animal
Animal (2010), 4:12, pp 2030–2047 & The Animal Consortium 2010 doi:10.1017/S1751731110001357
A teleonomic model describing performance (body, milk and intake) during growth and over repeated reproductive cycles throughout the lifespan of dairy cattle. 1. Trajectories of life function priorities and genetic scaling O. Martin- and D. Sauvant UMR Mode´lisation Syste´mique Applique´e aux Ruminants (MoSAR), INRA-AgroParisTech, 16, rue Claude Bernard, 75231 Paris cedex 05, France
(Received 25 February 2009; Accepted 12 May 2010; First published online 29 June 2010)
The prediction of the control of nutrient partitioning, particularly energy, is a major issue in modelling dairy cattle performance. The proportions of energy channelled to physiological functions (growth, maintenance, gestation and lactation) change as the animal ages and reproduces, and according to its genotype and nutritional environment. This is the first of two papers describing a teleonomic model of individual performance during growth and over repeated reproductive cycles throughout the lifespan of dairy cattle. The conceptual framework is based on the coupling of a regulating sub-model providing teleonomic drives to govern the work of an operating sub-model scaled with genetic parameters. The regulating sub-model describes the dynamic partitioning of a mammal female’s priority between life functions targeted to growth (G), ageing (A), balance of body reserves (R) and nutrient supply of the unborn (U), newborn (N) and suckling (S) calf. The so-called GARUNS dynamic pattern defines a trajectory of relative priorities, goal directed towards the survival of the individual for the continuation of the specie. The operating sub-model describes changes in body weight (BW) and composition, foetal growth, milk yield and composition and food intake in dairy cows throughout their lifespan, that is, during growth, over successive reproductive cycles and through ageing. This dynamic pattern of performance defines a reference trajectory of a cow under normal husbandry conditions and feed regimen. Genetic parameters are incorporated in the model to scale individual performance and simulate differences within and between breeds. The model was calibrated for dairy cows with literature data. The model was evaluated by comparison with simulations of previously published empirical equations of BW, body condition score, milk yield and composition and feed intake. This evaluation showed that the model adequately simulates these production variables throughout the lifespan, and across a range of dairy cattle genotypes. Keywords: teleonomic model, dairy cow, gestation, lactation, body reserves
Implications
Introduction
This model of lifetime performance of dairy cattle provides a basis for predicting nutrient partitioning across different physiological states and genotypes. The model has two tightly linked parts: a conceptual framework that focuses on priorities for life functions, and rules for modifying the outcomes when nutritional supply is inadequate. The conceptual framework described in this paper provides a holistic view of growth, reproduction and nutrition and scaling parameters allowing the simulation of different animal genotypes.
The objective of farm animal nutrition has evolved from the meeting of nutrient requirements, through the realization of genetic potential, to the prediction of multiple performance characteristics of a particular genotype in a particular environment (Sauvant, 1992). The animal is no more considered as a passive production unit but rather as an active living system elaborating performance through the complex interaction between physiological functions, mainly growth, reproduction and nutrition, and orchestrating nutrient partitioning. As stated by Friggens and Newbold (2007), ‘prediction of nutrient partitioning is a long-standing problem of animal nutrition that has still not been solved. Another substantial problem for nutritional science is how to incorporate
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Teleonomic model of dairy cattle performance genetic differences into nutritional models. These two problems are linked as their biological basis lies in the relative priorities of different life functions (growth, reproduction, health, etc.) and how they change both through time and in response to genetic selection’. This statement highlights the importance of being able to describe the changing priorities of an animal as it ages, through repeated reproductive cycles and over successive generations, and also in response to feeding and reproduction management practices. For the future, animal science needs models suitable for in silico experiments exploring changes in animal performance resulting from the interactions between genetic and environmental factors. The question we address in this study is how to represent in animal models (1) dynamic changes of performance throughout the lifespan, (2) genetic differences between individuals and breeds and (3) modulations of performance in response to nutritional challenges. The pioneering work of Baldwin et al. (1987a, 1987b and 1987c) has shown that animal models can provide suitable tools for quantitative evaluation of concepts, hypotheses and data regarding nutrient partition. Later, several other models of lactating animals, mainly in cattle, have been published in the last 20 years (e.g. reviews in Sauvant, 1992 and 1996; Chalupa et al., 2004; Tedeschi et al., 2005). The main objective of Baldwin’s work was to provide, at the level of metabolic pathways and throughout the lactation cycle, a modelling framework to embed knowledge and a simulation tool to aid interpretation of experimental data. His model was structured on the basis of biochemical and stoichiometric arguments. Regulations were formalized by way of the effect of plasma glucose concentration, capturing hormonal effects (catabolic and anabolic hormones), on the velocity of metabolic transactions such as lipogenesis, lipolysis and gluconeogenesis. Through this mechanistic representation, variations of wholeanimal performance emerged from the aggregation of several points of biochemical regulation. Similar attempts to incorporate regulation rules in animal models through control variables driving physiological processes were performed in several other studies, for example, ‘lactation hormone’ (Neal and Thornley, 1983; Baldwin et al., 1987c), ‘anabolic and catabolic hormones’ (Sauvant and Phocas, 1992; Baldwin, 1995; Martin and Sauvant, 2007) and ‘growth hormone and insulin’ (Danfaer, 1990). Aggregative models are based on the gathering of quantitative knowledge of underlying biological processes and are developed with the aim of reproducing complex interactions. In attempting to describe all the mechanisms involved, they frequently come to be exhaustive encyclopaedic compilations (Baldwin, 1995) that themselves become complex objects, difficult to manipulate and use for prediction. In a reverse approach, we propose to explicitly model a centralized regulating sub-system structured on the basis of teleonomic arguments. This approach is integrative rather than aggregative, intended to be predictive rather than explicative, and suitable for easy use. In our model, the different levels of performance variability, that is, through time, according to
genotype and in response to diet, are described with separate specific components: dynamic changes in performances are driven by goal-directed trajectories of life function priorities; genetic differences between individuals and breeds are defined by genetic scaling parameters; and modulations of performance in response to nutritional challenges are controlled by a theoretical model of energy partitioning regulation. The whole model simulates, on a daily basis, food intake, milk yield and composition, foetal growth, calf birth weight and body weight (BW) and composition changes in dairy cows throughout the lifespan, that is, during growth, over successive reproductive cycles and through ageing. The model is described in two companion papers. Paper 1 focuses on the simulation of a genetically scaled reference pattern of performance. Paper 2 focuses on the part of the model allowing simulation of a nutritionally altered pattern of performance. The objective of the present paper is to evaluate the efficacy of using teleonomic arguments and genetic scaling parameters in an integrated whole-animal model designed to describe performance throughout the lifespan of various genotypes of dairy cows. Model description
