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Ecological Modelling 270 (2013) 11– 29

Contents lists available at ScienceDirect

Ecological Modelling

jo ur nal ho me page: www.elsev ier .com/ locate /eco lmodel

model of diurnal grazing patterns and herbage intake of a dairy cow,INDY: Model description

ablo Gregorinia,∗, Pierre C. Beukesa, Alvaro J. Romeraa, Gil Levya, Mark D. Haniganb

DairyNZ, Ltd., Private Bag 3221, Hamilton, New ZealandVirginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

r t i c l e i n f o

rticle history:eceived 23 June 2013eceived in revised form 28 August 2013ccepted 3 September 2013vailable online 5 October 2013

eywords:odelingrazing behaviorerbage intakeattle

a b s t r a c t

Estimates of herbage intake and parallel measurements of ingestive and digestive behaviors of graz-ing ruminants pose considerable experimental and technical difficulties, owing to dynamic interactionsbetween the plant, the rumen and the animal. As a consequence, advances in the area have been slowand costly. Model simulations that capture such interactions are critical for research and managementdecisions involving the grazing process. This work describes MINDY, a mathematical, mechanistic anddynamic simulation model of the diurnal grazing pattern of a dairy cow. MINDY is based on a cluster ofthree models: (1) Molly (Baldwin, 1995), a model of ruminant digestion and metabolism; (2) a modelrepresenting feed consumption as a function of diurnal fluctuations in the internal state of the animal;and (3) a sward structure, herbage quality and grazing behavior model. The objective of the work wasto describe the diurnal grazing pattern, including ingestive actions and rumination behaviors, herbageintake, and nutrient supply to the animal in response to the animal’s internal state and grazing envi-ronment. The model was coded in ACSL and simulations were conducted using ACSLXtreme. In additionto dietary nutrient composition required by Molly, MINDY requires sward surface height and mass, andgrazing area offered to the cow. Key sub-model parameters were identified by sensitivity analyses andparameterized using two data sets from mid-lactation Friesian and late lactation Holstein dairy cowsbreeds under set stock conditions. The parameterized model predicted realistic estimates of ingestive

behavior for different cow genotypes managed under set stocking and rotational grazing. It also pre-dicted a realistic number of steps taken while eating and searching and sward defoliation dynamics aswell as diurnal fluctuations of digestion and metabolism. Additional evaluations are required and furtherdata may be needed to better define some parameters, but the model offers promise as an heuristic toolfor feed intake and grazing process research and as an informative tool for grazing and cow management decisions.

. Introduction

Herbage intake is the most important variable affecting animalerformance in pastoral production systems (Kolver and Muller,998; Burns and Sollenberger, 2002). No reliable means exist toeasure it, therefore, its prediction and modeling are critical for

upporting targeted research to improve management of intaken grazing systems. Herbage intake results from grazing (Gibb,996), a complex process involving animal decisions at multiple

patio-temporal scales (Arnold and Dudzinski, 1978; Senft et al.,987; Bailey et al., 1996). Considerable research has been con-ucted on several aspects of this process, from bite formation to

∗ Corresponding author. Tel.: +64 7 858 3787; fax: +64 7 858 375.E-mail addresses: Pablo.Gregorini@dairynz.co.nz (P. Gregorini),

ierre.Beukes@dairynz.co.nz (P.C. Beukes), Alvaro.Romera@dairynz.co.nzA.J. Romera), Gil.Levy@dairynz.co.nz (G. Levy), mhanigan@vt.edu (M.D. Hanigan).

304-3800/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.ecolmodel.2013.09.001

© 2013 Elsevier B.V. All rights reserved.

long-term digestive constraints and grazing distribution patternsin a landscape (Heitschmidt and Stuth, 1991; Jung and Fahey, 1999;Gregorini, 2012), and a large body of empirical data has been accu-mulated.

Modeling has focused on the mechanics and dynamics of thegrazing process. Ungar and Noy-Meir (1988) and Parsons et al.(1994) developed model to relate intake rate to herbage availabil-ity, sward structure, and leaf area index of two contrasting plantspecies. Baker et al. (1992) and Baumont et al. (2004) developedmore complex models based on sub-models of grazing behav-ior – sward structure and the animal. Brereton et al. (2005) andWoodward (1998) modeled herbage utilization by cattle for rota-tional grazing systems. In all cases however, the animal componentof these models was elementary, which constraints detailed rep-

resentations of the effect of animal metabolism and physiologicalstate on feeding decisions. Recently, Chilibroste et al. (2008) devel-oped a simulation model to predict nutrient supply to a dairy cowunder discontinuous feeding patterns. Regardless of complexity,

12 P. Gregorini et al. / Ecological Modelling 270 (2013) 11– 29

Fig. 1. Schematic representation of MINDY: a mechanistic and dynamic model to simulate diurnal patterns of herbage intake and grazing behavior of a grazing dairy cow.W l, whitr motiva

nwcoi

11v1arrmpThlo

g(siiiibattd

tiiaea

hite boxes with solid lines represent true pools (hard components) of the modeepresent modifiers. Grey boxes (functional components) and arrows represent thend Duncan (1988) and Smith (1996).

one of these models dynamically integrate animal internal stateith spatio-temporal fluctuations in sward structure and herbage

hemical composition. Nor they account for photoperiod effectsn diurnal, daily and seasonal changes in feeding motivation andntake for a grazing dairy cow.

Animal behavior is controlled by stimulation systems (Smith,996; Toates, 2002) that motivate certain responses (Day et al.,998), e.g. grazing, which is defined as the process of seeking, har-esting and orally processing herbage before swallowing (Gibb,996). Two types of stimulation systems motivate grazing: hungernd incentives (Staddon, 1983; Tolkamp et al., 1998). The formeresults from integration of direct and short-term nutritive (e.g.umen function) and physiological stimuli (e.g. hormone release)odulated by long-term stimuli (e.g. physiological state and adi-

osity) (Kissileff and Van Itallie, 1982; Weston, 1996; Geary, 2004).he incentives are an integration of the animal’s internal state (e.g.unger) in the context of the grazing environment, what estab-

ishes a functional relationship between direct and indirect controlf feeding motivation (Kyriazakis et al., 1999).

Spatio-temporal variability in sward characteristics means thatrazing environments are complex by nature. The sward canopystructure, morphology and chemical composition) changes inpace (horizontal and vertical planes) and time. These changesnfluence availability and accessibility of herbage and thereby graz-ng (Drescher, 2003; Thompson Hobbs et al., 2003). Ruminants eatn periodic and discrete meals, which add to total daily herbagentake (Gibb, 1996). Hence, behavioral decisions such as when toegin and end a meal, meal frequency, meal patterns within a day,nd harvesting intensity within each meal (cumulatively defined ashe diurnal grazing pattern) determine how animals allocate timeo feeding and thereby, the form and rate of nutrient supply forigestion, metabolism and growth (Gregorini, 2012).

The primary objective of the work reported here was to modelhe diurnal patterns of ingestive and digestive behavior (includ-ng rumination), the resulting herbage intake and nutrient supply

n response to the interaction between the animal internal statend the grazing environment of a dairy cow. This work extends thefforts of Baldwin (1995), Baker et al. (1992), Galli et al. (1999)nd Baumont et al. (2004). The mathematical formulation, first

e dashed with dashed lines represent soft components of the model, solid arrowsational system of feeding behavior adapted from Jensen and Toates (1993), Hughes

principles and model parameters are described in this paper. Forillustrative purposes, some model outputs are presented using anold and a modern New Zealand Holstein–Friesian biotype cowgrazed under set stocking and rotational grazing (24 h pasturestrips) methods on a Lolium perenne L. dominated sward. The modelhas wider application. Comparisons between experimental dataand simulated values will be presented in subsequent manuscripts,as well as a description of a supplementation and a time at pasturerestrictions scheme.

2. Model description: MINDY

MINDY is a mechanistic and dynamic simulation model of thediurnal grazing pattern of a dairy cow (Fig. 1). MINDY is based on acluster of three models: (1) the dairy cow digestion and metabolismmodel of Baldwin (1995) modified by Hanigan et al. (2013) andknown as Molly; (2) a model of diurnal fluctuations in feeding moti-vation; and (3) a model of sward canopy structure, herbage qualityand grazing behavior. The latter were derived from the models ofBaumont et al. (2004) and Galli et al. (1999).

A glossary of parameters and variable names, parameter val-ues, and definitions is included in the Appendix (Table A.1). Codewas developed and simulations were conducted using ACSLXtreme(Ver. 2.5.0.6 Aegis Technologies Group, Austin, TX). Numeri-cal integration was conducted using a fourth-order, fixed-step,Runge–Kutta method. The maximum integration interval was setto 1 min. Results were collected after 8 d of simulation to ensurethe model had reached a stable state.

2.1. Internal state: rumen digestion, metabolism and lactation

The internal state of the animal (internal stimulation systems,Fig. 1) and productive parameters are represented using Molly(Baldwin, 1995) with recent modifications to improve the accuracyprediction of lipid, glucose and energy metabolism (McNamara and

Baldwin, 2000), lactation curves (Palliser and Woodward, 2002),photoperiod effects on milk production (Beukes et al., 2005), lac-tation potential (Hanigan et al., 2008) and anabolic and catabolichormone dynamics, as well as gestational metabolism (Hanigan

P. Gregorini et al. / Ecological Modelling 270 (2013) 11– 29 13

F igan ei ers; anF

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2

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ig. 2. A simplified schematic representation of Baldwin (1995). Adapted from Hann the model; boxes with solid lines represent pools; solid arrows represent modifiA, fatty acids, VFA, volatile fatty acids.

t al., 2009) of dairy cows under grazing conditions. Recently theigestive elements of the model were reparameterized using aewer and broader data set and several representations of rumen

unction were updated (Hanigan et al., 2013). An overview of thatodel is depicted in Fig. 2. For details of this model, the reader is

eferred to Baldwin (1995) and the subsequent developments ofolly (Hanigan et al., 2008, 2009, 2013; Gregorini et al., 2013).

