title: Linear Models for Estimating the Nutritive Value of Sheep Diets
Creators: name: Christiansen, Michael L.
Publisher: name: Utah State University
Year: 1979

description: Digestibility data were determined in 2 replications of a 2 x 3 x 2 x 2 factorial arranged experiment to: (1) determine the effects of forage type (grass vs alfalfa), forage maturity (late vegetative vs midbloom vs fullbloom), diet ingredients (forage only vs 50:50 forage plus corn), and diet texture (coarsely chopped vs pelleted) on the digestibility of diet chemical constituents by sheep; (2) develop equations to estimate digestible energy of sheep diets from nutrient content of the diet; and (3) compare popular chemical methods used to partition feed dry matter into fibrous and soluble components. Diets were fed to growing wether lambs. Crude protein (CP) and available carbohydrates (AC) of diets were nearly 100% digestible (true digestibility) regardless of diet source. However, the apparent digestibility of CP and AC varied significantly with concentration of these components in the diet. Apparent digestibility of cellulose (CL) was significantly different between grass and alfalfa, early and late maturity stages, and coarse and pelleted diet textures. Interactions between forage type and stage of maturity and between stages of maturity and energy level also significantly altered the apparent digestibility of all diet fibrous constituents except hemicellulose (HC). An energy level-by-diet texture interaction significantly affected the apparent digestibility of HC, CL, CW, NDF, ADF and CF. simple (equation 1) and complex (equation 2) models were generated for estimating nutrient digestible amounts (YN) or diet digestible energy (DE) (YN) from nutrient content (XN) of the diet. Complex models were developed to adjust the estimation of the nutrient digestible amount or DE estimations for effects due to forage type (αi), stage of maturity (βj), feed combination (γk) and texture (δl). Two-way interactions (βij, βγK , . . ., γβKl) between qualitative variables were added in the equations when significant. Interactions between qualitative variables and the quantitative variable (αiXl, βjXl, γKXl, δlXl, &&alhpa;βijXl, etc) were also tried but did not significantly change the precision of the equations. Complex models gave significantly better estimates of digestible CP, AC, total lipid (TL), HC, CL, CW, NDF, ADR or CF and DE than simpler models. DE in the diets was determined by two methods: First, DE was estimated by the summation of the predicted decimal fraction of digested protein, carbohydrates, and lipids times respective caloric values (Mcal/kg) (equation 3). DE was also estimated directly from CL, CW, NDF, ADF, or CF content in the diet. Both approaches gave comparably precise estimations of diet DE when complex models were used. The CF
(1) YN = bo + blXN
(2) YN = bo + blXN + αi + βj + γK + δl + αβij+ . . . + γδKl
(3) DE = 5.65 (YCP) + 4.15 (YAC + YHC + YCL) + 9.40 (YTL)
Simple model gave poorer estimates of DE (R2 = .56) than CL, CW, NDF, and ADF simple models (R2 = .69, .69, .71, and .71 respectively). Added indicator variables compensated for differences between CF and other chemical parameters. Cl, CW, NDF, ADF, and CF complex models were similar in estimation of DE (average R2 = .89 for DE complex models). Complex models could be effectively used in a computer program for balancing rations for sheep. Additional experiments should be conducted to provide added information for comparison.