  Due to the availability of large molecular data-sets, covariance models are
increasingly used to describe the structure of genetic variation as an
alternative to more heavily parametrised biological models. We focus here on a
class of parametric covariance models that received sustained attention lately
and show that the conditions under which they are valid mathematical models
have been overlooked so far. We provide rigorous results for the construction
of valid covariance models in this family. We also outline how to construct
alternative covariance models for the analysis of geographical variation that
are both mathematically well behaved and easily implementable.
