identification of highly hereditable ‘chemical’ variables-components IN SCOTS pine populations

¹Efimov V.M, ²Tarakanov V.V, ³Naumova N.B, ¹Kovaleva V.Y.,

⁴Kutsenogyi K.P, ³Makarikova R. P, ⁴Chankina O.V.

Institute of Ecology and Systematics of Animals, SB RAS, Russia, vmefimov@ngs.ru

West-Siberian Office Of the Forestry Institute, SB RAS, Russia, vvtarh@yandex.ru

Institute of Soil Science and Agrochemistry, SB RAS, Russia, naumova@issa.nsc.ru

Institute of Chemical Kinetics and combustion, SB RAS, Russia, koutsen@kinetics.nsc.ru

Recently the methods of multivariate statistical analysis have been successfully employed for studying the role of genetic factors in the variability of natural populations. The multivariate genetic analysis of quantitative traits has been rapidly developing since the first half of the 20^th century.

C. Smith and L. Hazel solved the problem of estimating the adaptive hereditability of random linear combination of variables in the multidimensional space by means of phenotypic and genetic correlations. Besides that, they also raised and solved the problem of searching for the linear combination, maximally responsive to selection. R. Lande introduced the genetic matrix G – a multivariate analogue of the coefficient of hereditability between parents and offspring. So the multivariate analogue of the hereditability coefficient was written in a matrix form as H = GP^-1, where P is a phenotypic matrix of correlations between traits, and a so called “selectionists’s equation” ∆µ = GP^-1s, where s stands for a selection differential, and ∆µ represents the response to selection.

If the data about genetic correlations are absent, then the analysis may be reduced to the analysis of variables with high hereditability in a broad sense. R. Fisher and C. Smith laid the basics for such approach. For a case of several groups Fisher suggested to use the discriminant analysis, i.e. to search for the linear combination of variables that maximizes the ratio of between–group and total variance. If groups represent different clones, the problem automatically turns into the one of maximizing hereditability in a broad sense.

Identification of highly hereditable variables-components may be employed for genetic selection of woody plants. A useful experimental model to test and develop the approach is provided by the data about elemental composition of needles and soils from the long-term Scots pine field plantation. Detailed description of material and methods are provided by the authors elsewhere.

We applied the above-mentioned statistical approach to the analysis of elemental composition of winter needles. After analysis distribution and hereditability patterns we were left with the following set of elements: K, Ca, Mn, Cu, Zn, Se, Br, Rb, Sr, Y, Pb, Fe. Then the whole set was analysed by principal components’ extraction. Each principal component we considered to be a new variable and calculated the hereditability coefficient Н ² in a traditional way. The first principal components, accounting together for about 75% of the total variance, were used for the discriminant analysis, while the last components with small variances and nonsignificant hereditability coefficients were omitted from it. The analysis, i.e. the targeted search for axes with maximal hereditability, revealed one component with the hereditability coefficient of 0.9, which is much higher than the hereditability of any original variable.

So the applied statistical approach was shown to be quite efficient.

The study was supported by SBRAS Integration grant 5.23 and RFBR grant 07-04-01714-a.