Linear programming applied to dairy cattle selection

Paper 1 outlines a generalization to Hill\u27s equations for predicting response to selection. Equations are developed that account for multiple stage selection in either or both sexes and the flow of genes for animals selected at later stages. The asymptotic response to a single cycle of selection is shown to agree with classical selection theory. The equations applied to a dairy progeny testing scheme representative of an artificial insemination organization in the USA. The predicted asymptotic rates to a single cycle of selection were overestimated by 6% and the cumulative response to continuous selection over 20 years was overestimated by 8% when single stage male selection model was compared to two stage selection model;A linear programming model that accounts for the economic consequences of response to selection to the producer enterprise over a given planning horizon is described in Paper 2. A procedure is given in detail for defining upper lower bound constraints on variables that are correlated in the linear programming model. The optimal response to selection per year for the production traits was closest to their maximums achievable from a gene-flow model. Of all the non-production traits, days open had the greatest proportion of its maximum achievable from a gene-flow model. The linear programming model was used to compute relative economic weights (REV). The REVs for milk, fat, and protein production were considerably larger than the REVs for the non-production traits for all planning horizons. Somatic cell score had the largest REVs of the non-production traits in all planning horizons;In the third paper multiple-trait REML was used to estimate the heritabilities and the genetic and phenotypic correlations for 48- and 72-mo herd life from sire models incorporating sire relationships. Two traits were defined for 48- and 72-mo herd life, true herd life (THL) and functional herd life (FHL), which were adjusted for milk production prior to culling. The genetic correlations were used to compute weights for indirect prediction of true and functional herd-life PTA from linear-type traits PTA. (Abstract shortened by UMI.

Economic analysis of alternative breeding programs

An optimization method was developed for sire selection based on net return and risk of genetic merit of sires. Expected income (net present value) of a sire realized through the offspring was proposed as the composite criterion for selection. This considered the revenue corresponding to his predicted transmitting ability for milk, fat, and protein yields, cost of dystocia corresponding to his expected progeny difference for dystocia, and other fixed and variable costs. Variance of income (risk) of a sire was a function of his reliability estimates. Expected income-Variance frontier developed for a pool of sires based on quadratic programming provided the minimum risk combination of sires for an intended expected income. The combination of sires that maximizes the 95% lower confidence boundary of the frontier (that maximizes 95% guaranteed future income) determined the optimum set of sires to be selected;The optimization method explained above was applied to a simulated pool of young (pedigree tested) and proven (progeny tested) sires to determine the optimum proportion of young sire use. Young sires were riskier and, on the average, had higher expected income (low semen cost) than proven sires. The representation of young sires in the optimum set of sires that maximizes 95% guaranteed income determined the optimum proportion of young sire use. The optimum proportion of young sires was 34 percent for the pool that simulated the current Holstein population in the United States. The proposed method can be used to define the best set of sires where reliability estimates are included in the selection criteria in addition to predicted breeding values;Long term inbreeding, genetic and economic gains associated with cloning were estimated. Random and rotational mating systems for full-sib clones were considered. Production of more than 50 clones could keep inbreeding coefficient below 5 percent for 10 generations. Break-even costs per clone for modern progeny testing schemes were 83 and 41 per clone with one and five clones produced per dam, respectively. Technology of cloning and infrastructure enhancements should be developed further to lower the cost of cloning below the break-even levels for commercial use of cloning to be economically viable;Genetic and phenotypic (co)variance components were estimated from a multiple trait animal model for 305-day milk, fat, and protein yields, days open, number of services and percent cow mortality during lactation for Holsteins. Restricted maximum likelihood estimates based on expectation-maximization algorithm for the traits were similar to those from previous literature. Genetic and phenotypic relationships between yield and fertility were antagonistic. Genetic correlations between yield traits and cow mortality were unfavorable but phenotypic correlations were favorable. Evidently, modern management practices provide better management for better cows resulting in reduced mortality of high producing cows with poor genetic potential in terms of survival ability

Choosing the best forage species for a dairy farm: The Whole-farm approach

Although a handful of forage species such as perennial ryegrass are predominant, there are a wide range of forage species that can be grown in sub tropical and temperate regions in Australia as dairy pastures. These species have differing seasonal yields, nutrient quality and water use efficiency characteristics, as demonstrated in a large study evaluating 30 species University of Sydney in New South Wales, Australia. Some species can be grazed, while others require mechanical harvesting that incurs a further cost. Previous comparisons of species that relied on yields of dry matter per unit of some input (typically land or water) cannot simultaneously take into account the season in which forage is produced, or other factors related to the costs of production and delivery to the cows. To effectively compare the profitability of individual species, or combinations of species, requires the use of a whole-farm model. Linear programming was used to find the most profitable mix of forage species for an irrigated dairy farm in an irrigation region of New South Wales, Australia. It was concluded that a typical farmer facing the prevailing milk and purchased feed prices with average milk production per cow would find a mix of species including large proportions of perennial ryegrass (Lolium perenne) and prairie grass (Bromus willdenowii) was most profitable. The result was robust to changes in seasonal milk pricing and moving from year round to seasonal calving patterns.Dairy, Forage, Whole-farm, Linear programming