.2. Diurnal fluctuations of feeding motivation

.2.1. PhotoperiodThe diurnal timing of meals differs distinctly among animal

pecies (Collier and Johnson, 1990). In grazing ruminants the mealnd ingestive behavior patterns are circadian (Gregorini, 2012).razing during daylight hours is highly preferred (Rook and Huckle,997; Linnane et al., 2001), although short grazing bouts (5–15% ofaily grazing time) may occur during the night (Krysl and Hess,993). In temperate climates, ruminants have three to five majoreals per day (Hodgson, 1990; Gibb et al., 1998). This frequency

s flexible and affected by external stimuli (e.g. photoperiod) andehavioral adaptations to the grazing management and sward stateGibb, 1996; Gregorini, 2012). For example, during short days,

eals merge and the number of daily meals decreases, proba-ly in an attempt to maximize grazing time during light hours

Rook and Huckle, 1997). Regardless of frequency, the major mealsccur around twilight hours, dawn and dusk, with the latter hav-ng greater intensity and longer duration (Gibb et al., 1998; Taweelt al., 2004; Gregorini, 2012).

t al. (2008). Boxes with dashes lines represent conceptual compartments as definedd the circles associated with dashed arrows indicate the direction of the modifies.

The model of Forsythe et al. (1995) was used to determine daylength (including twilight) and the time of dawn and dusk basedon the day of the year (DayofYear) and latitude.

Daylight = sin [(T − 0.25) × 2�] −(

0.5 − DayTwlength

24

)× 3 (1)

where Daylight assumes a positive value when it is light and a nega-tive value when it is dark. T is time of day (unit: days). DayTwlength(hrs.) is the length of the day including twilight and calculated fromthe day of the year and latitude as:

DayTwlength = 24 − 24�

× acos (DayTwlengthP2) (2)

where,

DayTwlengthP2 =sin(

6�/180)

+ sin(

Latitude × �/180)

× sin (DaylengthP1)

cos (Latitude × � /180) × cos (DaylengthP1)(3)

and DaylengthP1, the daylength excluding Twilight hours for thelactation module in Molly,[ ( {

DaylengthP1 = asin 0.39795 × cos 0.2163108 + 2 × atan 0.9671396

×tan [0.0086 × (DayofYear − 186)]})]

(4)

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These equations do not perfectly reflect the length of day at lati-udes greater than 60◦. Thus, a set of conditional statements aresed to cap daylength to a value of not greater than 24 h (Appendix.2.1).

.2.2. Hunger hormoneAs a meal progresses, hunger signals (opposite of satiety)

erived from the gut and absorbed nutrient supply decrease, whichontributes to cessation of a meal and changes in ingestive behav-ors (Dufort and Wright, 1962; Teitelbaum, 1966; Allen et al., 2005;regorini et al., 2009c). Many of these signals communicate with

he brain via hormonal circulation in the blood and via peripheralerves (Morton et al., 2006; Roche et al., 2008b), and are integratedith signals coming from the animal (e.g. adipose tissue (Faverdin

t al., 1999; Geary, 2004)) and external stimuli (Smith, 1996) toetermine the level of feeding motivation (Fig. 1) (Rhind et al., 2002;il-Campos et al., 2006; Gregorini, 2011).

Hunger is represented in the model by a hormone denoted asHor (hunger hormone), which controls the onset and cessation of

eals. Although IHor represents an aggregated representation oftimuli, it is roughly patterned after ghrelin. The orexogenic prop-rties of ghrelin and its relationship with the onset, cessation andntra meal eating behavior are well documented (Miner, 1992; Gil-ampos et al., 2006; Roche et al., 2008b; Gregorini, 2011). Increased

Hor triggers a meal, while decreased IHor causes eating cessa-ion. IHor also modulates ingestive behavior within each meal asescribed in Section 2.5. IHor at any point in time is determinedy numerical integration of the differential equation describingynthesis and degradation:

d (IHor)dt

= IHorSyn − IHorDeg (5)

Hor =∫

(dIHor) + iIHor (6)

here iIHor represents the reference concentration of IHor; set to as for other hormones in Molly.

The differential equation describing IHor synthesis (IHorSyn) is:

HorSyn =1 +(

CVFA/kVFA × kFdRat

)xVFA +(

AHor/kaHor × kFdRat

)xaHor

here, VmIHorSyn, CVFA, RumDM, and Am represent, respectively, theaximum velocity of IHor synthesis, concentration of volatile fatty

cids (VFA), DM load (kg, dry matter basis) in the rumen and ammo-ia (mol/L). AmCor is a correction factor for Am. AHor representslood anabolic hormone, while kFdRat is a function adjusting forhanges in adiposity and genetic merit for milk production (seeHanigan et al., 2009, 2013) for further details on these variables).

The rationale for the various factors affecting IHorSyn is as fol-ows. Ruminal volatile fatty acids (VFA) are major satiety signals. Ofhe major VFA produced in the rumen, acetate and propionate arehought to produce the strongest satiety signals (Faverdin, 1999).

hile propionate seems to be the strongest signal (Farninghamnd Whyte, 1993) the concentration and rate of total VFA produc-ion in the rumen are considered to be the main satiety signalsAdams and Forbes, 1981; Illius and Jessop, 1996); they are neg-tively related to ghrelin secretion (Roche et al., 2007; Gregorini,011). Since the work of Cannon and Washburn (1912), for exam-le, the fill effect is also considered a major factor in determining

he amount and rate of feed consumed at each meal, meal inges-ive behavior (Baumont et al., 1990; Gregorini et al., 2007a,b, 2009c)nd the diurnal arrangement of meals (Gregorini, 2012). Gregorinit al. (2009c) reported negative relationships between the level

odelling 270 (2013) 11– 29

IHorSyn

umDM/kRumDM × kFdRat

)xRumDM +(

Am/AmCor/kAm × kFdRat

)xAm

(7)

of ruminal fill and plasma ghrelin in grazing dairy cows. Ruminalammonia has been related to the control of herbage intake and itsdiurnal pattern (Vuuren, 1993; Chapman et al., 2007). Conrad et al.(1977) also reported reductions in intake rate and meal durationas ruminal ammonia increased. High ruminal ammonia has beennegatively related to neuropeptide-Y and ghrelin secretion (Miner,1992). AHor is a proxy for insulin (Hanigan et al., 2009), which hasa negative feedback effect on intake, inhibiting feeding motivationand decreasing meal size (Asarian and Geary, 2006; Roche et al.,2008a), and indirectly related (negatively) to ghrelin secretion indairy cows (Roche et al., 2008a).

KFdRat (from Eq. (7)) includes a lag function based on the equationof Roseler et al. (1997) to represent the reduction of intake in earlylactation functionally. KFdRat is calculated as follows:

kFdRat = 1 +(

BCSTarget

BCS− 1

)× kBCS +

(MamCellsPart

1000− 1)

×kMamCells + LagDMIxLag − 1 (8)

where, BCSTarget, is the representation of the target adipose tissueweight defended by the animal depending on the stage of lactation.BCS BCSTarget MamCellsPart, and LagDMI are body condition scoretarget, actual BCS, number of milk secretory cells in the udder atparturition and the function representing the reduction of intakein early lactation, respectively.

Body condition score is used to represent changes in adipos-ity and thereby leptin secretion (Vega et al., 2013; Roche et al.,2009), and MamCellsParts represents genetic merit (potential formilk production) of the cow (Hanigan et al., 2008), respectively.Adipose tissue dynamics and BCS are dynamically represented inMolly (Section 2.1). Leptin acts to maintain adipose tissue reserves(Roche et al., 2008b), and thus leptin concentrations and BCS arepositively correlated (Vega et al., 2013; Delavaud et al., 2000; Leónet al., 2004). Leptin also controls feed intake (Vega et al., 2013;Faverdin et al., 1999; Delavaud et al., 2000) because reduced leptinsecretion stimulates feeding. The effect of leptin is thought to bemediated by glucose and ketone bodies (Delavaud et al., 2000), as

well as the orexigenic neuropeptide-Y (Schwartz et al., 1996; Gil-Campos et al., 2006). There is an interaction between leptin and theneuropeptide-Y (Gil-Campos et al., 2006) that explains the nega-tive relationship between leptin and ghrelin secretion (Stylianouet al., 2007). Leptin does not dictate the onset or cessation of ameal, it modulates feeding motivation (Houseknecht et al., 1998).Roche et al. (2006) observed that genetic selection for milk pro-duction increased plasma ghrelin concentrations and associatedherbage intake levels in dairy cows. This mechanism is representedby MamCellsPart, which represents secretory cell numbers and dif-ferentiates udder metabolic capacity between cows, enabling themodel to represent genetic merit for milk production.

A reduction of intake in early lactation (LagDMI) is generallyobserved in dairy cows. This relates to reductions in gut capacityand is potentiated by adipose tissue mobilization (utilization) andstatus (Faverdin et al., 1999). The lag function described by Roseleret al. (1997) captures this phenomenon.

IHor degradation is calculated as a mass action function of IHor,

kIHor being a constant for adjustments.

IHorDeg = kIHor × IHor (9)

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P. Gregorini et al. / Ecolog

Having defined IHor, trigger points for starting (StartIHor) andnding (StopIHor) a meal were determined from iIHor by defining

range (IHorRange),

StopIHor = iIHor − IHorRange

2

StartIHor = iIHor + IHorRange

2

(10)

A meal will start (IHor > StartIHor) and stop (IHor < StopIHor) sub-ect to additional constraints executed as a series of logical testsAppendix A.2.2). These include: (1) a primary meal cannot starthen Daylight < 0; (2) once started, a meal can continue past dusk;

3) a small meal can occur after dusk, and (4) a meal cannot occurhen the cow is out of the paddock and/or being milked. Because

topIHor and StartIHor are not equal, the time between meals andhe length of a meal are primarily determined by the magnitudef the range between the triggers (IHorRange), creating an inter-ittent grazing pattern. Because meals occurring during the late

fternoon and early evening are generally longer and more inten-ive compared to previous meals of the day (Gibb et al., 1998;aweel et al., 2004; Gregorini, 2012), StopIHor was adjusted down-ards 3 h before the end of the day, a period labeled Latefeeding,

nd a logical statement was used to reduce the StopIHor during thateriod (Appendix). Latefeeding was determined from DayTwlength;

atefeeding = sin [(T − 0.125) × 2�] − 3(

0.5 − DayTwlenght

24

)(11)

.3. Diurnal pattern of rumination

Similar to the model of Sauvant et al. (1996), rumination occurss a response to the size of the large particle pool in the rumen.he fraction of large particles swallowed is determined and used asn input to the pool (Fig. 2). During inter-meal periods, ruminationccurs if the pool of large particles (LP) is greater than the minimumP pool size (MinLPRumntn). Rumination continues until the LP poolalls to MinLPRumntn or another meal begins. When ruminating,he rate of particle breakdown to small particles is represented as a

ass action function (in Molly) governed by the rate constant kLPSP.hen MINDY is not grazing or ruminating, MINDY is considered to

e resting (Appendix, A.2.4.). Daily rumination time is calculatedy numerical integration.

