群体遗传学中的对偶性：新对偶性的新面貌
Dualities in population genetics: a fresh look with new dualities
摘要：
我们将我们在[Giardina '，Kurchan，Redig，J.Math.Phys.48，033301（2007）]中介绍的一般对偶方法应用于种群动力学模型。向前和祖先的过程之间的经典对偶可以被看作是在经典的创造和湮灭运营商的代表性的变化，无论是扩散对偶的合并的金曼的类型，以及与有限总体大小的模型。接下来，使用SU（1，1）提高和降低运营商，我们发现新的对偶之间的Wright-Fisher扩散与$d$类型和莫兰模型，在存在和不存在突变。这些新的二重性关系到两个向前的演化。从我们的一般方案，我们还确定了自对偶的Moran模型。
英文摘要：
We apply our general method of duality, introduced in [Giardina', Kurchan, Redig, J. Math. Phys. 48, 033301 (2007)], to models of population dynamics. The classical dualities between forward and ancestral processes can be viewed as a change of representation in the classical creation and annihilation operators, both for diffusions dual to coalescents of Kingman's type, as well as for models with finite population size. Next, using SU(1,1) raising and lowering operators, we find new dualities between the Wright-Fisher diffusion with $d$ types and the Moran model, both in presence and absence of mutations. These new dualities relates two forward evolutions. From our general scheme we also identify self-duality of the Moran model.
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