On the Ideal Value of Varying Characters

The aim of this study was to find, among groups of parts showing a variable character, one in which the variability is so strongly reduced that the character approaches constancy. This value, which we called the ideal one, is regarded as characteristic for the species. During this investigation it appeared that this ideal value can only be found, if attention is paid to the position the parts occupy in the plan on which the plant is built (I). First of all we have tried to find in our own material a definite regularity in the variability exhibited by the various characters we studied in different plants (II). After that this regularity was tested on data obtained from other investigators (III). In a number of leaves of Acer palmatum var. septemlobum the ratio between the length of the lateral main nerves and that of main nerve 1 (the longest nerve which at the same time is the middle one) was studied. By comparing the averages of the varying values found for this ratio in groups of leaves occupying a corresponding position on the shoot but differing in size, we found that these averages show a slight increase when we proceed from the smaller to the larger leaves. When we compare the averages found in groups consisting exclusively of leaves of the larger size but occupying different positions on the shoot, we saw that the averages show a continuous decrease when we begin with the leaves inserted at the base, and proceed towards those at the top of the shoot. The averages of the varying values found for the ratio between the length of the lateral main nerves and the central one, proved to reach their highest value in the leaves at the base of the shoot, no matter which of the lateral nerves was chosen. Besides one sees that the variation width decreases: 1) in leaves which occupy the same position on the shoot, when we proceed from the smaller to the larger ones, 2) in the groups of larger leaves when we proceed from the base of the shoot to the top. As the ratio between the length of the lateral main nerves and that of the central one reaches its highest value in the largest and best developed leaves, we may regard a higher value of this ratio as a criterium for a better development. Whereas an increase in the value of this ratio is always accompanied by a decrease in the variation width, a decrease in the latter too may be interpreted as indicating a higher development; the optimal degree of development, its ideal value, therefore, is recognizable by the decrease of the variation width to its lowest value. When we compare the averages found for the larger leaves inserted at the base of the shoots, which are more or less well-developed (the degree of development is measured by the number of leaf pairs) we see that they are nearly the same; the variation width is in each of these groups smaller than in the shoots with a smaller number of leaf pairs. The smallest value for the variation width was found in shoots with 3 leaf pairs and for this reason we will consider the average calculated for the leaves at the base of these shoots as the ideal value of this character, i.e. the value that is characteristic for this species. In this way the aim of this investigation, the discovery of a constant value that may be regarded as the ideal representation of a varying character, was reached (II A, a). The same state of things was observed when we studied in the same way the ratio between the length of the lateral main nerves and the central one in Acer cappadocicum (II A, b) in Platanus acerifolia (II A, c) and in Batrachium fluitans (II A, d). We found but one difference in this material, viz. that in the first named species the ideal value is, just as in Acer palm. v. sept., found in the leaves inserted at the base of the shoot, with a decrease of the average value in the direction of the top (a kathodic series), and that in the two last species the ideal value occurs in the leaves inserted at the top (an anodic series). When for a more accurate determination of the ideal value in each of these species the degree of development of the shoot is taken into account, an almost fully constant value is obtained; in these leaves too the variation width reaches its lowest value. In this way we obtain the ideal value which is to be considered representative for the species. From the study of the average value of the angle between the various main nerves too it appeared, that the variation width decreases as the angle approaches the ideal value. On account of this decrease in the width of variation the ideal value of this character was determined in Acer cappadocicum (II B, a) and in Platanus acerifolia (II B, b). In the foregoing investigations it was assumed that the difference in the relative length of the main nerves or in the size of the angle between the latter, are indicative of the degree of development of the leaf and must, therefore, undergo changes during the growth of the latter. The first-named assumption was based on the results of a comparison between average determined for groups of smaller and for groups of larger leaves occupying a corresponding position on the shoot. In order to test the soundness of this assumption we carried out measurements on the leaves of Tropaeolum lohbianum. In the first place the average values and the variation width of the proportion between the length of the main nerves and the angles between these nerves were calculated in separately gathered full-grown leaves of different size. After that similar measurements were carried out in the same leaf in successive stages of its development. The necessary material was obtained by means of contact photos. No difference of fundamental importance was found between these two series of measurements (II C). The study of the average length of leaves of Acer palmatum var. septemlobum (IID, a) Acer cappadocicum (II D, b) and Platanus acerifolia (II D, c) has shown that the average length of leaves inserted in successive positions on the shoot show a similar decrease or increase as the average of the proportion between the length of their main nerves. Besides this it appeared that the greatest average length is accompanied by the lowest variability, and that there is no difference in this respect between leaves at the base and leaves at the top of the tree. From a study of the averages obtained for the relative length of petiole and blade it appeared that the leaves with the highest average value show the smallest variation width. These measurements were carried out in Acer Platanoides, Acer pseudoplatanus and Batrachium fluitans (II E.) The relative width of leaves which was studied in Ligustrum ovalifolium also shows the same phenomenon, viz. that the greatest width is accompanied by the lowest variability (II F). The number of rays in the umbels of Aegopodium podagraria varies according to the position of the umbels on the stem, or to be more precise, according to the sequence in which they are produced. As an increase in the average number of umbel rays is always accompanied by a decrease in the variation width, the ideal value of this character is assumed to be present in the umbel which shows the lowest variation width (II G). The method applied in the foregoing studies carried out on material collected by ourselves has also been applied to data which other investigators have found for a number of varying characters. In the study of the size of the meshes formed by the reticulated veins of Vitis vulpina (111 A) it appears that the variation width reaches its lowest value in the leaves in which the meshes are largest. In a study of the internodium length of Fagus sylvatica (Ill B) the variation width proved to be smallest in those shoots in which the internodia were longest. In Teucrium chamaedrys (III C) the variation width in the proportion between the number of stomata and the number of epidermis cells proved to attain its minimum value in the leaves in which this proportion reached its highest average value. A study of the distribution of the frequency of the variates carried out for those characters of which we have ourselves investigated the variability, showed that the mean class is always best represented, as could be expected. In the curves representing the varying characters in the groups with the ideal value, the mean class sometimes contains a larger number of variates than there are found in material showing the binomial type of frequency distribution. The extreme plus and minus variates, which are, of course, present in a small number only, are always more numerous than was to be expected on the assumption that the frequency distribution is of the binomial type (IV).