Rumination is important, not only because of the physicalreakdown of ingested feed particles, but also because it affectsalivation. Saliva supplies between 70 and 90% of the fluid anduffering capacity entering the rumen and is the major determi-ant of liquid outflow rate from the rumen (Cassida and Stokes,986). Observations from Maekawa et al. (2002) and Cassida andtokes (1986) were used to set the previously encoded salivationates associated with eating, ruminating, and resting (225, 205 and14 mL/min, respectively) in Molly code.

.4. Grazing environment and behavior

Grazing ruminants prefer to graze swards and generally selectatches that enable them to maintain or increase herbage intakeDemment et al., 1993; Illius et al., 1999). Therefore, when the

MeanLM =

{[(ETHini + MeanSwardHeight) × LM] +

[(MeanSwardHeig

−[MeanSwardHeight × LM + (MeanSwardHeighteLMI × (LM

ETHin

odelling 270 (2013) 11– 29 15

sward canopy is relatively homogeneous (horizontal plane) andthe area offered and time allocated to graze are restricted, cattlegraze down available herbage in successive strata (Ungar and Ravid,1999). Even in relatively homogeneous swards, canopies presentvertical chemical and morphological heterogeneity, which changesthroughout the day (Delagarde et al., 2000; Gregorini, 2012). Thiscreates different spatio-temporal arrangements of availability andaccessibility of herbage mass and nutrients. Therefore, as cattle pro-gressively graze down a pasture, they define and then encountersuccessive and dynamically changing grazing strata with respectto feeding value.

2.4.1. Characteristics of the sward canopy, grazing strata andchemical composition of herbage

The sward canopy is modeled as a set of superimposed graz-ing strata (GS) as in Galli et al. (1999) and Baumont et al. (2004).The sward canopy depth (m) determines the vertical dimension ofthe sward canopy available to be grazed, which is determined bythe initial extended tiller height (ETHini), an input to the model.The number of accessible GS (Nstrata) within the sward canopyavailable to be grazed is calculated as follows:

Nstrata = 1 + [Log (ETHlim) − Log (ETHini)]Log (1 − DD)

(12)

where, ETHini (m) and ETHlim (m) are the initial extended tillerheight and the sward canopy barrier, respectively. The barrier is thesward canopy height under which cows are not allowed to (deter-mined by management) or able to graze (determined by swardcanopy structure; i.e. stem/pseudostem physical barrier). ETHlim isan input to the model. DD, a constant proportion of ETHini, repre-sents bite depth for each GS (Wade et al., 1989), thus defining thedepth (m) and ETH (m) of each GSi in the sward canopy. The latteris calculated as:

ETHi = ETHini × (1–DD)(i−1) (13)

For the purpose of calculations of vertical distribution of herbagemass and nutrients within the sward canopy, the median pointheight of each GS (Hi, m) is calculated as:

Hi = [ETHi + ETHi−1]2

(14)

Herbage biomass (kg DM/m2, input to the model) varies throughthe vertical plane of the sward canopy. Such a distribution isdescribed by a morphological analysis (mass, position and morpho-logical components) similarly to Baumont et al. (2004), utilizing alinear mass index (LMIi) that describes the vertical distribution ofherbage mass within the sward canopy.

LMIi = 1MeanLM

×

{LM +

[((SM − LM)

1 +(

MeanSwardHeight/Hi)eLMI

)]}(15)

where, LM and SM are the masses of lamina and sheath plus stem(kg DM/m) respectively. MeanSwardHeight is half of ETHini and eLMIis a parameter that changes the shape of the curve and so thedistribution of herbage mass in the vertical plane, allowing the

representation of different vertical distributions. MeanLM is themean linear mass (kg DM/m) of a grass tiller plus stem (or erectlegume) calculated from the integration of the Michaelis–Mentencurve between ETHini and MeanSwardHeight.

hteLMI)

× (LM − SM) / (ETHini + MeanSwardHeight)]}

− SM) /MeanSwardHeight)]

i(16)

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While herbage mass is an input to the model, mean bulk densityf the sward canopy (MBDsward, kg/m3) and each GS (MBDi, kg/m3)re calculated as:

BDsward = HM

ETHini(17)

BDi = MBDsward × LMIi (18)

Temporal changes in the nutrient composition of herbage massre represented using a set of polynomial equations to predicthanges in neutral and acid detergent fibers, crude protein, solu-le crude protein, and an estimate of the rumen undegradable acidetergent fiber concentrations continuously during daylight hoursAppendix A.3). The equations are of the form:

Adjustment = Cons tan t + a × T3 + b × T2 + c × T (19)

here FAdjustment is the adjustment factor to the herbage chemi-al composition, T represents time of day (days) calculated using aOD function; a, b and c are coefficients derived for each nutrient

rom the data of Gregorini et al. (2008c, 2009d). FAdjustment was cen-ered on a value of 1. As composition data were only available foraylight hours, the adjustment factors were calculated as a linear

nterpolation of the value at sunset and the value at sunrise duringark hours. Thus, the adjustments cycled each day. Fiber and pro-ein concentrations (g/kg DM) were then calculated continuouslyrom the herbage chemical composition inputs as:

utrientAdjusted = Nutrientinput × FAdjustment (20)

Soluble carbohydrates are calculated by difference after specifi-ation of all of the other nutrients in the herbage. Thus, net changesn the sum of temporally adjusted and explicitly defined nutrients

ere inversely proportional to the soluble carbohydrate contentf herbage. Changes in biomechanical (e.g. toughness) features oferbage affecting ingestive behavior are represented by the neu-ral detergent fiber content. Neutral detergent fiber content variesn the vertical plane of the sward canopy and by time of day. Thesepatio-temporal changes were represented using the equation ofaumont et al. (2004) with temporal adjustment using FAdjustment

or neutral detergent fiber (FAdjustmentNDF):

DFi = (1.15 − 7.33e − 4 × Hi) × NDFadjusted (21)

here, FAdjustmentNDF is defined by Eq. (19). The NDF content is usedn the model (see Molly code) to calculate nutrient inputs like hemi-ellulose, cellulose, and soluble carbohydrates. Thus, as NDF variesn time and space (by strata), reciprocal changes in herbage sol-ble carbohydrates, hemicellulose and cellulose occur across theertical plane of the sward canopy.

.4.2. Potential and actual herbage intake rate at each grazingtratum

The short-term herbage intake rate (kg DM/unit of time) of arazing animal can be represented by the product of two variablesite mass (BM, kg/bite) and bite rate (BR, bites/min). In the model,s in Baumont et al. (2004), the potential herbage intake rate atach GS, (PIRi, kg DM/min), is calculated as:

IRi = BMi

TBi(22)

here, is BMi given by:

Mi = BDi × BAi × MBDi (23)

here BDi and BAi are bite depth (m) and area (m2) and MBDi is theean bulk density (kg/m3). BDi and BAi are calculated as:

Di = ETHi × DD (24)

odelling 270 (2013) 11– 29

BAi =(

2 × DA2

1 + MeanSwardHeight/Hi

)× exp [−0.3 × (MBDi − 1)](25)

where DA (m) is the animal’s dental arcade width, which is cal-culated based on a modification of the Illius and Gordon (1987)allometric relationship to avoid the effect of gut fill, adipose tissueand gravid uterus on animal body weight (BW, kg):

DA = 8.6 × NonFatNonUterEmptyBW0.36 (26)

Because BA is dependent on DA (Illius and Gordon, 1987) andsward surface height, the asymptote of this relationship was set totwice the square of the DA (Gordon et al., 1996) and affected byMeanSwardHeight and Hi as in Baumont et al. (2004). The negativeexponential function represents the effect of sward density on BA,which has a neutral effect for a MBDi of 1 kg herbage dry matter perm3 (Laca et al., 1992).

The potential time per bite (TBi, min) is the sum of prehen-sion (PT, min) and potential ingestive chewing times (PCHT, min)for each GS, where the latter is a function of the herbage neutraldetergent fiber content and BM:

TBi = PT + PCHT (27)

PCHTi = (0.25 × NDFi − 12.5) × BMi (28)

where, PT is based on Illius and Gordon (1987) using empty BWminus fat and uterine weight (NonFatNonUterEmptyBW) so thatchanges in gut fill, BCS, and pregnancy state do not affect the esti-mate:

PT = 0.35 × NonFatNonUterEmptyBW0.125 (29)

Ingestive chewing is a variable function of the mass and fibros-ity of herbage and hunger (Pérez-Barbería and Gordon, 1998).Grazing cattle increase TB as BM and fiber content of harvestedherbage increase, but reduce it as hunger increases as a compen-satory mechanism to increase herbage intake rate (Greenwood andDemment, 1988; Gregorini, 2011). Therefore, from TBi and IHor, theactual chewing time (ACHT, min) required for each bite taken iscalculated as:

ACHTi = (TBi–PT) × ChewFactor (30)

where, ChewFactor is a variable representing the effect of feedingmotivation on ingestive chewing [See (Pérez-Barbería and Gordon,1998; Gregorini, 2011)] and calculated as:

ChewFactor = LowChewingMot − [(LowChewingMot

−HighChewingMot) × exp[−kChewfactor×GIHor]] (31)

where LowChewingMot and HighChewingMot are constants withvalues of 0.15 and 1, respectively, and kChewfactor is a parameter thatchanges the shape of the curve and so the time invested in ingestivechewing at different levels of hunger as a function of external fac-tors such as available herbage mass (AHM), time of day, and GIHor(See Section 2.4.3).

Therefore, the actual herbage intake rate (kg/min) for a partic-ular GSi at a given time of day (t) is calculated as:

ActualIRi = BMi

PT + ACHT(32)

2.4.3. Actual motivation to grazeModulation of hunger (IHor) by indirect controls (external

stimuli, incentives) represents (to some extent) the animal’s per-

ception of the feeding environment, which can change ingestivebehavior. Hunger and, thereby, ingestive actions are modulatedby time of day, herbage chemical composition, available herbage,light intensity and anti-predator strategies (Woods and Strubbe,

ical Modelling 270 (2013) 11– 29 17

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994; Strubbe and Woods, 2004; Gregorini, 2012). Therefore, actualotivation to graze is calculated as:

IHor = IHor × AHM × TimeOfDayEffect (33)

here, AHM is the available herbage mass modulator factor at aarticular T. AHM is calculated as:

HM = (HMtotavail + HMunavail)iHMtotal

(34)

Mtotavail =∑

(GSAii × MBDii) × BDi (35)

Munavail = iHMtotal–iHMtotavail (36)

HMtotal = HM × TA (37)

HMtotavail = TA × MBDsward × (ETHini–ETHlim) (38)

here, HMtotalavail is the sum of herbage mass (kg) remaining inach GSi. HMunavail is that herbage below ETHlim. iHMtotal is the totalre-grazing herbage mass (kg/m2). TA is total grazing area allocateder cow (m2). iHMtotavail is the AHM at the time pasture is allocatedpre-grazing herbage mass).

