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Measure representation of evolving genealogies
Max Grieshammer
We study evolving genealogies, i.e. processes that take values in the space of (marked) ultra-metric measure spaces and satisfy some sort of "consistency" condition. This condition…
Family size decomposition of genealogical trees
Max Grieshammer
We study the path of family size decompositions of varying depth of genealogical trees. We prove that this decomposition as a function on (equivalence classes of) ultra-metric meas…
Genealogical distance under selection
Max Grieshammer
We study the genealogical distance of two randomly chosen individuals in a population that evolves according to a two type Moran model with mutation and selection. We prove that th…
Partial orders on metric measure spaces
Max Grieshammer, Thomas Rippl
A partial order on the set of metric measure spaces is defined; it generalizes the Lipschitz order of Gromov. We show that our partial order is closed when metric measure spaces ar…