Trigonometric functions representing annual winter coat shedding and regrowth in Angus cows

Subjective scores (n=2603) representing (1) the shedding and regrowth of winter coat and (2) total quantity of hair were recorded monthly for 2yr for 135 Angus cows. Shedding scores of 1 indicated summer coats (all winter coat shed) and 5 indicated complete winter coats. Quantity scores of 1 and 5 indicated minimal and maximal amounts of hair in the coat, respectively. Scores of 2 through 4 for respective traits indicated intermediate conditions. A trigonometric function representing a sinusoid process was fitted to the residuals of scores across time: Asin[B(t−C)]+D, where A represents the height of peaks in the oscillatory function above a centralized baseline in the Cartesian plane; B represents the angular frequency, that is, the rate of change of scores across a complete fundamental cycle of the process; C represents the horizontal shift in the cycle; D represents the vertical offset of the function. The time dimension in months is represented as t. Parameters for this function were estimated for the two traits using least squares nonlinear regression procedures (1) across all data, (2) within cow age categories, and (3) within groups of cows representing distinct maternal lineages. In all cases, parameters representing amplitude (A) and angular frequency (B) seemed to be estimated most reliably (as indicated by magnitude of SE) and the parameter representing the vertical offset seemed to be estimated least reliably. The numerically larger estimate of the amplitude parameter (A) for winter coat shedding and regrowth score relative to the quantity of hair score suggested that it better characterized the process, as well as differences among cow age groups or maternal lineages. For both traits within all groupings of records the parameter representing the horizontal phase shift (C) appeared to be most informative: curves for younger cows were shifted to the right in the time space, indicating later shedding of winter coat. The phase shift parameter also best characterized differences in the process for cows in different maternal lineages; however, numerical differences in the parameter estimates representing amplitude (A) and angular frequency (B) also appeared to be responsible for the distinctiveness of group curves. Curves visually represented the shedding of winter coats (April–July in the time parameter space) better than the winter regrowth process. There may be value in considering parameters of such curves in some genetic improvement strategies for enhancing cow adaptability to local environmental conditions.