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J. agric. Sci., Gamb. (1978), 90, 47-68 4 7 With 6 text-figures Printed in Great Britain The estimation of the nutritive value of feeds as energy sources for ruminants and the derivation of feeding systems B Y K. L. BLAXTER AND A. W. BOYNE Rowett Research Institute, Bucksburn, Aberdeen AB2 9SB {Received 17 May 1977) SUMMARY The results of 80 calorimetric experiments with sheep and cattle, mostly conducted in Scotland, were analysed using a generalization of the Mitscherlich equation R = B(l-exp(-pG))-l, where R is daily energy retention and G daily gross energy intake, both scaled by dividing by the fasting metabolism. The relations between gross energy and metaboli- zable energy were also examined. Methods of fitting the Mitscherlich equation and the errors associated with it are presented. I t is shown that the gross energy of the organic matter of feed can be estimated from proximate principles with an error of ± 2-3 % (coefficient of variation) and that provided different classes of feed are distinguished, the metabolizable energy of organic matter can be estimated from gross energy and crude fibre content with an error of ±6-9%. Parameters of the primary equation made with cattle agreed with those made with sheep and there was no evidence of non-proportionality of responses on substitution of feeds in mixtures. The efficiency of utilization of gross energy for maintenance and for body gain of energy was related to the metabolizability of gross energy and, in addition, to fibre or to protein content. Prediction equations are presented which describe these relation- ships. It is shown that the primary equation can be manipulated to express a number of biological concepts and that its two parameters B and p can be simply derived from estimates of the two efficiency terms for maintenance and production. The results are discussed in relation to the design of feeding systems for ruminant animals and to the derivation of optima in their feeding. TNTTt ODTTPTTOW energy for maintenance, km, varied with the quality J.1M l H W U ^ l l U a o f ^ ^ d . e t from a b o u t Q 6 Q t Q Q ^g T h e g l o p e o f t h e The relationship between the rate of feed intake equation above maintenance, called the efficiency by a growing or fattening ruminant and the rate at of utilization of metabolizable energy for fattening, which it retains energy in its body is curvilinear. kf, varied more with quality of the diet than did Successive increments of daily intake result in km, ranging from O2 to 0-6. progressively smaller increments in daily energy In an attempt to devise a feeding system based on retention. Blaxter & Graham (1955) showed that these relationships Blaxter (1962) had to introduce this relationship could be described by a simple a component to accommodate the decline in pro- exponential equation and during the next few years portional retention of the gross energy of the feed it was shown that no great error was involved if the as the amount ingested each day was increased. This relationship between daily rate of energy retention term, the feeding level correction, in effect intro- and rate of feed intake expressed as metabolizable duced a curvilinearity to the system above main- energy was approximated by two straight lines tenance and it then approximated closely to the intersecting at zero energy retention, that is at underlying continuous curvilinear function. This energy maintenance (Blaxter & Wainman, 1961). system, usually called the metabolizable energy The slope ofthe linear equation below maintenance, system, was adopted by the Agricultural Research called the efficiency of utilization of metabolizable Council's Working Party on the Nutrient Require- 48 K. L. BLAXTER AND A. W. BOYNE ments of Ruminants and included in its 1965 publication (ARC, 1965). It was later adopted in principle in a slightly modified form by the Agricultural Departments of the United Kingdom (MAFF, DAFS & DANI, 1975) and replaced the older starch equivalent system which was shown to be less precise in estimating animal needs (Alderman, Morgan & Lessells, 1970). Even so, the system, although capable of accom- modating new findings, is cumbersome to use and probably leads to difficulty on extrapolation to high levels of production. Several attempts have been made to simplify the computation of rations by algebraic manipulation of the ARC System as exemplified in the Agricultural Departments' publication (MAFF et al. 1975), without taking into account that the system was an approximation to a continuous relationship. For these reasons, and in an attempt to provide a simple and firm basis for the development of feeding systems, we have under- taken a reassessment of the basic calorimetric data on feed evaluation for ruminants. A progress report has been published on this work based on fewer experiments than are now included (Blaxter & Boyne, 1970) and an account of some of the conclu- sions arising from preliminary calculations has been given (Blaxter, 1974). MATERIALS AND METHODS The Appendix Table lists details of the 80 experi- ments which were analysed. Most of these were carried out at the Hannah Dairy Research Institute, Ayr and at the Rowett Research Institute, Aberdeen and we are grateful to our colleagues for access to unpublished details. Fourteen experiments made in America, Australia or Japan were recorded in sufficient detail to permit their inclusion. The experiments comprise sets of determinations of energy retention when each animal was given various amounts of the same diet and also when it was starved to provide an estimate of its fasting metabolism. The methods used are described in the references to the Appendix Table. In 70 of the experiments the diets had been analysed chemically to give values for ash, N, crude fibre and ether extract contents and in 34 of these lignin content had been determined. The heat of combustion of each diet was also known. These diets were classified as shown in the Appendix Table into six classes: (1) Pelleted diets: mainly pelleted roughages including pelleted mixtures of roughages and cereals (13 diets). (2) First harvests of grasses: artificially dried herbages including not only very young spring grass but also more mature herbage which would normally have been made into hay rather than artificially dried (15 diets). (3) Begrowths of grasses: second and subsequent harvests of grasses which had all been artificially dried (11 diets). (4) Hays: both legumes and grasses distinguished from 2 above only because of the method of drying (10 diets). (5) Cereal mixtures: mixed diets of cereals and hay or dried herbage; the lowest cereal inclusion was 20% (24 diets). (6) Other mixtures: roughages together with oil- seed cakes and meals, animal products and some cereals (6 diets). This classification into six groups was found to be too fine; classes 5 and 6 were combined to give a group of 30 diets and classes 2 and 4 combined to give a group of 25 diets. One experiment, No. 61, was omitted from the analysis since it gave com- pletely anomalous results compared with the remainder. The results of analysing these data are presented in two parts. In the first a simple mathematical model is developed which describes the relationship between rate of energy retention and rate of energy intake; the estimation of the parameters of the model is described and aspects of the parameters themselves discussed. The algebraic derivation of efficiency terms is presented and their relation to the ARC (1965) system described. In the second part these efficiency terms are then related to attributes of the diet to provide prediction equa- tions. Finally further simplification of the approach is presented. RESULTS Development The basic descriptive equations relating energy reten- tion to feed energy intake The Mitscherlich equation, which describes a system to which the law of diminishing returns applies, was first used by Wiegner & Ghoneim (1930) to analyse the two calorimetricexperiments made with cattle which had been carried out at the time. Brody (1945) re-analysed these same experiments and a third using the same form of the equation and Blaxter & Graham (1955) followed a similar approach to analyse the results of two experiments they had made with sheep. The present treatment derives from these approaches but is more general; its derivation is given in full: LetB' = the rate of energy retention of an animal (kj/day) and G' the rate at which it ingests feed energy (kJ/day). Then — = p'(A-R'), where A is the maximal attainable rate of energy Nutritive value of feeds as energy sources 49 retention and p' is a constant. On integration this gives R'= A-B'(exp(-p'G')), (1) where B'is a constant of integration. When G' = 0, R' = A-B' =-Hb, where 2?» is the rate of fasting metabolism. Sub- stituting for A = B' — Hb in equation (1) and divid- ing throughout by Hb gives .