Rationale The model consists of two connected sub-models, representing the regulating and operating parts of the model. The regulating sub-model describes, throughout the lifespan of dairy cows, the dynamic partitioning of relative priorities to elementary life functions (growth, reproduction, ageing and balance of reserves) and is structured on a teleonomic basis (Table 1), embodying the idea that the coordination of life functions is goal directed towards the preservation of life for the reproduction of life form (Bricage, 2002). The operating sub-model describes the dynamics of performance (body, milk and intake) and is structured on the partitioning of metabolizable energy intake with genetic parameters scaling individual performance (mature weight, milk potential, milk composition and body reserves lability). Performance, denoted by the generic term Q (daily material flow), is converted into energy denoted by the generic term E (daily energy flow) with appropriate conversion coefficients (eQ 5 E/Q, energy/material). At any time, priorities to life functions together with genetic scaling parameters are used to define a reference pattern of performance Q*, which determines a reference energy requirement E* 5 eQ 3 Q*. Given the actual intake, the difference between energy supply and requirement is apportioned between energy flows, giving energy deviation qE. The actual energy flow is thus calculated such that E 5 E* 1 qE, leading to the actual performance Q 5 E/eQ, which expresses a deviation from the reference performance such as qQ 5 Q 2 Q*. In this paper, the model deals with a non-challenged feeding context such as qE 5 0, E 5 E*, Q 5 Q* and qQ 5 0, that is, assuming that intake supplies the realization of the genetically scaled reference pattern of performance (description of the deviations qE and qQ is given in Martin and Sauvant, 2010). 2031
Martin and Sauvant Table 1 Teleonomic-based priority control: use of priorities, combination of priorities and differential priorities to elementary life functions for model regulation Variable Priority to G A R U N S Combination of priorities as priority to 12G 1 2 (G 1 A) G1A1R Differential priorityc as ability to (1 2 G)x (1 2 G)y NkjN SkjS
Definition
Main regulation function in model
Acquire maturitya (growth) Age and dieb (ageing) Balance body reserves (reserve) Support gestation (unborn) Support initiation of lactation (newborn) Support persistency of lactation (suckling)
Inhibition of growth at maturity Inhibition of life functions with age Inhibition of reserve storage peripartum Activation of foetal growth during pregnancy Activation of mobilization at parturition Basis for differential priority Sk
Functions of the mature individual Functions of the procreating individual Non-reproductive functions
Basis for differential priority (1 2 G)x or y Inhibition of reproduction in young and elderly Inhibition of growth during reproductive cycles
Balance labile body mass Secrete milk constituents Secrete milk constituent j after parturition Secrete milk constituent j during lactation
Delay in reserve storage in early growth stage Delay in maturity of the mammary gland Modulation of milk dynamics after parturition Modulation of milk dynamics during lactation
a
Maturity is considered as the achievement of a mature non-labile body mass. Priority A to ageing represents a loss of other priorities. With exponent parameters x, y and kjN and kS for milk constituent j (fat j :F ; protein j :P ; lactose j :L ; water j :H ).
b c
Figure 1 Regulating sub-model diagram. Compartments refer to animal priorities G: growth, A: ageing, R: balance of body reserves, U: ensuring survival of the unborn calf, N: ensuring survival of the newborn calf and S: ensuring survival of the suckling calf.
Structure of the regulating sub-model The regulating sub-model (Figure 1) describes the partitioning of a mammal female’s priority over lifetime t (d) between six components of the goal of maximizing the generation of viable offspring: (i) G achieve growth to maturity by body mass accretion during the developmental stage of life; 2032
(ii) A undergo ageing by reducing investment in repair processes resulting in a decline of the ability to perform vital functions; (iii) R balance body reserves by storage or mobilization to maintain favourable reproductive conditions; (iv) U achieve foetal development of the unborn calf during pregnancy;
Teleonomic model of dairy cattle performance (v) N supply nutrients to the newborn calf by initiation of lactation and body reserve mobilization at the transition time between gestation and lactation; (vi) S supply nutrients to the suckling calf (substitute by the milking machine in dairy production context) by lactation persistency. The so-called priorities to the unborn, newborn and suckling correspond to stages of maternal investment in reproduction, soliciting different physiological functions to ensure offspring survival: gestation, lactation and the transition phase between them, which involves mobilization of
body reserves and initiation of lactation. At parturition, the function of supplying nutrients to the offspring is transferred from the placental uterine unit to the mammary gland. Priority N represents the priority to this transfer. Priority is formalized as a dimensionless quantity flowing through these compartments: from G to R during growth, from R to A with ageing, and cyclically through R, U, N and S during reproductive cycles (Figures 2 and 3). An essential feature of the model is that it describes the pattern of relative priorities of different life functions, the sum of which always remains equal to 1: G þ A þ R þ U þ N þ S ¼ 1:
ð1Þ
Figure 2 Trajectories of priorities G: growth, A: ageing, R: balance of body reserves, U: ensuring survival of the unborn calf, N: ensuring survival of the newborn calf and S: ensuring survival of the suckling calf over 20 years of life.
Figure 3 Trajectories of priorities G: growth, A: ageing, R: balance of body reserves, U: ensuring survival of the unborn calf, N: ensuring survival of the newborn calf and S: ensuring survival of the suckling calf over 1500 days of life. Arrows indicate parturition times of two successive reproductive cycles.
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Formalism of the regulating sub-model Full details are given in Appendixes A to G in the supplementary online appendix available at: http://www.animaljournal.eu/. The list of equations used to define priority components G, A, R, U, N and S is given in Table 2. These equations are described in detail in Appendix A. Growth. Priority G to growth represents the investment in the construction of a mature individual and is linked to the level of achievement of a mature structural body mass, assumed to be an individual genetic trait. The main component of this investment is the allocation of available energy to build tissue. In a general model for ontogenetic growth, West et al. (2001) defined the quantity 1 2 (current weight/ mature weight)1/4 as the proportion of total available metabolic energy fuelling the production of new biomass, the remaining quantity (current weight/mature weight)1/4 being the proportion of total available metabolic energy allocated to maintenance and other functions. This formalism is used to describe the priority to grow and the differential equation for G (see Table 2) is defined consistently with the analytical rule given by 1 W 4 ; G ¼ 1 WM
ð2Þ
where W and WM are, respectively, the current and mature non-labile body mass weights (see Table 3). The flow d (development) from G to R is defined to update G according to changes in W with respect to (2).
