Evaluating parameters of survival for the components of nonhomogeneous population of productive animals: analysis of problem, development of approximate solution
In recent years, in the field of lifetime biology, the concept of the need to take into account the heterogeneity of populations in terms of survival parameters has been developed. The purpose of this work is to justify the formulation of the problem and preliminary development of techniques for the approximate evaluation of survival parameters in a population of productive animals that is inhomogeneous in terms of mean and maximum length of productive life in subpopulations or groups. Features of two methodological approaches for such estimation are considered: 1) iterative procedures of sequential analytical approximation by the least squares method (LSM), 2) methods of computational experiment using the discrete age scale. When assessing survival parameters from the age structure of a herd of cows using LSM, it is necessary to take into account the influence of a number of "disturbing" factors: 1) a small number of "points" (pairs of values of culling intensity and lactation number) commensurable with the number of parameters to be determined; the increase in the number of points is possible, but this requires a transition to another, more informative system of registration and electronic archiving of production data; 2) the statistical reliability of estimating the culling intensity is higher on the first lactations, and on subsequent ones it decreases, the scatter of points increases, the requirement of equality of deviation variances is violated, the risk of obtaining "pop-up values" causing increase in estimates bias; 3) in the period after the exhaustion of the "short-lived" group (when the predicted culling intensity reaches a single value), the appearance of artifact values of group size is possible. In the study of the diagrams obtained using the "truncated" distribution of the cohort population by the length of productive life (LPL) in the mode of computational experiment with a discrete age scale, it was shown that the maximum LPL in the model subpopulations is approximately 2 times larger than the mean LPL. The possibility of obtaining numerical estimates of LPL for subpopulations is shown under the condition that the values of c in the exponent of the Gompertz function are close in size, while the different lifetimes of the corresponding cohorts are mainly due to differences in the magnitude of the pre-exponential factor. According to empirical data, the value of this factor correlates with the level of constitutive resistance in the early phase of reproductive period. The variants used to solve this problem testify the need to take into account the inhomogeneity of populations in survival parameters in studies and in practical work. It is also advisable to search for ways of obtaining an additional empirical base, in addition to the dynamics of the cohort number, including data on the frequency of occurrence of genetic markers associated with survival.