Game Mapping Of Allometry

Many biological processes,from cellular metabolism to population dynamics,are characterized by particular allometric scaling(power-law)relationships between size and rate.Although such allometric relationships may be under genetic determination to a certain degree,their precise genetic mechanisms have not been clearly understood due to a lack of a statistical analytical method.In this study,we construct a basic statistical framework,game mapping model,for mapping quantitative trait loci(QTL)responsible for universal quarter-power scaling laws by combining the power law equation of allometric growth and differential equation system.By considering the whole traits as the summation of independent growth and dependent growth as a dynamic system,we can use game theory to explain the model of allometric growth regulated by the QTL.Applying the model to the real data of Populus euphratica,122 SNPs related to allometric growth of aboveground biomass and underground biomass were successfully detected,of which 50 were hybridized,72 were crossed and distributed on 97 scaffolds.Functional annotations found that all SNPs may participate in biological processes.Some significant SNPs were found to be related to growth regulators and cytokinin synthesis.It has been proved that root system plays an important role in root development and coordinated growth with other parts under adverse environmental conditions.The application of our model in a real example from Populus euphratica leads to successful detection of a QTL governing the allometric relationship of aboveground biomass and belowground biomass.The genetic analysis of allometric growth of Populus euphratica by game mapping developed in this study can provide important theoretical guides for further genetic mapping of Populus euphratica.The game mapping model of allometric growth can also provide a powerful tool for the study of allometric growth of animals,microorganisms and humans and can further promote the development of genetic breeding more efficiently and accurately.