Objective Height and diameter are two important growth traits in the life cycle of trees. This paper quantifies the interaction between the stem height and diameter of Populus szechuanica var. tibetica, explores the growth process and patterns of these two traits, and reveals the genetic regulatory mechanism of the dynamic growth of P. szechuanica var. tibetica stems.

Method We constructed dynamic growth interaction differential equations for the height and diameter traits of P. szechuanica var. tibetica based on the allometric growth model and game theory, and used system mapping to build a statistical model for genetic analysis of the stem growth of P. szechuanica var. tibetica. Furtherly, a natural population of P. szechuanica var. tibetica was used to investigate the dynamic stem growth in greenhouse. Combined with the high-throughput molecular marker data of this population, the genome-wide gene mapping of Populus tibetica was carried out.

Result The overall growth curves of main stem height and diameter of P. szechuanica var. tibetica conformed to the logistic growth curve. By splitting the overall growth curve, it was indicated that the diameter growth of P. szechuanica var. tibetica stems had an inhibitory effect on height growth, while height growth had a promoting effect on diameter growth. The individual fitting goodness of height and diameter of P. szechuanica var. tibetica was R² > 0.90, and the residuals of the fitting of the two traits followed a random distribution, indicating that using the generalized Lotka-Volterra differential equations to fit the height and diameter of P. szechuanica var. tibetica was effective. Based on the functional plotting method, 78 significant loci were co-located, annotating 52 candidate genes. Taking the most significant SNP on chromosome 2 as an example, genetic analysis of height and diameter of P. szechuanica var. tibetica showed that the three genotypes of this SNP, AA, AC, and CC had similar height-diameter interaction patterns. This SNP exhibited different genetic effects on overall growth, independent growth, and dependent growth. Functional annotation of the significant loci identified genes related to lignin/cell wall synthesis, growth and development, disease resistance, and photosynthesis.

Conclusion A gene localization model combining allometric growth model and game theory can detect how genes regulate the size of the trunk of Populus szechuanica var. tibetica through cooperative or competitive strategies, identify the process and pattern of dynamic trunk growth, and provide reference for deep genetic analysis of important traits in other species.