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The scale patterns of 6000 cones from one single tree of Pinus nigra Arn. have been examined. Apart from the main Fibonacci pattern with 8 and 13 parastichies, nine aberrant spiral patterns with Fibonacci-type sequences have been found. They are quite rare and occur with different frequencies. The parastichy quotient 8/13 of the prevalent pattern is very close to the golden ratio 0.618. In case of the black pine it appeared that the greater the deviation of the parastichy quotient m/n from 0.618, the rarer the pattern. Similar results obtained for the sample of 1506 cones collected from three individual trees of larch (Larix decidua Mill.) suggest a true correlation between the frequency of a pattern and the deviation of its parastichy quotient from the golden ratio.
Compared to the formation of male generative organs, the development of female sporogenous tissue of the European larch (Larix decidua Mill.) is considerably delayed. The young megaspore mother cell (megasporocyte, MMC) is not observable until late October, a short time before the period of dormancy. In early spring, MMCs become moderately enlarged, with intensive accumulation of starch grains around the nucleus. At the end of the first 10 days of March the MMCs become more rounded in section and the nucleus moves towards the basal part of the cell (near the chalaza). The integument and nucellus become observable at that time and chromosomal strands are visible in the MMC nuclei. Meiosis of MMCs was observed from mid-March to early April. During that period the tip of the integument grows gradually over the nucellus and creates the stigmatic apparatus of the ovule. Instead of the expected tetrads, triads of linearly arranged unequal megaspores were observed in individual ovules at the beginning of pollen shedding. Immediately after meiosis of the MMC, massive growth of the functional chalazal megaspore occurs, along with intensive free-nuclear divisions. The nuclei become located near the megaspore membrane, whereas the whole central part of the developing female gametophyte is filled with an extraordinarily large central vacuole. During intensive growth of the functional megaspore, the innermost layer of the nucellar tapetum gradually disintegrates. This development stage lasts until early May, when the megaspore membrane segregates partially from the nucellar tapetum and the free-nucleate female gametophyte assumes an irregular sac-like shape. The cellular stage of the female gametophyte with typical pyramidal cells at its micropylar end is visible at mid-May. Then the vacuolated (so-called frothy) archegonia gradually forms. The disappearance of vacuoles and the division of the central cell were registered in late May. At the stage of the large female gamete (egg cell) and the small ventral canal cell, the archegonia become fully receptive for fertilization. Our observations indicate that the development of the free-nucleate gametophyte and the formation of cell walls among the nuclei are the most sensitive phases of ovule development in the European larch before fertilization. During these stages, numerous cases of degeneration of the female gametophyte were observed, along with the complete deformation of ovules. The reasons for frequent irregularities are discussed here; the influence of meteorological and nutrient conditions seems especially important.
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