Ageing. Priority A to ageing represents the relative loss in other priorities. The increase in A with time relies on the progressive decline with age of the ability to perform the work of life, including survival and reproduction (Brody, 1924). The flow s (senescence) from R to A is arbitrarily formalized to induce a sigmoid shape for A (Figure 2) and to cause the integral transfer of the sum of relative priorities to A (A-1 and G 1 R 1 U 1 N 1 S-0 with age). Reserves. Priority R concerns the goal of balancing body reserves assuming the existence of an optimal target level of body reserves (Friggens, 2003) maintained by physiological processes of storage and mobilization. Accumulation of body reserves to reach this target level occurs during the developmental stage of life, and also for the reconstitution of this target level during reproductive cycles. Mobilization occurs at parturition as part of the lactation process and is targeted by N (see Newborn section) but also takes place for the deconstruction of excessive levels of body reserves constituted during periods of overfeeding (see Martin and Sauvant, 2010). Relying on Friggens (2003), the view taken here is that the changes in body reserves are to a large extent genetically driven and follow a trajectory that is a natural component of the reproductive cycle to support the evolu2034
tionary goal of maximizing reproductive success. The body reserve reconstitution at the end of a reproductive cycle has the goal of safeguarding the subsequent reproductive cycle. From that standpoint, through the balance of a body condition compatible with reproduction, priority R expresses a potential maternal investment in reproduction: R is charged (using the analogy of a battery) during the developmental stage of life (flow d ), progressively discharged by senescence (flow s) and cyclically discharged (flow p, pregnancy) and recharged (flow w, weaning) during reproductive cycles (Figure 2). Since U 1 N 1 S 5 0 during the non-reproductive stages of life, priority R 5 1 2 (G 1 A), quantifies the level of potential investment in reproduction, that is, a ‘quantity of priority’ potentially conveyable from R to U, which increases during development and decreases in older animals. The key role of R as a source for priority to reproduction in the model reflects the crucial importance of energy storage in body tissues in reproduction of mammals (Pond, 1984; Oftedal, 2000). As seen in Figure 2, priority R oscillates during the reproductive stages of life defining ‘opportunity peaks’ for reconstitution of body reserves between reproductive cycles. During the non-reproductive stages, R shows a continuous and undisturbed pattern implying a priority to stabilize body reserves at an optimal level.
Unborn. Priority U to the unborn represents the maternal investment to complete successfully the current pregnancy. The flow p (pregnancy) from R to U is derived from a model of foetal growth (Laird, 1966) with the assumption that priority U to pregnancy is proportional to foetal growth (see Appendix B). The equation for p is designed to yield R 5 1 after p days of pregnancy and the time of parturition is defined as the integral transfer of U to N, that is, the time of maximal investment in the current reproductive cycle (Friggens, 2003). Newborn. Priority N to the newborn represents the maternal investment in physiological functions allowing the initiation of lactation to provide nutrients for the neonate’s requirements. The expression of this investment is the mobilization of body reserves of the mother and lactogenesis. Structurally, N can be seen as an intermediary compartment that ensures continuity between gestation and lactation within the reproductive cycle. The flow l (lactation) from N to S describes, with a simple mass action, the transfer of maternal investment from N (priority, inherited from U at parturition, to initiate lactation) to S (priority to maintain lactation). Suckling. Priority S to the suckling calf represents the maternal investment in physiological functions allowing lactational persistency. As previously mentioned, both N and S are priorities to the survival of the same physical calf through lactation, but N and S are priorities to specific components of this process, namely its short-time initiation and its long-time course, respectively. The flow w (weaning) describes the trade-off between priorities S and R, that is, the shift between the priority to continue to invest in the lactation (the current reproductive cycle) and the priority to
Table 2 Compendium of regulating sub-model equations giving the dynamics of priorities G, A, R, U, N and S Reproductive eventc Conception Definition
Unit
t c milking pregnant parity tC (c) tP (c) dim dip G A R U N S
day – {0,1} {0,1} – day day day day – – – – – –
Equationa,b 0 to 7300 by dt 5 1
tc(c ) 5 tP (c ) 1 PCI(c ) dimt 1 1 5 dimt 1 milking dipt 1 1 5 dipt 1 pregnant dG/dt 5 2d dA/dt 5 s dR/dt 5 d 2 s 2 p 1 w dU/dt 5 p dN/dt 5 2l dS/dt 5 l 2 w
Initial value 0 0 0 0 0 PCI(0) 0 0 0 1 2 (WB/WM)1/4 0 (WB/WM)1/4 0 0 0
c50
c.1
c5c11
c5c11
pregnant 5 1
pregnant 5 1
Parturition
Drying off d
milking 5 1 pregnant 5 0 parity 5 parity 1 1
milking 5 0
tP(c) 5 t dim 5 0 dip 5 0
At 1 1 5 At 1 1023 Rt 1 1 5 Rt 2 e 2 1023 Ut 1 1 5 Ut 1 e
Rt 1 1 5 Rt 2 e Ut 1 1 5 Ut 1 e
Ut 1 1 5 0 Nt 1 1 5 Nt 1 Ut
a W: non-labile body mass; WB: W at birth; X: labile body mass; WM: scaling parameter of mature W ; PCI(0): age at first conception; PCI(c . 0): parturition to conception interval; (p,a,v): pregnancy scaling parameters; (m,l0,1,g,t,s): fractional rates; (xM,xS): body reserves threshold parameters. 1=4 b d ¼ ð4 WM W 3=4 Þ1 A ð1AÞ; p ¼ a lnðZ=UÞ U if Uo1ðG þ AÞ; l ¼ m N; w ¼ ðl0 þ LX þ g U þ t ð1milkingÞÞ S; ¼ $=WB ; Z ¼ exp lnðÞ= dW=dt; s ¼ s 5 ð1 expða pÞÞÞ; LX ¼ l1 ð1 þ ððX=WÞ=wS Þ Þ. c Conception if A , 0.2 at t 5 tC(c); parturition triggered when U >1 2 (G 1 A) 2 e. d Drying off at dim > 320.
