Estimating probability of insemination success using milk progesterone measurements.

The aim of this study was to quantify the effects of progesterone profile features and other cow-level factors on insemination success to provide a real-time predictor equation of probability of insemination success. Progesterone profiles from 26 dairy herds were analyzed and the effects of profile features (progesterone slope, cycle length, and cycle height) and cow traits (milk yield, parity, insemination during the previous estrus) on likelihood of artificial insemination success were estimated. The equation was fitted on a training data set containing data from 16 herds (6,246 estrous cycles from 3,404 lactations). The equation was tested on a testing data set containing data from 10 herds (8,105 estrous cycles from 3,038 lactations). Predictors were selected to be implemented in the final equation if adding them to a base model correcting for timing of insemination and parity decreased the overall likelihood distance of the model. Selected variables (cycle length, milk yield, cycle height, and insemination during the previous estrus) were used to build the final model using a stepwise approach. Predictors were added 1 by 1 in different order, and the model that had the smallest likelihood distance was selected. The final equation included the variables timing of insemination, parity, milk yield, cycle length, cycle height, and insemination during the previous estrus, respectively. The final model was applied to the testing data set and area under the curve (AUC) was calculated. On the testing data set, the final model had an AUC of 58%. When the farm effect was taken into account, the AUC increased to 63%. This equation can be implemented on farms that monitor progesterone and can support the farmer in deciding when to inseminate a cow. This can be the first step in moving the focus away from the current paradigm associated with poorer estrus detection, where each detected estrus is automatically inseminated, to near perfect estrus detection, where the question is which estrous cycle is worth inseminating?

Prediction of the lifetime productive and reproductive performance of Holstein cows managed for different lactation durations, using a model of lifetime nutrient partitioning.

The GARUNS model is a lifetime performance model taking into account the changing physiological priorities of an animal during its life and through repeated reproduction cycles. This dynamic and stochastic model has been previously used to predict the productive and reproductive performance of various genotypes of cows across feeding systems. In the present paper, we used this model to predict the lifetime productive and reproductive performance of Holstein cows for different lactation durations, with the aim of determining the lifetime scenario that optimizes cows' performance defined by lifetime efficiency (ratio of total milk energy yield to total energy intake) and pregnancy rate. To evaluate the model, data from a 16-mo extended lactation experiment on Holstein cows were used. Generally, the model could consistently fit body weight, milk yield, and milk components of these cows, whereas the reproductive performance was overestimated. Cows managed for repeated 12-, 14-, or 16-mo lactation all their life were simulated and had the highest lifetime efficiency compared with shorter (repeated 10-mo lactations: scenario N-N) or longer lactations (repeated 18-, 20-, or 22-mo lactations). The pregnancy rates increased slightly from a 10-mo to a 16-mo lactation but not significantly. Cows managed for a 16-mo lactation during their first lactation, followed by 10-mo lactations for the rest of their lives (EL-N scenario), had a similar lifetime efficiency as cows managed for 16-mo lactation all of their lives (EL-EL scenario). Cows managed for a 10-mo lactation during their first lactation, followed by 16-mo lactations for the rest of their lives (N-EL scenario), had a similar lifetime efficiency as that of the N-N scenario. The pregnancy rates of these 4 scenarios (N-N, EL-EL, N-EL, and EL-N) were similar to one another. To conclude, the GARUNS model was able to fit and simulate the extended lactation of Holstein cows. The simulated outputs indicate that managing the primiparous cows with a 16-mo extended lactation, followed by 10-mo lactations, allows their lifetime efficiency to increase and become similar to cows managed for 16-mo lactation during their entire lives. Further work should include health incidence (i.e., diseases) in the prediction model to have more accurate and realistic predictions of lifetime efficiency.

A minimal model for hepatic fatty acid balance during fasting: application to PPAR alpha-deficient mice.

The purpose of this study is to identify the hierarchy of importance amongst pathways involved in fatty acid (FA) metabolism and their regulators in the control of hepatic FA composition. A modeling approach was applied to experimental data obtained during fasting in PPARalpha knockout (KO) mice and wild-type mice. A step-by-step procedure was used in which a very simple model was completed by additional pathways until the model fitted correctly the measured quantities of FA in the liver. The resulting model included FA uptake by the liver, FA oxidation, elongation and desaturation of FA, which were found active in both genotypes during fasting. From the model analysis we concluded that PPARalpha had a strong effect on FA oxidation. There were no indications that this effect changes during the fasting period, and it was thus considered to be constant. In PPARalpha KO mice, FA uptake was identified as the main pathway responsible for FA variation in the liver. The models showed that FA were oxidized at a constant and small rate, whereas desaturation of FA also occurred during fasting. The latter observation was rather unexpected, but was confirmed experimentally by the measurement of delta-6-desaturase mRNA using real-time quantitative PCR (QPCR). These results confirm that mathematical models can be a useful tool in identifying new biological hypotheses and nutritional routes in metabolism.

Coupling a reproductive function model to a productive function model to simulate lifetime performance in dairy cows.

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?

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.

Overview of progesterone profiles in dairy cows.

The aim of this study was to gain a better understanding of the variability in shape and features of all progesterone profiles during estrus cycles in cows and to create templates for cycle shapes and features as a base for further research. Milk progesterone data from 1418 estrus cycles, coming from 1009 lactations, was obtained from the Danish Cattle Research Centre in Foulum, Denmark. Milk samples were analyzed daily using a Ridgeway ELISA-kit. Estrus cycles with less than 10 data points or shorter than 4 days were discarded, after which 1006 cycles remained in the analysis. A median kernel of three data points was used to smooth the progesterone time series. The time between start of progesterone rise and end of progesterone decline was identified by fitting a simple model consisting of base length and a quadratic curve to progesterone data, and this luteal-like phase (LLP) was used for further analysis. The data set of 1006 LLP's was divided into five quantiles based on length. Within quantiles, a cluster analysis was performed on the basis of shape distance. Height, upward and downward slope, and progesterone level on Day 5 were compared between quantiles. Also, the ratio of typical versus atypical shapes was described, using a reference curve on the basis of data in Q1-Q4. The main results of this article were that (1) most of the progesterone profiles showed a typical profile, including the ones that exceeded the optimum cycle length of 24 days; (2) cycles in Q2 and Q3 had steeper slopes and higher peak progesterone levels than cycles in Q1 and Q4 but, when normalized, had a similar shape. Results were used to define differences between quantiles that can be used as templates. Compared to Q1, LLP's in Q2 had a shape that is 1.068 times steeper and 1.048 times higher. Luteal-like phases in Q3 were 1.053 times steeper and 1.018 times higher. Luteal-like phases in Q4 were 0.977 times steeper and 0.973 times higher than LLP's in Q1. This article adds to our knowledge about the variability of progesterone profiles and their shape differences. The profile clustering procedure described in this article can be used as a means to classify progesterone profiles without recourse to an a priori set of rules, which arbitrarily segment the natural variability in these profiles. Using data-derived profile shapes may allow a more accurate assessment of the effects of, e.g., nutritional management or breeding system on progesterone profiles.

Modelling impacts of performance on the probability of reproducing, and thereby on productive lifespan, allow prediction of lifetime efficiency in dairy cows.

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.