TimeOfDayEffect (unitless) was patterned after the natural diur-al grazing patterns of ruminants, using data (patterns of ingestiveehavior) from set stocked dairy cows (Gibb et al., 1998; Taweelt al., 2004), sheep (Orr et al., 1997) and beef heifers (Gregorini et al.,007a). It stimulates the motivation to graze as dusk approachesGregorini, 2012) and reduce it overnight. TimeOfDayEffect calculuss presented in the Appendix (A.2.6).

.4.4. Grazing strata, foraging decisions and actual herbagentake dynamics.4.4.1. Dynamics of grazing strata area availability and accessibility.s in Baumont et al. (2004), a GS is considered relatively homoge-eous and thus can be represented as cluster of contiguous bitesFig. 3a). Therefore, if iHMtotavail occupies the TA, each grazabletratum area (GSA, m2) initially equals the sum of the potential BAn the GS. As the pasture is grazed down, the next lower GS will pro-ressively become accessible. Therefore, GSA accessibility for eachS changes as grazing occurs.

dGSAi

dt= SGRi − CRi (39)

here, SGRi and CRi are the rates of change in the area (m2) ofach GS due to sward canopy growth (m2/min) and consumption,espectively (Also see Fig. 3a). SGRi and CRi are calculated similarlyo Baumont et al. (2004).

GRi = [(TA–GSAi) × HGR]BDi

dGSAi

dt= SGRi − CRi (40)

Ri = BRi × BAi (41)

here GSAi (m2) is the ungrazed and accessible area for GSi (derivedy numerical integration of Eq. (39)); HGR is the herbage growthate (m/min); and BRi is bite rate (bites/min) for GSi (see Section.4.5).

.4.4.2. Foraging decisions. As successive GS become accessible, thenimal can either (1) completely graze the upper GS before startingo graze the next lower GS, or (2) graze completely down the swardanopy at each feeding station (FS, Section 2.4.6) before moving to

he next FS. The former is consistent with an attempt by the animalo maximize intake rate given that BM successively becomes lessn each lower GS (Demment et al., 1993; Illius et al., 1999). Underotation grazing management, cattle graze by stratum (Wade et al.,

Fig. 3. a) A schematic representation of the bite features and grazing strata duringgrazing; b) a schematic representation of the harvesting step length calculus.

(Adapted from Galli et al. (1999) and Baumont et al. (2004)).

1989). They start consuming the next lower GS as the area of theupper stratum shrinks. In MINDY, it was assumed that the animalwould only graze from the upper two available GS, and the pref-erence for each strata (PREFi and PREFi − 1) was calculated from theproportion of the upper GSA remaining using a Michaelis–Mentenfunction to achieve a continuous shift in preference from the upperto the lower GS as the GSA of the upper stratum declined. A series oflogical statements (Appendix A.2.5.) was used to shift grazing downto the next pair of GS (i.e. GSi − 1 and GSi − 2) when GSAi reached anegligible area (minimumGSA).

2.4.5. Real herbage and nutrient intake and bite rateHerbage intake rate (FdRat, kg/min) is a function of ActualIR and

PREF for each of the pair of available GS:

FdRat = (PREFCurrentStratum × ActualIRCurrentStratum + PREFCurrentStratum−1

×ActualIRCurrentStratum−1) (42)

where PREFCurrentStratum and PREFCurrentStratum − 1 are the relativepreferences for the upper and next lower GS, respectively.

Therefore, the rate of each particular nutrient intake is calcu-lated as:FdRatNutrient = FdRatCurrentStratum × NutrientCurrentStratum + FdRatCurrentStratum−1

×NutrientCurrentStratum−1 (43)

where, NutrientCurrentStratum is calculated as described in Section2.4.1. Eqs. (19–21).

Daily herbage DM intake (HDMI, kg/d) and particular nutrientintake (kg/d) are determined by numerical integration, for exam-ple:

HDMI =t∫0

FdRat (44)

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Having determined PREF, ActualIR, and BM, bite rate (BR,ites/min) can is calculated as:

R =[(

PREFCurrentStratum × ActualIRCurrentStratum

BMCurrentStratum

)+(

PREFCurrentStratum−1 × ActualIRCurrentStratum−1

BMCurrentStratum−1

)](45)

.4.6. Walking and searching while grazingGrazing includes a series of animal decisions at different scales

Senft et al., 1987). Once the animal has made the decision to graze,t selects an area to place the bites, exploits it and then abandonst. Grazing encompassed two main actions, harvesting (prehension,ngestive chewing and swallowing) and searching. A feeding stationFS) is the area of pasture a grazing animal can reach from a givenosition without taking a step. The number of FS would then bequal the number of steps taken while the cow is head down har-esting (Ruyle and Dwyer, 1985; Rook et al., 2004; Wade et al.,006; Gregorini et al., 2011). The area of a FS is calculated as a semi-ircle, where the step length while harvesting (HSL, m) is used as theadius (m). Based on the works of Ruyle and Dwyer (1985) and Rookt al. (2004) and assuming a 30◦ angle for the neck when the cows head down harvesting, the HSL is trigonometrically calculated asFig. 3b):

SL = CowHeight × tan 30◦ (46)

here, CowHeight (m) is the shoulder height of the cow.Assuming random searching for FS while grazing, a maximum

alking speed while harvesting (MVeleating, m/min) (Ungar andoy-Meir, 1988; Galli et al., 1999) and that such a velocity slowsown as grazing motivation declines (Gregorini, 2011; Gregorinit al., 2011), the momentary rate of FS (FSR, FS/min) is calculateds:

SR =(

MVeleating × GIHor)

HSL(47)

The momentary average speed while harvesting (MSH, m/min)s derived as:

SH = FSR × HSL (48)

and the distance walked while harvesting (DWH, m)

WH =t∫0

MSH (49)

Searching time (STI, days) and distance (SDI, m) covered whileearching are calculated assuming that maximum searching veloc-ty (MVelsearching, m/min) also changes in response to grazing

otivation as shown by Gregorini et al. (2007a,b). Considering thathe grazing process is equal to harvesting plus searching, searchingime is calculated only when the cow is grazing but is not harvestingerbage:

STI = 1 − [BR × (PT + ACHT)] (50)

here, pSTI momentary proportion of time searching (unitless), andTI calculated as:

TI =t∫0

pSTI (51)

Then, momentary average searching speed (SSpeedS, m/min)

SpeedS = pSTI ×(

MVelsearching

GIHor

)(52)

odelling 270 (2013) 11– 29

and SDI calculated as:

SDI =t∫0

SSpeedS (53)

Therefore, the searching step rate (SSR, searching steps/min) andthe total number of steps while searching (TSS) are calculated as:

SSR = SSpeedS

(HSL × 1.4)(54)

TSS =∫

y

xSSR

y − x(55)

where, 1.4 is a scalar to calculate searching step length (m) whichis 40% longer than HSL (Gregorini et al., 2007a,b).

During lactation, in addition to HTD, cows walk from the pastureto the milking parlor. This extra walking (RacesDistance, m) dependson milking frequency and distance to the parlor. Therefore, it ispossible to calculate the total distance walked during a particularday (DailyWalking, m).

DailyWalking = DWH + SDI + RacesDistance × milking frequency

(56)

3. Model parameterization

Due to the complex interactions among the sub-models, multi-dimensional sensitivity analyses were run to identify patterns ofchange in HDMI, grazing time, rumination time, resting time, num-ber of meals per day, and meal length in response to variablesaffecting the diurnal pattern of IHor. Model parameters were ini-tially set to achieve the approximate number and length of mealsper day. Variables were perturbed in both a positive and a nega-tive direction from their assumed values by 20% in two steps. Thenmodel outputs were regressed on the change in the variables esti-mates to estimate the model sensitivity (Appendix A.4, Table A.3).Herbage dry matter intake and daily grazing time responded tomost of the variables tested as expected. They were particularlywell correlated with changes in parameters controlling IHor syn-thesis and degradation and the minimum interval between meals atnight. Rumination time was sensitive to IHor synthesis and degra-dation, the multiplier to expand the IHor range during dusk, therate of reduction of large particles to small particles in the rumen,and the pool of DM in the rumen. Resting time mirrored rumina-tion time. Meals per day was most sensitive to factors controllingIHor synthesis and degradation, like anabolic hormone, pool of DMand VFA concentration in the rumen. Intake per meal was not sen-sitive to any single parameter but was moderately sensitive toIHor synthesis, reduction of large particles to small particles in therumen, and VFA and ammonia concentration in the rumen. Thelength of meals was not sensitive to any of the parameters but wasmoderately sensitive to IHor synthesis and to VFA and ammoniaconcentration in the rumen. This test provided a better understand-ing of how each of the variables affected model outputs, therebyidentifying which parameters determined total intake and patternsof intake within a day.

Parameter estimation was conducted by fitting the model to thedata of two experiments conducted with grazing dairy cows underset stocking grazing management, Gibb et al. (1998) and Taweelet al. (2004), since under this management, domestic ruminantsshow a natural grazing pattern Gregorini (2012). The experiment

of Gibb et al. (1998) was conducted in summer and used Friesianscows in mid-lactation (∼160 days in milk) with an approximateliveweight of 470 kg, grazing a L. perenne dominated sward of5–7 cm surface height and an approximate mass of 2200 kg DM/ha.

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ows were milked twice a day at 5 am and 2:30 pm. The exper-ment of Taweel et al. (2004) was conducted in the spring andsed Holstein cows in late lactation (310 days in milk) with anpproximate liveweight of 600 kg, grazing a L. perenne dominatedward of approximately 10–15 cm surface height and a mass of700 kg DM/ha. Cows were milked twice a day at 6:30 am and 6 pm.he model inputs were configured to reproduce the above swardharacteristics, time of year, latitude, and milking schedule. Thebserved discrete patterns of grazing activity were reconstructedsing a time scale of minutes and smoothed to create a continuousariable using the following equation. This was required for param-ter estimation as the available optimizers in ACSLX are not able toandle discrete data.

