  In this paper we study Weil-Petersson volumes of the moduli spaces of conical
hyperbolic surfaces. The moduli spaces are parametrised by their cone angles
which naturally live inside Hassett's space of stability conditions on nodal
curves. Such stability conditions produce weighted pointed stable curves which
define compactifications of the moduli space of curves generalising the
Deligne-Mumford compactification. The space of stability conditions decompose
into chambers separated by walls. We assign to each chamber a polynomial
corresponding to the Weil-Petersson volume of a moduli space of conical
hyperbolic surfaces. The chambers are naturally partially ordered and the
maximal chamber is assigned Mirzakhani's polynomial. We calculate wall-crossing
polynomials, which relates the polynomial on any chamber to Mirzakhani's
polynomial via wall-crossings, and we show how to apply this in particular
cases. Since the polynomials are volumes, they have nice properties such as
positivity, continuity across walls, and vanishing in certain limits.