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Teleonomic model of dairy cattle performance
Age Reproductive cycle Milking status Pregnancy status Parity Age at conception Age at parturition Days in milk Days in pregnancy Growth priority Ageing priority Reserves priority Unborn priority Newborn priority Suckling priority
Symbol
Equationa,b,c Definition
Symbol
Non-labile body mass
W
kg
dW=dt ¼ AW =eW
Labile body mass
X
kg
dX=dt ¼ AX =eXa CX =eXc
Gravid uterus weight
GU
kg
dGU=dt ¼ P=eU (GU 5 0 at parturition)
Digestive tract contents weight
DT
kg
dDT=dt ¼ DMI=DMCk0 ðDTd WÞ
n dW=dt ¼ G ðG þ A þ RÞ In =eW n dX=dt ¼ ð1GÞx b0 1 X=W M wM Rm0 N X nX n dGU=dt ¼ dU=dt WB =f n dDT=dt ¼DMIn =DMCk0 ðDTd WÞ
DMI
kg/day
MY
kg/day
DMI ¼ DMIn þdDMI P MY ¼ j:F;P;L;H MYj
Daily yield of milk constituent j
MYj
kg/day
MYj ¼ milking Yj ej
DMIn ¼ In =eD P MYn ¼ j:F;P;L;H MYnj
Energy intaked
I
kg/day
I ¼ eD DMI ¼ In þ dI
MYnj ¼ milking ð1 GÞy ðkjn Nyjn þ kjs Syjs Þ WM nY nj In ¼ ðMn þ Y n þ P n þ AnX CXn Þ ð1 G ðG þ A þ RÞÞ
Maintenance energy requirement
M
MJ/day
M ¼ Mn þ dM
Milk energy requirement
Y
MJ/day
Y ¼ Y n þ dY
Mn ¼ eM BW0:75 P Y n ¼ j:F;P;L;H ej MYnj
Pregnancy energy requirement
P
MJ/day
P ¼ P n þ dP
P n ¼ eU ðdGU=dtÞn
Energy for non-labile mass growth
AW
MJ/day
AW ¼ AnW þ dAW
AnW ¼ eW ðdW=dtÞn
Energy for labile mass anabolism
AX
MJ/day
AX ¼ AnX þ dAX
Energy from labile mass catabolism
CX
MJ/day
CX ¼ CXn þ dCX
AnX ¼ eXa ðdX=dtÞn if ðdX=dtÞn 40 ð0 elsewhereÞ n n CXn ¼ eXc dX=dt if dX=dt o0 ð0 elsewhereÞ
Dry matter intake
d
Daily raw milk yielde e
Unit
Actual
Reference
a Parameters: d, xM, bW , bX, f: body mass composition; WM, nY , nX, nj: genetic scaling; b0, m0, k0: BW change; x, y, yjN , yjS : scaling exponents of differential priority; kjN, kjS: milk constituents secretion; DMC: diet DM factors. content; eD , eU , eM, eW, eXa, eXc, ej : MEconversion 0:83 b Birth value: EBWB ¼ 0:197 WM 1 þ wM ; BWB ¼ EBWB þ DTB ; WB ¼ 0:97 EBWB ; XB ¼ 0:03 EBWB ; GUB ¼ 0; DTB ¼ d WB . c 2 5 EBW Leading 1 GU 1 DT; empty body weight (kg): EBW 5 W 1 X; empty body fat (kg): EBF ¼ bW W WM þ bX X; body condition score (0–5): BCS ¼ to: body weight (kg): BW3:7235 17:9 39:8; milk constituent j content (kg/kg): MCj 5 MYj/MY if MY . 0. EBF 1 expð0:0068 ðEBW EBFÞÞ d Assumption of non-challenged feeding: dDMI 5 0 and dI 5 dM 5 dY 5 dP 5 dAW 5 dAX 5 dCX 5 0 v. challenging feeding in Martin and Sauvant (2010). e Milk fat: j:F; milk protein: j :P; milk lactose: j :L; milk water : j :H; milking: milking status.
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Table 3 Compendium of operating sub-model equations giving reference and actual performance and energy flows for age t ranging from 0 to 7300 days where G, A, R, U, N and S are priorities defined in the regulating sub-model
Teleonomic model of dairy cattle performance restore body reserves to start a new reproductive cycle. The flow w is influenced by the effect of the level of body reserves, the effect of pregnancy and the effect of mammary gland stimulation. First, when body reserves are low, the transfer from S to R is accelerated and priority to maternal investment in the suckling calf is decreased to support the priority to reconstitution of maternal body reserves (Wade and Schneider, 1992). In challenging contexts such as food restriction, ‘homeostatic controls for survival can overwhelm homeorhetic mechanisms’ (Bauman and Currie, 1980), so that the priority of staying alive prevails. Formally, this effect represents the synchronization of the regulating sub-model with the operating sub-model according to the level of body reserves. An emerging property of this formalism is that as the level of body reserves is higher before the first reproductive cycle (O. Martin, unpublished results), the transfer of S to R is slower in the first reproductive cycle, which induces a better persistency of the priority to lactation in primiparous cows, which is a known feature of lactation. Second, the start of a new reproductive cycle induces a decrease in priority to the suckling generation in favour of the next generation to be born (Coulon et al., 1995). Third, the transfer from S to R is accelerated when the young are no longer suckling after weaning or death, or when the animal is no longer milked after drying off in the dairy production context.
Structure of the operating sub-model The performance measures considered in the operating sub-model concern BW(kg), body condition score (BCS, 0 to 5 scale defined by Mulvany, 1977), milk yield (MY, kg/day), milk fat (j: F), protein (j: P), lactose (j: L) and water ( j : H) yields (MYj:F,P,L,H, kg/day) and content (MCj:F,P,L,H, g/kg), and dry matter intake (DMI, kg/day). The daily raw milk yield is defined as the sum of yields of milk lactose, protein, fat and water, such that: MY 5 Sj:F,P,L,HMYj. BW (kg) is given by BW 5 EBW 1 GU 1 DT, where EBW (kg) is the empty BW given by EBW 5 W 1 X, where W (kg) is the weight of the non-labile body mass, X (kg) is the weight of the labile body mass (body reserves), DT (kg) is the weight of the digestive tract contents and GU (kg) is the weight of the gravid uterus including the foetus and products of conception (placentome, membranes and fluids). The operating sub-model describes the metabolizable energy flows associated with material flows expressing intake, growth and milk production. The central energy compartment of the model is the zero pool of metabolizable energy (ME, MJ), which links the inflow and outflow of energy. The differential equation for ME is dME ¼ IAW AX þ CX PYM; dt
ð3Þ
where I (MJ/day) is the energy inflowing from diet, AW (MJ/ day) is the energy for growth in W, AX (MJ/day) is the energy for anabolism of X, CX (MJ/day) is the energy from mobilization of X, P (MJ/day) is the energy for pregnancy, Y (MJ/day) is the energy for milk secretion and M (MJ/day) is the energy for
maintenance. The principle of energy conservation (dME/dt 5 0) implies I 1 CX 5 M 1 AW 1 AX 1 P 1 Y. The diagram of this operating sub-model linking energy flows to performance (material flows) is presented in the companion paper. The generic term Q for performance refers to any one of {DMI,W,X,DT,GU,MY,(MY,MC)j:L,F,P,H} and the generic term E for energy flows refers to any one of {I,M,AW,AX,CX,P,Y}.
