# Structured Population Dynamics

### Beetle Model

Macroscopic equations:

Has the corresponding variance-covariance dynamics

Where g_i is the second jump moment, which is a function of the state (E, L, P, A) just as f_i is. (In this case it will correspond to the sum of all birth and death terms).

### General Form & Algorithm

Consider the dynamics are given by

and define variance-covariance matrix M and the Jacobian matrix of f as J. Then the dynamics of the diagonal elements (variance terms) are written as

While the dynamics of the off-diagonal elements (covariance terms) are given by

Track current implementation of the algorithm here.