„ G'\\ Hh (2) which may be written R = B{l-exp(-pG))-l, where R, B and G are scaled as multiples of fasting metabolism. B— 1 is equal to the scaled asymptote of equation (1), namely A\Hb. The relationship expressed by equation (2) is general in form. We have applied it to sealed energy retention and sealed gross energy intake. Our reason for choosing gross energy instead of meta- bolizable energy is that each estimate of energy retention depends on the same measurements of energy lost as methane and in faeces and urine as does the corresponding estimate of metabolizable energy; thus errors in both estimates are correlated, a situation which gives spurious information on the relationship between them. Examination of the relationship between scaled gross energy intake (G) and the scaled metabolizable energy (M) showed that in any one experiment the two were closely associated by an equation of the form M = c + bG. (3) Equation (2) can be written as R = B{l-exp(-p(M-c)lb)-l, (4) where retention is expressed in terms of metaboli- zable energy. The asymptotic energy retention remains B — 1, unaffected by the way in which the energy of the feed intake is described. Metabolizability, q, of the diet is the ratio of meta- bolizable to gross energy, i.e. q = ME\GE = M\G = b + cjG. In particular metabolizability at maintenance, It will be noted that if c in equation (3) is zero, q does not vary with feed intake; if c is positive, q falls as feed intake increases. Finally, the device of dividing energy intake and retention by fasting metabolism enables observations on more than one animal on the same diet to be combined for esti- mation of the parameters B, p, c and 6. The regression of scaled metabolizable energy intake, M, on scaled gross energy intake, G Appendix Table 1 lists the slopes (6) and inter- cepts (c) of equation (3). All the regressions were highly significant statistically and the proportion of the total sum of squares accounted for by the re- gression averaged 0-988 with a standard deviation of ± 0-063. Clearly a linear regression provided a very satisfactory fit to the data. The 80 experiments can be grouped according to the number of animals used in each and the residual standard deviation from the regressions calculated for each group. Table 2 (column 5) shows a tendency for the residual standard deviation to increase with increasing number of animals used in an experiment. Even so, the standard deviations were very small, about 2 % of the mean value. The slopes and intercepts of the individual equa- tions were negatively correlated and both appeared to be related to the crude fibre content, F, of those diets for which chemical data were available. This Table 1. Within-experiment dependence of M, the scaled metabolizable energy and of q, the metabolizability, upon G, the scaled gross energy. The standard error of each regression coefficient is given below it Class of diet Pelleted (1) First harvests (2 and 4) Regrowths (3) Mixed diets (5 and 6) Change in M with unit change in G (i.e. 6 in regression equation M = c + bG) 0-661 -O-OOORF* + 0-025 + 0-0001 0-976- 0-0016F* + 0023 ±00001 0-928 -0-0015.F* 0-054 + 0-0002 0-803-0-0012^* ±0-015 + 0-0001 Change in q with unit change in O (i.e. 6 in regression equation q = c + bG) -0-0067 ±0-0014 0-0187-0-000079.F* ±0-0058 ±0-000022 -0-0057 ±00017 0-0627-0-000322^* + 0-0136 + 0-000087 • Where change in M or q is of the form d, —&2.F, then the effect of unit change in 0 is smaller in diets of high crude fibre content than in diets with little crude fibre in them, ACS 90 50 K. L. BLAXTBR AND A. W. BOYNE Table 2. Residual standard deviations of the scaled metabolizable energy from equation (3) and of scaled energy retention from equation (2)f Residual standard deviations (+) No. of animals used in the experiments One Two Three Four Six All No. of experiments 5 6 42 18 6 79 Mean no. of observations per animal 6-8 3 1 2-8 1-9 1-5 , D.F.J 24 25 272 102 41 510 Scaled metabolizable energy (M) from equation (3) 0046 0054 0067 0-067 0-057 0-063 Scaled energy- retention (B) from equation (2) 0060 0-084 0096 0097 0-109 0093 t Equation (2) R = B ( l - exp ( - p G ) ) - 1 , Equation (3) M = c + bG. I Two degrees of freedom deducted for constants. was examined further by carrying out, for each of the four main groups of diets, a within-experiment re- gression analysis of M on Q and GxF, where F was expressed as g crude fibre per kg of organic matter. The regression coefficients are given in Table 1. The relationship between M and G, which accounted for 0-99 of the variability in M, clearly depended upon F in that the yield of metabolizable energy for each unit increment of gross energy intake fell as the crude fibre in the diet increased. From these expressions the intercepts were cal- culated for each experiment and no relationship was found between them and crude fibre. For each of the groups, the mean intercept, its standard deviation and the number of experiments are given below: Diet class Pelleted diets (1) 1st harvests (2, 4) Regrowths (3) Mixtures (5, 6) Intercept 0142 0085 0025 0-016 S.D. (±) 0-113 0-163 0-056 0136 No. of expts 25 12 11 22 Thus for most of the diets the intercept was + ve, indicating that metabolizability usually fell as in- take increased. This effect of intake on metaboliza- bility was examined directly via the relationship between q, G and GxF. The regression coefficients are also presented in Table 1. These show that for pelleted diets and re- growths, metabolizability fell as intake (G) in- creased, whereas for first harvests and mixtures the effect of intake was conditional upon the crude fibre content of the diet; for first harvests q fell with intake if crude fibre content was greater than 238 g/kg organic matter (OM), and for mixtures the corresponding fibre value was 196 g/kg OM. Fitting the exponential relationship between scaled energy retention, R, and scaled gross energy intake, G An iterative calculation method, similar to that outlined by Williams (1959), was used to fit equation (2) to each data set. The method was devised to give approximate estimates of error variability and is described below. Fitting the equation R = B{1 — exp (— pG)) — 1, or R = f(B, p, G) was accomplished by making pre- liminary estimates Bo and p0 of the parameters and making adjustments to them SB and 8p. R was then estimated by where the partial derivatives are evaluated at Bg, p0. The procedure was repeated at ad j usted values of B and p until the magnitude of the adjustments in B and p and the change in the residual mean square became negligible. Appendix Table 1 lists for all experiments the values of B and p together with the residual mean squares. In Fig. 1 the best estimates of B and p in the equation R = B(l — exp (— pG)) — 1 are plotted against one another. It seemed possible at first that the relationship between these two parameters might be so close as to enable one to be expressed in terms of the other. If this had been so then estima- tion of one parameter wouldhave been enough to describe the relationship between energy retention and intake. This, however, did not prove possible, largely because of the nature of the correlation be- tween estimates of B andp for any one experiment. In Fig. 2 for two experiments, 46 and 52, the best estimates of B andp are plotted along with contours of values of B and p for which the residual mean square in retention are respectively twice and four Nutritive value of feeds as energy sources 51 a o _ A A • • O l 0° «52 #46 o . s • °n o 4 " 0-2 0-3 0-4 Pig. 1. Scatter diagram of best estimates of B and p for all 79 experiments. A, Hays; • , hay-cereal; D, hay-cereal-protein; A, pelleted; O» 1st cut grass; • , 3rd cut grass. # 46 