  Polyploidization whereby an organism inherits multiple copies of the genome
of their parents is an important evolutionary event that has been observed in
plants and animals. One way to do this is in terms of the ploidy level of the
species that make up a dataset of interest. It is therefore natural to ask the
following question which we address here: How much information about the
evolutionary past of a dataset can be gleaned from the ploidy levels of the
species that make up the dataset? To help answer this question we introduce and
study the novel concept of a ploidy profile which allows us to formalize our
question in terms of a multiplicity vector indexed by the species that make up
the dataset. Using the framework of a phylogenetic network, our results include
a closed formula for computing a ploidy profile's hybrid number (i.e. the
minimal number of polyploidization events required to explain a polyploid
dataset). Reflecting the fact that that formula relies on the availability of a
prime factor decomposition of a number we also present a non-trivial upper
bound for it.
