Between 1980 and 1986, six field experiments were conducted to investigate the relations between planting density, total dry matter and pod yield of groundnut (Arachis hypogaea L. cv. TMV2) grown at different levels of irrigation and rainfall at two sites in central India. In general, the relationship between total dry matter and planting density for most treatments was well described by the function:

where W is the crop dry weight per unit ground area, wm is the maximum weight per plant, Wm is the maximum crop weight per unit ground area and P is the plant population. Because the harvest index, h, was constant for each treatment irrespective of plant population, a similar equation described the relationship between pod yield and planting density. When nine of the eleven treatments planted in a square (i.e. 1:1) arrangement were compared, the asymptotic value Wm varied between treatments depending on available soil water and atmospheric demand. To quantify the effects of plant and environmental factors on crop productivity, a ‘transpiration equivalent’ (ωw; (g/kg)/kPa), i.e. the product of the dry matter/water ratio and mean seasonal saturation deficit D, was used as a crop constant to calculate productivity at each site or season from a knowledge of seasonal rainfall and/or irrigation and soil water-holding capacity. Thus, total crop productivity, W'8, was calculated using the equation W'8 = ωwS/D where S (mm) is a soil supply term dependent on soil water-holding capacity and monthly values of rainfall and/or irrigation. When values for Wm and W'8 were plotted against each other, a linear regression was obtained with a slope = 1·02 (R2 = 0·78). The mean harvest index of 0·38 was used to predict pod yield from a knowledge of W'8. It was concluded that of all the climatic, soil and management factors that influence crop growth in semi-arid situations, it is the interaction between the supply of and demand for water that ultimately determines total productivity, pod yield and optimum plant population.