and # 52 are the best estimates for Expts 46 and 52, respectively. times the residual associated with the best estimates. The contours for these two experiments do not inter- sect anywhere indicating that no point-pair of B, p can satisfactorily fit the data from both experiments. The best estimates of Expts 46 and 52 are indicated on Fig. 1, showing that these are by no means the least compatible experiments in the series. It can also be seen from Fig. 2 that a large change in B may be accompanied by a compensatory change in p with little effect on the goodness of fit. To illus- trate and amplify this, estimates of B and p for Expt 52 were used corresponding to x, the best fit, and to (1), (2), (3) and (4), 'corners' of the contour corresponding to twice the minimal residual mean square. The resulting values of 0*, EG, m and Eg, t (vide infra for their definition) are given in Table 3 where it can be seen that although values of B and p may differ from the best estimate by as much as 40%, the differences in O*, EQ m and EG. t are no greater than 9%. There is, however, 4-2 52 K. L. BLAXTER AND A. W. BOYNE 010 0-15 0-20 0-25 0-30 0-35 Fig. 2. Envelopes for Expts 46 and 52 enclosing values of B and j> for which residual mean square does not exceed twice and four times minimum. Table 3. Estimates of O*, EGt n and EG,ffor Expt 52, derived from the best estimates of B and p, and from estimates corresponding to each 'corner' of the contour in Fig. 2 at which the residual mean square is twice the minimum. Point X (1) (2) (3) (4) B 3-38 4-78 2-68 3-43 3-32 P 0193 0122 0-280 0-199 0-188 G* 1-82 1 92 1-67 1-73 1-91 E0,m 0-55 0-52 0-60 0-58 0-52 Eg, t 0-39 0-41 0-38 0-41 0-37 no doubt, as was shown by Blaxter & Graham (1955), that a curvilinear relationship more closely describes the results of energy metabolism studies in which different amounts of the same diet are given than does a linear equation. Estimates of retention of energy within the effective range are little affected by the inability to predict B and p precisely. Studies made with both cattle and sheep (Schie- mann, 1958;Blaxter, 1967) suggest that the error of a single estimate of scaled energy retention is likely to be about ± 0-07 kJ /kJ fasting metabolism, the precise value depending largely on the duration of the experiment. As shown in Table 2, the residual standard deviation from equation (2) was on average ± 0-093, which is slightly greater than the error of a single trial. There was a tendency, as with the estimation of scaled metabolizable energy, for the precision of the estimated scaled retention to worsen as the number of animals included in the experiment increased. In our opinion the increase in residual variability is more than compensated for by the facility that equation (2) provides for combining the results from a number of animals. Algebraic definition of biological terms Manipulation of the two basic equations (2) and (3) provides expressions for a number of the more commonly accepted measures of energy exchange such as maintenance, level of feeding and efficiency of energy utilization. These are developed below, extending the approach used by Blaxter & Graham (1955). The gross energy required for maintenance is the Nutritive value of feeds as energy sources 53 amount of feed energy which results in zero energy- retention and from equation (2) is ln p B—l (5) and, from equation (3), the metabolizable energy required for maintenance is Mm = M* = c + bG*. The metabolizability of the gross energy of the diet measured precisely at maintenance is q* = M*\Q*. (6) The level of feeding of an animal is defined in terms of multiples of the amount of feed required for maintenance. The gross energy concentration of feed is independent of level, so L = GIG*. (7) The efficiency with which the gross energy of feed is used for maintenance is 1 E°. - = G* (8) because in the scaled equations the fasting meta- bolism is axiomatically unity. Similarly, the effi- ciency with which the metabolizable energy is used for maintenance is E M, m = j£i = km (9) The shape of the relationship between energy reten- tion and feed intake dictates that the efficiency with which feed energy is used to promote retention above maintenance declines with increasing intake. To obtain comparable estimates of the efficiencies with which different feeds are used above main- tenance, the points between which such efficiencies are measured must be standardized. We measure efficiency for production between maintenance and a feeding level precisely 2 x maintenance. The gross energy retained by an animal at any feeding level, L, is from equations (2), (5) and (7) from which B2 = B-l B ' The efficiency of utilization of gross energy for production measured between maintenance and 2 x maintenance is thus EG,t = B-l BG* ' (10) If the metabolizability of the gross energy is taken to be that at maintenance, then at 2G*, the efficiency of utilization of metabolizable energy for production is (11) This is the definition we have used. The terms derived algebraically above are for the most part formally equivalent to those currently adopted in describing the energy metabolism of animals. Thus EM. m is identical to km, the efficiency of utilization of metabolizable energy for maintenance in the ARC (1965) system, and L, the feeding level, is also pre- cisely the same. The efficiency of utilization of metabolizable energy for production, EM /, is very closely analogous to kf, the ARC coefficient of efficiency of utilization for fattening. It is not pre- cisely the same, because it is calculated over a de- fined range and also because it refers to a constant metabolizability of gross energy. In the ARC (1965) scheme hf was obtained directly from the observed metabolizable energy intakes above maintenance and any decline in the proportional retention with increase in feeding level was dealt with separately. These quantities EG, m and EG, f are simply related to B andp of equation (2). Thus from equation (10) it follows that B = EG,mj(EG_n-EG,t), (12) and from this result and equation (5) p = EG,m]n(EG.mIEG.f). (13) (From these it is simple to derive the equations re- lating B andp to EM, m and EM, /•) Knowledge of the two efficiencies enables energy retention to be predicted at any level of intake, and not solely at maintenance and 2 x maintenance. When, additionally, EG, m and EG, f are found to be related to composition of diets in terms of their proximate constituents, it becomes possible to pre- dict for a diet the energy retention at any level of feeding from its proximate composition. Table 4 summarizes the mean values and coeffi- cients of variation of these biological terms as de- fined above together with the mean chemical com- positions of the feeds. Figure 3 gives frequency distributions of the proximate chemical constituents. In each distribution the abscissae are in units of 50 g/kg. These feeds varied considerably in quality; metabolizability of gross energy varied from 0-38 to 0-83, crude fibre from 20 to 390 g/kg, and crude pro- tein from 54 to 256 g/kg. The efficiency terms also varied considerably, especially when expressed in terms of gross energy. 