Seed Size Variation in Grain Crops: Allometric Relationships between Rate and Duration of Seed Growth

Genetic control and environmental modulation of seed size operate through their influences on rate and duration of seed filling, and their interaction. To account for this interaction, here we advance an allometric model centered on the scaling exponent α calculated as the slope of the linear regression between duration and rate of grain filling in a log-log scale. The scaling exponent allows for three types of responses: seed size is stable as a result of full compensation between rate and duration (α = -1), seed size is variable as a result of rate (α > -1), or duration-dominated growth (α < -1). The concept was tested with 45 data sets from the literature involving nine crop species, and sources of variation including genotype, environment, and their interaction. Relative variation in seed size ranged from 5 to 274%, and the scaling exponent was strongly concentrated in the range from 0 (large, rate-driven seed size range) to -1 (narrow seed size range due to mutually cancelled effects of rate and duration). The range of seed size declined when the scaling exponent declined from approximately 0 to -1. An α approximately equal to -1 (rate and duration effects cancel each other) is necessary and sufficient for small variation in seed size, whereas α approximately equal to 0 is necessary but not sufficient for large seed size variation. The magnitude of seed size variation is dependent on the variation in the rate of seed growth when α approximately equal to 0. This double condition for seed size variability is summarized in a multiple regression model with α and range of rate of grain filling as independent variables, which accounted for 73% of the variation in range of seed size.