GrazingSmotothed = (SmoothingCons tan t × time step + Grazing)(1 + SmoothingCons tan t × time step)

razingSmoothed =t∫0

dGrazingSmoothed

here GrazingSmoothed is a moving average of grazing activity with ratio of 10 to 1 for the previous moving average, SmoothingCon-tant is 10 and grazing is the discrete meal patterns shown by theata.

The same equation form was used in the model to converthe predicted discrete meal patterns into a continuous variablehich was then compared to the function values derived from

he observed data. Fig. 4 shows a plot of smoothed meal patternor observed and predicted values. Parameters for estimation werehosen based on the sensitivity analyses and estimated using theelder–Mead algorithm available in ACSLX.

Model parameter estimates and an analysis of residual errors areresented in Table 1. In all cases, the model parameters were wellefined by the data as evidenced by the STD of the parameter esti-ates being less than 1% of the respective estimates. Synthesis of

Hor was most sensitive to changes in ruminal VFA concentrationss evidenced by the sensitivity exponent of 10.35. Sensitivity of thequation to changes in AHor, ruminal ammonia, and ruminal DM fillere more modest assuming sensitivity exponents near the initial

alues of 1. The evening and night-time range between StopIHornd StartIHor was found to expand to 1.24 times the range duringhe daytime. This helped trigger initiation of a late afternoon, earlyvening meal and expanded the length of such a meal to ensure

dequate ruminal mass through the night. The length of meals initi-ted after dark was limited to 64 min. With the derived settings, theodel had 36% error in predicting the timing and length of the var-

ous meals throughout the day as reported in Gibb et al. (1998) and

able 1odel parameter estimates derived by fitting to the data of Gibb et al. (1998) and Taweel

Parameter1 Final STD of estimates

VmIHorSyn 73.26 0.0027

kIHor 6.01 0.009

NightMealInter 0.10 0.00001

NightMealTime 0.04 0.000003

NightMult5 1.24 0.003

kLPSP 2.78 0.00081

kaHor 1.53 0.00023

kAm 2.99 0.00013kRumDM 3.38 0.00047kVFA 0.11 0.000033xaHor 0.85 0.00036xAm 1.16 0.00025xRumDM 1.02 0.00016xVFA 10.35 0.0056

SMPE, square root of mean prediction error; STD, standard deviation; MSPE, mean squa1 Parameters are described in Table A.1.

odelling 270 (2013) 11– 29 19

Taweel et al. (2004). The model did not display mean bias (0.35%of the MSPE) and slope bias was minor (20% of the MSPE). Thissuggests that most of the variance was due to random biologicalvariation (79% of the MSPE).

4. Illustration, application and discussion

The present work focused on formulating and parameterizingthe model with an initial validation conducted under contrastingscenarios. This validation was performed by assessing its abilityto simulate realistic diurnal grazing patterns and herbage intakesfor dairy cows of two distinct genotypes, old (∼1970s origin)and modern (∼1990s origin) New Zealand Holstein–Friesian inmid-lactation (late spring) subjected to two contrasting grazingmanagements: (1) set stocking and (2) rotational grazing (24 h pas-ture allocation) on a L. perenne dominated sward. Stocking rate wasthe equal for both management scenarios; while grazing pressure(stock density per unit of area over a 24 h period) was lower forset stocking. In rotational grazing the area allocated per cow perday was 100 m2, while the area available to graze over 24 h in setstocking was 2000 m2 (equivalent to a rotation length of ∼20 days).The parameters and inputs used to describe cows and swards arepresented in Table 2. The results of the simulation are presented inTable 3 and Fig. 5 and discussed in the following sections.

4.1. Daily herbage intake and hunger level

The results of the simulation show a marked effect of animalgenotype on daily herbage intake. The predicted level of intake,and the magnitude of its difference between cow genotype, agreewith the empirical data of Macdonald et al. (2008) collected underNew Zealand grazing conditions and management. Macdonald et al.(2008) reported intakes of 13.9 and 13.7 and 16.8 and 15.7 kg for theold and modern cows at 90 and 240 days in milk, respectively. Previ-ous empirical modeling (Gregorini et al., 2009b) for these two cowgenotypes indicated that modern cows of NZ origin have greaterfeeding drive (hunger) in comparison with the older cows’ typewhich is consistent with Roche et al. (2006) who reported greaterlevel of plasma ghrelin for modern cows (301 vs. 241 pg/mL, respec-tively). MINDY predicted not only a different diurnal pattern of thehunger hormone (IHor ∼ ghrelin) across cow genotypes, especiallyunder rotational grazing management (Fig. 5), but also different

daily means (Table 3). Increments in intake come with geneticimprovements for milk production (Linnane et al., 2004; Kolveret al., 2005). Although detailed statistical validation is required, thepresent example suggests that MINDY can predict realistic levels of

et al. (2004), and residual error analyses.

Residual error analyses

RMSPE, % of mean 36.18Mean bias, % of MSPE 0.35Slope bias, % of MSPE 20.71Random error, % of MSPE 78.92N 5264Mean of observed 0.46Mean of predicted 0.47

re prediction error.

20 P. Gregorini et al. / Ecological Modelling 270 (2013) 11– 29

Fig. 4. Plot of smoothed observed values from Gibb et al. (1998) and Taweel et al. (2004), overlaid with the smoothed predicted values for grazing activity (i.e. meal throughoutthe day).

Table 2Input parameters used to represent cow genotype and sward features for simulations of cows with historic or current genetic potential subjected to set stocked or rotationalgrazed pastures.

Parameter Sward characteristicsa

Set stocking Rotational grazinga

Herbage mass (kg DM/ha) 2300 3000Extended tiller height (cm) 15 30eLMI (unitless) 0.00001 1SM (g/cm) 0.001 0.0015Area available to graze over 24 h (m2) 2000 100Herbage growth rate (cm/d) 0.6 0.6Crude protein (g/kg herbage DM) 178 178Lipids (g/kg herbage DM) 40 40Non-structural carbohydrates (g/kg herbage DM) 60 60Neutral detergent fiber (g/kg herbage DM) 385 385Acid detergent fiber (g/kg herbage DM) 206 206Lignin (g/kg herbage DM) 16 16Ash (g/kg herbage DM) 100 100

Cow genotype

Old Modern

Mature weight (kg) 500 550Height (from ground to shoulders, m) 1.4 1.6Liveweight (kg) 440 470MamCellPart (unitless) 710 860Body condition score (points, 1–5 scale) 3.25 3.0Days in milk (days) 180 180Milking times (hours) 5 am, 3 pm 5 am, 3 pm

a Strips of new pasture were allocated every 24 h right after morning milking (5:30 am). Chemical composition of the grass at noon (12:00 pm).

Table 3Effect of cow genotype and grazing method on model predictions of variables associated with hunger, dry matter intake, grazing pattern, and distance walked.

Cow genotype Old Modern

Grazing method Set stocking Rotational grazing Set stocking Rotational grazing

Output variableIHor (unitless) 0.91 0.99 0.95 1.43Herbage intake (kg DM/d) 15.2 15.3 17.8 16.6Grazing time (min/d) 492 485 544 560Harvesting time (min/d) 487 297 537 351Searching time (min/d) 5 187 7 208Number of meals per day 5 5 5 5Average meal length (min) 102 59 115 75Average meal intake (kg DM) 3.04 3.01 3.55 3.32Rumination time (min/d) 442 471 441 435Idling time (min/d) 505 483 455 446Distance walked while eating (m/d) 2444 3192 2455 3357Distance walked while searching (m/d) 30 1044 33 956

P. Gregorini et al. / Ecological Modelling 270 (2013) 11– 29 21

F horm[ ’ axis

hi

i

ig. 5. Diurnal pattern of grazing behavior, rumen function and anabolic and hungerset stocking and rotational] as simulated by MINDY model. (Solid lines belong to ‘y

erbage intake (Table 3), and thus be used to evaluate the responsen herbage intake of cows with different genetic merit.

Grazing management also altered the level of intake. Herbagentake was lower for the modern cow under rotational grazing

ones of two genotype of cows [Old (a) and Modern (b)], under two grazing methodsand dotted lines belong to the ‘z’ axis).

as a result of herbage depletion, which constrains compensatoryingestive behavior and thereby herbage intake rate, as shown inFig. 5b and supported by Dillon (2007). Relatively small differencesin herbage intake were predicted between grazing methods for

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he old cow type. This prediction matches previous observationsMcMeekan and Walshe, 1963; Bluett and Macdonald, 2001) of amall, or no, difference in herbage intake between these grazingethods when availability of herbage is not limiting and feeding

rive is relatively low. This premise is reinforced by the predictedaily means of IHor (Table 3), in other words, hunger.

.2. Daily and diurnal patterns of ingestive behavioral activities

.2.1. GrazingPredicted daily grazing times by MINDY fell within the ranges

481–608 min/d) reported in a meta-analysis by Pérez-Prieto andelagarde (2012) for grazing dairy cows with similar characteristicnd feeding in similar grazing environments to the ones simulatedor the present illustration. More specifically, MINDY predicted dif-erent grazing times, along with different harvesting and searchingime budgets, depending on cow genotype and grazing manage-

ent (Table 3). These predictions follow the pattern observed byossi et al. (2004, 2005), who reported different daily grazing times

or the old and modern cow genotypes during early lactation, 489nd 509 min/d, respectively. These considerations indicate realis-ic prediction of daily grazing time by MINDY and its potential toepresent grazing time as affected by cow genotype.

MINDY predicted consistently different mean meal length anderbage intake per meal for cows of different type subjected to dif-

erent grazing management (Table 3). When combined with Fig. 5,he data indicate distinct grazing, herbage and nutrient intake pat-erns. Modern cows demand more nutrients, leading to longer,

ore intense meals, as previously suggested by Roche et al. (2006)nd Linnane et al. (2004). Rotational grazing reduced the lengthnd level of intake of the average meal. These two meal features,lus within meal ingestive behaviors (bite rate, chewing time, eat-

ng and searching steps rates) and their diurnal pattern follow theiurnal grazing pattern described by Gregorini (2012). Set stockeduminants show the longest and most intensive meal during thefternoon and early evening, and rotationally strip-grazed onesoncentrate their eating activity on the first meal after a newasture strip is allocated, and MINDY simulated it. Despite these

nteractions, both cow genotype maintained the same number ofeals. The lack of difference in the daily number of meals matches

revious empirical data (Linnane et al., 2004) where cow genotypeid not affect daily meal number. However, more data are requiredo clarify this point and increase confidence in model predictions.

