metabolizable energy
#     CP  [g kg-1 (DM)]   crude protein
#   */
#
#   uCP = function (ME, CP):
#
#     return 8.76 * ME + 0.36 * CP
#
#   }
#
#
#   #
#     Apart from satisfying the cow´s requirement of uCP, the German system also calculates the ruminal nitrogen balance
#     in order to ensure an adequate supply of ruminally available protein for the ruminal microbes.
#
#     Equation for calculating the ruminal nitrogen balance (RNB) taken from GfE (2001) page 45
#
#     RNB [g kg-1 (DM)] ruminal nitrogen balance, e.g. 4
#     CP  [g kg-1 (DM)] crude protein, e.g. 235
#     uCP [g kg-1 (DM)] utilizable crude protein, e.g. 220
#   */
#
#   RNB = function (CP, uCP):
#
#     return (CP - uCP) / 6.25
#
#   }
#
#   return:
#       GE: GE
#     , ME: ME
#     , E_f: NEL
#     , E_c: NEL
#     , uCP: uCP
#     , RNB: RNB
#   }
#
# }())
#
# fi = (function ():
#
#   #
#     The last description of the Finnish system of feed evaluation published in print is MTT (2006). Since then all
#     updates have been published online, hereafter quoted as MTT (2014).
#
#     Equations for calculating the energy contents of forages taken from the sub-site "Energy value, ruminants" of
#     MTT (2014)
#
#     Energy is expressed in MJ metabolizable energy (ME)
#
#     ME_f  [MJ kg-1 (DM)]      metabolizable energy content of a forage, e.g. 11.4
#     OM    [g kg-1 (DM)]       organic matter, e.g. 915
#     OMD   [kg kg-1]           digestibility of organic matter, e.g. 0.78
#     type  [enum]              grasssilage (default), hay, straw, wholecropsilage
#
#     TODO: Im finnischen System gibts eine correction equation for energy intake, die auf der supply-Seite angewendet
#     wird. Das ist noch zu klären ob und wie wir das anwenden.
#   */
#
#   ME_f = function (OMD, OM, type):
#
#     # In the MTT feed tables, the content of digestible organic matter in dry matter is called D-value, but because
#     using the same terminology in all country-specific systems makes SOLID-DSS less susceptible to errors, the term dOM
#     is used instead [g kg-1 (DM)]*/
#     dOM = OM * OMD
#
#     # fresh forages, fresh maize, fresh sorghum and grasssilage*/
#     ME_f = 0.016 * dOM
#
#     #in Finland, maize silage is not commonly used. However, in case of using maize silage, the equation for wholecrop
#     cereal silages can be used for maize silage as well. Consequently, the equation for maize silage is the same as the
#     one for whole crop silage.*/
#
#     if (type === 'hay')
#       ME_f = 0.0169 * dOM - 1.05
#     if (type === 'maizesilage')
#       ME_f = 0.0155 * dOM
#     elif (type === 'straw')
#       ME_f = 0.014 * dOM
#     elif (type === 'wholecropsilage')
#       ME_f = 0.0155 * dOM
#
#     return ME_f
#
#   }
#
#   #
#     Equations for calculating the energy contents of concentrates taken from the sub-site "Energy value, ruminants" of
#     MTT (2014)
#
#     Energy is expressed in MJ metabolizable energy (ME)
#
#     The feed table included in SOLID-DSS gives the NfE digestibility of the feeds, but the plant growth models in
#     SOLID-DSS don´t supply the digestibility of NfE, therefore the following calculation is mainly given for reasons of
