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The coalescent in population models with time-inhomogeneous environment. (English) Zbl 1064.92034
Summary: The coalescent theory, well developed for the class of exchangeable population models with time-homogeneous reproduction law, is extended to a class of population models with time-inhomogeneous environment, where the population size is allowed to vary deterministically with time and where the distribution of the family sizes is allowed to change from generation to generation. A new class of time-inhomogeneous coalescent limit processes with simultaneous multiple mergers arises. Its distribution can be characterized in terms of product integrals.
MSC:
92D15Problems related to evolution
60J70Applications of Brownian motions and diffusion theory
60F17Functional limit theorems; invariance principles