A statistical model is a family of probability distributions where joint probabilities are often specified parametrically. If the joint probabilities are specified parametrically by polynomials, then the closure of the model is an algebraic variety. An underlying idea in algebraic statistics is that information about the variety yields statistical information about the model. Mixtures of independence models form a class of models that falls under this paradigm, indeed, their closures are sets of tensors with bounded border rank, i.e. secant varieties. In this talk, we will introduce mixture models, their closure, and their applications to phylogentics and evolutionary biology.