Method Of Path Coefficients Research Articles

The Concept of Path Coefficient and Its Impact on Population Genetics

The method of path coefficients was first published by Professor Sewall Wright thirty-five years ago. In 1921 there appeared in the Journal of Agricultural Research (Vol. 20) a general account of the method and the relationship between correlation and path coefficients, together with some examples of application; and in Genetics (Vol. 6) a series of five papers dealing exclusively with the application of path coefficients to genetic problems. Previously known results of various mating systems, obtained by laborious arithmetical procedures, were confirmed by the more elegant method, and many new results were reached, some of which were later corroborated by the method of matrix algebra while others are still difficult to obtain by any other method today. These classical papers, together with the pioneer work of Fisher (1918), still constitute the basic readings for students of population genetics, although the method has since taken a more sophisticated form and the field of application has been widened. However, one must admit that the method of path coefficients, as powerful and flexible as it is, was not immediately very popular among geneticists, still less so among professional statisticians. It was much later that its usefulness became gradually and generally appreciated. Path coefficients can be treated at various mathematical levels. The most important properties, however, can be deduced and studied by standard statistical tools. To understand the method requires little more than a knowledge of multiple and partial regression and correlation. It is a special type of multi-variate analysis a method of dealing with a closed system of variables that are linearly related. (For nonlinearly related variables, an appropriate transformation of scales may

The Derivation of Joint Distribution and Correlation between Relatives by the Use of Stochastic Matrices

The absolute frequencies of the various genotypic parent-offspring and sib-pair combinations with respect to one pair of genes, autosomal or sex-linked, are well known to geneticists, for they are of practical value in certain types of studies in human heredity. These frequencies are, however, obtained by a rather long process, even for the simple case of full sibs. The procedure of obtaining the frequencies of unclenephew or first cousinl combinations is entirely too tedious evenly with the help of matrix notations (Hogben, 1933). The purpose of the present communication is three-fold. The first is to give a simple procedure of finding the frequencies of the various genotype combinations of near relatives by using matrices of conditional probabilities. The second purpose is to express such matrices of conditional probabilities of relatives in the form of a linear function of some basic matrices. The third is to deduce the correlations between relatives from such linear functions of the basic matrices. The meaning of these statements will be made clear in later sections. For many years there existed two apparently very different methods of obtaining the genotypic correlations between relatives. One is a straightforward but long procedure by which the frequencies of the various combinations of the stated relatives in the general population are first found and then the is calculated from such a correlation table. On the other hand, they may be obtained by the method of path coefficients, developed by Wright (1921 and later). The latter method gives the required coefficient almost instantly once the relationship is specified, but does not give us any information about the frequencies of the various combinations of the relatives in the population. Moreover, one has to be familiar with the mathematical theorems concerning the path coefficients before he can use them to derive the required correlations. The method of stochastic process and its final reduction to some basic matrices, as described in the following pages, will give us both the frequencies of relative-pairs and their in a very simple manner. It is hoped that the present method will bridge the gap between the two existing procedures.

Statistical Analysis of Factors Which Make for Success in Initial Encounters between Hens

Initial encounters lie at the basis of the social order in flocks of chickens, as is known to be the case with a number of other vertebrates. To gain some insight into the factors which decide the outcome of initial encounters 200 pair contacts were staged in a neutral pen using normal, moderately inbred white leghorn hens from different flocks. Controlled factors included sex, territorial familiarity, and social facilitation. Evaluation of the less easily controlled factors was made mainly by the use of a modified biserial correlation formula. The degrees to which success in encounters was controlled by the more important factors were determined by the method of path coefficients which in the present instance was the same as the method of multiple regression. Factors of major importance were male hormone output as indicated by comb size and thyroxin secretion as indicated by the complex of changes which accompany moulting. Social rank in the home flock had much less influence, and weight was of only small importance. The multiple correlation coefficient of success with the four factors analyzed was 0.75. Forty-four per cent. of all factors were unknown or unmeasured in this analysis.

The Method of Path Coefficients

The Method of path coefficients was suggested a number of years ago (Wright 1918, more fully 1920, 1921), as a flexible means of relating the correlation coefficients between variables in a multiple system to the functional relations among them. The method has been applied in quite a variety of cases. It seems desirable now to make a restatement of the theory and to review the types of application, especially as there has been a certain amount of misunderstanding both of purpose and of procedure.

THE METHOD OF PATH COEFFICIENTS AN ANSWER TO WRIGHT

THE METHOD OF PATH COEFFICIENTS AN ANSWER TO WRIGHT