54 K. L. BLAXTER AND A. W. BOYNE Table 4. The variationpresent in the 70 experiments for which chemical data were available. Mean values and coefficients of variation of the estimates derived from the equations and for chemical constituents. The results for all 79 experiments are given in brackets^ Symbol 6* E(3,m EO. 1 M* EJI, m •^if, / 9* Name Gross energy for maintenance Efficiency of utilization of gross energy for maintenance Efficiency of utilization of gross energy for production Metabolizable energy (ME) for maintenance Efficiency of utilization of ME for maintenance Efficiency of utilization of ME for production Ash, g/kg dry matter N x 6-25, g/kg organic matter Ether extractives, g/kg organic matter Crude fibre, g/kg organic matter N-free extractives, g/kg organic matter Heat of combustion, MJ/kg organic matter Metabolizability of gross energy at maintenance Mean value 2-59 (2-55) 0-405 (0-409) 0-262 (0-267) 1-45 (1-43) 0-696 (0-705) 0-443 (0-453) 68 147 28 244 582 20-2 0-578 (0-571) Standard deviation (+) 0-60 (0-57) 0-087 (0-084) 0094 (0091) 0 1 5 (0-15) 0-070 (0-074) 0118 (0-117) 24 55 14 92 104 0-80 0-086 (0-082) Coefficient of variation (%) 23-0 (22-4) 21-5 (20-5) 36-0 (34-0) 10-3 (10-7) 10-1 (10-4) 26-5 (25-7) 35-4 37-6 49-8 37-7 17-8 4-0 14-9 (14-2) "f In any one experiment the efficiencies for maintenance are the reciprocals of the amounts of scaled energy required for maintenance. The reciprocals of the means of a series of estimates of efficiencies are unlikely to be the same as the means of a series of amounts. Analysis The relationship between the gross energy and the metabolizable energy of feed and its chemical com- position The heat of combustion of the organic matter of the wide range of feeds was subject to little varia- tion, the mean value being 20-17 MJ/kg with a standard deviation of ±0-80, corresponding to a coefficient of variation of ±4-0%. The distribution is shown in Fig. 3. Eegression of the heat of combus- tion on chemical composition was undertaken to provide estimates of the heats of combustion of crude protein, ether extractives, crude fibre and nitrogen-free extractives which together sum to give the organic matter. The results are given in Table 5 where they are compared with those derived by Schiemann et al. (1971) from calorimetric studies in East Germany. The only major discrepancy relates to the low heat of combustion of ether extractives. Triacylglycerols have heats of combustion of about 38kJ/g; other ether-soluble constituents, notably carotenoids and chlorophyl, have lower ones. In any event, the error caused by the use of the coefficients given in Table 5 is not likely to be great since ether extractives in ruminant diets rarely exceed 60 g/kg. The residual standard deviation which results from use of the regression equation was + 0-47 MJ/kg, corresponding to a coefficient of variation of only 2-3 %. There were no significant differences between classes of feeds. A similar analysis was made of the relationship between the metabolizable energy/kg organic matter, measured at the maintenance level of nutri- tion, and chemical composition. The overall rela- tionship gave the coefficients shown in Table 5 which includes a set derived by MAFFetal. (1975) from the work of Schiemann et al. (1971) based on assumed digestibility coefficients for the individual nutrients. They permit the estimation of metabolizable energy of feeds from their crude chemical composition with an error of + 1-09 MJ/kg. The factors derived in the present analysis give higher values for most rumi- nant feeds than do the factors of MAFF et al. (1975) 64 60 24 20 51 16 I Nutritive value of feeds as energy sources 201- 55 16 12 0 100 Ether extract (g/kg OM) 100 200 Fibre (g/kg OM) 300 400 19 20 21 22 23 Gross energy (MJ/kg OM) 20 16 <U 82 100 200 Protein (g/kgOM) = 1 f = 300 400 500 600 700 NFE (g/kgOM) 900 Fig. 3. Histograms representing the frequency distributions of the proximate chemical constituents (g/kg) and of the gross energy (MJ/kg) of the organic matter of the experimental diets. Table 5. The gross energy and metabolizable energy of crude protein, ether extractives, crude fibre and N-free extractives estimated by regression methods (MJjkg) Crude protein (N x 6-25) Ether extractives Crude fibre N-free extractives BSD Coefficient of variation Gross energy 1 Estimated 26-8 27-2 21-8 17-4 ±0-47 ±2-3 Schiemann et al. (1971) 22-6 40-7 19-2 17-7 — — Metabohzable energy Estimated 161 33-7 8'6 13-9 ±l'O9 + 9-4 MAFF et al. (1975) 12 31 5 14 — 1 for which no great precision has been claimed. A number of other possibilities of estimating meta- bolizable energy/kg organic matter were explored. The best estimate was given by the equation tion (MJ/kg), x is the gross energy of the organic matter (MJ/kg), F is the crude fibre content of the organic matter (g/kg) and c is the intercept which varies from class to class of diet: y = 0-412a;-0-0205.F + (14) where y is the metabolizable energy of the organic matter measured at the maintenance level of nut ri- Diet class Pelleted (1) First harvests (2 and 4) Regrowths (3) Mixed diets (5 and 6) Intercept 7-57 9-29 8-79 7-44 56 K. L. BLAXTER AND A. W. BOYNE This equation has a residual standard deviation of + 0-80 corresponding to a coefficient of variation of ± 6-9 % of the mean value. It will be noted that either the coefficients in Table 5 or the equation above enable the metaboliza- bility of gross energy at the maintenance level to be derived from crude chemical composition alone with relatively little error. Agreement of estimates of parameters made with sheep and cattle Seven experiments were duplicated with sheep and cattle (Blaxter & Wainman, 1961) and Table 6 summarizes the mean values of the parameters ob- tained with each species. The seven diets covered a wide range of diets as exemplified by the metaboliza- bility of the gross energy which ranged from 0-5 to 0-8. The table shows that there were no differences attributable to species. It can be concluded, there- fore, that the device of scaling by the fasting meta- bolism equates for the wide differences in body size of different ruminant species. The coefficient of variation in the final column refers to an individual determination of the parameter based on these replicated trials. Additivity of dietary characteristics If two diets of different nutritive values are mixed in a given proportion, it is important to know whether their nutritive values combine additively to give the nutritive value of the mixture, or whether there is evidence of synergism. Three experiments to test this were carried out by Blaxter & Wainman (1961) and by Blaxter, Wainman & Smith (1970). The characteristics examined were the metaboliza- bility at maintenance, q*, the gross energy required for maintenance, G*, and EG, f, the efficiency of utilization of gross energy for production. Each experiment contained six mixtures, and there was no evidence of non-additivity of q* or of EG, /. In only one experiment, in which cattle were given mixtures of hay and maize, was there evidence of eynergism in G*, significant at the 5 % level, but in that experiment there was a small residual mean square, and the departure from linearity was negligible. Recent work carried out by the Feed Evaluation Unit at the Rowett Institute (DAFS, 1976) also shows that there is linearity of substitution of grains for long roughages or of grains for silages in the determination of q*. It can be concluded from this limited evidence that no error is likely to accrue if linearity of substitution of feeds is assumed in terms of metabolizable energy. The prediction of the utilization of the energy of feed In the preliminary analysis of the data, EM, m and EM. f, the efficiencies of utilization of metabolizable energy for maintenance and fattening, had been related to attributes of the feed (see Blaxter, 1974). A more direct analysis is now preferred on logical grounds. Itwas pointed out earlier that the relation- ship between energy retention and gross energy is preferred, to that between energy retention and metabolizable energy since measurements of faecal, urinary and methane energy are common to meta- bolizable energy and energy retention. The same preference applies to efficiency measurements; they are less open to bias when based on relationships between retention and gross energy. Accordingly, the efficiencies related to attributes of the feed were EG, m and EG. /, which are defined by equations (8) and (10). The corresponding equations in terms of metabolizable energy may be derived from the relationship = EG, Jq*, EM. t = EG, ,\q*. Maintenance Analysis of all 79 experiments showed that there was a statistically highly significant regression (P < 0-001) of the efficiency of utilization of gross energy for maintenance on metabolizability of energy measured at the maintenance level of nutri- tion. The slope of the relationship was common to all feeds but intercepts differed. The equation was Eo. m = 0-817g* + c, Table 6. Comparison of the values of parameters determined with both cattle and sheep. Results of seven experiments in which the two species were given tlie same diets Parameter Metabolizability of gross energy measured at maintenance Scaled amount of gross energy required for maintenance (kJ/kJ fasting metabolism) Efficiency of utilization of gross energy for production measured between maintenance and 2 x maintenance Mean Sheep 0-625 2-32 0-288 values Cattle 0-621 2-21 0-287 Difference