The Influence of the Length of the Growth Period and Planting Density on Total Crop Yield

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Abstract
The growth rate of plants in a crop can be approximated by the product of three functions, each depending on one of the variables—plant weight, yield per unit area, and time. Assuming such an equation, several possible models of the relationship between total yield per unit area (or mean plant weight), the plant density and the length of the growth period are constructed by giving simple forms to the three functions. The connection between various yield-density models that have previously been suggested and the present work is indicated. With growth rate assumed to be independent of time, one or more of the derived equations fitted five sets of published experimental data reasonably well. However, only the most general of the equations considered gave consistently good fits to the five data sets. The fits to a sixth data set were much improved when growth rate depended directly on time, probably because of temperature changes during growth. Some slight but systematic differences between the models and experimental data are discussed.

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