Formalism of the operating sub-model Equations. Given the terms of body composition W and X at any time t (age in days) and the so-called GARUNS pattern of priority defined with the formalism given in Table 2, the reference pattern of performance (Q* and associated E*) is calculated with the formalism given in Table 3 and detailed in Appendixes C and D (energetics of body tissues). This formalism involves (1) a teleonomic-based priority control and (2) genetic scaling parameters. The resulting reference energy flow I* 5 M* 1 AW* 1 AX* 2 CX* 1 P* 1 Y* corresponds to the energy required to realize the reference pattern of performance. In the present paper, energy intake is assumed to cover reference requirements (non-challenged feeding) such that DMI 5 DMI* and I 5 I*. This leads each energy flow to its reference level (E 5 E*) and to the full expression of the reference performance (Q 5 Q*). The alternative situation where DMI 6¼ DMI* and I 6¼ I* leads to a deviation from the reference pattern (E 5 E* 1 qE and Q 5 Q* 1 qQ) and implies deviations of the trajectories of priorities. This situation is dealt with in the companion paper (Martin and Sauvant, 2010). Teleonomic basis. Priorities to functional goals are used to drive physiological functions. This control, summarized in Table 1, is formalized by way of (1) priorities, (2) combinations of priorities and (3) differential priorities. Combinations of priorities to elementary functions allow the construction of specific regulation rules. For instance, U 1 N 1 S is the priority to reproductive functions and the complementary U 1 A 1 R 5 1 2 (U 1 N 1 S) is the priority to non-reproductive functions, which is used to inhibit growth during reproductive cycles. The notion of differential priority embodies the idea that a given physiological process, though contributing to a priority goal, may be only partially effective according to the level of that priority. The formalism of a priority raised to the power of a given exponent is used to capture this idea (Figure 4). It allows the construction of the so-called ability indexes aimed at regulating physiological functions. For instance, given 1 2 G, which is the priority to functions of the fully developed individual, the differential priority (1 2 G )x is defined as the ability to store and mobilize body reserves, where x is the exponent parameter. During development, the differential priority (1 2 G )x increases at a proportionally lower rate than the priority 1 2 G. This formalism accounts for the delayed deposition of fat during growth (allometry). The priority control allows the formalization of the following physiological phenomena concerning BW and milk yield. Increase in W is inhibited during reproductive cycles, 2037
Martin and Sauvant
Figure 4 Trajectories of global priorities (1 2 G, G 1 A and R 1 U 1 N 1 S), and differential priority (1 2 G)K for K 5 {2,5,10,100} over 20 years of life (with priorities G: growth, A: ageing, R: balance of body reserves, U: ensuring survival of the unborn calf, N: ensuring survival of the newborn calf and S: ensuring survival of the suckling calf).
when gestation and lactation prevail. Changes in X during its lifetime are defined through the balance of a target equilibrium level of body fatness (Friggens et al., 2004) and the mobilization of body reserves. The constitution of body reserves is postponed relative to the growth of the non-labile body mass in early developmental stages (Owens et al., 1993; Vernon et al., 1999). The balancing of labile body reserves to an optimal level prevails during the developmental stages of life (constitution of body reserves) and during the transition between the lactational and gestational stages of two successive reproductive cycles (reconstitution of body reserves by mobilizing surplus or filling deficit). The balancing of body reserves is also inhibited at the onset of lactation, consistently with the fact that anabolism of body tissues is known to be hindered in early lactation (Vernon and Flint, 1984; Chilliard and Robelin, 1985; McNamara, 1997). Mobilization of X at parturition contributes to the supply of energy for milk secretion dedicated to the survival of the neonate, which is the main feature in mammals (Pond, 1984; Oftedal, 2000). Moreover, mobilization is assumed to be proportional to the level of body reserves (Broster and Broster, 1998; Martin and Sauvant, 2002). Milk yield increases with age (Brody et al., 1923) as the mammary gland reaches maturity.
Genetic scaling. Given the dynamics incorporated by the GARUNS pattern of priority, genetic parameters are used to scale individual body and milk performance. Animal size is scaled with the genetic parameter WM (kg) defined as the non-labile body mass weight at maturity and set to 500 kg during model development. Mobilization of labile body mass is modulated by the dimensionless genetic parameter nX scaling mobilization of body reserve. The yield of each milk 2038
constituent j is modulated by the dimensionless genetic parameter nj:F,P,L,H. Moreover, milk yield is modulated by the dimensionless genetic parameter nY scaling milk production potential. Genetic parameters nX, nj:F,P,L,H and nY were set to 1 during model development.
Parameters The list of parameters of the regulating sub-model is given in Table 4 and the list of parameters of the operating submodels is given in Tables 5 and 6. Numerical values were either fixed as user-defined input (genetic parameters, timing of reproductive events and diet energy content) or assessed on a literature basis or estimated through a fitting procedure (see Methods section). A detailed description of the literature-based assessment of parameter values is given in Appendix E. Methods Implementation. The model was implemented with the Modelmaker 3.0 software (Cherwell Scientific Ltd, 2000) using the Runge–Kutta 4 numerical integration procedure and a fixed integration step of 1 day for t ranging from 0 to 7300 days ( , 20 years, arbitrary long-term horizon). Evaluation of performance dynamics. Our first specific objective was to evaluate the efficacy of using teleonomic arguments to describe performance throughout the lifespan of dairy cows. To address this issue, a fitting procedure was achieved on literature data to capture an average profile of dairy cow performance (15 references, see Calibration data sets in the Literature resources section). Numerical values of parameters of the operating sub-model (b0, m0, x, y and {kjn , yjn , kjs , yjs}j:L,F,P,W) together with parameters of the regulating
Teleonomic model of dairy cattle performance Table 4 Parameters of the regulating sub-model describing the dynamics of priorities G, A, R, U, N and S Assessment basis Parameter Fractional rate of priority transfer m l0 l1 g t s Pregnancy scaling p a v Reproductive events timing PCI(0) PCI(c)
Description
Transfer from N to S Basal transfer from S to R X-dependant transfer from S to R Pregnancy dependant transfer from S to R Milking dependant transfer from S to R Transfer from R to A
Value
Unit
0.06 0.0017 0.0063 0.032 0.1 0.0018
day day day day day day
Maximal pregnancy length Rate of decay of foetal growth rate Initial value of foetal growth
285 0.0111 3.5 3 1026
day – kg
Age at first conception Parturition to conception interval of cycle c . 0
450 120
day day
sub-model (m, l0, l1 and g) were thus simultaneously estimated through a least square procedure performed with the simplex algorithm of the Modelmaker 3.0 software with default parameter values and 100 convergence steps. These parameters define the reference dynamic pattern of performance. In addition, the realism of the resulting reference dynamic pattern of intake was evaluated. Model simulation of DMI* was generated with default values of genetic parameters to produce an average intake curve from birth to 2000 days of life, focusing on a 5-year productive lifetime. This curve was graphically compared with curves produced with literature models of intake (21 references, see Intake models in the Literature resources section).