and S.E. of difference 0-004 + 0-007 0-11 + 0-06 0-001 ±00076 Coefficient of variation 20 4-6 7-1 Nutritive value of feeds as energy sources 57 where the intercept, c, had the following values: Diet class Pelleted (1) Forages (2, 3 and 4) Mixed diets (5 and 6) Intercept -0069 -0-078 - 0 0 4 0 The residual standard deviation was + 0-037 which is ± 9 % of the mean value. Further analysis was made of the 70 experiments for which compositional data were available in which metabolizability and the content of proxi- mate principles in the organic matter were tested as predictors, separately and in combination. For the 70 feeds, the simple relationship with q* was again highly significant and very similar to that obtained with the complete data; again there were differences between classes of feed. It was found, however, that these differences were removed by inclusion in the equation of either crude fibre or crude protein along with metabolizability. No other combination elimi- nated class differences or gave lower residual mean squares. These equations were: EG.m = 0-838g*- 0-00012.F -0-050, (15) USD = + 00353, CV = ± 9%, EG m = 0-947g*-0-00010P-0-128, (16) RSD = ± 0-0354, CV = ± 9%, where F is the content of crude fibre in the organic matter (g/kg) and P is the content of crude protein in the organic matter (g/kg). Values of Eg, m predicted from these two equations are given in Tables 7 and 8 together with the derived values of EM_ m. Analyses in which only the proximate principles were regarded as independent variables singly and in combination showed that the regression on crude fibre gave the lowest residual standard deviation Table 7. Prediction of the efficiency of utilization from the metabolizability of gross energy and Metabolizability of gross energy («•) 0-40 0-50 0-60 0-70 0-80 0-40 0-50 0-60 0-70 0-80 of gross energy and metabolizable energy for maintenance the crude fibre content of the organic matter Crude fibre, g/kg organic mattei 50 100 200 Efficiency of utilization of gross energy, EOt „ — — — 0-441 0-531 0-525 0-614 0-608 Efficiency of utilization — — — — — 0-735 0-759 0-750 0-766 0-761 0-345 0-429 0-512 — i of metabolizable energy, i — 0-690 0-715 0-731 •(F) 300 0-249 0-333 0-417 — — '11, m 0-623 0-666 0-695 — of the feed 400 0-237 0-321 — — — 0-592 0-642 — — Table 8. Prediction of the efficiency of utilization of gross energy and metabolizable energy for maintenance from the metabolizability of the gross energy and the crude protein content of the organic matter of the feed Metabolizability of gross energy (?*) 0-40 0-50 0-60 0-70 0-80 0-40 0-50 0-60 0-70 0-80 Crude protein, g/kg organic matter (P) 50 100 150 200 250 Efficiency of utilization of gross energy, EQi m 0-246 0-241 0-236 — — 0-340 0-336 0-330 0-326 — 0-435 0-430 0-425 0-420 0-415 0-530 0-525 0-520 0-515 — 0-625 0-620 — — — Efficiency of utilization of metabolizable energy, EM: m 0-615 0-602 0-590 — — 0-680 0-670 0-660 0-650 — 0-725 0-717 0-708 0-700 0-692 0-757 0-750 0-743 0-736 — 0-781 0-775 — — — 58 K. L. BLAXTER AND A. W. BOYNE and no other combination reduced it. Class dif- ferences were, however, apparent and the equation was Ea.m = c - 0-000862*' RSD = ±0-0505, CV = 12-5%, where the intercept, c, had the following values: Diet class Intercept Pelleted (1) -0-573 First harvests (2 and 4) -0-644 Regrowths (3) -0-609 Mixed diets (5 and 6) -0-604 It will be noted from comparison of the residual standard deviations that there is distinct advantage in using metabolizability in the prediction. Growth and fattening Analysis of 79 experiments showed highly signifi- cant regressions of the efficiency of utilization of gross energy for production on its metabolizabiiity. The regressions varied from class to class of diet and these differences were statistically significant (P = 0-014). These regression equations are given in Table 9. Further analysis was undertaken with the 70 experiments for which chemical data were available. When crude fibre and metabolizability were in- cluded in the analysis, it was found that for pellets fibre had no effect and that all other diets could be described by the same regression coefficients. For first harvested material, however, the intercept term was 0-06 greater than for the remainder. The equa- tion was EG., = 0-6002*-0000622^ + 0, (17) where F is the crude fibre content of organic matter (g/kg) and the intercept, c, was 0-036 for classes 3, 5 and 6 (regrowths and mixed diets) and for first harvests and hays (classes 2 and 4) it was 0-096. The residual standard deviation from this regression was ± 0-0353. Values predicted from the equation are given in Table 10. Hoffmann, Schiemann & Nehring (1962) gave pure starch to oxen in a number of experiments and found it to have a mean metabolizability of 0-868 and that its metabolizable energy was utilized with an efficiency of 0-641 ± 0-017 for fattening. For a fibre-free diet with a metabolizability of 0-868 the above equation predicts an efficiency of 0 • 641, which is precisely the same. A similar analysis was undertaken with crude Table 9. Relation between Class of feed Pellets First harvests and Aftermaths Mixed diets All diets and the hays . the efficiency of utilization of gross energy for production Eg , metabolizability of the gross energy of feed q* No. in class Equation 12 Eg , = 0-494g*-0-008 25 Eg , = M15g*-0-380 11 Eg, = 0-874J*-0-299 30 Eg[, = 0-774g*-0-157 78 Eg., = 0-899g*- 0-251 Residual standard deviation( +) 0-015 0-048 0023 0046 0-052 Table 10. Values of EG, , and EMi , predicted from the metabolizability at maintenance of the 9* 0-40 0-50 0-60 0-70 0-80 0-40 0-50 0-60 0-70 0-80 gross energy, q* PftllRtfiH rHfit<3 . t UA1«31/UvL Lliv 09 (Class 1) 0-186 0-236 0-285 0-335 0-385 0-465 0-472 0-475 0-478 0-481 , and the 50 — — — 0-425 0-485 crude fibre content, F, of the organic matter < Regrowths and mixed diets (Classes 3, 5 and Crude fibre, g/kg organic matter (F) 100 200 300 Efficiency of utilization of gross energy, Eo. — — 0089 — 0-212 0-149 0-334 0-272 0-209 0-394 0-332 — 0-454 — — Efficiency of utilization of metabolizable energy, — — — 0-607 0-606 — — 0-222 — 0-424 0-298 0-556 0-453 0-348 0-563 0-474 — 0-567 — — of the diet (g\kg) 6) Addition for first harvests 400 and 4) 0027 0-06 0087 0-06 — 0-06 — 006 — 006 Eu t 0070 0-150 0-174 0-120 — 0-100 — 0-086 — 0-075Nutritive value of feeds as energy sources 59 Table 11. Values of EG, t and Em, t predicted from q*, the metabolizability of gross energy at maintenance, and the crude protein content, P, of the organic matter (gfhg) for diets other than Glass 1 (pelleted diets) First harvests and mixed diets (Classes 2, 4, 5 and 6) 9* 0-40 0-50 0-60 0-70 0-80 0-40 0-50 0-60 0-70 0-80 50 0-158 0-254 0-348 0-444 Crude protein, g/kg organic matter (P) 100 A 150 200 Efficiency of utilization of gross energy, EBi f 0081 0-177 0-272 0-367 0-462 0-100 0196 0-290 0-386 — — 0-214 0-309 0-404 — Efficiency of utilization of metabolizable energy, Eu 0-319 0-423 0-497 0-555 0-203 0-354 0-453 0-524 0-578 0-250 0-392 0-483 0-551 0-428 0-515 0-577 250 — — 0-328 — — r, / — — 0-547 — Adjustment for regrowths (Class 3) -0070 -0-070 -0-070 -0-070 -0-070 -0-175 -0-140 -0117 -0-100 -0-088 protein replacing crude fibre. Its inclusion did not improve the prediction of Eg, / for pelleted diets. For all other diets the inclusion of crude protein significantly reduced residual error and between feed classes there were no differences in the regression coefficients. The intercept was, however, signifi- cantly greater for regrowths of herbage (class 3) than for the remainder. The equation was EG, , = 0-951g*+ 0-00037P + C, where P is crude protein content of organic matter (g/kg) and the intercept, c, was — 0-336 for all diets other than regrowths for which it was —0-406. The residual standard deviation was +0-0349. Values estimated from the equation are given in Table 11. DISCUSSION The effect of crude fibre It is unfortunate that the feedingstuffs had been described chemically in terms of the Weende methods of analysis; more modern ones based on the use of detergents and enzymes (see Clancy & Wilson, 1966; MacRae & Armstrong, 1968; van Soest & Wine, 1967) would have been more meaningful. Of the other proximate constituents, only crude protein appears to be as useful as crude fibre for predicting nutritive value, and an