Abstract
Summary.The problems of phyllotaxis are re‐examined from the standpoint of the initial adjustment of the units of shoot growth. The structure of the shoot apex is reviewed in relation to the origin of leaf primordia and it is pointed out that such primordia, once formed, are competing centres of activity and consequently tend to arise as nearly as possible opposite to one another, as exemplified by the simplest case of alternate or 1/2 phyllotaxis.When more than two primordia are growing simultaneously at the apex, successive ones cannot be exactly opposite, as in this case the position of the new primordium is influenced by all the others which are growing at the same time.By application of this conception of competing growth centres, it is shown that, as the number of growing primordia at the apex rises, the fraction denoting the new type of phyllotaxis is likely to fall in the Fibonacci series, because analysis shows that these are the only ones which satisfy the requisite spacing of the primordia in relation to the number of time intervals or “plastochrones” separating them in origin.It is pointed out that systems belonging to the higher fractions in the Fibonacci series are practically impossible to recognise with certainty, unless external observations are supported by anatomy. The case of Iberis amara is analysed in detail and it is shown that the 5/13 system could be derived from anatomy.A rise in the number of primordia growing simultaneously involves readjustment of the units of shoot growth and it is shown that, as the system rises from one fraction to the next, characteristic displacements take place, which vary in direction in different transitions.The higher systems are usually associated with a wider pith.It is concluded that the direction of the spiral is determined by the positions of the two first primordia, the genetic spiral being merely an abstraction from the developmental standpoint. This is illustrated by the fact that the direction of the spiral on branches seems to vary irrespective of the spiral on the axis of the same plant.A decussate system with an angular divergence of 1/2 between members of a pair and 1/4 between successive pairs is regarded as a stable system, provided that the primordia of a pair arise almost simultaneously and time intervals between the pairs lengthen proportionately. This argument is analysed from measurements of the plastochrones in whorled and spiral plants of the same species. Although decussate types often show slight differences in the time and position of development of the members of a pair, this merely demonstrates the tendency to successive emergence of primordia and not the evolutionary derivation of the system from a theoretical spiral system. If a plant has a tendency to decussate phyllotaxis, this system naturally appears in the seedling because of the temporary halt in the embryonic growth at a stage when two cotyledons occupy the apex. In axillary branches, the symmetry of the phyllotaxis is affected by the subtending leaf and often starts with an approximately spiral system.In many decussate dicotyledons, the lateral expansion of the primordia causes them to extend over more than half the circumference. In such types, if in abnormal specimens the primordia arise in spiral succession instead of simultaneously, spiral torsion results, the successive primordia remaining “bound” together by one fused margin. Other types of torsion and variations from normal decussate phyllotaxis are also discussed.In whorled systems of more than two members, the members of successive whorls alternate. Similar torsions and abnormalities to those discussed for decussate types may also occur.In such whorled types, it is shown that, from the developmental standpoint, 2n leaf primordia (or units of shoot growth) must be growing simultaneously, n being the number of members in a whorl.
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