“…(Abbreviations in Model II) y ijk , measured value for the ith annual ring number from pith at the jth height position above the ground of the kth individual tree; ARN ijk , ith annual ring number from pith at the jth height position above the ground of the kth individual tree; β 0 , β 1 , and β 2 , the fixed effect parameters; e ijk , residual; u 0k( j) , u 1k( j) , or u 2k( j) , random effect parameters for β 0 , β 1 , or β 2 , respectively, at the jth height position above the ground nested within the kth individual tree. species mean level (Sarkhad et al 2020(Sarkhad et al , 2022. Even in the boundary cambial age was almost the same among four species, the distance from pith to boundary cambial age in transverse section was different among species: the ratios of distance from the pith to boundary cambial age to radius were 0.45, 0.50, 0.61, and 0.67 for Pinus sylvestris, Pinus sibirica, Picea obovata, and Larix sibirica, respectively (Figure 2).…”