A polytomy (also called a polychotomy) is a section of a phylogeny in which the evolutionary relationships can not be fully resolved to dichotomies. In a phylogenetic tree, a polytomy is represented as a node which has more than two immediate descending branches. They present an analytical problem, but can usually be better studied by utilizing more flexible phylogenetic network software such as SplitsTree, which can represent some polytomies as median networks.
Two types of polytomies are recognised, soft and hard polytomies. Soft polytomies are the result of insufficient phylogenetic information: though the lineages diverged at different times – meaning that some of them are closer relatives than others – the available data does not allow to recognize this.
On the contrary, hard polytomies represents several speciation or lineage divergence events occurring at the same time, i.e. without their ancestral population, lineage or gene pool evolving in between, the resultant daughter species are equally distant from each other. While some researchers doubt that hard polytomies occur at all, there is little reason to assume that they don't. In particular situations they may even be not uncommon, for example when a species that has rapidly expanded its range and/or is highly panmictic undergoes peripatric speciation in different regions.
An example is the Drosophila simulans species complex. Here, the ancestor seems to have colonized two islands at the same time but independently, yielding two equally old but divergently evolved species.
As DNA sequence evolution is usually much faster than evolution of complex phenotypic traits, it may be that genetic lineages diverge a short time apart from each other, while the actual organism has not changed if the whole ancestral population is considered. As few if any individuals in a population are genetically alike in any one population – especially if lineage sorting has not widely progressed – it may be that hard polytomies are indeed rare or nonexistent if the entire genome of each individual organism is considered, but rather widespread on the population genetical level if entire species are considered as interbreeding populations (see also species concept).
Note that "speciation or lineage divergence events occurring at the same time" refers to evolutionary time measured in generations, as this is the only means that novel traits (e.g. germline point mutations) can be passed on. Also note that in practical terms, our ability to distinguish between hard and soft polytomies is limited: if for example a kilobase of DNA sequences which mutate approximately 1% per million years is analysed, lineages diverging from the same ancestor within the same 100,000 years cannot be reliably distinguished as to which one diverged first.
In that respect, it is also important to realize that founder effects and genetic drift may result in different rates of evolution. This can easily confound molecular clock algorithms to the point where hard polytomies become unrecognizable as such.