FRACTAL DESCRIPTION OF TEMPORAL YIELD VARIABILITY OF 10 CROPS IN THE UNITED-STATES

Fractal analysis has been used to characterize both temporal and spati al variability in plant and soil parameters. A plant parameter of prim e concern is crop yield. Consequently, the temporal variability of 10 crops commonly grown in the USA was described using fractal analysis. Average yields of nine grain crops along with fiber yield of cotton (G ossypium hirsutum L.) from 1930 to 1990 in the USA were used for semiv ariogram and fractal analyses. Semivariance was calculated for each cr op for different year intervals (h). The slope of the regression line of log semivariance vs. log h for each crop was used to calculate frac tal dimension [D = (4 - slope)/2], which is an indication of the patte rn of yield variability. A small D-value (near 1) indicates the domina nce of long-term variation, while a large D-value (near 2) indicates d ominance of short-term variation and nondominance or lack of longterm variation or trend. From 1930 to 1990, yield of all crops increased, r anging from about twofold in soybean [Glycine mar (L.) Merr.], oat (Av ena sativa L.), and barley (Hordeum vulgare L.) to about sixfold in ma ize (Zea mays L.). Crop improvement through plant breeding and the use of fertilizers and pesticides are presumably the main reasons for inc reased yield. Large yield differences were observed after 1960 for mos t of the crops studied, suggesting that risk resulting from year-to-ye ar yield differences increased with improved yields. Fractal dimension s ranged from 1.20 to 1.47 for the crops studied, identifying longterm trend as well as short-term variation in yield of these crops. Rice ( Oryza sativa L.) had the smallest D-value, indicating that this crop h ad the least short-term variation, while oat and soybean had the large st D, indicating greatest short-term variation. Temporal variability i n average crop yield in the USA was much smaller than typical spatial variability values reported by others for soil parameters. It appears that fractal analysis is useful in quantifying temporal variability in yield of various crops and can be applied to agronomic research to ch aracterize temporal variations.