examination of their values in the 70 diets shows that, apart from mixed diets, crude protein and crude fibre are negatively corre- lated. It is possible that more precisely defined attributes of the carbohydrate fraction of the feeds would have been of even greater value. It has been shown that metabolizable energy/g of organic matter of feed can be predicted from the heat of combustion of the feed and its crude fibre content with a residual error of only + 6-9 % of the mean value. Inclusion of crude fibre as a variable in regressions of efficiency on metabolizability abolishes class differences be- tween feeds for maintenance, and for production enables a separation of feeds into two classes, pellets and other feeds, to be made, again removing class differences and reducing residual variability. Increase in the fibre content of the organic matter of a diet markedly reduces its metabolizability: irrespective of the class of diet an increase of 1 g/kg in its crude fibre content causes a fall of 0-0010 + 0-00008 in q*, the metabolizability at maintenance. In equations (15) and (17), however, fibre content contributes along with metabolizability to estima- tion of EQ_ m and EG f. This suggests that crude fibre, however poorly it describes the fibrous con- stituents of diets, has relevance to the nutritive value over and above that accounted for by its part in determining metabolizability. Feeding systems The attributes of a feeding system which are important in practice are that it should enable calculation of the performance of an animal knowing the amount and quality of the feed consumed, the amount of feed of a given quality necessary to support a particular performance, and the amount of a feed of one particular quality which substitutes for another of different quality in a diet without af- fecting the performance of the animal. The per- formance of growing and fattening animals with which this analysis has been concerned is repre- sented practically by a gain or loss in body weight. Any system designed to meet the energy needs of animals implies that these gains or losses of body weight can be expressed in terms of a rate of energy 60 K. L. BLAXTER AND A. W. BOYNE retention. For example, the loss of body weight on fasting an animal represents a loss from the body of energy equivalent to fasting heat production, while a gain in body weight represents a retention of energy. The use of the descriptive equation (2) requires that measures of body weight gain should be con- vertible into rates of energy retention. This entails a tabulation of fasting heat production according to breed, size, sex and other attributes and of the energy retentions associated with gains in body weight. Given such a tabulation the model enables most of the computations required of a feeding system to be undertaken. If the metabolizability of a feed and its protein content are known, the efficiencies of utilization of gross energy for maintenance and production can be estimated and the constants of the basic equation derived. For example, for a diet with a metabolizability of 0-6 and a protein content of the organic matter of 150 g/kg, EG, m = 0-425 (Table 8) and .EG. , = 0-290 (Table 11). insertion of these efficiencies in equations (12) and (13) yields the constants, B and p, of equation (2), thus: B = EG 0-425 EG_m-EGit 0-425-0-290 = 315, = 0 - 4 2 5 1 ^ = 0-162. For any value of scaled gross energy intake, G, 1-6 1-4 1-2 10 0-8 0-6 0-4 0-2 0 -0-2 -0-4 -0-6 -0-8 -10 ."8 0 1 2 -3 4 5 6 7 8 9 10 11 12 Scaled gross energy intake Fig. 4. Energy retentions, R, corresponding to energy intakes, O, of pelleted diets of differing metabolizabi- lities. (The corresponding metabolizable energy intakes, M, are also indicated.) scaled energy retention B can then be estimated from equation (2): B = 3-15(l-exp(-0-162G))-l. Conversely for any desired energy retention, B, the gross energy intake is: B In this example, O = • I n 315 0162 3 -15 - .R -1 ' Figures 4 and 5 show the corresponding scaled gross energy intakes and retentions for diets with different metabolizability. Figure 4 refers to pelleted diets and Fig. 5 to diet classes 2, 4, 5 and 6 with a constant protein content of 100 g/kg organic matter. Similar graphs can be constructed for feeds with different attributes. Using tabulations of fasting metabolic rates these scaled values can be converted to absolute gross energy intakes and retentions for any given animal. Absolute retentions can be expressed as changes in body weight and absolute gross energy intakes as amounts of organic matter either on the assumption of constancy of the heat of combustion of organic matter or more precisely if the composition of the diet is known. The basic relationship thus enables 1-6 1-4 1-2 10 0-8 0-6 0-4 0-2 0 -0-2 -0-4 co 1 >e u -0-6 -0-8 - 1 0 0-4 0 2 4 6 8 Scaled gross energy intake 10 Fig. 5. Energy retentions, E, corresponding to gross energy intakes, 0, of first harvests of forage crops and of mixed diets (classes 2, 4, 5 and 6) all containing 100 g crude protein/kg organic matter but differing in metabolizability. (The corresponding metabolizable energy intakes, M, are also indicated.) Nutritive value of feeds as energy sources 61 either performance of animals to be predicted from their feed intake or vice versa more simply than by the methods proposed in the ARC (1965) system. The computation of the relative value of feeds as components of diets is more difficult since replace- ment value is not constant but depends on the level of performance. Evidence is accumulating in support of the hypothesis that metabolizability is an additive attribute of feeds; the metabolizable energy of a mixture is thus the sum of the products of the weight of each feed present and its metabolizable energy per unit weight. Replacement value of feeds on a weight basis is not, however, proportional to metaboliza- bility since energy retention is not directly propor-tional to the amount of metabolizable energy supplied, but varies with the metabolizability of the mixture as a whole, and also with fibre or protein content. It is evident that there is no unique replacement value of one feed for another, either as complete diets or as constituents. It depends upon feeding level and upon the metabolizability and protein or fibre content of each of the feeds involved in an iterative way which precludes solution by single algebraic expressions. Nevertheless, provided a statement can be made of the context in which replacement value is to be measured, it is not diffi- cult to devise numerical or graphical solutions. Table 12. Maximal efficiencies of utilization of the gross energy of feed (RjO)^^, and the feed intakes at which these maxima occur (0^^ for diets of classes 2, 4, 5 and 6 Protein content of organic matter (g/kg) Efficiency when intake is optimal (B/G)m0I Scaled feed intakes at which efficiency is maximal (?mu Metabolizability of gross energy 0-4 0-5 0-6 0-7 0-8 0-4 0-5 0-6 0-7 0-8 , 50 0031 0081 0135 0-192 0-254 7-91 6-87 6-08 5-46 500 100 0041 0092 0-149 0-208 0-270 8-66 7-42 6-52 5-85 5-35 . —* 150 0-051 0-105 0162 0-225 — 9-54 8-10 7-07 6-34 200 0118 0-180 0-244 — 8-88 7-75 6-94 — 250 — 0-200 — — — 8-68 — — 12 10 3 ~ \ 1 I — — 2G* G' 1 0-4 0-5 0-6 0-7 Metabolizability of gross energy, q 0-8 Pig. 6. Scaled gross energy intake at which maximal efficiency of utilization occurs (<?mox)> the intakes at nutritional levels of 1, 2 and 3 x maintenance, and estimated maximal intake plotted against meta- bolizability of gross energy, q, for diets of classes 2, 4, 5 and 6 with protein content of 100 g/kg OM. 62 K. L. BLAXTER AND A. W. BOYNE Some derivations from the primary equation Equation (2) can be manipulated algebraically to define optimal amounts of feed to be given to an animal. Since the primary descriptive equation relates rate of energy retention to rate of feed intake so also do the solutions, which describe optimal amounts of feed to be given on a single day rather than over weeks or months. First, equation (2) can be used to define gross efficiency, the ratio of retention to intake, viz. which on maximizing shows that overall production is maximal when Differentiating this equation and equating to zero shows that a maximum occurs when dG' From the efficiencies of utilization of gross energy for maintenance and production