In this paper, Madouasse et al. (2021) present a generalisable Bayesian method for calculating the probability that a herd is free from disease, based on its prior disease status, and using data (herd status over time over a sufficient number of herds to inform the model) and reasonable prior estimates of the sensitivity and specificity of tests being used to determine animal infection status.  Where available, the modelling approach can also include relevant additional risk factors. 

By bringing all these factors together, it allows for most countries to use the same analytical approach on their data, with differences across datasets expressed in terms of the uncertainty around the central estimates. 

Having a single methodology that generates both a central estimate of disease freedom, and uncertainty thus provides the opportunity (given typically available data) to compare the probability of freedom across different systems. This is relevant in terms of the context of trade (since international trade of livestock in many cases depends on disease freedom). It is also important when evaluating, for example, transnational burdens of disease - and with different regulations in place in different countries, this is invaluable and can be used, for example, to assess risks of zoonotic infection including for zoonotic infection emergence. In the BVD example provided, the point is made that, since regular testing would probably pick up infection rapidly, the addition of risk factors is most valuable where testing is infrequent. This emphasizes the advantages of direct incorporation of risk factors into a single modelling framework. 

From a technical point of view, the analysis compares two different packages for the Markov Chain Monte Carlo (MCMC) implementation necesary to run the model. They show that, while there are some slight systematic differences, the estimates provided by the two methods are similar to each other; as one method is approximate but substantially more stable and generally much more computationally efficient, this is an important outcome. Both implementations are freely available and  with relevant additional software made similarly available by the authors. This is extremely welcome and should encourage its general adoption across different countries. 

No single model can of course account for everything. In particular, the reliance on past data means that there is an implicit assumption common to all purely statistical methods that the underlying risks have not changed. Thus projections to altered circumstances (changing underlying risk factors or systematic changes in testing or test performance) cannot so easily be incorporated, since these factors are complicated by the dynamics of infection that lie outside the modelling approach. Of course the well known quote from George Box that "all models are wrong" applies here - the generality of approach, statistical robustness and open source philosophy adopted make this model very useful indeed.  

Madouasse A, Mercat M, van Roon A, Graham D, Guelbenzu M, Santman Berends I, van Schaik G, Nielen M, Frössling J, Ågren E, Humphry RW, Eze J, Gunn GJ, Henry MK, Gethmann J, More SJ, Toft N, Fourichon C (2021) A modelling framework for the prediction of the herd-level probability of infection from longitudinal data. bioRxiv, 2020.07.10.197426, ver. 6 peer-reviewed and recommended by PCI Animal Science. https://doi.org/10.1101/2020.07.10.197426

The idea of altering the growth rate of replacement heifers to improve reproductive and productive indicators of dairy cattle is not new. In the late 1970s, Gill and Allaire [1] indicated that the first parturition between 22.5 to 23.5 months of age yielded the optimum lifetime performance as long as the heifers had adequate body size [2]. Since 1980s, many studies have been conducted to understand the partitioning of energy between growth and lactation, including the impact of growth rates on the heifer puberty [3] as well as growth and development of the mammary gland [4,5]. The senior author of the recommended study has written previously about this research topic [6].
 

In the present manuscript, Le Cozler et al. studied the effect of feeding programs to increase the growth rate of late-born heifers to catch up with the growth of those born earlier in the calving season on their reproductive and productive performance. The authors analyzed 217 heifers for three consecutive years, split into three dietary treatments: control (C), accelerated growth rate from birth to 6 months of age (ID1), or accelerated growth rate from birth to 12 months of age (ID2). In this study, the late-born heifers receiving the ID2 treatment were able to partially reach the bodyweight of the early-born heifers at 24 months of age. In part, the incomplete understanding of the prioritization of the use of energy (and other nutrients) for different physiological stages (e.g., maintenance, growth, lactation, and pregnancy) of the dairy animal [7] undercuts the development of more robust feeding strategies to improve the reproductive and productive performance of the animal. In the recommended study by Le Cozler et al., although there was no impact on reproductive performance among groups, heifers in the group ID2 produced less milk (about 400 kg for the whole first lactation) than heifers in the groups C and ID1, apparently suggesting that energy allocation for growth had priority over that needed for lactation. The question then becomes what would have happened with energy partitioning if energy intake was restricted. Studies like this one are important to shed some light on the prioritization of the use of energy and other nutrients in support of growth, pregnancy, and lactation of dairy animals, and how compensatory growth differs between meat versus dairy growing animals, both physiologically and energetically.

