Deciphering individual triticale grain weight patterns: A gaussian mixture model approach

by Bo Hwan Kim, Hyeok Kwon, Wook Kim

Grain weight is one of the key phenotypic traits in crops, closely related to yield. However, the actual structure of grain weight distribution is often overlooked. In this paper, to analyze the characteristics of grain weight, we interpret the weight distribution and structure of individual grains of triticale (× Triticosecale Wittmack) from the perspective of a sum of normal distributions, rather than a single normal distribution, using the Gaussian Mixture Model (GMM). We analyzed the individual grain weight distribution of three triticale cultivars (Gwangyoung, Minpung, Saeyoung) bred in Republic of Korea, cultivated under three different seeding rates (150 kg grains per ha, 225 kg grains per ha, and 300 kg grains per ha), over time from 2 to 5 weeks post-heading. Each distribution was fitted using a GMM and evaluated using the Corrected Akaike Information Criterion (AICc) and Bayesian Information Criterion (BIC). It suggests that the distribution of the grain weight is not a single normal distribution, but rather more closely to the distribution composed of two normal distributions. This is hypothesized to be due to the physiological characteristics of the spikelet of Poaceae, including triticale, wheat, rye, and oats. Through these results, we recognize the importance of understanding the distribution structure of data and their physiological traits, which is often overlooked in measuring the characteristics of crops.