Modelling New Zealand dairy farm systems to design greenhouse gas mitigation strategies

Dairy cattle in New Zealand account for about 17% of the country’s total greenhouse gas (GHG) load. As the nation progresses in its efforts to reduce these emissions, is likely that the dairy industry will face physical constraints and/or financial costs associated with their mitigation. For this study, a non-linear optimization model was developed to analyse the cost-effectiveness of diverse mitigation strategies for reducing GHG loads between 10–30% within systems of different production intensity in the main dairy farming regions of New Zealand: Waikato and Canterbury. Pastoral dairy farms, as found in New Zealand, are complex farming systems with many interdependent management variables and any change in one of these variables in order to reduce GHG emissions will inevitably affect the system as a whole, generating changes in its physical and economic outputs. Computer modelling is thus highly suited to evaluate alternative strategies, given its capacity to represent and consider these interdependencies simultaneously. De-intensification, by reducing any combination of stocking rate, nitrogen fertiliser and supplement use, was a key strategy in reducing GHG emissions in an economic manner across the whole range of farming systems and regions considered in this study, as well as for all levels of emissions constraints tested. The mean farm profit reduction found under this level of mitigation across all studied systems was 6%, when no other mitigation strategies were available. To achieve this, the mean reduction in stocking rate was 8.8% and the mean nitrogen fertilizer reduction was 36%. Nitrogen fertiliser usage increases GHG emissions by increasing the available mineral nitrogen in soil and thus increasing denitrification and also by increasing enteric methane emissions as more fibrous feed is available to be consumed. The mean profit reduction was 6.9% and 4.9% for the Waikato and Canterbury regions, respectively. The Canterbury medium-input system had a lower cost of mitigation than the other systems, associated with the use of more supplements with high embedded GHG emissions in the baseline. Accordingly, the use of this kind of supplement was quickly reduced by the optimization model in the mitigation scenarios. At the other end, the Canterbury high input system had the highest cost of mitigation, arising from a combination of larger GHG-e reductions required in absolute terms and the low profitability of the baseline plan, given its high use of imported supplement. In contrast, the abatement cost in the Waikato systems was intermediate between these two extremes. Improved reproductive performance and improved genetic merit of the herd were selected as optimal in all cases where specific mitigation strategies were available. Profit was reduced by 1.6%, on average, in this case when 10% GHG emissions reductions were imposed. To adapt to this constraint, stocking rate was reduced by 8.1%, while N fertilizer was reduced by 30.7%, on average. Thus, although the availability of specific mitigation strategies was valuable in reducing the profit losses arising from mitigation, these were not sufficient to reduce emissions without some degree of de-intensification. Other mitigation strategies, like removing cows from pasture or the use of denitrification inhibitors, were not always cost effective and only entered the optimal solution when higher levels of mitigation were imposed. This demonstrates that the high cost of adopting these specific mitigation strategies is only warranted when systems are exposed to larger profit reductions associated with higher levels of de-intensification. A quick calculation using average reduction in milksolids production found in this study shows that the loss of revenue of the dairy industry if 30% mitigation of GHG is imposed can represent as much as half the export earnings of the entire beef industry of the nation

A Robust Statistical Model to Predict the Future Value of the Milk Production of Dairy Cows Using Herd Recording Data

The future value of an individual dairy cow depends greatly on its projected milk yield. In developed countries with developed dairy industry infrastructures, facilities exist to record individual cow production and reproduction outcomes consistently and accurately. Accurate prediction of the future value of a dairy cow requires further detailed knowledge of the costs associated with feed, management practices, production systems, and disease. Here, we present a method to predict the future value of the milk production of a dairy cow based on herd recording data only. The method consists of several steps to evaluate lifetime milk production and individual cow somatic cell counts and to finally predict the average production for each day that the cow is alive. Herd recording data from 610 Danish Holstein herds were used to train and test a model predicting milk production (including factors associated with milk yield, somatic cell count, and the survival of individual cows). All estimated parameters were either herd- or cow-specific. The model prediction deviated, on average, less than 0.5 kg from the future average milk production of dairy cows in multiple herds after adjusting for the effect of somatic cell count. We conclude that estimates of future average production can be used on a day-to-day basis to rank cows for culling, or can be implemented in simulation models of within-herd disease spread to make operational decisions, such as culling versus treatment. An advantage of the approach presented in this paper is that it requires no specific knowledge of disease status or any other information beyond herd recorded milk yields, somatic cell counts, and reproductive status

An Optimal Milk Production Model Selection and Configuration System for Dairy Cows

