Ability of mathematical models to predict faecal output with a pulse dose of indigestible marker

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Abstract
The aim of the work was to compare the faecal output and digestibility estimated by two mathematical approaches with the actual amount of faeces excreted or feed digested by Siental cows. Experimental data (intakes and digestibility measured over 5 d) and faecal Cr concentrations (measured at 0, 4, 8, 12, 16, 24, 32, 48, 56, 72, 96, 120 and 144 h after a pulse dose of Cr-mordanted forage) were collected from published experiments and fitted to a multicompartmental (MC) model and a γ age-dependent (AD) model. From a statistical point of view, the MC model was very satisfactory while the AD model produced lower r2 and higher SE values and reached satisfactory statistical values only for higher DM intakes (lactating animals). The MC model produced higher correlations with the digestibility values while the AD model generated better correlations with the intake data; DM intake and digestibilities were more highly correlated with the model's parameters than neutral-detergent fibre terms. The regression between the estimated faecal outputs obtained with the two models showed an intercept closeto 0 (P>0·05) and angular coefficients near 1; there was a good correspondence of the estimates especially for the lowest values of output. The r2 values of the regressions were 0·800 and 0·829 for the MC and AD models respectively and their SE were 2·93 and 2·63. The ability of the two models to predict faecal output and digestibility was very similar, independent of the statistical accuracy of fitting the Cr- concentration data. The results indicate that variation of Cr concentration is the result of the entire digestive process, i.e. dilution and passage, which interact in a competitive or associative way.