Evaluation of performance diversity. Our second specific objective was to evaluate the efficacy of using genetic scaling parameters to describe the performance of various genotypes of dairy cows. To address this issue, model simulations were generated with different values of parameters scaling individual size (WM 5 {300; 450; 600}) and performance (nX 5 {0.2; 1.0; 1.8}, nY 5 {0.5; 1.0; 1.5}, nj:F,P,L 5 {0.9; 1.0; 1.1}) to produce a set of curves expressing the model variability relying on genetic diversity. These curves were graphically compared with curves produced with literature models on body, milk and intake performance (37 references, see Performance models in the Literature resources section). Literature resources Calibration data sets. The data sets (15 references, 696 records) used for model calibration concerned BW changes during growth (2, 81), BCS changes during growth and over successive gestation/lactation cycles (10, 355) and milk yield (1, 63) and composition (5, 197) over successive lactations in dairy cows (mainly of the Holstein–Friesian type). References of literature data are detailed in Table 7.
Input
Fitting
Article
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> > >
> >
Intake models. A series of 21 intake models published between 1965 and 2007, listed in Appendix F and discussed in Faverdin (1992), Ingvartsen (1994) and Roseler et al. (1997), was considered. Each literature model was applied to calculate an estimated intake pattern with specific input variables provided by model output performance Q*. Predictors used in these empirical models relate to BW and milk production (MY*, MY*j :F,P, MY*F , MY4* 5 MY* 3 (0.4 1 15 3 MYF*), BW*, (dBW/dt )* and BCS*), physiological times (day in milk: dim; week in milk: wim ¼ ðdim þ6Þ=7 , where b x c is the integer part of x ; day in pregnancy: dip; week in pregnancy: wip ¼ ðdip þ 6Þ=7 ; age at parturition of the reproductive cycle c: tp(c )*), and feed characteristics set to an average standard diet (concentrate: DMCO 5 0.40 kg/kg DM, crude fibre: CF 5 0.26 kg/kg DM, acid detergent fibre: ADF 5 0.31 kg/kg DM, neutral detergent fibre: NDF 5 0.43 kg/kg DM), digestible energy: DE 5 3.3 MJ/kg DM). Performance models. A survey of 37 articles published between 1928 and 2007 provided parameter values of different empirical models for BW, BCS, MY, MCF and MCP fitted by authors to successive lactation data recorded worldwide on cows of various dairy cattle breeds (see Appendix G). Published models simulating the growth pattern of dairy cattle from birth to maturity without particular representation of BW changes during reproductive cycles were also considered. Results
Evaluation of performance dynamics Model simulations of BW*, BCS* and MY* from birth to 3000 days of life and MC*j:F,P,L over the first three lactations are plotted with data used in the global fitting procedure in Figures 5 and 6. The goodness of fit is given through reported root mean square errors: BW*: 15.0 kg (2 references, 81 2039
Martin and Sauvant Table 5 Parameters of the operating sub-model: performance Assessment basis Parameter Body mass compositional ratio d xM xS f bX bW Body mass change rate b0 m0 k0 Individual Performance scaling (genetic parameter) WM nX nY nF nP nL nH Scaling exponent for differential priority x y Scaling exponent for milk constituent secretion ability yFN yPN yLN yHN yFS yPS yLS yHS Scaling coefficient of milk constituent secretion kFN kPN kLN kHN kFS kPS kLS kHS
Description
Value
Unit
Digestive contents:non-labile body mass Mature labile:non-labile body mass Safeguarded labile:non-labile body mass Foetus:gravid uterus mass Fat:labile body mass Fat:non-labile body mass
0.17 0.33 0.20 0.58 0.75 0.03
kg/kg kg/kg kg/kg kg/kg kg/kg kg/kg
Balancing Mobilization Digestive tract removal
1.6 0.03 1.1
day day day
Mature non-labile body mass Labile body mass mobilization index Milk yield Milk fat secretion Milk protein secretion Milk lactose secretion Milk water secretion
Input
Fitting
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> > >
500.0 1 1 1 1 1 1
kg – – – – – –
Labile body mass balance ability Milk secretion ability
5.7 5.0
– –
>
Fat Protein Lactose Water Fat Protein Lactose Water
1.26 1.59 1.13 1.15 0.97 0.89 1.27 1.21
– – – – – – – –
>
Fat Protein Lactose Water Fat Protein Lactose Water
0.0035 0.0030 0.0037 0.0632 0.0032 0.0027 0.0049 0.0848
kg/kg kg/kg kg/kg kg/kg kg/kg kg/kg kg/kg kg/kg
>
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>
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Table 6 Parameters of the operating sub-model: metabolizable energy conversion factors Assessment basis Parameter
Description
Value
eD eU eM eF eP eL eH
Dietary content (DM basis)a Pregnancy requirement Maintenance requirement Milk fat secretion requirement Milk protein secretion requirement Milk lactose secretion requirement Milk water secretion requirement
11.3 29.299 0.599 56.814 32.287 25.799 0.603
a
Diet DM content : DMC 5 0.6 kg DM/kg.
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Unit MJ/kg MJ/kg MJ/kg0.75 MJ/kg MJ/kg MJ/kg MJ/kg
Input
Article
Article
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BCS BCS, BW BCS, BW BCS BCS BCS BCS BCS BCS BCS (0, 11) month pp (0, 24) months of life (28, 7) week pp (0, 50) week pp (0, 400) day pp (200, 600) day of life (1, 44) week pp (2, 224) day pp (150, 600) day of life (0, 305) day pp {1, 2, 3, 41} {0} (1 to 7) {1} {1, 21} {0} {1} {1, 2, 31} {0} {1, 2, 3}
records); BCS*: 0.3 unit of the 0 to 5 scale (10, 355); MY*: 0.8 kg/day (1, 63); MCF*: 1.2 3 1023 kg/kg (1, 63); MCP*: 1.0 3 1023 kg/kg (1, 63); MCL*: 0.8 3 1023 kg/kg (4, 71). Model efficacy to simulate BW and condition changes during growth and reproductive cycles and milk yield and composition during lactation was found to be satisfactory. In particular, the increase in peak milk yield and the associated change in milk persistency along the lactation course from the first to the third parity are well represented. Model simulations of DMI are plotted in Figure 7 together with predictions of literature models from birth to 2000 days of life. The lifetime shape of intake simulated by the model falls in the range of predictions of these models: 45% of literature model-based predictions of intake are within the reference pattern DMI* 6 1.0 kg/day; 72% are within DMI* 6 2.0 kg/ day; 87% are within DMI* 6 3.0 kg/day. The early lactation period (3 months post partum) is the period of maximal deviation between the reference model and literature models (average overestimation of 1.0 kg/day).
