the selected order $\nu$.]{} Alternatively, the set of equations could be closed using moment closure techniques based on common expressions for well known probability distributions [@Milner2011]. In this paper we will use truncation as well as closure based on a Gaussian distribution.

Results
=======

We illustrate the approach in a range of applications that serve to highlight both the basic properties of the moment expansion method as well as the advantages this method offers in situations where other methods [@Ito2010; @Komorowski2012; @Wallace2012] tend to fail.

Dimerisation
------------

We first illustrate the moment approximation method using a simple dimerisation reaction [@Wilkinson2012]. The system describes the reversible formation and disintegration of a dimeric molecule, $$\begin{aligned}
X_1+X_1 \xrightleftharpoons[k_2]{k_1} X_2.\end{aligned}$$ The system can be written in terms of two propensities $$\begin{aligned}
\begin{array}{cc}
a_1: k_1x_1(x_1-1);&\hspace{7mm} a_2: k_2x_2,
\end{array}\end{aligned}$$ and the stoichiometry matrix $$\begin{aligned}
S=\left[\begin{array}{cc}
-2 & 2\\
1 & -1\end{array} \right],\end{aligned}$$ where the columns correspond to reactions and the rows to variables.

The exact kinetics of the system can be straightforwardly simulated using the Stochastic Simulation Algorithm (SSA) [@Gillespie1976]. One realisation of the SSA is equivalent to observing the kinetics of the system inside a single cell (Figure \[dimer1\]a), whereas the average over many realisations 