system clearly demonstrate that failure to take a sufficient number of moments into account can lead to incorrect conclusions and biased parameter estimates. Ideally we would like to know from the outset whether a deterministic approach or a two moment approximation is sufficient to capture the general statistical behaviour of the stochastic system. But without recourse to a large number of SSA runs it is impossible to predict the statistical properties of the solutions to non-linear stochastic systems. And in such cases it is generally not feasible to perform large numbers of SSA simulations and we need a different approach. We should look at the assumption made at the beginning of our derivation, where we assumed that we can approximate the propensity functions with a Taylor expansion. For a single variable a Taylor expansion of a function $f(x)$ about the point $c$ has the general form $$\begin{aligned}
f(x)=f(c)+\frac{f'x}{\partial x}\left(x-c\right)+\frac{f''x}{\partial^2 x}\left(x-c\right)^2+\ldots\end{aligned}$$ By taking into account only the first term, we assume that the function value in point $x$ is the same as for point $c$; by taking into account also the second term we assume that $f(x)$ can be approximated by a straight line between points $x$ and $c$, etc.. Truncating 