New Paper: MaThRad team proves a new many-to-few result for general branching processes

In their recent research paper Simon Harris (Auckland), Emma Horton (Inria Research Centre & MaThRad), Andreas Kyprianou (Warwick & MaThRad) and Ellen Powell (Durham) prove a many-to-few result for general branching processes.

The many-to-few result is a well known formula that enables one to link the k-th moment of a population of individuals that undergo asexual reproduction to the average behaviour of k “special’’ particles. It is a powerful tool for understanding the genealogical structure of the aforementioned population of individuals.

In this article, they extend this formula to a general class of branching processes where particles move around in space, produce offspring at a spatially dependent rate and where the locations of the offspring can be scattered in space (non-local branching). They demonstrate an application of this formula by calculating the time to the most recent common ancestor of two individuals sampled from the current population, when the population has been conditioned to stay alive until a large time.

Similarly, one may use this formula to reconstruct the genealogy of a sample of any number individuals chosen from a population conditioned to stay alive until a large time. The team believe that these types of results are useful for understanding how close a population is to an equilibrium and for statistical inference, with applications in ecology, physics and chemistry.

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