#     completeness.
#
#     ME_c  [MJ kg-1 (DM)]      metabolizable energy of a concentrate, e.g. 12.2
#     CP    [g kg-1 (DM)]       crude protein content, e.g. 125
#     CPD   [kg kg-1]           digestibility of crude protein, e.g. 0.71
#     CF    [g kg-1 (DM)]       crude fibre, e.g. 103
#     CFD   [kg kg-1]           digestibility of crude fiber, e.g. 0.30
#     EE    [g kg-1 (DM)]       ether extract content, e.g. 60
#     EED   [kg kg-1]           digestibility of ether extracts, e.g. 0.84
#     NFE   [g kg-1 (DM)]       nitrogen free extracts, e.g. 500
#     NFED  [kg kg-1]           digestibility of nitrogen free extracts, e.g. 0.83
#   */
#
#   ME_c = function (CP, CPD, CF, CFD, EE, EED, NFE, NFED):
#
#     dCP = CP * CPD
#     #content of digestible crude protein*/
#     dEE = EE * EED
#     #content of digestible ether extracts*/
#     dCF = CF * CFD
#     #content of digestible crude fiber*/
#     dNFE = NFE * NFED
#     #content of digestible nitrogen free extracts*/
#
#     ME_c = (15.2 * dCP + 34.2 * dEE + 12.8 * dCF + 15.9 * dNFE) * 1e-3
#
#     return ME_c
#
#   }
#
#   return:
#       E_f: ME_f
#     , E_c: ME_c
#   }
#
# }())
#
# gb = (function ():
#
#   #
#     The British system of feed evaluation is described in Feed into Milk (2004)
#
#     Energy is expressed in MJ metabolisable energy (ME)
#
#     Only the energy values of forages are calculated, the energy values of concentrates are taken from the feed table
#     that comes with SOLID-DSS. The reason is that the plant growth models can´t supply the parameters NCGD and AHEE,
#     which are needed for the calculation of the energy content of concentrates. NCGD is the neutral detergent cellulase
#     plus gammanase digestibility, which is a modified version of Van Soest´s NDF. AHEE is the acid hydrolysed ether
#     extract, meaning that before ether extraction the feed is hydrolysed with hydrochloric acid.
#
#     ME              [MJ kg-1 (DM)]  metabolizable energy, e.g. 12.8
#     OM              [g kg-1 (DM)]   organic matter, e.g. 911
#     OMD             [kg kg-1]       digestibility of organic matter, e.g. 0.88
#     is_grass_or_hay [bool]
#   */
#
#   ME_f = function (OM, OMD, is_grass_or_hay):
#
#     # In Feed into Milk, the content of digestible organic matter in dry matter is called DOMD, expressed in %, so the
#     equation is ME = 0.16 * DOMD. Because using the same terminology in all country-specific systems makes SOLID-DSS less
#     susceptible to errors, the term dOM is used instead [g kg-1 (DM)], so the equation is ME = 0.016 * dOM*/
#     dOM = OM * OMD
#
#     ME_f = 0.016 * dOM
#
#     if (is_grass_or_hay)
#       ME_f = 0.015 * dOM
#
#     return ME_f
#
#   }
#
#   return:
#       E_f: ME_f
#     , E_c: ME_f
#   }
#
# }())
#
# fr = (function ():
#
#   #
#     The French system of feed evaluation is described in Agabriel (2010)
#
#     Energy is expressed in unité fourragére lait (UFL). One UFL equals the net energy for lactation of 1 kg standard
#     barley.
#
#     Equations for calculating energy values (UFL) of forages taken from Agabriel (2010) Tables 8.1, 8.8 and 8.9.
#
#     In order to provide values for feeding level (L), the requirements (req_m, req_t) according to the French system are
