Use of grain size distribution parameters to explain variation in small grain screenings of wheat in multi-environment trials involving new cultivars

The proportion of small grain screenings is a worldwide problem for wheat growers in water-limited environments and is known to be influenced by both genetic and environmental factors including crop management. This paper follows our previous finding that parameters mu (reflecting point of majority mass of the grain size distribution) and 1/alpha (reflecting the slope of grain size distribution up to the majority point) of a skew-Laplace distribution can be used to differentiate the tendency of cultivars to produce small grains. The variability of these parameters over environments (15 Cultivar x Time of sowing and 2 Cultivar x Plant population x Nitrogen rates experiments) was investigated in order to indicate their utility in breeding cultivars and managing wheat crops. The estimated values of both m and 1/alpha varied over experiments but the relative cultivar ranking remained similar. Of the genetic and management factors, cultivar had more effect on variance of m than of 1/alpha, while applied nitrogen level significantly influenced 1/alpha. We conclude that: (i) cultivars can be grouped according to their m and 1/alpha values; (ii) cultivars owing their lower screenings to high 1/alpha need a careful optimising of nitrogen inputs, while breeding for high m is likely to provide stability against small grain screenings; (iii) both the parameters were associated with kernel weight and grains/spike but not grains/m(2); and (iv) future research establishing the relationship of 1/alpha with specific kernel position within the plant will be useful in proposing an ideal ear and plant structure for minimising small grain screenings. When using parameters of the suggested grain size distribution, we suggest the following relevant points be considered: (i) 1/alpha is not a linear slope, it is related to 'skewness'; (ii) the peak at majority mass (MM) reflects the tendency to concentrate grain mass and therefore provides an opportunity to increase skewness (1/alpha) despite a lower m and a lower mean grain weight; (iii) there is a point up to which skewness of grain size distribution can sufficiently protect against high screenings and is highly dependent upon the value of m; and (iv) 1/alpha is a potentially useful parameter nonetheless, because in practice, grain weight may be reduced as number of grains/area is increased in pursuit of high yield through breeding and agronomic practices.