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A Power Parabola for an Asymmetrical Response

As plant density increases, crop yield often increases, reaches a plateau, then decreases at a different rate. It is difficult to find a simple equation that will adequately describe this situation. A FORTRAN IV program is presented which can be used to fit a parabola to such an asymmetrical response by the transformation of abscissa and ordinate values to calculated powers, i.e. Y^w = a + bX^z + c(X^z)². The procedure is illustrated with the response of sugar beet (Beta vulgaris L.) root yield to plant density in field plots and resulted in a power parabola of excellent fit (R² = 0.955).

Key Words: Curve fitting • Sugar beet • Plant density

Received for publication May 14, 1976.