Evaluation of performance diversity BW and condition. Model simulations of BW* from birth to 2500 days of life generated with three different values of the genetic parameter scaling body size (WM 5 {300; 450; 600}) are shown in Figure 8. The generated diversity of patterns during growth and throughout the reproductive cycles is consistent with the range of variation of literature models. The range of variation of the scaling size parameter WM allows simulation of growth pattern differences within breeds (between animals of different strains) and between breeds. The model was additionally fitted to curves derived from the models proposed by Turner (1928) and Rotz et al. (1999) to determine values of the scaling parameter WM to simulate growth patterns for the Jersey (WM 5 275) and Guernsey (WM 5 340) breeds and for animals of small (WM 5 440), average (WM 5 500) and large (WM 5 560) sizes within the Holstein breed. The variability of BCS at calving results from previous feeding regimens (Garnsworthy and Topps, 1982; Ruegg and Milton, 1995). The current version of the model produces a reference pattern BCS*, nutritionally non-challenged, and the parameter nX only governs the intensity of body reserves mobilization post partum. Consequently, to evaluate the model simulations v. previously modelled dynamics of BCS during lactation, all curves are expressed in percentage of the 2nd parity postcalving BCS and are shown in Figure 9. The generated diversity of patterns with three different values of the genetic parameter scaling body reserves mobilization potential (nX 5 {0.2; 1.0; 1.8}) is consistent with the range of variation of literature models. pp 5 post partum. a
Holstein US and Canadian Holstein Holstein Holstein Holstein Italian Holstein-Friesian Holstein and Dutch Friesian Holstein Israeli-Holstein Holstein–Friesian US, Washington, 1988 to 1990 Field survey US, Missouri, 1989 to 1991 US, New York Belgium Italy, 1992 to 1993 The Netherlands, 1998 to 1999 Denmark, 1997 to 2001 Israe¨l, 1999 to 2002 Ireland, 1995 to 2002
350 ? 728 265 926 31 108 809 100 40 422
MCL MCL MY, MYF,P, MCF,P MCL MCL (1, 45) week ppa (1, 320) day pp (7, 315) day pp (5, 328) day pp (1, 38) week pp {11} {21} {1, 2, 31} {1} {21} Dairy cattle Dairy cattle Holstein Danish Holstein Friesian, Jersey and cross
Milk performance Jenness (1985) O’Mahony (1988) Schutz et al. (1990) Ostersen et al. (1997) Roche (2003) Body performance Waltner et al. (1993) Hoffman (1997) Kertz et al. (1997) Van Amburgh et al. (1998) Drame et al. (1999) Abeni et al. (2000) Koenen et al. (2001) Mao et al. (2004) Shamay et al. (2005) Berry et al. (2006)
? Ethiopia, 1984 to 1986 US, Minnesota, 1983 to 1984 Denmark New Zealand, 1995 to 2001
? ? 155 527 39 77
Variables Period Parity Number Data source Reference
Table 7 References of data used for model calibration
Breed
Animals
Teleonomic model of dairy cattle performance
Milk performance. Model simulations of MY* generated with three different milk potential values (nY 5 {0.5; 1.0; 1.5}) are shown in Figure 10. The raw milk yield shape and scale changes with parity are consistent with the previously published models and genetic parameters allow the simulation of the variability of milk production levels. For a 2041
Martin and Sauvant
Figure 5 Model simulations of body weight (BW, kg), body condition score (BCS, 0 to 5 scale), and milk yield (MY, kg/day) from birth to 3000 days of life plotted with data used for model calibration.
Figure 6 Model simulations of milk fat (MCF , kg/kg), protein (MCP , kg/kg) and lactose (MCL, kg/kg) contents (kg/kg) during the first and second parities plotted with data used for model calibration.
reference third parity Holstein cow (WM 5 500), peak milk yields of 15 and 50 kg/day are generated with nY 5 0.5 and nY 5 1.5, respectively. These values are associated with 305-day milk, milk fat, milk protein and milk lactose yields of 3215, 123, 106, 159 and 10 151, 389, 338, 501 kg, respectively, for the 15 and 50 kg/day peak milk, with the average milk fat, protein and lactose contents remaining stable at 38, 33 and 49 g/kg, respectively. The same conclusion on the ability of the model to produce a realistic diversity of milk composition pattern is drawn for model simulations of MC*j:F,P generated with three different values 2042
of milk composition genetic parameters (nj:F,P 5 {0.9; 1.0; 1.1}). This range of variation produces average milk fat contents ranging from 35 to 43 g/kg, milk protein content ranging from 31 to 38 g/kg and milk lactose ranging from 44 to 54 g/kg. Genetic parameters WM, nX and nj:F,P,L can thus be used to specify a particular genotype of a given dairy breed. Discussion The results presented in this paper illustrate the capacity of the model to describe the dynamics and diversity of dairy
Teleonomic model of dairy cattle performance
Figure 7 Model simulations of dry matter intake (DMI, kg/day) from birth to 2500 days of life plotted with simulations of published models.
Figure 8 Model simulations of BW (kg) for increasing values of the input parameter scaling body size (WM 5 {300,450,600} kg) plotted with simulations of literature models for different dairy cattle breeds and sizes within breeds.
cows’ performance during growth and over repeated reproductive cycles throughout their lifespan, which indicates the potential of basing a model on teleonomic arguments and genetic scaling parameters.
Teleonomic arguments The teleonomic basis was to consider the animal ‘as an active biological entity with its own ‘‘agenda’’ ’ (Friggens and Newbold, 2007). Following this idea, the modelling of a trajectory, that is, a schedule of priority of life functions, was the starting point (Friggens et al., 2004). Ultimately, relative priorities change to ensure the survival of the individual and to maximize the production of viable offspring. Trajectories
of life function priority pertain to a schedule of changing dominance of the following main goal-directed functions: growth to reach maturity, investment in reproduction to produce and rear offspring, and modulation of body reserves to safeguard physiological requirements for future reproduction and counter seasonal changes in food availability. Homeorhesis is the tendency to home on to such a physiological dynamic process (Kennedy, 1967) and refers to the orchestrated changes in metabolism necessary to support a dominant physiological state (Bauman and Currie, 1980). The term homeorhesis (‘similar flow’) was introduced by Waddington (1957) to expand the concept of homeostasis (‘similar state’; Bernard, 1865; Cannon, 1929) and to capture 2043
Martin and Sauvant
Figure 9 Model simulations of BCS (0 to 5 scale) expressed in % of BCS at second calving (t 5 1121 day of age) for increasing values of the input genetic parameter scaling individual body reserves mobilization potential (nM 5 {0.2,1.0,1.8}) plotted with simulations of literature models.