#     used, details see dairy.requirements.
#
#     UFL_f   [UFL kg-1 (DM)] energy content of a forage, e.g. 0.89
#     OMD     [kg kg-1]       digestibility of organic matter, e.g. 0.72
#     OM      [?]
#     CP      [g kg-1 (DM)]   crude protein content, e.g. 134
#     CF      [g kg-1 (DM)]   crude fibre content, e.g. 296
#     type    [enum]          type of feed
#     DM      [%]             dry matter content
#     delta_F1
#     pH      []              pH of grass silage
#     wilted  [bool]          grasssilage wilted (true) or grassilage short cut and directly ensiled
#     req_m   [UFL]           maintenance requirements
#     req_t   [UFL]           total requirements
#   */
#
#   UFL_f = function (OMD, OM, CP, CF, type, DM, delta_F1, pH, wilted, req_m, req_t):
#
#     UFL_f = 0
#         # default in case grass silage pH is not available */
#       , pH = pH || 4.8
#
#
#     #contents of crude protein and crude fibre in organic matter, g kg-1 OM*/
#     CP_o = CP / OM * 1000
#     CF_o = CF / OM * 1000
#
#  # gross energy [kcal kg-1 (OM)] content per kg organic matter of fresh fodder, hay and haylage */
#     GE_o = 4531 + 1.735 * CP_o + delta_F1
#     if (type === 'freshsorghum'):
#       GE_o = 4478 + 1.265 * CP_o
#     } elif (type === 'freshmaize'):
#       GE_o = 4487 + 2.019 * CP_o
#     } elif (type === 'maizesilage'):
#       if (DM <= 30)
#         GE_o = 1.02 * (4487 + 2.019 * CP_o)
#       else
#         GE_o = 4487 + 2.019 * CP_o + 25
#     } elif (type === 'grassilage'):
#       if (wilted)
#         GE_o = 1.03 * (3910 + 2.45 * CP_o + 169.9 * pH)
#       else
#         GE_o = 3910 + 2.45 * CP_o + 169.9 * pH
#   #the gross energy content of wholecropsilage is calculated the same way as wilted grasssilage, that´s why the equations
#   are the same*/
#     } elif (type === 'wholecropsilage'):
#       GE_o = 1.03 * (3910 + 2.45 * CP_o + 169.9 * pH)
#     } elif (type === 'dehydrated alfalfa'):
#       GE_o = 4618 + 2.051 * CP_o
#     }
#
#     #
#     delta_F1  []  feed material correction coefficient:
#                     grasses = -71
#                     clover, sainfoin, grass from mountainous areas, hay from leys and whole crops = -11
#                     fresh alfalfa and fresh fodder and hay from permanent grassland = + 82
#     */
#
#     #For the remaining steps of the energy calculation, GE is needed on dry matter basis*/
#     GE = (GE_o * OM) / 1000
#
#     # digestibility of energy [%] in fresh grasses and legumes, e.g. 68
#     In INRA the values for OMD are in %, e.g. 80. Because using the same terminology in all country-specific systems
#     makes SOLID-DSS less susceptible to errors, OMD is used in kg kg-1, just like in the other systems. Consequently,
#     the French equations for dE (%) were adjusted.*/
#     dE = 0.957 * (OMD * 100) - 0.068
#     if (type === 'freshmaize')
#       dE = 0.997 * (OMD * 100) - 2.53
#     if (type === 'maizesilage')
#       dE = 1.001 * (OMD * 100) - 2.86
#     if (type === 'grasssilage')
#       dE = 1.0263 * (OMD * 100) - 5.723
#     #dE of wholecropsilage is calculated the same way as wilted grasssilage, that´s why the equations are the same*/
#     if (type === 'wholecropsilage')
#       dE = 1.0263 * (OMD * 100) - 5.723
#     if (type === 'dehydrated alfalfa')
#       dE = 1.003 * (OMD * 100) - 3.00
#     if (type === 'straw')
#       dE = 0.985 * (OMD * 100) - 2.949
#     elif (type === 'hay')
#       dE = 0.985 * (OMD * 100) - 2.556
#
#     # feeding level, e.g. 1.5 */
#     L = req_t / req_m
#
#     #energy losses due to urine excretion and gaseous losses products of digestion = the energy loss between digestible