Predicted, differences in the number of bites and ingestivehewing time per bite reflect within and between meals fluctu-tions in feeding motivation (Fig. 5). They are consistent withbserved reductions in ingestive chewing with increments inerbage intake rate for cattle and deer (Greenwood and Demment,988; Spalinger and Hobbs, 1992; Gregorini et al., 2009a). More-ver, Orr et al. (1997) and Gibb et al. (1998) and Taweel et al. (2004)eported fewer chews per bite for sheep and dairy cows as the dayrogresses, a pattern also predicted by MINDY. However, MINDYredicted (Fig. 5) greater bite rates and lower ingestive chewingime than the daily averages of 53 and 59 bites per min and 0.44nd 0.33 s per bite, reported by Gibb et al. (1998) and Taweel et al.2004), respectively, for set stocked dairy cows. Under rotationalrazing, however, bite rate (daily and meal means) fell within theange of 40–65 bites per minute reported in the literature (Rossit al., 2004; Gregorini et al., 2009a). Gregorini et al. (2009a) reported

hunger related decrease in bite rate during meals, from 55 to9 bites/min. Although the model represented this reduction, pre-icted bite rates were greater at the beginning of a meal, suggesting

hat time per bite may be underestimated (see Eqs. (45 and 27),espectively). MINDY predicted prehension time of ∼0.7 s, whichs similar to reported values (Illius and Gordon, 1987). Ingestivehewing time, the other action determining time per bite, is driven

odelling 270 (2013) 11– 29

by bite mass, fiber content and feeding motivation. Spatial (grazingstrata) and diurnal changes in toughness of herbage (fiber content)are used in the model to calculate ingestive chewing time, but thisphenomenon requires further development in the model (see Eq.(30)). Moreover, sward canopy is assumed to be relatively homo-geneous, which may add to the potential underestimation of timeper bite.

Predicted daily harvesting and searching times differed betweencow genotypes and grazing management (Table 3). Under rota-tional grazing both genoypes reduced harvesting time andincreased searching time as the time in the paddock progressed orherbage was depleted, which is consistent with previous observa-tions for sheep (Ruyle and Dwyer, 1985), blesboks and springboks(Noville, 1978), wapiti (Hudson and Nietfeld, 1985), beef heifers(Wade et al., 2006) and dairy cows (Gregorini et al., 2011). Thesestudies also showed that when these ruminants entered a paddock,they tended to show higher bite rates than later when the samepastures had become depleted which is consistent with modelpredictions (Fig. 5) for rotationally grazed dairy cows irrespec-tive of genotype. On the other hand, MINDY predicted that underset stocking grazing management, grazing and harvesting times(data not shown, but reflected by harvesting step rate and herbageintake rate; Fig. 5) increased and searching step rate decreasedthroughout the day. This phenomenon reflects the effect of diur-nal fluctuation of feeding motivation to increase herbage intakerate as darkness approaches (Gregorini, 2012). MINDY also pre-dicts changes in the dynamics of steps taken while harvesting andsearching within a meal for both grazing methods and cow geno-type (Fig. 5) consistent with previous observations of rotationallygrazed dairy cows (Gregorini et al., 2009a) and beef heifers (Wadeet al., 2006; Gregorini et al., 2007a,b) with different hunger levels.As the meal progresses, the model predicted a decrease in harvest-ing and an increase in searching step rates. Finally, daily walkingdistances while grazing fall within observed ranges (Thomson andBarnes, 1993; Clark et al., 2010) with surprisingly no substantial dif-ference between cow genotype, but there was a difference betweengrazing management (Table 3). Rotational grazing resulted in cowswalking longer distances while harvesting and also when searching.Despite the novelty of modeling locomotion while grazing, moredata is required in this area.

4.2.2. RuminatingIn MINDY, the length of the rumination bout was modeled as

a function of the size of the ruminal large particle pool whichresponds to meal size, rumination rate, and dietary fiber con-tent (See Section 2.3). This represents a step forward from Molly(Baldwin, 1995) where rumination is set to either occur contin-uously under continuous feeding or periodically using a cosinefunction. In the latter case, the proportion of the day during whichrumination occurred was modulated by the amount of dietary fiberso that low dietary fiber diets reduced proportional time spentruminating. However, the timing of the rumination bouts could notdeviate from the cosine function.

Predicted daily rumination times (Table 3) fall within the range(387–530 min) previously reported by Pérez-Prieto and Delagarde(2012). Daily rumination time was not affected by genotype underset stocking, which is consistent with the lack of difference amongcow genotypes reported by McCarthy et al. (2007) and Gregorini(unpublished data). However, under rotational grazing ruminationtime was lower for the modern cow type. This phenomenon is con-sistent with previous observations of Gregorini et al. (2012) andGibb et al. (1997) who reported that restricted animals reduced

rumination time as a compensatory behavior to increase grazingtime. Diurnal rumination patterns were affected by cow geno-type and grazing management (Fig. 5), which is consistent withprevious observations in dairy cows (Gibb et al., 1997; Gregorini,

ical M

urbb

4

wgfisnfessRfiSfipaFttatTa

cp(erammPwmappp

dc2nfiTtaG

tmsidctMt

P. Gregorini et al. / Ecolog

npublished data) and beef heifers (Gregorini et al., 2008b). Theseesults indicate realistic prediction of rumination time and patterny MINDY and its potential to represent rumination time as affectedy cow genotype.

.3. Rumen function

Ruminal fill and its rate of change within and between mealsere affected by cow type (Fig. 5), indicating that modern, higher

enetic merit (hungrier) cows must either tolerate greater rumenll in order to achieve desired intake rates or that rumen fill pere is not such a strong satiety signal. The strength of satiety sig-als was set by exponents regulating the effect of each controlling

actor on IHor synthesis (see Eq. (7)). The parameterization of suchxponents (Table 1) indicates that rumen fill is a weaker satietyignal than rumen VFA (1.02 vs. 10.35, respectively). This greatertrength rumen VFA is concomitant with previous arguments ofoche et al. (2007) and Sheahan et al. (2011). The effect of rumenll in modulating intake pattern should not be discarded though.ince the sensitivity analysis indicated a significant effect of rumenll on daily grazing and ruination time, as well as number of mealser day (Table A.3). The differential diurnal pattern of rumen fill,ccording to cow genotype and grazing method, can be observed inig. 5. Under set stocking, predicted rumen fill increased throughouthe day to peak at the end of the day, responding to the eating pat-ern, as previously reported for dairy cows by Taweel et al. (2004)nd Thiago (1988). Under rotational grazing, rumen fill also followshe eating pattern as reported by Thomson et al. (1985) with sheep.hese results, therefore, evidences realistic prediction of rumen fillnd its effect on intake pattern by MINDY.

The greater satiation power of VFA compared to rumen fillould also be supported by empirical data showing some com-ensatory increase of intake when dietary digestibility decreaseConrad, 1966). Moreover, increments in milk production are gen-rally explained by an increased rate of removal of VFA from theumen and blood, which may explain the increase in feed intake,s satiety signals from VFA would be reduced, resulting in a longereal (Storm et al., 2012). Predicted increments in intake for theodern cow genotype (Table 3) are consistent with these premises.

redicted pattern and magnitude of the anabolic hormone changesith cow genotype and grazing management (Fig. 5). This hor-one is a proxy for insulin, which reflects the balance of nutrient

bsorption and nutrient utilization. Thus, the predicted changesrovide a further link between nutrient demand and intake, sup-orting intake changes associated with genetic potential for milkroduction.

Predicted concentrations of ruminal VFA fluctuated during theay (Fig. 5), which can be related to intake rate and diurnalhanges in chemical composition of the herbage (Taweel et al.,004; Gregorini, 2012). From dawn to dusk, herbage accumulateson-structural carbohydrates (sugars and starch), which dilutesber and protein content. This dilution is represented in MINDY.hese diurnal fluctuations cause variation in ruminal VFA concen-rations from a given meal occurring at different times of the day,nd thus can modulate diurnal intake patterns (Taweel et al., 2004;regorini et al., 2008a,b).

Predicted levels and rate of production of ammonia changedhrough the day (Fig. 5), which seemed to be related to grazing

anagement and therefore meal characteristics (length and inten-ity) and pattern. Under rotational grazing, predicted incrementsn ammonia in the rumen were the greatest for the first meal of theay, and were greater in the modern than the older genotype of

ow. Concentration of ammonia in the rumen has been consideredo control herbage intake at the meal level (Conrad et al., 1977;

iner, 1992; Chapman et al., 2007). The sensitive analysis showedhat meal frequency, length and level of intake are affected by

odelling 270 (2013) 11– 29 23

rumen ammonia (Table A.3). However, the parameterized sensitiv-ity exponents in Eq. (7) (Table 1) reflect the relative importance ofrumen ammonia in controlling IHor synthesis compared to rumenVFA. The exponent for VFA is approximately 10× that for ammonia.Rumen VFA concentration, in particular, has been postulated as akey factor controlling intake (Illius and Jessop, 1996), which is sup-ported by the reported marked reductions in plasma ghrelin relatedto increments rumen fermentation rates as a results of concentratesupplementation (Roche et al., 2007). Due to rumen fermentationpattern and rate of production of VFA are related to ammonia avail-ability in the rumen, level of ammonia in the rumen should not bedisregarded and cannot be discarded from the Eq. (7).

Collectively, rumen fermentation end-products and the result-ing hormonal changes are the overwhelming modulators of mealcessation (Pittroff and Soca, 2006; Roche et al., 2008b; Gregorini,2011). The structure of MINDY allows consideration of this phe-nomenon and shows it interacting with patterns of intake andingestive behavior. Previous modeling efforts, as stated by Allen(1996); (Allen, 2000), have not been comprehensive enough toinclude these more complicated concepts. Therefore, MINDY rep-resents a step forward.

5. Conclusions

The model presented herein, MINDY, makes explicit the func-tional relationships among direct and indirect controls of feedingmotivation of grazing ruminants. MINDY reproduces the observedpatterns of meals achieving the correct temporal occurrence andthe relative meal lengths of a grazing dairy cow as compared tothose reported in the literature. The model’s sensitive response tothose functional relationships also allows it to simulate realisticdaily herbage intake and within meal behavior for contrasting graz-ing environments and cows of different genetic merit. Therefore,the concepts encoded in the model capture much of the underly-ing biological mechanisms that drive the diurnal grazing patternand ultimately daily herbage intake. This is a considerable advancein the understanding and modeling of herbage intake and grazingbehavior patterns of free range ruminants.