References

[1] Gill, G. S., & Allaire, F. R. (1976). Relationship of Age at First Calving, Days Open, Days Dry, and Herdlife to a Profit function for Dairy Cattle1. Journal of Dairy Science, 59(6), 1131–1139. doi: 10.3168/jds.S0022-0302(76)84333-0
[2] Hoffman, P. C. (1997). Optimum body size of Holstein replacement heifers. Journal of Animal Science, 75(3), 836–845. doi: 10.2527/1997.753836x
[3] Cardoso, R. C., Alves, B. R. C., Prezotto, L. D., Thorson, J. F., Tedeschi, L. O., Keisler, D. H., … Williams, G. L. (2014). Use of a stair-step compensatory gain nutritional regimen to program the onset of puberty in beef heifers. Journal of Animal Science, 92(7), 2942–2949. doi: 10.2527/jas.2014-7713
[4] Sejrsen, K., Huber, J. T., Tucker, H. A., & Akers, R. M. (1982). Influence of Nutrition on Mammary Development in Pre- and Postpubertal Heifers1. Journal of Dairy Science, 65(5), 793–800. doi: 10.3168/jds.S0022-0302(82)82268-6
[5] Sejrsen, K., & Purup, S. (1997). Influence of prepubertal feeding level on milk yield potential of dairy heifers: a review. Journal of Animal Science, 75(3), 828–835. doi: 10.2527/1997.753828x
[6] Le Cozler, Y. L., Lollivier, V., Lacasse, P., & Disenhaus, C. (2008). Rearing strategy and optimizing first-calving targets in dairy heifers: a review. Animal, 2(9), 1393–1404. doi: 10.1017/S1751731108002498
[7] Tedeschi, L. O., and D. G. Fox. 2018. The Ruminant Nutrition System: An Applied Model for Predicting Nutrient Requirements and Feed Utilization in Ruminants. (2nd ed.). XanEdu, Acton, MA."

The ability to adequately characterize the lactation curve of livestock is important not only to ensure proper nutrition of the lactating animal but, among many other benefits, it can assist in diagnosing the incidence of diseases, predicting the quantity of milk production, and comparing animals within the herd for managerial strategies such as culling. Eventually, such smart fitting algorithms can lead to improved genetic selection of more productive animals after genetic-unrelated noises are removed from the data, systematically.
The manuscript by Ben Abdelkrim et al. developed and explained an algorithm to detect perturbations in lactation curves of dairy goats. Researchers have been interested in accurately describing lactation curves since the early-1960s. Johansson [1] proposed a nonlinear decay function, Nelder [2] described an inverse polynomial, and Wood [3] proposed the incomplete gamma function to describe milk production of dairy cows. Unfortunately, many of the lactating animals that yielded lactation curves that did not comply with the typical, expected pattern of milk production were usually discarded and, until then, efforts to address this lack of adherence were not conducted. The recommended manuscript provides a different perspective in which rather than discarding the lactation profile, one can model the perturbations of the lactation curve as an attempt to identify possible problems (e.g., mastitis) and minimize their occurrence. Such an algorithm is important to separate females that show resilient attributes from those females that show sustainable attributes, as per existing definitions proposed by Tedeschi et al. [4].
The recommended manuscript proposes the Perturbed Lactation Model to explicitly account for multiple perturbations in the time-series milk production in dairy goats. When perturbations occur in biological processes, a typical negative impact is observed in the animal’s response, but on rare occasions, positive impacts can occur. In this case, the animal responds positively to the perturbation (i.e., responsive), and as a result, there is an increase in their output when compared to unperturbed animals. The recommended manuscript only considered negative impacts due to perturbations in the lactation curve of dairy goats. Future modifications should include positive responses due to perturbations. In this case, animals would be “positively responsive” to perturbations, and examples of such behavior include feed intake and growth curves.

References

[1] Johansson, I. (1961). Genetic Aspects of Dairy Cattle Breeding. University of Illinois Press, Urbana, IL.

[2] Nelder, J. A. (1966). Inverse polynomials, a useful group of multi-factor response functions. Biometrics. 22 (1):128-141. doi: 10.2307/2528220
[3] Wood, P. D. P. (1967). Algebraic model of the lactation curve in cattle. Nature. 216 (5111):164-165. doi: 10.1038/216164a0
[4] Tedeschi, L. O., J. P. Muir, D. G. Riley, and D. G. Fox. (2015). The role of ruminant animals in sustainable livestock intensification programs. Int. J. Sustainable Dev. World Ecol. 22 (5):452-465. doi: 10.1080/13504509.2015.1075441