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In this paper we study relations between trunks and tops of pines in natural Siberian forests. By statistical methods we show that the tops tend to deviate in the direction away from the nearest neighbour tree or from a summary of the trees in a given neighbourhood. In an alternative approach we show that the tops deviate into the direction of the empty space near the trunk position defined by the corresponding Voronoi polygon.

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Research Highlights: For the first time, the Pinus sibirica Du Tour and Abies sibirica L. conifer forest at the West Sayan ridge timberline has been explored to reveal which species is likely to react to climate change and a shift of the timberline. Such a shift may modify the ecological functions of the forests. Background and Objectives: Long-term climate change has become obvious in the mountains of southern Siberia. Specifically, a half-century rise in annual mean temperatures has been observed, while precipitation remains unchanged. Trees growing at the timberline are likely to strongly react to climate alterations. The objective was to estimate which of the two species sharing the same habitat would benefit from climate alteration and shifting of the timberline. Materials and Methods: At several altitudes (from 1413 to 1724 m a.s.l.), samples of P. sibirica and A. sibirica needles have been collected and contents of chlorophyll a and b as well as carotenoids were measured in June 2019. The temperature of needles of the two species was measured in both cloudy and sunny weather conditions. Results: The studied species have been shown to have different patterns of pigment variations with the growth of altitude. The decline of chlorophylls and carotenoids was more pronounced in P. sibirica (ratio at timberline ca. 2.2) than in A. sibirica (ratio ca. 3.1). Accordingly, the electron transport rate decreased more strongly in P. sibirica at the timberline (ca. 37.2 μmol of electrons/m−2 s−1) than in A. sibirica (56.9 μmol of electrons/m−2 s−1). The temperatures of needles in both cloudy and sunny weather were higher in A. sibirica (10.5 and 43.3 °C, respectively) than in P. sibirica (3.8 and 24.2 °C, respectively). Conclusions: The considered physiological and ecological traits show that P. sibirica is better protected from higher-altitude hazards (excess insolation, rise of temperature etc.) than A. sibirica. P. sibirica may be therefore a more likely winner than A. sibirica in the movement of the mountain timberline under climate warming in the area.

Some properties of diagonal binomial coefficients were studied in respect to frequency of their units' digits. An approach was formulated that led to the use of difference tables to predict if certain units' digits can appear in the values of binomial coefficients at quadratic terms of the binomial theorem. Frequency distributions of units' digits of binomial coefficients contain gaps (zero frequency) under most common numbering systems with supposed exclusion to systems with 2 n bases. In the work, an application of binomial coefficient arithmetic to model cell population dynamics was suggested. For a multicellular organism, the growth of number of cells was presented as a succession of binomial coefficients. It was inferred that the number of cells in a multicellular organism may obey power function laws.