#     energy (DE) and metabolizable energy (ME), e.g. 0.81*/
#     ME_DE = (84.17 - 0.0099 * CF_o - 0.0196 * CP_o + 2.21 * L) / 100
#
#     # ME [kcal kg-1 (DM)], e.g. 2536 */
#     ME = GE * (dE/100) * ME_DE
#
#     # efficiency of utilizing metabolizable energy for milk production = energy lost as heat, e.g. 0.60*/
#     k_l = 0.463 + 0.24 * ME / GE
#
#     #net energy for lactation, NEL [kcal kg-1 (DM)], e.g. 1512*/
#     NEL = ME * k_l
#
#     #UFL_f kg-1 DM, e.g. 0.89*/
#     UFL_f = ME * k_l / 1700
#
#     return UFL_f
#
#   }
#
#   #
#     Equations for calculating energy values (UFL) of concentrates taken from Agabriel (2010) Tables 8.1, 8.8 and 8.9.
#
#     UFL_c     [kg-1 (DM)]     energy content of a concentrate
#     OMD       [kg kg-1]       digestibility of organic matter, e.g. 0.72
#     OM        [?]
#     CP        [g kg-1 (DM)]   crude protein, e.g. 111
#     EE        [g kg-1 (DM)]   ether extracts, e.g. 67
#     CF        [g kg-1 (DM)]   crude fibre, e.g. 135
#     NDF       [g kg-1 (DM)]   neutral detergent fibre, e.g. 336
#     ash       [g kg-1 (DM)]   ash, e.g. 30
#     req_m     [UFL]           maintenance requirements
#     req_t     [UFL]           total requirements
#     delta_C1  []              feed material group correction coefficient taken from Tran et Sauvant (2002)
#
#     corn gluten meal = 308
#     alfalfa protein concentrate = 248
#     wheat distillery by-products, wheat gluten feed, maize bran, rice bran = 138
#     full fat rapeseed, full fat linseed, full-fat cottonseed, cottonseed meal = 116
#     oats, wheat milling by-products, corn gluten feed and other maize starch by-products, maize feed
#     flour, sorghum = 75
#     dehydrated grass, straw = 46
#     barley = 36
#     linseed meal, palm kernel meal, full fat soybean, soybean meal, sunflower meal, sunflower seed = -46
#     cassava = -55
#     faba bean, lupin, pea = -87
#     sugar beet pulp, molasses, vinasse, potato pulp = -103
#     whey = -177
#     soybean hulls = -231
#     all others = 0
#   */
#
#   UFL_c = function (OMD, OM, CP, EE, CF, NDF, ash, delta_C1, req_m, req_t):
#
#     UFL_c = 0
#
#     #contents of crude protein and crude fibre in organic matter, g kg-1 OM*/
#     CP_o = CP / OM * 1000
#     CF_o = CF / OM * 1000
#
#     # gross energy content per kg dry matter [kcal kg-1 DM]*/
#     GE = 4134 + 1.473 * CP + 5.239 * EE + 0.925 * CF - 4.44 * ash + delta_C1
#
#
#     # digestibility of energy [%], e.g. 72
#     In INRA the values for OMD are in %, e.g. 80. Because using the same terminology in all country-specific systems
#     makes SOLID-DSS less susceptible to errors, OMD is used in kg kg-1, just like in the other systems. Consequently,
#     the French equations for dE (%) were adjusted.*/
#     dE = (OMD * 100) - 3.94 + 0.0104 * CP + 0.0149 * EE + 0.0022 * NDF - 0.0244 * ash
#
#     # feeding level, e.g. 1 */
#     L = req_t / req_m
#
#     #energy losses due to urine excretion and gaseous losses products of digestion = the energy loss between digestible
