Pollen Quantitative and Genetic Competitiveness of Rice (Oryza sativa L.) and Their Effects on Gene Flow

The gene flow rate in rice (<i>Oryza sativa</i> L.) is a critical factor for establishing safe isolation distances between genetically modified (GM) and non-GM varieties and for ensuring varietal purity in rice breeding programs. This study refines existing gene flow models by disentangling two key components of rice pollen dynamics: quantitative pollen competition and genetic competitiveness. We define <i>B</i> as the proportion of GM pollen within mixed pollen, representing quantitative pollen competitiveness. The outcrossing parameter <i>C_b</i> reflects the likelihood of successful fertilization and seed development by foreign pollen, while the hybrid compatibility parameter <i>C_p</i> captures the relative fertilization success of GM versus non-GM pollen within the same pollen pool. Together, <i>C_b</i> and <i>C_p</i> characterize the genetic competitiveness of rice pollen. Our findings reveal a nonlinear relationship between <i>B</i> and the observed GM pollen rate <i>G</i>, which may exhibit either upward or downward curvature. A nonlinear model provides a significantly better fit to this relationship than a linear model, improving <i>R</i>² by 4.1-21.4% and reducing <i>RMSE</i> by 9.9-47.8%. The parameters <i>C_b</i> and <i>C_p</i> play central roles in determining gene flow; higher values correspond to stronger GM pollen competitiveness, resulting in higher gene flow rates and greater dispersal distances. Specifically, <i>C_b</i> sets the range of the <i>B</i>-<i>G</i> curve, while <i>C_p</i> determines its curvature.