[Computer technology of gene geographic analysis of a gene pool: III. Derivation of trend surfaces].

A computer technology for obtaining a set of trend (background) maps on the basis of an original geographic map is reported. These trend maps reveal the patterns of distribution of the mapped trait. The technology allows one to shape the reliefs of the genetic surfaces that reflect patterns having different origin and appearing at different times, via changing the parameters of algorithms for averaging and approximation. The set of maps, which is obtained with the use of approximation methods, simulates the hypotheses of the through trend and of the mono-, di-, or polycentric distribution of the trait. New methods for deriving the trend surfaces on the basis of averaging throughout the area of either the "moving window" or the window of variable size ("changing window") are proposed. The informative significance of maps that are obtained with the use of Chebyshev polynomials of high (up to several tens of) degrees is demonstrated.