Figure 10 Model simulations of milk yield (MY, kg/day) in first to third parity for increasing values of the input genetic parameter scaling individual milk yield potential (nY 5 {0.5,1.0,1.5}) plotted with simulations of literature models.
the idea that what living things really hold ‘constant is not a single parameter, but a time-extended course of change, that is to say, a trajectory’. Waddington introduced the term chreod (‘necessary path’) to describe the trajectory itself. From the modelling standpoint, this distinction between the end and the means-to-the-end is an essential point, and has motivated the explicit modelling of a trajectory compatible with life, genetically determined and evolutionarily targeted to ensure species continuation. Relying on Waddington’s concept of chreod, it was assumed that from birth to death, relative priorities of life functions follow a specific dynamic pattern of changes adapted to the realization of the work of life. The introduction of the idea of goal-directed process as a driving 2044
force referred to the teleonomy concept of Monod (1970): ‘organisms are endowed with a purpose which is inherent in their structure and determines their behavior’. This deterministic point of view focuses on the biological significance of physiological processes giving rise to performance rather than focusing on their biochemical determinants, which is the basis of aggregated mechanistic models such as Baldwin’s model (Baldwin et al., 1987a, 1987b and 1987c; Baldwin, 1995). The proposed model falls into the category of ‘teleonomic models’ according to the typology of Thornley and France (2007), that is, explicitly incorporating an apparent goal-directed process. The main originality of this approach is to describe lifetime performance over successive reproductive cycles, allowing
Teleonomic model of dairy cattle performance the focus on long-term residual effects, mainly by way of body reserves. The use of teleonomic arguments involves a reference pattern of performance, expressing a potential. The notion of potential refers to an optimal equilibrium between life functions rather than a maximum possibility, which is the classical view used for instance by Faverdin et al. (2007) for milk production potential. The trajectory involves an optimal body condition balanced during the transition between successive reproductive cycles and safeguarded to ensure individual survival. This idea was already captured by Friggens et al. (2004) in developing a genetically driven pattern of body lipid change through pregnancy and lactation in dairy cattle, seen as a trajectorysafeguarding reproductive success (Friggens, 2003), and used in a model of feed intake regulation in dairy cows (Petruzzi and Danfaer, 2004). Published models considering lifetime performance were mainly built with a herd level perspective with a simple and operational representation of nutrient partitioning at the animal level (Blackburn and Cartwright, 1987; Sorensen et al., 1992; Tess and Kolstad, 2000). Several models of dairy animals have already incorporated an explicit representation of a ‘driving force’ underlying physiological processes. The first attempt was performed by Neal and Thornley (1983) by way of a theoretical hormone controlling the division rate of basic udder cells to provide active secretory cells in the mammary gland. Further developments were carried out by Dijkstra et al. (1997), Vetharaniam et al. (2003a and 2003b) and Pollott (2004). This principle of modelling was also used to direct adipose tissue anabolism and catabolism (Sauvant and Phocas, 1992; Baldwin, 1995; Martin and Sauvant, 2007) or to provide kinetics of plasma growth hormone and insulin driving exchanges between the tissues and udder (Danfaer, 1990). However, none of these approaches focused on a centralized regulating model. The model presented here is a generalization of the approach proposed in Puillet et al. (2008) in which the modelling of dynamic drives for gestation and lactation was considered within a dedicated sub-model in dairy goats. The main strength of the centralized regulating system is that it formalizes a coordination of functions. Thus, gestation and lactation are naturally stages of the same reproductive cycle and the elasticity of body reserves is considered as a full-fledged component of reproductive success. The integration of teleonomic arguments is nevertheless only one way to develop a usable model and is not intended to formalize a biological theory of nutrient partitioning. The model can be used as a ‘virtual cow’ to simulate individual lifetime performance, formalize hypotheses and provide inputs to run scientific models focusing on particular physiological aspects, such as the control of fertility or the description of main metabolic pathways associated with performance (Martin and Sauvant, 2007). For instance, a model of reproduction predicting conception times could use simulations of milk yield, intake and body reserves as predictors and in turn set the timing of reproductive events. However, by its nature, the regulating sub-model of priority cannot be directly fit or fed with experimental data. The priority formalism applied here to drive performance could be extended to directly drive a reference pattern of
hormone kinetics and/or metabolite transactions in a mechanistic whole-animal model, and thus give quantitative milestones for aggregative modelling approaches. The ability of the GARUNS pattern to control underlying processes such as lipolysis and lipogenesis, gluconeogenesis or mammary gland amino acid uptake, for instance, would have to be explored to do so.
Scaling parameters The incorporation of scaling parameters is proposed as a way to formalize individual patterns of performance, interpreted as genetic profiles. This feature is intended to open perspectives of connecting this approach with works focusing on genetic aspects of animal performance and their elaboration from genotypes to animal products (Bryant et al., 2005; DoeschlWilson et al., 2007). These so-called genetic parameters have been conceived as command buttons allowing the use of the model as a simulation tool for differentiated profiles of performance. Each genetic parameter modulates a particular trait, the structure of the model being preserved. The model is thus flexible and suitable for simulations of a large range of variability, between individuals within a breed as well as between individuals of different breeds. Nevertheless, the ability of the model to describe individual performance has to be evaluated. Do these genetic parameters provide sufficient flexibility? Does ad libitum recorded performance correspond to the reference pattern of performance? Which profiles among the possible combinations of genetic parameters are realistic patterns of performance? These questions will have to be addressed to corroborate these first promising results. Moreover, for simplicity and to preserve the generic feature of the regulating sub-model, these parameters have only been incorporated into the operating sub-model. Further work will be necessary to evaluate the need to incorporate deformations of the regulating sub-model pattern of priorities pertaining to genetics. Although such questions remain to be answered, this model has been found to have the necessary structure to reproduce genetic differences in a biologically meaningful way. In the future, the model could be specifically designed as a generic tool to simulate genetic selection effects on dairy livestock performance. Conclusion We propose a conceptual framework for modelling lifetime performance of dairy livestock based on the dynamic partitioning of life function priorities. This approach formalizes performance as the realization of a goal-directed and genetically scaled trajectory. We applied this framework to dairy cows to build a whole-animal and lifetime predictive tool. As such, it provides a dynamic pattern of the body, milk and intake performance in which the monitoring of body reserves is considered as a full-fledged function. The conceptual framework, based on teleonomic arguments and incorporation of genetic scaling keys, is proposed as a way to tackle the question of nutrient partitioning prediction in nutritional models and as a postulate to be tested in 2045
Martin and Sauvant other lactating species. The companion paper contains the description of nutritional effects implying deviations from the reference pattern of performance. Acknowledgements The authors are indebted to the reviewers for their constructive criticism and comments, which helped in improving the manuscript, and also thank Laurence Puillet and Muriel Tichit for stimulating discussions relating to the ideas contained in this paper.
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