Variogram investigation of covariance shape within longitudinal data with possible use of a krigeage technique as an interpolation tool: Sheep growth data as an example

Abstract

Most quantitative traits considered in livestock evolve over time and several continuous functions have been proposed to model this change. For individual records (longitudinal data), it is evident that measures taken at close dates are generally more related than these further apart in time. Since milk production involves several parities, the covariance structure within this trait has been analysed by time series methodology. However, the covariance structure within traits that are not repeated during life, such as those linked to growth, has not yet been formally modelled by considering time lags as is done in time series analysis. We propose an adaptation of the variogram concept to shape this structure; which gives the possibility of kriging missing data at any particular time. A new parameter, the halftime variogram, has been proposed to characterise the growing potential of a given population. The weight records of a Barbarine male lamb population were used to illustrate the methodology. The variogram covering the whole growth process in this population could be modelled by a logistic equation. To estimate the missing data from birth to 105 days of age, a simple linear interpolation was sufficient since kriging on a linear model basis gives a relatively more accurate estimation than kriging on a logistic model basis. Nevertheless, when both known records around the missing data are distant, a krigeage on the basis of the logistic model provides a more accurate estimation.