蒙古羊的群体遗传研究

本研究用Markov随机过程模型解释、模拟和预测了蒙古羊的起源、演变 ，主要品种特征的形成，若干突变在世代交替过程中的随机波动规律，遗传漂变特征，自然选择压力与人工选择压力的随机变化对若干目标基因频率的影响。结合Wright提出的移动平衡理论与随机微分方程的数值解，提出了蒙古羊Homeobox基因在定向与非定向选择条件下，最终可能消失或固定的概率，及其在任意世代时的频率求值问题和解法。本研究的主要数学工具是Markov随机过程理论与方法，其中包括Feller提出的扩散方程，Kolmogorov的前向方程与后向方程，Wright的移动平衡理论，Kimula的扩散近似方程。此外地也吸收了Haldane,Malecot,Fisher等的有关论点与方法。在实验方面，利用了蒙古羊历史久，分布广，群体大，亚群多，变异广泛，特点突出等优点，为理论分析和模拟研究提供了最好的实验材料和佐证。

STUDIES ON POPULATION GENETICS IN MONGOLIA SHEEP

The origin,evolution,the main breed characteristics,the rules of influences on some mutants among the generations,genetic drift,the pressures of natural and artificial selections and the interactions from these factors were explained,simulated and predicted by Markov stochastic procedures.Combinning with shifting balance theory and the results of random parcial differential equation methods,the probabilities of disappearing or fixing of homeobox genes in Mongolia sheep,and the conditions of direct and indirect selection and how to get the results of gene frequencies in any generation were proposed. The major tools in this study were the theories and methods of Markov stochastic procedures,including Feller`s diffusion equations,Kolmogorov forward equation and backward equation,Wright`s shifting balance theory,Kimula`s diffusion equation.On the other hand,some related conceptes and methods from Haldane,Malecot,Fisher etc.were absorbed. On the experiments of this study,taken advantages of the long history,broad distribution,large poppulation,more subpopulations,lots of varies,significant characters in Mongolia sheep,it was proved that those were the best data and evidences for the theoratical analysis and simulation research.