Mathematical models of lineage selection
The writings by Samir Okasha (philosopher of biology/science) could be a good starting point. In his book Evolution and the Levels of Selection, he explicitly uses the Price equation to discuss selection at multiple levels (e.g. chapter 2.3: Price's equation in a hierarchical setting), and also derives a multi-level version of the Price equation:

$$\bar{w}\Delta\bar{z} = Cov(W,Z) + E(Cov_k(w,z))$$

where the first part on the right hand side represents collective-level selection and the second part particle-level selection. This is mostly aimed at aspects of group-level selection though. There is also a chapter on "Species Selection, Clade Selection, and Macroecolution" (ch. 7), but this is not directly tied to the Price equation. A note though; I own the book and have read parts of it casually, but I haven't worked with the Price equation myself, and I haven't checked exactly how the extended version of the Price equation is developed and used in the book.

A couple of references that might be useful are Frank (1998) (and other papers by him) and papers by Vrba. The work presented in this recent conference abstract by Rankin, Fox et al (2014), "Using the Extended Price Equation to Analyze Species Selection in Mammalian Body Size Evolution Across the Paleocene/eocene Thermal Maximum", seems to describe exactly the type of theoretical developments that you are looking for (I didn't attend the conference, and haven't heard the talk though).