Darwin and Modern Science [165]
experimentale des Vegetaux", Corbeil, 1895.) or vice versa. Such variations are by no means isolated examples. All plants exhibit a definite alteration in form as the result of prolonged cultivation in moist or dry air, in strong or feeble light, or in darkness, or in salt solutions of different composition and strength.
Every individual which is exposed to definite combinations of external factors exhibits eventually the same type of modification. This is the type of variation which Darwin termed "definite." It is easy to realise that indefinite or fluctuating variations belong essentially to the same class of phenomena; both are reactions to changes in environment. In the production of individual variations two different influences undoubtedly cooperate. One set of variations is caused by different external conditions, during the production, either of sexual cells or of vegetative primordia; another set is the result of varying external conditions during the development of the embryo into an adult plant. The two sets of influences cannot as yet be sharply differentiated. If, for purposes of vegetative reproduction, we select pieces of the same parent-plant of a pure species, the second type of variation predominates. Individual fluctuations depend essentially in such cases on small variations in environment during development.
These relations must be borne in mind if we wish to understand the results of statistical methods. Since the work of Quetelet, Galton, and others the statistical examination of individual differences in animals and plants has become a special science, which is primarily based on the consideration that the application of the theory of probability renders possible mathematical statement and control of the results. The facts show that any character, size of leaf, length of stem, the number of members in a flower, etc. do not vary haphazard but in a very regular manner. In most cases it is found that there is a value which occurs most commonly, the average or medium value, from which the larger and smaller deviations, the so-called plus and minus variations fall away in a continuous series and end in a limiting value. In the simpler cases a falling off occurs equally on both sides of the curve; the curve constructed from such data agrees very closely with the Gaussian curve of error. In more complicated cases irregular curves of different kinds are obtained which may be calculated on certain suppositions.
The regular fluctuations about a mean according to the rule of probability is often attributed to some law underlying variability. (de Vries, "Mutationstheorie", Vol. I. page 35, Leipzig, 1901.) But there is no such law which compels a plant to vary in a particular manner. Every experimental investigation shows, as we have already remarked, that the fluctuation of characters depends on fluctuation in the external factors. The applicability of the method of probability follows from the fact that the numerous individuals of a species are influenced by a limited number of variable conditions. (Klebs, "Willkurl. Ent." Jena, 1903, page 141.) As each of these conditions includes within certain limits all possible values and exhibits all possible combinations, it follows that, according to the rules of probability, there must be a mean value, about which the larger and smaller deviations are distributed. Any character will be found to have the mean value which corresponds with that combination of determining factors which occurs most frequently. Deviations towards plus and minus values will be correspondingly produced by rarer conditions.
A conclusion of fundamental importance may be drawn from this conception, which is, to a certain extent, supported by experimental investigation. (Klebs, "Studien uber Variation", "Arch. fur Entw." 1907.) There is no normal curve for a particular CHARACTER, there is only a curve for the varying combinations of conditions occurring in nature or under cultivation. Under other conditions entirely different curves may be obtained with other
Every individual which is exposed to definite combinations of external factors exhibits eventually the same type of modification. This is the type of variation which Darwin termed "definite." It is easy to realise that indefinite or fluctuating variations belong essentially to the same class of phenomena; both are reactions to changes in environment. In the production of individual variations two different influences undoubtedly cooperate. One set of variations is caused by different external conditions, during the production, either of sexual cells or of vegetative primordia; another set is the result of varying external conditions during the development of the embryo into an adult plant. The two sets of influences cannot as yet be sharply differentiated. If, for purposes of vegetative reproduction, we select pieces of the same parent-plant of a pure species, the second type of variation predominates. Individual fluctuations depend essentially in such cases on small variations in environment during development.
These relations must be borne in mind if we wish to understand the results of statistical methods. Since the work of Quetelet, Galton, and others the statistical examination of individual differences in animals and plants has become a special science, which is primarily based on the consideration that the application of the theory of probability renders possible mathematical statement and control of the results. The facts show that any character, size of leaf, length of stem, the number of members in a flower, etc. do not vary haphazard but in a very regular manner. In most cases it is found that there is a value which occurs most commonly, the average or medium value, from which the larger and smaller deviations, the so-called plus and minus variations fall away in a continuous series and end in a limiting value. In the simpler cases a falling off occurs equally on both sides of the curve; the curve constructed from such data agrees very closely with the Gaussian curve of error. In more complicated cases irregular curves of different kinds are obtained which may be calculated on certain suppositions.
The regular fluctuations about a mean according to the rule of probability is often attributed to some law underlying variability. (de Vries, "Mutationstheorie", Vol. I. page 35, Leipzig, 1901.) But there is no such law which compels a plant to vary in a particular manner. Every experimental investigation shows, as we have already remarked, that the fluctuation of characters depends on fluctuation in the external factors. The applicability of the method of probability follows from the fact that the numerous individuals of a species are influenced by a limited number of variable conditions. (Klebs, "Willkurl. Ent." Jena, 1903, page 141.) As each of these conditions includes within certain limits all possible values and exhibits all possible combinations, it follows that, according to the rules of probability, there must be a mean value, about which the larger and smaller deviations are distributed. Any character will be found to have the mean value which corresponds with that combination of determining factors which occurs most frequently. Deviations towards plus and minus values will be correspondingly produced by rarer conditions.
A conclusion of fundamental importance may be drawn from this conception, which is, to a certain extent, supported by experimental investigation. (Klebs, "Studien uber Variation", "Arch. fur Entw." 1907.) There is no normal curve for a particular CHARACTER, there is only a curve for the varying combinations of conditions occurring in nature or under cultivation. Under other conditions entirely different curves may be obtained with other