Path and ridge regression analysis of seed yield and seed yield components of soybean under different irrigation regimes

Seed yield, a quantitative character, is largely influenced by the environment, and thus has a low heritability. Therefore, the response to direct selection for seed yield may be unpredictable unless environmental variation is well controlled. The objective of this study was to examine the mathematical relationships between seed yield and its components by using a path analysis and ridge regression modeling approach to forecast the seed yield in seed production. To do this, a split-plot experimental based on randomized complete block design with three replication was conducted in 2004. Irrigation treatments were assigned to main plots, and two soybean cultivars were allocated to the subplots. Irrigation treatments I1, I2, I3 and I4 were defined based on the cumulative evaporation of 60±3, 80±3, 100±3 and 120±3 mm, from pan (class A), respectively. The seed yield components considered in this study, were number of pods per plant (x1), number of seeds per pod (x2), number of seeds in plant (x3), pod-bearing nods in plant (x4) and seed weight (x5). Pearson correlation coefficients and path analysis of components x1 through x5 to Y showed that the strongest indirect effect on Y was x1 via x3 (the coefficients is 0.29), x1 via x4 (the coefficients is 0.24) and x3 via x1 (the coefficients is 0.24). All of the ridge coefficients were positive except x2 that in two levels of I1 and I4 irrigation treatments was negative. This result showed that number of seeds per pod trait in the soybean crop is very sensitive to the amount of water so that with the maximum and minimum amounts of water, its value was related to yield inversely. This study developed an original exponential model for estimating yield from the values of yield components under influenced different irrigation regimes. The model was statistically reliable. In the present trial, the genetic controls were more general than the environmental controls for x1 to x5. Therefore, we tentatively propose that x1, x3 and x4 were orderly more genetic and less environmental control than x2 and x5.