Inverse modeling to estimate deep phenotypes of the feed utilization complex in dairy cows

Deep phenotypes of the feed utilization complex reflect the underlying meta-mechanisms that determine differences in feed efficiency among cows, such as net energy for maintenance and net energy efficiency for milk synthesis. In animal breeding, deep phenotypes are hypothesized to provide better measures for improving feed efficiency than currently used traits. Although deep phenotypes cannot be measured easily on a large scale, they can be estimated by inverse modeling, combining LiGAPS-Dairy (a mechanistic model simulating lifetime feed efficiency of a cow), a genetic algorithm (GA; an optimization algorithm based on natural selection) and measured phenotypes (fat- and protein-corrected milk; FPCM, DMI, BW, and gross feed efficiency). The GA estimates deep phenotypes by minimizing differences between LiGAPS-Dairy simulated and measured phenotypes. Therefore, the objective of this study was to estimate deep phenotypes by using inverse modeling, and subsequently to evaluate the precision of these estimates and to assess the effect of 4 different levels of feed quality data used in estimating deep phenotypes. These estimated deep phenotypes were expected to reflect biological traits rather than mere model-dependent proxies. Data included 173 Holstein-Friesian cows with 20,027 weekly records for FPCM, 10,815 for DMI, 16,783 for BW, and 8,212 for feed quality from experimental farms in the Netherlands. For each cow, and for each of the 4 levels of feed quality data, 9 deep phenotypes were estimated. The precision of estimated deep phenotypes was evaluated by model fitness, phenotype prediction accuracy, and reproducibility of deep phenotypes across different random initial values in the GA and across randomly split data sets for the same animal. Model fitness was assessed using the objective function value, which is the standardized residual mean squares between simulated and measured FPCM, DMI, BW, and gross feed efficiency. Reproducibility was assessed by the concordance correlation coefficient (CCC). The average objective function value across feed quality scenarios was -48.2 with an average rRMSE of 19% for FPCM, 18% for DMI, and 7% for BW, indicating relatively good model performance. Unexpectedly, model fitness did not improve by using increasingly detailed feed quality data. Reproducibility across different initial values was acceptable for 8 deep phenotypes (CCC ranged from 0.58 to 0.95), but not for PROTNE (CCC = -0.07), and results for reproducibility across split data sets were similar, possibly indicating that the estimated 8 deep phenotypes tended toward biological traits. In conclusion, 8 out of 9 deep phenotypes (except PROTNE) of the feed utilization complex were estimated with reasonable precision by using inverse modeling. The present study is a foundational step in investigating deep phenotypes as novel traits of feed efficiency, where further investigations can explore the use of the 8 estimated deep phenotypes in animal breeding.