  Intratumour phenotypic heterogeneity is nowadays understood to play a
critical role in disease progression and treatment failure. Accordingly, there
has been increasing interest in the development of mathematical models capable
of capturing its role in cancer cell adaptation. This can be systematically
achieved by means of models comprising phenotype-structured nonlocal partial
differential equations, tracking the evolution of the phenotypic density
distribution of the cell population, which may be compared to gene and protein
expression distributions obtained experimentally. Nevertheless, given the high
analytical and computational cost of solving these models, much is to be gained
from reducing them to systems of ordinary differential equations for the
moments of the distribution. We propose a generalised method of
model-reduction, relying on the use of a moment generating function, Taylor
series expansion and truncation closure, to reduce a nonlocal
reaction-advection-diffusion equation, with general phenotypic drift and
proliferation rate functions, to a system of moment equations up to arbitrary
order. Our method extends previous results in the literature, which we address
via two examples, by removing any \textit{a priori} assumption on the shape of
the distribution, and provides a flexible framework for mathematical modellers
to account for the role of phenotypic heterogeneity in cancer adaptive
dynamics, in a simpler mathematical framework.
