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The coalescent in population models with time-inhomogeneous environment

2002

AbstractThe 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.

Statistics and ProbabilityWeak convergencePopulation geneticsApplied MathematicsPopulation sizeVarying environmentPopulation geneticsProduct integralHeavy traffic approximationProduct integralStirling numbersCoalescent theoryFamily SizesDiffusion approximationPopulation modelAncestorsModelling and SimulationModeling and SimulationEconometricsQuantitative Biology::Populations and EvolutionCoalescentStatistical physicsWeak convergenceMathematicsStochastic Processes and their Applications
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