Milk production forecasting in the dairy industry has been an independent research topic since the early 20th century. The accurate prediction of milk yield can benefit both the processor (creameries) and the producer (dairy farmer) through developing short-term production schedules, planning long-term road maps, facilitating trade and investment in the dairy industry, improving business operations, optimising the existing infrastructure of the dairy industry, and reducing operating costs. Additionally, due to the innate characteristics of the milk production process, the accurate prediction of milk yield has been a challenging issue in the dairy industry. With the abolishment of EU milk quotas in 2015, the business requirements of milk production forecasting from the dairy industry has become increasingly important. However, to date, most of the existing modelling techniques are data dependent and each case study utilises specific data based on unique conditions. Consequently, it is difficult to compare the prediction performance of each candidate model for forecasting milk as both the data types and origins are independent from study to study. This body of work proposes an integrated forecasting framework XIX concentrating on milk production forecasting using heterogeneous input data combinations based on animal data, milk production, weather variables and other possible records that can be applied to milk yield forecasting on either the herd level or the individual cow level. The first objective of this study concerned the development of the Milk Production Forecast Optimisation System (MPFOS). The MPFOS focused on data processing, automated model configuration and optimisation, and multiple model comparisons at a global level. Multiple categories of milk yield prediction models were chosen in the model library of the MPFOS. Separated databases existed for functionality and scalability in the MPFOS, including the milk yield database, the cow description database and the weather database. With the built-in filter in MPFOS, appropriate sample herds and individual cows were filtered and processed as input datasets for different customised model simulation scenarios. The MPFOS was designed for the purpose of comparing the effectiveness of multiple milk yield prediction models and for assessing the suitability of multiple data input configurations and sources. For forecasting milk yield at the herd level, the MPFOS automatically generated the optimal configuration for each of the tested milk production forecast models and benchmarked their performance over a short (10-day), medium (30-day) and long (365-day) term prediction horizon. The MPFOS found the most accurate model for the short (the NARX model), medium and long (the surface fitting model) terms with R2 values equalling 0.98, 0.97 and 0.97 for the short, medium and long term, respectively. The statistical analysis demonstrated the effectiveness of the MPFOS as a model configuration and comparison tool. For forecasting milk yield at the individual cow level, the MPFOS was utilised to conduct two exploratory analyses on the effectiveness of adding exogenous (parity and meteorological) data to the milk production modelling XX procedure. The MPFOS evaluated the most accurate model based on the prediction horizon length and on the number of input parameters such as 1) historical parity weighting trends and 2) the utilisation of meteorological parameters. As the exploratory analysis into utilising parity data in the modelling process showed, despite varying results between two cow groups, cow parity weighting profiles had a substantial effect on the success rate of the treatments. Removal of the first lactation and applying static parity weight were shown to be the two most successful input treatments. These results highlight the importance of examining the accuracy of milk prediction models and model training strategies across multiple time horizons. While the exploratory analysis into meteorological data in the modelling process demonstrated that based on statistical analysis results, 1) the introduction of sunshine hours, precipitation and soil temperature data resulted in a minor improvement in the prediction accuracy of the models over the short, medium and long-term forecast horizons. 2) Sunshine hours was shown to have the largest impact on milk production forecast accuracy with an improvement observed in 60% and 70% of all predictions (for all test cows from both groups). However, the overall improvement in accuracy was small with a maximum forecast error reduction of 4.3%. Thus, the utilisation of meteorological parameters in milk production forecasting did not have a substantial impact on the overall forecast accuracy. One possible reason for this may be due to modern management techniques employed on dairy farms, reducing the impact of weather variation on feed intake and lessening the direct effect on milk production yield. The MPFOS architecture developed in this study showed to be an efficient and capable system for automatic milk production data pre-processing, model configuration and comparison of model categories over varying prediction horizons. The MPFOS has proven to be a XXI comprehensive and convenient architecture, which can perform calculations for milk yield prediction at either herd level or individual cow level, and automatically generate the output results and analysis. The MPFOS may be a useful tool for conducting exploratory analyses of incorporating other exogenous data types. In addition, the MPFOS can be extended (addition or removal of models in the model library) and modularised. Therefore the MPFOS will be a useful benchmark platform and integrated solution for future model comparisons

Sire Selection and Mating Practices in United States Dairy Herd Improvement Association Holstein Herds.

Over two million Holstein mating records was used to investigate selection and mating practices. Population statistics revealed non-random mating and selection. Herd production level was associated with higher breeding value sires and price paid per unit of semen. The decision to use an Artificial Insemination (AI) sire or natural service sire was studied and a discriminant function was derived that accurately categorized matings in a test data set of 117,000 observations, with an error rate less than 2.5 percent. Discriminating variables were herd production level, lactation number, service number, breeding month, cow status code, and days in milk at breeding. Natural service bulls were used to breed heifers and dry cows, but not milking cows---especially high producers. Selection of AI bulls was examined using stepwise regression on transformed frequency of bull use. Responses were regressed on 17 variables representing genetic and phenotypic characteristics of the bull. A model with 8 variables was selected using Mallow\u27s coefficient. Variables included breeding values for production traits, final score, somatic cell score, and reliabilities. Major factors in AI sire selection were type, fat merit, net merit dollars, and somatic cell score. Mating of AI bulls and production cows showed that both tended to group independently of mate, based upon genetic values. Residual correlations reflected genetic correlations between production and type traits, except that there was a large negative association between type and production. This could have resulted from the way that production and type bulls have developed over time, or could indicate producers are willing to give up more production for type than was economically justifiable