Crop Science Journal of Natural Resources and Life Sciences Education
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Published in Crop Sci 18:948-951 (1978)
© 1978 Crop Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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Optimal Nutrient Combinations Determined from Isoprobs1

S. Geng, W. A. Williams and D. J. DaVia2

Response surface models are frequently used in estimating optimal levels of nutrient inputs. Experimental observations are subject to errors; therefore, results obtained by differentiation of a response surface function do not provide an estimate with due consideration of reproducibility. Walker and Carmer in 1967 related the probability of obtaining an increase in an observed response with an increased input level for a one variable case. We have developed a general procedure to estimate combinations of nutrients that will produce maximal yield based on a specified probability. A contour of combinations of nutrients that have the same probability to produce maximal yield is called an "isoprob". A unique optimal nutrient-combination can then be determined from an isoprob under some economic constraints. Data obtained from a greenhouse study of the effects of Ca and P on the yield of ‘Hykon’ rose clover (Trifolium hirtum All.) were used for an illustration. For a given probability level of 0.75, the estimated optimum combination of the two nutrients that depends on their relative costs ranged from 1,296 and 105 ppm to 1,530 and 83 ppm for Ca and P, respectively.

Key Words: Maximum yield • Response surface • Isoquant • Isocost

1 Contribution from the Dep. of Agronomy and Range Science, Univ. of California, Davis, CA 95616.

2 Associate professor, professor, and staff research associate, Dep. of Agronomy and Range Science, Univ. of California, Davis.

Received for publication October 4, 1977.




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