given in Tables 8 and 11, values of B and p were derived by means of equations (12) and (13) for classes 2, 4, 5 and 6. Maximal efficiency of feed utilization was then estimated for each pair of values of B and p by the use of iterative methods to solve the equation above. The results are given in Table 12 and plotted in Fig. 6 for diets with protein content of 100 g/kg OM. They show that irrespective of feed quality intakes for maximal efficiency lie between twice and slightly in excess of three and a half times main- tenance . From the Figu re it may be seen that only for diets with metabolizability in excess of 0-65 is there evidence that the intakes necessary for maximal efficiency can be achieved (on the basis of voluntary intake estimated from Blaxter's (1964) relationship for sheep and a fasting energy loss of 230 kj/kg PP°'7S). This agrees with a conclusion reached by Blaxter & Graham (1955). The relationship between efficiency and scaled feed intake, however, is rather flat around the optimum. Thus for a diet with 100 g crude protein/kg organic matter and a metaboliza- bility of 0- 7 a 20 % reduction in feed intake from the optimal of 5-85 to 4-68 changes efficiency by only 3%, from 0-208 to 0-202. This suggests that animals can gain at widely different rates in the region of maximal efficiency without much change in their overall efficiency. In the above instance the 20% reduction in feed intake from that which gave maxi- mal efficiency reduced gain by 23 %. An analogous problem relates to the allocation of a fixed resource of feed to animals. Denoting the total feed by T and the number of animals as n the problem can be formulated / / T\\ Z = nR = nJBll-expl -p-\\-n, \ \ n)J n d(Tjn)' which is equivalent to dG and identical to the expression for maximal effi- ciency in the individual. Thus, there is no advantage to be gained by feeding animals other than at maxi- mal efficiency. Maximal profit is estimated by maximizing the difference between the price of output and the cost of inputs. If a is the price ascribed to output (R) and y is the cost ascribed to input (G) Profit, Z = aR-yG = ot(B- l-B(exp(-pG))) — yG, which on maximizing gives the exact solution = - ln- PL 7 and this occurs when 1_dR <x~ dG' that is when the inverse price ratio is equal to the first differential of the relationship between output and input. Proportional profit, that is profit as a proportion of input can be formulated as which is maximal when «-§• This solution is identical to that for optimal effi- ciency of feed utilization. All the above relationships deal with rates of energy intake and retention, scaled as multiples of fasting metabolism. If, however, equation (2) ia supplemented by two additional relationships, the first to convert energy retention into weight gain, and the second relating fasting metabolism to body weight, it is then possible to formulate a model describing body weight gain over a period of weeks or months. Nutritive value of feeds as energy sources 63 REFERENCES ALDERMAN, G., MORGAN, D. E. & LESSELLS, W. J. (1970). A comparison of live weight gains in beef cattle with values predicted from energy intakes measured as starch equivalents or metabolizable energy. In Energy Metabolism of Farm Animals (ed. A. Schiirch and C. Wenk), pp. 81-4. EAAP Publication No. 13. ARC (1965). 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A P P E N D IX T A B L E 1 R ef er en ce no . 2 30 33 46 47 48 59 60 68 71 73 80 82 3 4 5 6 27 42 43 44 64 N o. a nd sp ec ie s of an im al IS 6S 8S 6S 6S 2S 4S 4S 3 S 4 S 4S 3S 4S 3S 3S 3S 3S IS 4S 4S 4S 3S N o. o f ob se rv at io ns in a dd it io n to f as ti ng 7 11 16 6 | 6 ;;} 9 12 8 1 7 8) 12 f 12) 8 CD 00 00 00 6 5 66 3S 3S P la n of e xp er im en t R an do m a ll oc at io n 2 am ou nt s of e ac h di et gi ve n in a f or m al s eq ue nc e 1 m ai nt en an ce a nd 1 di ff er en t am ou nt S ep ar at e sh ee p gi ve n di ff er en t am ou nt s In cr ea si ng a m ou nt s of f ee d M ea n va lu es o nl y an al ys ed L at in s qu ar e 1 ad l ib it um a nd 2 l es se r am ou nt s 2, a m ou nt s 1 ad l ib it um 2 ob se rv at io ns o n 1 sh ee p, an d w it h re m ai ni ng 2 ra nd om a ll oc at io n of 5 am ou nt s R an do m a ll oc at io n P ai re d ob se rv at io ns w it h ea ch a ni m al L at in s qu ar es M at er ia l fe d P el le te d dr ie d gr as s (f es cu e) Fe sc ue h ay p el le te d D ri ed g ra ss p el le ts P el le te d gr as s, m ed iu m gr ou nd P el le te d gr as s, f in e gr ou nd D ri ed g ra ss p el le ts 8 m ea ls o f a pe ll et ed di et /d ay 1 m ea l of a p el le te d di et /d ay 40 % b ar le y pe ll et s, E xp t 9 04 B /R R I R um in an t D ie t A P el le te d gr as s H ay p el le t Sa in fo in p el le t C on st an ts o f th e en er gy e qu at io ns F or e st im at in g en er gy F or e st im at in g m et ab ol iz ab le re te nt io n fr om g ro ss en er gy f ro m g ro ss en er gy i nt ak e en er gy i nt ak e 4- 04 3- 35 40 4 S. 23 r ye gr as s dr ie d, 1s t cu t 4 0 4 2n d cu t 61 0 3r d cu t 3 1 6 4t h cu t 1- 82 Sp ri ng c ut f re ez e- dr ie d 2- 39 gr as s T im ot hy d ri ed , 1s t cu t 2- 67 2n d cu t 3 0 8 3r d cu t 3- 55 1s t ha rv es t pa st ur e gr as s, 34 2 2 cw t fe rt ili ze r 1s t ha rv es t pa st ur e gr as s, 3- 56 5 cw t fe rt ili ze r 1s t ha rv es t he rb ag e, 33 7 E xp t 7 1C T /R R I B p R M S c 6 R M S P el le te d di et s 5- 98 00 55 0 00 05 84 -0 0 1 4 9 5 0- 48 46 00 04 99 2- 45 01 68 7 00 22 26 00 99 77 0- 39 67 00 11 83 2- 74 0- 21 37 00 06 65 2- 59 0- 22 69 00 06 71 L it er at ur e re fe re nc e 1 7 2- 36 0- 26 30 00 01 50 2- 97 01 30 5 00 32 92 3- 98 00 977 00 06 77 3 0 6 01 28 0 00 03 41 5- 89 0- 07 21 00 14 72 5- 91 0- 04 85 0- 01 40 0 01 87 47 0- 53 86 00 23 81 01 73 23 0- 51 59 00 00 04 0- 26 32 2 0- 48 56 00 00 09 0- 21 30 6 0- 44 55 00 13 64 0- 15 60 0- 49 48 00 07 77 0- 08 59 3 0- 45 52 00 04 33 0- 07 62 8 0- 58 81 00 06 56 00 34 72 0- 47 66 00 03 15 00 87 0 0- 01 04 5 0- 21 17 1 0- 43 91 00 09 84 01 13 9 00 07 00 01 92 29 0- 40 83 00 24 76 00 76 6 00 15 35 00 52 50 0- 38 92 00 04 94 L on g dr y gr as s 1s t cu t 0- 14 68 00 05 87 -0 -0 26 73 0- 67 95 00 01 47 00 80 5 0- 00 50 3 -0 0 7 5 8 5 0- 65 85 0- 00 21 4 0- 16 86 00 09 76 -0 0 0 0 3 9 0- 61 92 00 02 32 0- 28 54 00 13 65 01 22 12 0- 47 16 00 05 30 01 94 0 00 04 35 -0 0 0 6 1 4 0- 51 62 00 01 30 0- 20 05 00 08 62 0- 10 97 9 0- 54 67 0- 00 15 9 01 39 2 00 13 39 00 95 76 0- 50 51 00 03 19 00 97 6 00 03 51 00 28 80 0- 45 13 00 02 52 01 35 4 00 04 48 00 34 32 0- 61 37 00 02 90 0- 12 83 0- 00 95 5 00 13 56 0- 61 26 00 02 40 01 33 2 00 05 75 01 60 12 0- 57 50 00 02 93 11 11 12 19 19 23 24 25 22 ^ S TO 05 s O5 Ox A P P E N D IX T A B L E 1 (c on t.) O 5 er en ci n o . 39 40 4 1 7 1 8 9 10 11 N o. a nd B sp ec ie s of an im al 4S 4S 4S 4 S IS 3S 3 S 3 S 3S N o. o f ob se rv at io ns in a dd it io n to f as ti ng 00 00 00 8 51 9 / 9 1 9 9J 28 29 45 67 72 74 1 2 13 14 15 16 31 IS 6S 6S 3S 4S 3S 2S 2S 2S 3S 3C 6S 12 6 9 8 6J 12 C on st an ts o f th e en er gy e qu at io ns F or e st im at in g en er gy re te nt io n fro m g ro ss en er gy i nt ak e F or e st im at in g m et ab ol iz ab le en er gy f ro m g ro ss en er gy i nt ak e M at er ia l fe d S. 37 c oc ks fo ot d ri ed , 1s t cu t B 6 0 0 2n d cu t 4- 62 3r d cu t 2- 83 S. 24 r ye gr as s dr ie d 1s t cu t 4- 54 P la n of e xp er im en t P ai re d ob se rv at io ns w it h ea ch a ni m al P ai re d ob se rv at io ns R an do m a ll oc at io n L at in s qu ar es i n w hi ch ea ch a ni m al r ec ei ve d 3 am ou nt s of f ee d R an do m a ll oc at io n 2 am ou nt s of e ac h di et F es cu e ha y fe d as c ha ff gi ve n in a f or m al s eq ue nc e L on g dr ie d gr as s (f es cu e) 3r d cu t pa st ur e gr as s, 2 cw t N f er til iz er 3r d cu t pa st ur e gr as s, 3 cw t N f er til iz er 3r d cu t pa st ur e gr as s, 4 cw t N f er til iz er 3r d cu t pa st ur e gr as s, 5 cw t N f er til iz er A ut um n cu t fr ee ze -d ri ed S ep ar at e sh ee p gi ve n di ff er en t am ou nt s L at in s qu ar e 2 am ou nt s, 1 a d li bi tu m L at in s qu ar e P ai re d ob se rv at io ns w it h ea ch s he ep E ac h an im al r ec ei ve d a m ai nt en an ce a m ou nt o f fe ed a nd a n am ou nt do ub le t hi s in a r un do w n al lo ca ti on s ch em e 2 am ou nt s of e ac h di et gi ve n in a f or m al s eq ue nc e C ho pp ed d ri ed g ra ss 3r d ha