A new model predicting intake at pasture for beef cows

We developed a simple model predicting dry matter intake and diet digestibility at pasture, for a simulator of grassland-based suckler systems. Herbage is divided into structural components described by their biomass and digestibility. Diet composition is calculated assuming that the most digestible and abundant components are preferred. Dry matter intake depends on diet digestibility, animal intake capacity (function of animal characteristics), and sward biomass. The model is sensitive to digestibility of herbage components. Its predictions were satisfactory, since errror represented 5% of the mean observed value for diet digestibility and 10% for the dry matter intake.


INTRODUCTION
Based on INRA fi ll unit system for beef cows (INRA, 1989), we developed a model predicting intake at pasture that takes into account specifi c grazing features: the selective intake between the structural components of herbage and the intake limitation by herbage availability.This intake model was designed for a larger beef cow production model (Jouven et al., 2007) in a simulator of grasslandbased suckler systems.Therefore, we kept it simple and defi ned its inputs to be connectable with the outputs of a vegetation model (Jouven et al., 2006).We present here the conceptual basis and the equations of the intake model, and its evaluation through sensitivity analysis and comparison with experimental data for Charolais cows at pasture.

MODEL DESCRIPTION
According the fi ll unit system (INRA, 1989), dry matter intake (DMI, kg/d) is calculated as the ratio of the intake capacity (IC, CFU) to the diet fi ll value (FV diet, CFU/kg DM).Both are expressed in cattle fi ll unit (CFU): by defi nition 1 CFU is the "standard" voluntary dry matter intake of a reference herbage by a 400 kgheifer, set to 95 g/kg metabolic LW.
IC represents the amount of forage an animal can eat when fed ad libitum.It depends exclusively on animal characteristics, since the effect of diet ingestibility is taken into account by FV diet .The IC of the lactating beef cow is calculated according to INRA tables (1989) from cow liveweight (LW cow , kg), milk production (MP, kg), and body condition score (BCS, /5). (1) The present model integrates the effect of sward structural composition on diet digestibility, and thus on diet FV, as a result of selective intake of sward structural components differing in quality and abundance.The sward is described by total standing biomass (BM) and by the proportions (PR) in the grazeable stratum (>3 cm above ground level) and the organic matter digestibility (OMD) of four structural components: green leaves and sheath (GV), dead leaves and sheath (DV), green stems and fl owers (GR) and dead stems and fl owers (DR).The proportion of each structural component ingested in the diet (PRI) depends on both its relative abundance and its digestibility: we considered that animals prefer the most abundant and digestible plant components.In order to represent different levels of selectivity, we introduced a selectivity coeffi cient κ, which we calibrated for cattle to the value of 1, according to data by Farruggia et al. (2006).
(2) and similarly for GR, DV and DR.
Once the composition of the diet is known, its digestibility (OMD diet ) is calculated as the weighted average of the digestibility of the individual components.Diet FV is calculated as the ratio between the voluntary dry matter intake of the reference herbage by a 400 kg heifer, set to 95 g/kg LW 0.75 (INRA, 1989), and the voluntary dry matter intake of the selected diet.Voluntary dry matter intake depends on a number of forage characteristics, the most infl uential being organic matter digestibility (OMD) and forage type (INRA, 1989).The following equation is used for permanent pasture: (3) Finally, to integrate the established limitation of intake by herbage availability at pasture, we used data gathered in the literature to construct a function relating DMI to standing biomass per hectare (Figure 1).Thus, DMI is calculated as: (4) Figure 1.Limitation of intake by the biomass of the sward grazed (BM).The function (solid line) was constructed using 74 data (dots) from 12 experiments from the literature involving beef cattle grazing either continuously or rotationally (Jouven et al., 2007) The model was developed in Python 2.3 for Windows (Copyright 1991-1995 by Stichting Mathematisch Centrum, Amsterdam, The Netherlands).

MODEL EVALUATION
The ability of the model to represent a range of animal and sward types was evaluated by sensitivity analysis and by comparison with experimental data.

