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Coupling a reproductive function model to a productive function model to simulate lifetime performance in dairy cows
- O. Martin, P. Blavy, M. Derks, N.C. Friggens, F. Blanc
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Reproductive success is a key component of lifetime performance in dairy cows but is difficult to predict due to interactions with productive function. Accordingly, this study introduces a dynamic model to simulate the productive and reproductive performance of a cow during her lifetime. The cow model consists of an existing productive function model (GARUNS) which is coupled to a new reproductive function model (RFM). The GARUNS model simulates the individual productive performance of a dairy cow throughout her lifespan. It provides, with a daily time step, changes in BW and composition, fetal growth, milk yield and composition and food intake. Genetic-scaling parameters are incorporated to scale individual performance and simulate differences within and between breeds. GARUNS responds to the discrete event signals ‘conception’ and ‘death’ (of embryo or fetus) generated by RFM. In turn, RFM responds to the GARUNS outputs concerning the cow’s energetic status: the daily total processed metabolizable energy per kg BW (TPEW) and the net energy balance (EB). Reproductive function model models the reproductive system as a compartmental system transitioning between nine competence stages: prepubertal (PRPB), anestrous (ANST), anovulatory (ANOV), pre-ovulating (PREO), ovulating (OVUL), post-ovulating (PSTO), luteinizing (LUTZ), luteal (LUTL) and gestating (GEST). The transition from PRPB to ANST represents the start of reproductive activity at puberty. The cyclic path through ANST, PREO, OVUL, PSTO, LUTZ and LUTL forms the regime of ovulatory cycles, whereas ANOV and GEST are transient stages that interrupt this regime. Anovulatory refers explicitly to a stage in which ovulation cannot occur (i.e. interrupted cyclicity), whereas ANST is a pivotal stage within ovulatory cycles. Reproductive function model generates estradiol and progesterone hormonal profiles consistent with reference profiles derived from literature. Cyclicity is impacted by the GARUNS output EB and clearance of estradiol is impacted by TPEW. A farming system model was designed to describe different farm protocols of heat detection, insemination, feeding (amount and energy density), drying-off and culling. Results of model simulation (10 000 simulations of individual cows over 5000 days lifetime period, with randomly drawn genetic-scaling parameters and standard diet) are consistent with literature for reproductive performance. This model allows simulation of deviations in reproductive trajectories along physiological stages of the cow reproductive cycle. It thus provides the basis for evaluation of the relative importance of different factors affecting fertility at individual cow and herd levels across different breeds and management environments.
Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?
- R. Muñoz-Tamayo, L. Puillet, J. B. Daniel, D. Sauvant, O. Martin, M. Taghipoor, P. Blavy
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What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.
Modelling impacts of performance on the probability of reproducing, and thereby on productive lifespan, allow prediction of lifetime efficiency in dairy cows
- H. N. Phuong, P. Blavy, O. Martin, P. Schmidely, N. C. Friggens
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Reproductive success is a key component of lifetime efficiency – which is the ratio of energy in milk (MJ) to energy intake (MJ) over the lifespan, of cows. At the animal level, breeding and feeding management can substantially impact milk yield, body condition and energy balance of cows, which are known as major contributors to reproductive failure in dairy cattle. This study extended an existing lifetime performance model to incorporate the impacts that performance changes due to changing breeding and feeding strategies have on the probability of reproducing and thereby on the productive lifespan, and thus allow the prediction of a cow’s lifetime efficiency. The model is dynamic and stochastic, with an individual cow being the unit modelled and one day being the unit of time. To evaluate the model, data from a French study including Holstein and Normande cows fed high-concentrate diets and data from a Scottish study including Holstein cows selected for high and average genetic merit for fat plus protein that were fed high- v. low-concentrate diets were used. Generally, the model consistently simulated productive and reproductive performance of various genotypes of cows across feeding systems. In the French data, the model adequately simulated the reproductive performance of Holsteins but significantly under-predicted that of Normande cows. In the Scottish data, conception to first service was comparably simulated, whereas interval traits were slightly under-predicted. Selection for greater milk production impaired the reproductive performance and lifespan but not lifetime efficiency. The definition of lifetime efficiency used in this model did not include associated costs or herd-level effects. Further works should include such economic indicators to allow more accurate simulation of lifetime profitability in different production scenarios.