Estimates of herbage intake and parallel measurements ofingestive behavior and rumen function of grazing ruminants poseconsiderable experimental and technical difficulties. As a conse-quence, advances in knowledge of herbage intake under grazingconditions have been slow and costly. Therefore, upon completionof additional testing and evaluation, MINDY can be used to designand organize experimental programs. The model could also enableinvestigators interested in different aspects of the control of intakeand grazing behavior of ruminants (nutrition, physiology, ecologyetc.) to have a common and heuristic tool for mechanistic research.Thus, MINDY can help to accelerate advances in the knowledge ofthe grazing process at low cost.

Acknowledgments

This work was funded by New Zealand dairy farmers thruDairyNZ Inc. The authors thank Drs. David Chapman and JeremyBryant from DairyNZ (New Zealand) for reviewing this manuscriptand Dave Clark (DairyNZ, New Zealand), Prof. John McNamara(Washington State University, USA) and Dr. Juan Villaba (Utah StateUniversity, USA) for their useful comments during the developmentof this work and writing of the manuscript.

Appendix A.

A.1. Model variables and parameters

Table A.1.

24 P. Gregorini et al. / Ecological Modelling 270 (2013) 11– 29

Table A.1Model variables definitions and units.

Symbol Definition Value/Unit

ACHT Actual chewing time DaysActualIR Actual herbage intake rate of the grazing stratum i kg/minAHM Available herbage mass modulator UnitlessAHor Anabolic hormone UnitlessAm Ruminal ammonia concentration mmol/LAmCor Ruminal ammonia correction factor UnitlessBAi Bite area of the grazing stratum i m2

BCS Body condition score PointsBCSTarget Body condition score target PointsBDi Bite depth of the grazing stratum i mBMi Bite mass of the grazing stratum i kgBR Bite rata Bites/dayChewingfactor Motivation to chew UnitlessCowHeight Animals height to the shoulder mCRi Consumption rate area of grazing stratum i m2/dayCurrentStratum Upper stratum from the pair strata currently being grazedCurrentStratum−1 Lower stratum from the pair strata currently being grazedCVFA Ruminal concentration of volatile fatty acids mmol/LDA Dental arcade mDailydistancewalked Daily distance walked mDaylengthP1 Daylength excluding twilight hours for lactation moduleDaylight Value representing light intensity UnitlessDayTwlength Length of the day including twilight hours DaysDayTwlengthP2 Daylength including twilight hours DaysDD Defoliation depth ProportionDWH Distance walked while harvesting meLMI Shape factor UnitlessETHi Extended tiller height of the grazing stratum i mETHini Initial extended tiller height mETHlim Physical barrier under what cows are not allowed to or are not capable to graze mFadjustment Adjustment factor to the herbage chemical composition UnitlessFdRat Herbage intake rate kg/dayFSR Number of feeding stations per unit of time FS/dayGACurrentStratum Area harvested at the upper grazing stratum from the pair of grazing strata being grazed at the time m2

GACurrentStratum − 1 Area harvested at the lower grazing stratum from the pair of grazing strata being grazed at the time cm2

GAi Rates of changes in GSAi due to herbage consumption in grazing stratum i m2/dayGIHor Motivation to graze UnitlessGrazingSw Switch to turn on and off grazing UnitlessHDMI Daily herbage dry matter intake kg/dayHGR Herbage growth rate m/dayHi Median point height of each grazing stratum i mHighChewingMot Constant 1, unitless, 31HM Herbage mass kg/m2

HMtotalavail Sum of the herbage mass remaining in each grazing stratum kgHMunavail Unavailable herbage mass kgHSL Length of a step while harvesting miHMtotal Pre-grazing herbage mass kgiHMtotalavail Pre-grazing available herbage mass kgIHor Hunger hormone UnitlessIHorCor Scalar 1.0, unitlessIHorDeg Intake hormone degradation UnitlessIHorRange Constant, Range of IHor 0.02, unitlessIHorSyn Intake hormone synthesis UnitlessiIHor Initial IHor 1.0, unitlesskaHor Scalar 1.0, unitlesskAm Scalar 0.75, unitlesskChewfactor Scalar UnitlesskFdRat Function adjusting for adiposity and genetic potential UnitlesskIHor Constant 6.037, unitlesskMamCells Scalar (it scales FdRat with genetic potential) 0.1, unitlesskLPSP Rate of particle breakdown while ruminating UnitlesskmPref Scalar to correct PIR(i − 1)/PIR(i) to achieve a proper curve shape UnitlesskRumDM Scalar 9.5, unitlesskVFA Scalar 0.11, unitlessLagDMI Intake lag function UnitlessLateFeeding Adjusting variable to reduce MinIHor DaysLM Linear masses of lamina kg/mLMIi Linear mass index of each grazing stratum i UnitlessLowChewingMot Constant 0.15, unitlessLP Large particle size pool in the rumen kgMamCellPart Number of milk secretor cells in the udder UnitlessMBDi Mean bulk density of the grazing stratum i kg/m3

MBDsward Mean bulk density of the sward kg/m3

MeanLM Mean linear mass of the tiller kg/mMeanSwHeight Half of the ETHini m

P. Gregorini et al. / Ecological Modelling 270 (2013) 11– 29 25

Table A.1 (Continued)

Symbol Definition Value/Unit

minimunGSA Area threshold at which hrazing strating has ‘0′ preference m2

MinLPRumntn Minimum LP size required to initiate a ruination bout kgMSH Momentary speed of harvesting m/dNightMealInter Length of the last meal of the day 0.1, unitlessNightMealTime Interval of the last meal of the day and the next meal during the night 0.044, unitlessNstrata Number of sward canopy accessible grazing strataNutrientadjustment Adjustment factor to the herbage nutrients UnitlessPCHT Potential chewing time DaysPIRCurrent stratum Potential intake rate in the upper stratum from the pair strata currently being grazed kg/dayPIRCurrent stratum+1 Potential intake rate in the lower stratum from the pair strata currently being grazed kg/dayPIRi Potential herbage dry matter intake rate of the grazing stratum i kg/dayPREFCurrentStratum Partial preference for the upper stratum from the pair strata currently being grazed UnitlessPREFinter Constant to affect the intercept of the curve of partial preference for current currently being grazed UnitlesspSTI Momentary average proportion of time searching UnitlessPT Prehension time DaysRest Resting (idling) time DaysRumDM Ruminal dry matter load kg DMRumntn Rumination time DaysSDI Distance walked while searching mSGR Sward growth rate m2/dSM Linear masses of sheath kg/mSSpeedS Momentary average speed while searching m/daySSR Searching step rate Searching steps/dayStartIHor Constant, trigger point for starting a grazing bout UnitlessSTI Searching time DaysStopIHor Constant, trigger point for ending a meal UnitlessT Time of day DaysTA Total area offered m2

TBi Time per bite at the grazing stratum i DaysVmIHorSyn Maximum velocity of IHor synthesis UnitlessxaHor Scalar 1.0, unitlessxAm Scalar 1.12, unitlessxFdRatLag Scalar (it rescales Roseler et al. (1997) lag function) 0.25, unitlessxRumDM Scalar 1.0, unitlessxVFA Scalar 10.0, unitless

Table A.2Regression parameters relating changes in the nutrient composition of grass with respect to time of day (t, fraction of a day).

Variable name Constant a b c

Organic matter 88.69 2.93 4.73 6.46Crude protein 17.20 2.33 −41.18 59.93Acid detergent fiber 31.33 −10.37 24.20 −30.66Neutral detergent fiber 50.74 −14.14 11.05 14.89Non-structural carbohydrates 12.32 7.54 50.64 −84.43Soluble crude protein 5.00 0.77 −13.28 19.30Non-protein nitrogen 22.86 −6.14 76.41 −108.86Rumen undegradable acid detergent fiber 31.96 10.76 −25.37 34.85Cellulose 31.33 −9.56 18.59 −24.60

F

A

Am

Al

wtg

Hemicellulose 16.40

adjustment = Constant + a × t3 + b × t2 + c × t.

.2. Conditional statements

.2.1. Conditional statements used to ensure proper outputs atore extreme latitudes

DayTwlengthP2 = −1.0 If DayTwlengthP2 < −1

DayTwlengthP2 = 1.0 If DayTwlengthP2 > 1

.2.2. Conditional statements used to reduce the StopIHor duringate afternoon and early evening

StopIHor = StopIHorIf LateFeeding ≤ 0

NightMult5

here, StopIHor is the minimum IHor (intake hormone level) levelo stop grazing. NightMult5 is a constant set to 2.0095 to elongaterazing bout occurring during late afternoon and early evening. This

−4.57 −7.54 39.49

value was derived by fitting the model to the observations (Gibbet al., 1998; Taweel et al., 2004).

A.2.3. Conditional statements used to start or stop grazingStart grazing

GrazingSw = 1T interMeal = T − TMealStopT interStart = T

∣∣∣∣∣If IHor≥startIHor

If Daylight≥0

End If Daylight < 0 and TInterMeal≥NightMealInter

Stop grazing ∣

T interMeal = T − TMealStart

GrazingSw = 0T interStop = T

∣∣∣∣If GrazingSw = 1

If IHor ≤ StopIHor

End If Daylight < 0 and TMeal > NightMealTime

26 P. Gregorini et al. / Ecological M

Tab

le

A.3

Res

pon

ses

in

mod

el

outp

uts

asso

ciat

ed

wit

h

two

step

s

of

a

10%

chan

ge

in

the

valu

e

of

each

mod

el

par

amet

er. T

he

regr

essi

on

equ

atio

n

rela

tes

vari

able

chan

ges

to

par

ticu

lar

resp

onse

dat

a.

Var

iabl

e

Mod

el

outp

uts

Her

bage

inta

ke

(kg

DM

/d)

Dai

ly

graz

ing

tim

e

(%/d

)

Dai

ly

rum

inat

ion

tim

e

(%/d

)

Dai

ly

rest

ing

tim

e

(%/d

)

Mea

ls

per

day

Ave

rage

inta

ke

per

mea

l (kg

DM

)

Ave

rage

len

gth

per

mea

l (d

)

Vm

IHor

Syn

0.08

2x

+

13.8

17

R2

=

0.92

**0.

001x

+

0.21

7R

2=

0.92

56**

0.00

09x

+

0.30

6

R2

=

0.83

*=−

0.00

2x

+

0.47

5

R2

=

0.97

0.00

2x

+

4.04

R2

=

0.02

0.05

4x

+

2.15

R2

=

0.64

*0.

