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Title:   Author  item
                                            Vanraden, Paul
  Submitted to: Journal of Dairy Science
                                    Publication Type: Abstract Only
                                    Publication Acceptance Date: 6/22/2003
                                    Publication  Date: N/A
                                    Citation: N/AInterpretive Summary:
                                Technical Abstract: Cow fertility and longevity traits often have distributions similar to coin tosses that are repeated if tails are observed. Methods to evaluate repeated binomial observations were compared by simulation. Dependent variables included 21-d pregnancy rate, length of time to achieve pregnancy, and log of length of time. Pregnancy rate and mean number of 21-d opportunities required to achieve pregnancy are reciprocals, but the product-moment (linear) correlation of true transmitting abilities was -0.987 rather than -1.00 because of curvature. An evaluation of pregnancy rate in which more weight is given to lactations for which the cow requires more cycles to become pregnant was preferred slightly to an unweighted evaluation but was not more accurate than evaluation of days open. Of the several models of analysis compared in simulation, none had an accuracy advantage of >1% over the others. With actual days-open data, heritability decreased from 4.1 to 3.0% when the upper limit on days open was increased from 150 to 305 d, probably because heritability of days to first breeding is higher (6.6%). The economic benefits of very early pregnancy are not as great as the costs of delayed pregnancy. Thus, breeding dates up to 250 d (rather than 150 d) are used routinely so that the more severe fertility problems are identified. As compared with days open or calving interval, pregnancy rate can be computed sooner, cows that do not become pregnant are included more easily, and larger (rather than smaller) values are desirable. Pregnancy rate can be obtained from days open using a nonlinear formula, pregnancy rate = 21/(days open - voluntary waiting period + 11), or by a linear approximation, pregnancy rate = 0.25(233 - days open), obtained from the derivative of the nonlinear formula evaluated at the mean. Voluntary waiting period is the initial phase of lactation during which no inseminations occur (assumed to be 60 d) and the factor of +11 adjusts to the middle day of the 21-d cycle. With either formula, 154 d open converts to a pregnancy rate of 20%  and 133 d open to a pregnancy rate of 25%.


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