  Methods of phylogenetic inference use more and more complex models to
generate trees from data. However, even simple models and their implications
are not fully understood.
  Here, we investigate the two-state Markov model on a tripod tree, inferring
conditions under which a given set of observations gives rise to such a model.
This type of investigation has been undertaken before by several scientists
from different fields of research.
  In contrast to other work we fully analyse the model, presenting conditions
under which one can infer a model from the observation or at least get support
for the tree-shaped interdependence of the leaves considered.
  We also present all conditions under which the results can be extended from
tripod trees to quartet trees, a step necessary to reconstruct at least a
topology. Apart from finding conditions under which such an extension works we
discuss example cases for which such an extension does not work.