0007

x +

0.03

7

R2

=

0.75

*

k IH

or−1

.1x

+

22.8

R2

=

0.93

*0.

018x

+

0.35

8

R2

=

0.93

*−0

.016

x

+

0.42

0

R2

=

0.96

**0.

034x

+

0.22

1

R2

=

0.98

**0.

175x

+

3.46

R2

=

0.53

−3.4

65x

+

19.9

2

R2

=

0.72

−0.0

43x

+

0.26

2

R2

=

0.73

Nig

thM

ealIn

ter

−55.

484x

+

16.7

81

R2

=

0.75

−0.9

31x

+

0.26

4

R2

=

0.75

−0.4

67x

+

0.33

3

R2

=

0.75

1.39

85x

+

0.40

26

R2

=

0.75

−450

x

+

5.02

R2

=

0.75

31.1

05x

+

4.16

5

R2

=

0.75

5.49

7x

+

0.05

3

R2

=

0.75

Nig

htM

ealT

ime

−9.7

35x

+

17.1

26

R2

=

0.36

−0.1

54x

+

0.26

9

R2

=

0.37

0.09

5x

+

0.32

9

R2

=

0.12

0.05

8x

+

0.40

1

R2

=

0.05

−60x

+

6.42

R2

=

0.66

57.1

66x

+

2.08

0

R2

=

0.73

0.91

21x

+

0.03

0

R2

=

0.76

Nig

htM

ult5

=0.2

86x

+

16.6

4

R2

=

0.32

0.00

4x

+

0.26

1

R2

=

0.33

0.00

8x

+

0.31

6

R2

=

0.92

*=−

0.01

3x

+

0.42

2

R2

=

0.74

**−8

.425

x

+

42.1

8

R2

=

0.78

=0.3

02x

+

3.45

8

R2

=

0.07

−0.2

17x

+

1s.0

28

R2

=

0.51

KLP

SP−0

.46x

+

17.3

29

R2

=

0.29

−0.0

07x

+

0.27

2

R2

=

0.29

−0.2

18x

+

0.66

2

R2

=

0.99

***

0.22

5x

+

0.06

5

R2

=

0.99

***

−0.4

x

+

4.6

R2

=

0.45

0.65

2x

+

3.46

1

R2

=

0.56

*0.

005x

+

0.05

9

R2

=

0.34

k fdr

atah

or1.

18x

+

13.1

63

R2

=

0.98

**0.

018x

+

0.20

6

R2

=

0.98

**0.

024x

+

0.25

1

R2

=

0.97

***

−0.0

451x

+

0.54

3R2

=

0.99

***

1.2x

+

0.3

R2

=

0.95

**−1

.061

7x

+

7.77

R2

=

0.81

−0.0

165x

+

0.11

9

R2

=

0.93

**

k fdr

atA

m3.

3782

x

+

15.2

68

R2

=

0.83

**0.

0528

x

+

0.24

04R

2=

0.83

**0.

023x

+

0.32

0

R2

=

0.32

−0.0

76x

+

0.43

9

R2

=

0.88

*−2

.75x

+

5.08

R2

=

0.64

2.16

9x

+

3.59

8

R2

= 0.

51

0.05

2x

+

0.04

5

R2

=

0.71

k fdr

atR

umD

M0.

667x

+

11.2

71

R2

=

0.96

***

0.01

05x

+

0.17

7

R2

=

0.96

***

0.01

16x

+

0.23

5

R2

=

0.92

***

−0.0

22x

+

0.58

7

R2

=

0.94

***

0.22

5x

+

2.04

R2

=

0.78

**−0

.212

x

+

6.27

6

R2

= 0.

65

−0.0

02x

+

0.08

6

R2

=

0.61

k fdr

atV

FA11

4.63

x

+

6.07

1

R2

=

0.93

**1.

799x

+

0.09

5

R2

=

0.93

**1.

728x

+

0.16

7

R2

=

0.88

*−3

.528

x

+

0.73

9

R2

=

0.91

**8.

888x

+

3.18

R2

=

0.5

18.6

4x

+

2.68

1

R2

=

0.72

**0.

3196

x

+

0.03

7

R2

=

0.78

*

x aH

or−1

78.4

x

+

18.4

94

R2

=

0.96

**−2

.836

x

+

0.29

1

R2

=

0.96

**−1

.463

x

+

0.34

6

R2

=

0.70

4.30

0x

+

0.36

2

R2

=

0.91

**−2

00x

+

5.98

R2

=

0.93

**18

1.91

x

+

2.61

9 R

2=

0.65

2.75

9x

+

0.03

9

R2

=

0.83

*

x Am

−0.4

109x

+

17.0

83R

2=

0.77

*−0

.006

x

+

0.26

8

R2

=

0.80

*0.

008x

+

0.31

9

R2

=

0.13

−0.0

02x

+

0.41

1

R2

=

0.01

−13.

5x2

+

26.6

x

−

8.9R

2=

0.64

**13

.4x2

− 25

.7x

+

16.6

R2

=

0.55

**0.

2x2

−

0.4x

+

0.3

R2

=

0.65

**

x Rum

DM

1.06

8x

+

11.2

7

R2

=

0.96

***

0.01

6x

+

0.17

7

R2

=

0.96

**0.

018x

+

0.23

5

R2

=

0.92

**−0

.035

x

+

0.58

7

R2

=

0.94

***

0.36

x

+

2.04

R2

=

0.78

*−0

.339

x +

6.27

6

R2

=

0.65

−0.0

03x

+

0.08

6

R2

=

0.61

x VFA

0.00

14x

+

0.17

R2

=

0.91

**3E

−06x

+

0.70

85R

2=

0.65

***

3E−0

5x

+

0.00

4

R2

=

0.51

3E−0

5x

+

0.28

47

R2

=

0.57

N/A

0.00

01x

+ 0.

0163

R2

=

0.50

2E−0

7x

+

0.06

35

R2

=

0.50

*P

<

0.05

.**

P

<

0.01

.**

*P

<

0.00

1.

odelling 270 (2013) 11– 29

where, IHor is the level of the intake hormone, StartIHor is theminimum IHor level to start grazing, Daylight is the intensity, EatSwis the switch to turn on and off grazing, NightmealInter is length ofthe last meal of the day, MinIHor is the minimum IHor level to stopgrazing and NightMealTime is the interval of the last meal of the dayand the next meal during the night.

A.2.4. Conditional statements used to start or stop ruminationbouts

Rest = 0∣∣If FdRat > 0.1

Rumntn = 0Else If LP > MinLPRumntn

Rumntn = 1Rest = 0

ElseRumntn = 0

Rest = 1

where, FdRat is intake rate (g/min); Rest (∼idling) is resting(min); Rumntn is ruminating (min); LP is pool (kg) of large par-ticles in the rumen; and MinLPRumntn (kg/kg empty BW0.75)is the minimum LP size required to initiate a ruination bout.Empty BW is the weight of the cow without the conceptusweight.

A.2.5. Conditional statements used to represent foragingdecisions and partial preference for grazing strata

CurrentStratum = CurrentStratum

∣∣∣ If GSAcurrentStratum < min imumGSAIf CurrentStratum < NStrata

KmPREF = TACurrentStratum × PIRCurrentStratum(PIRCurrentStratum/FKmPref

) IfCurrentStratum < NStrata

Else

KmPREF = 0

End If PREFCurrentStratum = (1.0–PrefInter)

1 +(

KmPREF/GSAexp PREFCurrentStratum

)+ PREFInter

PREFCurrentStratum−1 = 0 If CurrentStratum > 1

PREFCurrentStratum−1 = 1 − PREFCurrentStratum If CurrentStratum < NStrata

Else

PREFCurrentStratum = 1

where, GSACurrentStratum is the accessible area (m) of the upper graz-ing stratum from the pair of grazing strata being grazed at thetime. GSACurrentStratum−1 is the accessible area of the lower grazingstratum from the pair of grazing strata being grazed at the time.PREFCurrentStratum is the relative preference for the upper grazingstratum from the pair of grazing strata being grazed at the time.PREFCurrentStratum−1 is the relative preference for the lower grazingstratum from the pair of grazing strata being grazed at the time.minimumGSA is a constant that needs to be large enough that thearea consumed per integration interval does not exceed this num-ber. PrefInter, FKmPref and expPREF are also constants. PrefInter is0.3 affects the intercept of the curve of partial preference for cur-

rent currently being grazed. FKmPref, 0.2, is a scalar to correct theratio PIRi−1: PIRi to achieve a proper curve shape. expPREF, 3.0, cre-ates a sigmoid shape to the PREFCurrentStratum (upper stratum of thepair being grazed at the time).

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.2.6. Conditional statements used to represent the modulatoryffect of time of day

TimeOf DayEffect =[DawnSwitch × (T − Dawn) × SunriseGIHOR + (Sunrise − T)×(NightGIHOR)]

(Sunrise − Dawn)+

[MorningSwitch × (T − Sunrise) × NoonGIHOR + (Noon − T) × (SunriseGIHOR)](Noon − Sunrise)

+[AfternoonSwitch × (T − Noon) × SunsetGIHOR + (Sunset − T) × (NoonGIHOR)]

(Sunset − Noon)

+ [DuskSwitch × (T − Sunset) × NightGIHOR + (Dusk–T) × (SunsetGIHOR)](Dusk–Sunset)

+NightSwitch × NightGIHOR

awn < Tod ≤ Sunrise(i.e.Dawn.DawnSwitch = 1)

unrise < Tod ≤ Noon(i.e.Morning.MorningSwitch = 1)

oon ≤ Tod ≤ Sunset(i.e.Afternoon.AfternoonSwitch = 1)

unset < Tod ≤ Dusk(i.e.Dusk.DuskSwitch = 1)

awn < Tod < Dusk(i.e. Night. NightSwitch = 1)

here, T is time of day (days) and DawnSwitch, MorningSwitch,fternoonSwitch, DuskSwitch and NightSwitch indicate the time ofay to the model, and Night, Sunrise, Noon and SunsetGIHOR areonstants, being, 5, 19.5, 21, and 27.8 their respective values scaledScalerTimeofDay) to 15. These values were based on herbagentake rates reported by Gibb et al. (1998), Gregorini et al. (2007a)nd Orr et al. (1997) in dairy cows, beef heifers and sheep, respec-ively, under set stocking.

.3. Diurnal fluctuation of herbage chemical composition:onstants

Table A.2

.4. Local sensitivity analysis

Table A.3

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