#     energy (DE) and metabolizable energy (ME), e.g. 0.83*/
#     ME_DE_ratio = (84.17 - 0.0099 * CF_o - 0.0196 * CP_o + 2.21 * L) / 100
#
#     # ME [kcal kg (DM)], e.g. 2818 */
#     ME = GE * (dE / 100) * ME_DE_ratio
#
#     # efficiency of utilizing metabolizable energy for milk production = energy lost as heat, e.g. 0.61*/
#     k_l = 0.463 + 0.24 * ME / GE
#
#     #net energy for lactation, NEL [kcal kg-1 (DM)], e.g. 1709*/
#     NEL = ME * k_l
#
#     #UFL_c kg-1 DM, e.g. 1.01*/
#     UFL_c = NEL / 1700
#
#     return UFL_c
#
#   }
#
#   #
#     In SOLID-DSS, feed intake is predicted according to GrazeIn (details see dairy.intake). For the calculation of the
#     fill values of forages, the parameters QIL (for dairy cows) and QIB (for dairy heifers) are required.
#
#     Equations for calculating QIL and QIB are taken from Agabriel (2010), Table 8.14.
#
#     In GrazeIn, OMD is called dOM and is expressed in %, e.g. 72. Because using the same terminology in all country-
#     specific systems makes SOLID-DSS less susceptible to errors, OMD is used in kg kg-1 (e.g. 0.72), just like in the
#     other systems. Consequently, the equations for QIL and QIB were adjusted.
#
#     The one expection is straw, for which Agabriel (2010) doesn´t supply an equation for calculating the fill value.
#     Therefore linear regressions for the fill values of straw depending on OMD were produced based on data from the
#     feed tables in Agabriel (2010) and expressed as QIL = ... and QIB = ... The linear regressions are valid for OMD
#     values between 0.42 and 0.68 and fill values between 1.00 and 1.60 (QIL) and 1.07 and 2.00 (QIB). The coefficients
#     of determination of the regressions are 0.23 (QIL) and 0.23 (QIB).
#
#     QIL       [g kg-1]      ingestibility in g per kg metabolic live weight, dairy cows
#     QIB       [g kg-1]      ingestibility in g per kg metabolic live weight, heifers
#     OMD       [kg kg-1]     digestibility of organic matter, e.g. 0.72
#     CP        [g kg-1 (DM)] crude protein content, e.g. 235
#     DM        [g kg-1]      dry matter content
#     type      [enum]        type of forage (fresh, grasssilage, hay, maizesilage)
#     delta_FR1 []           species adjustment parameter fresh:
#                               cows (QIL)
#                                 perm. grassland = 0
#                                 grasses = -3.7
#                                 legumes = 1.0
#                               young stock (QIB)
#                                 perm. grassland = 0
#                                 grasses = -1.6
#                                 legumes = 4.1
#     delta_S1  []            species adjustment parameter silages:
#                               cows (QIL)
#                                 perm. grassland = 0
#                                 grasses = -1.4
#                                 legumes = 2.8
#                               young stock (QIB)
#                                 perm. grassland = 0
#                                 grasses = -1.9
#                                 legumes = 2.8
#     delta_H1  []            species adjustment parameter hay:
#                               cows (QIL)
#                                 perm. grassland = 0
#                                 grasses = -0.9
#                                 legumes = 2.6
#                               young stock (QIB)
#                                 perm. grassland = 0
#                                 grasses = -1.4
#                                 legumes = 3.4
#     delta_S2  []            technical adjustment parameter silage:
#                               cows (QIL)
#                                 unwilted & w/o additives = -10.1
#                                 unwilted & w additives = -0.8
#                                 wilted = 1.6
#                                 haylage = 0
#                               young stock (QIB)
#                                 unwilted & w/o additives = -9.9
#                                 unwilted & w additives = -0.9
#                                 wilted = 1.9
#                                 haylage = 0
#     delta_H2  []            technical adjustment parameter hay:
#                               cows (QIL)
#                                 ventilated = 6.6
#                                 wilted in sun & good weather = 5.5
#                                 wilted in sun = 0
#                               young stock (QIB)
#                                 ventilated = 6.6
#                                 wilted in sun & good weather = 5.2
#                                 wilted in sun = 0
#   */
#
#   QIL = function (OMD, CP, DM, type, delta_FR1, delta_S1, delta_H1, delta_S2, delta_H2):
#
#     QIL = 0
#
#     if (type === 'fresh')
#       QIL = 66.3 + 0.655 * (OMD * 100) + 0.098 * CP + 0.626 * (DM / 10) + delta_FR1
#     elif (type === 'grasssilage')
#       QIL = 99.3 + 0.167 * (OMD * 100) + 0.128 * CP + delta_S1 + delta_S2
#     elif (type === 'hay')
#       QIL = 82.4 + 0.491 * (OMD * 100) + 0.114 * CP + delta_H1 + delta_H2
#     elif (type === 'maizesilage')
#       QIL = -76.4 + 2.39 * (OMD * 100) + 1.44 * (DM / 10)
#     elif (type === 'straw')
#       QIL = 140 / (1.938 - 0.013 * (OMD * 100))
#     else
#       QIL = 66.3 + 0.655 * (OMD * 100) + 0.098 * CP + 0.626 * (DM / 10)
#
#     return QIL

#   }
#
#   QIB = function (OMD, CP, DM, type, delta_FR1, delta_S1, delta_H1, delta_S2, delta_H2):
#
#     QIB = 0
#
#     if (type === 'fresh')
#       QIB = 6.44 + 0.782 * (OMD * 100) + 0.112 * CP + 0.679 * (DM / 10) + delta_FR12
#     elif (type === 'grasssilage')
#       QIB = 47 + 0.228 * (OMD * 100) + 0.148 * CP + delta_S12 + delta_S22
#     elif (type === 'hay')
#       QIB = 30.3 + 0.559 * (OMD * 100) + 0.132 * CP + delta_H12 + delta_H22
#     elif (type === 'maizesilage')
#       QIB = -45.49 + 1.34 * (OMD * 100) + 1.15 * (DM / 10)
#     elif (type === 'straw')
#       QIB = 95 / (2.380 - 0.018 * (OMD * 100))
#     else
#       QIB = 6.44 + 0.782 * (OMD * 100) + 0.112 * CP + 0.679 * (DM / 10)
#
#     return QIB
#
#   }
#
#   return:
#       E_f: UFL_f
#     , E_c: UFL_c
#     , QIL: QIL
#     , QIB: QIB
#   }
#
# }())
#
# return:
#     de: de
#   , fi: fi
#   , gb: gb
#   , fr: fr
# }
#
# }())
#
#