Sensitivity analysis
The sensitivity analysis was done on the input values of the main animal and sward characteristics, by altering by ±20% one input value at a time (Table 1).The standard situation consisted in a sward containing only GV and DV components with a 75/25 ratio.In this situation the estimates of PRI GV , OMD diet and DMI reached 0.83 g/g, 0.70 g/g and 12.9 kg DM, respectively.Cow liveweight was the animal characteristic to which the model was the most sensitive.Sensitivity to the selectivity coeffi cient κ was small in the range of variations tested (Table 1): to increase OMD diet by 2 points with the sward described, it would have been necessary to multiply the selectivity coeffi cient by 2. The sward characteristic to which the model was most sensitive was OMD GV .

Comparison with experimental data
Two groups of eight cows (4 to 7 years old) with their calves (calving date: 22 January ± 14 days) were grazed continuously (from 13 May to 4 November 2004) at two stocking rates (low: 0.70 cow ha -1 , high: 1.23 cow ha -1 ) on permanent pastures dominated by Festuca rubra and Agrostis tenuis (Baumont et al., 2006).Five experimental periods were set up at six-week intervals.During each period, sward biomass (BM) was measured, sward structural composition was assessed visually, and the quality of structural sward components was estimated by pepsincellulase digestibility.The intake of the cows was measured for each experimental period using ytterbium oxide (Yb 2 O 3 ) as an indigestible marker to estimate faecal output and using faecal nitrogen content to estimate diet OMD (Baumont et al., 2006).We simulated the intake of the average cow in the two treatments, for the fi ve experimental periods.
The model reproduced the decreases in OMD diet and DMI observed during the grazing season in the two treatments (Figure 2).Consistently with the experimental observations, the model predicted a higher OMD diet for the high stocking rate, a higher DMI in period 1 for the high stocking rate, and a higher DMI in period 4 for the low stocking rate.Model precision, estimated by root mean squared deviation was 0.04 for OMD diet and 1.5 kg for DMI.The model tended to underestimate OMD diet (Figure 2a), and consequently DMI (Figure 2b).Selectivity between plant components has already been modelled: Armstrong et al. (1997) predicted the proportion of different vegetation types and of green vs dead matter in the intake of sheep grazing hill vegetation based on the abundance and potential intake allowed by each component; Freer et al. (1997) predicted the proportion of vegetation and digestibility classes in intake based on their abundance in the sward and their digestibility.Our model uses a selectivity coeffi cient to modulate the selective behaviour of the grazing animal, which should allow applying the model to different animal types.Though, our model does not take into account the spatial distribution of structural components.
The limitation of intake by biomass availability, was previously modelled in relation to sward architecture and bite mass (e.g., Baumont et al., 2004), or directly in relation to sward height or biomass per animal and per day (see for a review in dairy cattle, Delagarde and O'Donovan, 2005).In our model, relating intake to biomass per hectare makes it possible to apply the same equation to rotational and continuous grazing systems, as well as to a range of vegetation types differing in sward height and density.Though, this approach assumes a homogeneous distribution of sward height in the paddock, which is rarely the case in large paddocks grazed continuously at a low stocking rate.

Figure 2 .
Figure2.Observed (dots, means ± SEM) and predicted (lines) intake at pasture across the fi ve experimental periods set up at six-week intervals between May and November: (a) organic matter digestibility of the herbage ingested (OMD diet ), and (b) dry matter intake (DMI), for suckler cows grazed continuously on permanent pasture at two stocking rates.Solid line and black squares: low stocking rate; dotted line and white squares: high stocking rate

Table 1 .
Results of sensitivity analysis, assessed for a ± 20% variation of the standard input values, on selected diet digestibility and on dry matter intake NSC) is the ratio of the rate of variation of the output variable to the rate of variation of the input value tested.A positive (or negative) NSC indicates positive (or negative) correlation.A higher absolute value for NSC means a higher sensitivity of the output variable to the input value tested