rv es t he rb ag e, E x p t 7 3C T /R R I C ho pp ed g ra ss A ll gr as s, E x p t 6/ T T I 1s t cu t fe sc ue h ay 2n d cu t fe sc ue h ay 3r d cu t fe sc ue h ay A ll m ed iu m h ay 2- 71 2- 13 P 0- 08 32 01 03 4 01 60 2 01 23 0 01 53 9 0- 23 54 R M S 0- 00 87 2 00 09 82 00 04 30 00 16 38 -0 -0 27 70 0- 00 19 8 00 49 24 00 18 51 6 0- 65 73 0- 59 87 0- 53 84 0- 69 98 L on g dr y gr as s 3r d cu t 00 01 63 00 97 40 0- 54 37 00 11 91 -0 -3 29 4 0- 57 46 R M S 00 02 93 00 13 69 00 02 75 0- 00 59 0 0- 00 19 7 0- 00 39 2 L it er at ur e re fe re nc e 2 2 2 2 1 3 1- 87 0- 33 00 0- 00 71 4 0- 12 16 1 0- 53 49 0- 00 29 7 1- 75 0- 35 85 0- 00 40 4 00 15 72 0- 52 32 0- 00 33 4 2 0 5 0- 22 13 00 04 28 -0 0 1 3 4 5 0- 55 73 00 00 94 2- 11 01 95 3 0- 00 20 4 -0 0 5 9 6 6 0- 51 16 0- 00 12 9 1- 23 0- 43 96 2- 24 0- 27 43 2- 45 01 84 9 2- 49 01 55 1 2 1 9 0- 29 05 1- 98 0- 27 47 2- 25 0- 22 01 1- 51 0- 37 87 00 09 16 01 03 00 00 17 06 0- 12 35 3 0- 00 74 2 0- 08 20 4 0- 32 01 4 00 03 25 0- 12 96 7 00 07 67 H ay s: 00 00 90 0- 17 80 8 00 02 81 0- 14 99 6 0- 00 05 9 0- 30 39 5 0- 38 98 0- 58 15 0- 56 16 0- 49 00 0- 58 40 0- 49 81 0- 47 90 0- 38 13 00 06 55 00 00 02 00 01 08 00 10 75 00 01 58 00 00 14 0- 00 04 7 00 00 28 [ 1 -5 1 0- 34 47 00 00 97 I 1- 37 0- 44 42 00 04 78 01 54 92 0- 44 90 00 12 65 0- 23 44 4 0- 42 36 00 01 62 3 3 7 7 11 22 25 26 4 4 4 5 5 o F es cu e ha y fe d as a m ea l 1- 36 0- 37 14 00 15 00 01 75 42 0- 36 66 00 02 14 A P P E N D IX T A B L E 1 (c o n t. ) C on st an ts o f th e en er gy e qu at io ns R ef er en ce n o . 62 63 3 2 81 17 18 19 20 21 22 2 3 24 25 26 34 3 5 36 37 38 4 9 50 51 5 7 N o. a n d sp ec ie s of an im al 3S 3S 3 S 4S 3S 3C 3S 3C 3S 3C 3 S 3C 3S 3C 3C 3C 3C 3C 3C 3C 3 S 2C 2C N o. o f ob se rv at io ns in a dd it io n to f as ti ng 12 ( 4) "j 12 ( 4 )/ 9 \ 8j 6' 6 6 6 6 6 6 6 6 6 9 ] 9 9 1 15 17 11 8 P la n of e x p er im en t M ea n v al u es o nl y an al y se d L at in sq u ar e E ac h an im al r ec ei v ed a m ai n te n an ce a m o u n t of fe ed a n d an a m o u n t d o u b le t h is i n a ra n d o m al lo ca ti o n sc h em e L at in sq u ar e R an d o m al lo ca ti o n R an d o m a ll o ca ti o n p lu s a fi na l h ig h le ve l 5 o b se rv at io n s on o n e, 6 on t h e o th er 2 am o u n ts o f fe ed fo r ea ch a n im al M at er ia l fe d F re sh h er b ag e H a y m ad e fr om fr es h h er b ag e C ha ff ed l u ce rn e h ay H a y lo ng A ll f la ke d m ai ze , 95 % f la ke d m ai ze , 5 % h ay 20 % f la ke d m ai ze , 8 0 % h ay 20 % f la ke d m ai ze , 8 0 % h ay 40 % f la ke d m ai ze , 6 0 % h ay 40 % f la ke d m ai ze , 60 % h ay 60 % f la ke d m ai ze , 4 0 % h ay 60 % f la ke d m ai ze , 40 % h ay 80 % f la ke d m ai ze , 2 0 % h ay 80 % f la ke d m ai ze , 2 0 % h ay M ix tu re o f 50 % d ri ed g ra ss an d 50 % o f a co n ce n tr at e • p el le t M ix tu re o f h ay a n d o at s M ix tu re o f h ay a n d o at s 50 % m ai ze , 50 % l u ce rn e b ay 50 % m ai ze , 50 % l u ce rn e h ay F o r es ti m at in g en er g y re te n ti o n fr om g ro ss B 5- 80 3- 83 3- 79 1- 72 4- 07 4- 58 1- 69 2- 20 2- 89 2- 86 2- 69 2- 46 4 0 4 2- 59 (" 4- 03 4- 76 2 1 1 3 0 6 4- 92 2- 76 4- 02 2- 72 3 0 1 en er g y in ta k e P 0- 08 00 0 1 2 9 2 0 1 2 3 0 0- 17 68 0- 17 80 0- 15 12 0- 35 52 0- 23 05 0- 18 27 0- 18 99 0- 21 47 0- 26 87 0- 15 39 0- 27 88 0- 11 89 0- 10 62 0- 31 42 0- 18 68 0 1 0 5 3 0- 20 27 0 1 1 3 2 0- 24 19 0 1 9 7 8 R M S 0 0 0 1 2 4 0 0 0 7 6 3 0- 00 48 5 0 0 1 0 3 2 F o r es ti m at in g m et ab o li za b le en er gy f ro m g ro ss en er gy i n ta k e c 0 0 1 7 3 8 0- 0278 8 0 0 4 9 5 8 0- 05 38 8 b 0- 5 99 2 0- 56 56 0- 53 55 0- 37 00 H ay -c er ea l m ix tu re s: 0- 00 25 6 0- 00 74 7 0 0 1 7 3 8 0- 01 22 5 0- 00 80 3 0- 00 24 5 0- 00 52 2 0 0 0 4 4 8 0 0 1 4 9 3 0 0 2 6 4 9 0- 01 78 6 0 0 1 2 8 3 0 0 6 7 3 0- 24 95 0 0 0 3 2 3 0 0 0 3 0 9 0 0 1 5 1 6 0- 00 48 3 0 0 0 0 6 4 -0 0 0 0 9 5 0 0 0 1 0 3 0- 23 45 9 0 0 0 0 3 2 0 0 9 4 4 6 0- 07 05 0 -0 0 3 6 9 5 -0 0 1 5 3 3 -0 -0 3 8 3 5 -0 0 0 3 2 3 -0 -1 0 9 6 1 -0 1 6 5 1 0 0 0 2 9 5 1 -0 -1 2 8 6 8 -0 0 8 0 3 7 -0 0 0 0 2 3 0 0 2 0 4 7 0 0 5 2 5 2 0 0 1 4 2 6 0- 83 53 0- 79 29 0- 45 61 0- 55 66 0- 58 10 0- 58 25 0- 64 78 0- 65 10 0- 74 01 0- 71 34 0- 61 39 0- 63 71 0- 57 41 0- 65 43 0- 60 57 0- 52 48 0- 51 84 0- 56 59 0- 59 10 R M S 0 0 0 0 2 8 0 0 0 0 3 5 0- 00 48 5 0 0 0 1 3 3 0- 00 39 2 0- 00 26 0 0 0 0 9 6 9 0 0 0 3 5 0 0- 00 64 0 0 0 1 0 4 0 0 0 0 9 0 3 0 0 0 4 5 7 0 0 0 8 5 6 0 0 0 5 3 9 0 0 0 6 3 2 0 0 0 5 4 1 0- 00 43 6 0- 00 57 2 0- 00 47 9 0 0 0 1 3 1 0 0 0 9 4 0 0- 00 15 8 0 0 0 1 6 4 L it er at u re re fe re nc e 21 21 8 5 5 5 5 5 5 5 5 5 5 1 0 10 10 10 10 13 13 14 17 < i" TO | 'feeds a 03 s 2 i O S 0 0 A P P E N D IX T A B L E 1 (c on *. ) N o. a nd N o. o f ob se rv at io ns R ef er en ce sp ec ie s of in a dd it io n to f as ti ng 9 9 9 9 75 76 77 78 79 52 53 54 55 56 58 an im al 3S 3S 3S 3S 3S 1C 4C 4C 4C 4C 7S P la n of e xp er im en t L at in s qu ar es S eq ue nt ia l fe ed in g T w o am ou nt s of f ee d fo r ea ch a ni m al 34 W it h on e ex ce pt io n ea ch sh ee p gi ve n 5 am ou nt s 8 \ C on st an ts o f th e en er gy e qu at io ns F or e st im at in g en er gy re te nt io n fro m g ro ss en er gy i nt ak e F or e st im at in g m et ab ol iz ab le en er gy f ro m g ro ss en er gy i nt ak e M at er ia l fe d 20 % -| ba rl ey E x p t 6/ R R I 40 % I u np ro - E x p t 6/ R R I 60 % j ce ss ed E x p t 6/ R R I 80 % ! E x p t 6/ R R I A ll ba rl ey E x p t 6/ R R I B 3- 22 2- 58 6 1 6 5- 60 7- 86 P 0- 14 62 0- 23 47 00 83 3 0 09 47 00 55 4 R M S 0- 00 61 8 00 13 13 0- 00 27 5 0- 00 19 9 0- 05 13 6 00 17 36 00 94 85 00 99 63 00 98 89 0- 26 63 6 0- 59 34 0- 65 50 0- 66 93 0- 71 58 0- 79 62 R M S 0- 00 25 2 00 01 63 0- 00 64 5 00 01 17 0- 00 97 9 M ix ed d ie ts ; h ay , ce re al , p ro te in c on ce nt ra te : 0- 16 49 6 0- 57 65 00 00 97 3- 38 0- 19 32 00 04 43 73 % m ai ze , 24 % h ay , 2- 0 % l in se ed o il m ea l 30 % l uc er ne h ay , 40 % m ai ze , 30 % l in se ed m ea l 30 % t im ot hy h ay , 50 % ba rl ey , 20 % m ea t sc ra ps 1 5 % r ed c lo ve r ha y, 6 0 % 2- 72 01 65 9 00 02 03 -0 0 5 6 3 6 oa ts , 25 % c ot to ns ee d 20 % o at s tr aw , 45 % w he at , 20 % s oy a- be an m ea l P el le ts o f 50 % w he at , 40 % 3 0 2 lu ce rn e ha y, 1 0 % m ol as se s 7- 82 00 61 9 00 08 23 -0 0 2 2 6 7 5- 63 0- 08 47 00 05 02 -0 1 3 0 6 8 2- 67 0- 16 93 00 08 89 -0 0 7 4 6 5 0- 22 05 00 07 39 -0 0 5 7 0 4 0- 64 44 00 00 01 0- 65 97 00 00 03 0- 55 60 00 00 03 0- 58 80 00 00 06 0- 72 98 0- 00 27 6 L it er at ur e re fe re nc e 26 26 26 26 26 1 5 16 16 16 16 18 R ef er en ce s: 1 . B la xt er & G ra ha m ( 19 55 ); 2 . A rm st ro ng ( 19 64 ); 3 . B la xt er , W ai nm an , D ew ey , D av id so n, D en er le y & G un n (1 97 1) ; 4 . B la xt er & W ils on ( 19 63 ); 5 . B la xt er & W ai nm an ( 19 64 ); 6 . C or be tt , L an gl an ds , M cD on al d & P ul la r (1 96 6) ; 7. K . L . B la xt er & N . M cC . G ra ha m ( 19 57 E xp t, u np ub li sh ed ); 8 . B at em an & B la xt er ( 19 64 ); 9. K . L . B la xt er & J . L . C la pp er to n (1 96 6, u np ub li sh ed ) an d B la xt er ( 19 68 ); 9 a. B la xt er ( 19 68 ); 1 0. B la xt er , C la pp er to n & W ai nm an ( 19 66 ); 1 1. B la xt er & G ra ha m (1 95 6) ; 12 . G ra ha m , W ai nm an , B la xt er & A rm st ro ng ( 19 59 ); 1 3. B la xt er & W ai nm an ( 19 61 ); 1 4. F or be s, B ra m an , K ri ss , S w if t, F re nc h, S m yt he , W il li am s & W ill ia m s (1 93 0) ; 15 . M it ch el l, H am il to n, M cC lu re , H ai ne s, B ea dl es & M or ri s (1 93 2) ; 16 . M itc he ll & H am il to n (1 94 1) ; 17 . F or be s, B ra m an & K ri ss ( 19 28 ); 1 8. M ar st on ( 19 48 ); 19 . G ra ha m ( 19 67 ); * 20 . H as hi zu m e, K ai sh io , A m bo , M or im ot o, M as ab uc hi , A be , H or ii , T an ak a, H am ad a & T ak ah as hi ( 19 62 ); 2 1. G ra ha m ( 19 64 ); 2 2. F . W . W ai nm an & K . L . B la xt er ( 19 69 , u np ub li sh ed ); 2 3. B la xt er , W ai nm an & S m it h (1 97 0) ; 2 4. W ai nm an , B la xt er & P ul la r (1 97 0) ; 2 5. W ai nm an , B la xt er & S m it h (1 97 2) ; 2 6. W ai nm an & B la xt er ( 19 72 ). * T he c on st an ts f or t hi s Ja pa ne se e xp er im en t ar e no t in cl ud ed i n th e ta bl e. A s m en ti on ed i n th e te xt , th e re su lts w er e an om al ou s. w > w o
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