On the Relationship between the Length of the Pod and Fertility and Fecundity in Cercis

Abstract

1. In considering the influence of the number of seeds developing upon the dimensions attained by the fruit, the number of ovules formed cannot be disregarded, since a correlation attributed directly to the influence of the development of the seeds may be in part at least due to an interdependence between the number of ovules formed and the dimensions of the fruit. The influence of the number of ovules can be neglected only when the coefficient of correlation between number of ovules and size of fruit is demonstrated to be zero. This point is well illustrated by a series of 3,000 pods of Cercis, where the correlations for ovules and length is rol = 0.428±0.010; while the correlation for seeds per pod and length is only rsl = 0.506±0.009. 2. Two methods for freeing the correlation between the number of seeds developing and the length of the fruit from the influence of the relationship between the number of ovules formed and the length of the pod are suggested; the first is the determination of the partial correlation coefficient, that is, the correlation between number of seeds and length for constant values of numbers of ovules per pod; the second is the determination of the correlation between the index \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{wasysym} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document}$$\frac{\mathrm{Seeds\ developing\ per\ pod}}{\mathrm{Ovules\ formed\ per\ pod}}$$\end{document} and the length of the pod. The results from the data in hand are in close agreement,\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{wasysym} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\begin{eqnarray} \rho_{\mathrm{sl}} & = & 0.313 \pm 0.011 \nonumber \\ r_{\mathrm{il}} & = & \underline {0.291} \pm 0.011 \nonumber \\ \rho_{\mathrm{sl}}-r_{\mathrm{il}} & = & 0.022 \nonumber \end{eqnarray}$$ \end{document} and we conclude that of the gross correlation of about ρ = 0.500 for number of seeds and length of pod a considerable portion, say ρ = 0.300 roughly, is due to some morphogenetic or physiological relationship between the number of seeds developing and the length of the pod.

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