The coalescent in population models with time-inhomogeneous environment

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.