Title: The sequential loss of allelic diversity,
Abstract: This paper gives a new flavor of what Peter Jagers and his co-authors call
`the path to extinction'. In a neutral population with constant size $N$, we
assume that each individual at time $0$ carries a distinct type, or allele. We
consider the joint dynamics of these $N$ alleles, for example the dynamics of
their respective frequencies and more plainly the nonincreasing process
counting the number of alleles remaining by time $t$. We call this process the
extinction process. We show that in the Moran model, the extinction process is
distributed as the process counting (in backward time) the number of common
ancestors to the whole population, also known as the block counting process of
the $N$-Kingman coalescent. Stimulated by this result, we investigate: (1)
whether it extends to an identity between the frequencies of blocks in the
Kingman coalescent and the frequencies of alleles in the extinction process,
both evaluated at jump times; (2) whether it extends to the general case of
$\Lambda$-Fleming-Viot processes.