Fractal Description of Temporal Yield Variability of 10 Crops in the United States

Abstract Fractal analysis has been used to characterize both temporal and spatial variability in plant and soil parameters. A plant parameter of prime 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 ( Gossypium hirsutum L.) from 1930 to 1990 in the USA were used for semivariogram and fractal analyses. Semivariance was calculated for each crop for different year intervals ( h ). The slope of the regression line of log semivariance vs. log h for each crop was used to calculate fractal dimension D = (4 — slope)/2, which is an indication of the pattern of yield variability. A small D ‐value (near 1) indicates the dominance of long‐term variation, while a large D ‐value (near 2) indicates dominance of short‐term variation and nondominance or lack of long‐term variation or trend. From 1930 to 1990, yield of all crops increased, ranging from about twofold in soybean Glycine max (L.) Merr., oat ( Avena sativa L.), and barley ( Hordeum vulgare L.) to about sixfold in maize ( Zea mays L.). Crop improvement through plant breeding and the use of fertilizers and pesticides are presumably the main reasons for increased yield. Large yield differences were observed after 1960 for most of the crops studied, suggesting that risk resulting from year‐to‐year yield differences increased with improved yields. Fractal dimensions ranged from 1.20 to 1.47 for the crops studied, identifying long‐term 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 had the least short‐term variation, while oat and soybean had the largest D , indicating greatest short‐term variation. Temporal variability in 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 characterize temporal variations.