Modelling The Neolithic

A database of the 302 sites used in my work can be found here

In my role at Newcastle University I investiagting reaction-diffusion models of the spread of Neolithic farmers, from the near-East into Europe. This work is in collaboration with Graeme Sarson, Anvar Shukurov, Richard Boys and Andrew Golightly.

I developed a numerical code to solve the Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation with an advective velocity employed on coastlines and rivers,

(1)
\begin{align} \frac{\partial N(\mathbf{x},t)}{\partial t}+\nabla \cdot (\mathbf{V}N)=\gamma N\left(1-\frac{N}{K}\right)+ \nabla \cdot (\nu \nabla N), \end{align}

on a 2D mesh, in spherical coordinates.
Here $\gamma$ is the growth-rate of the population, which is estimated from the generation time of the population, and is fixed in our simulations.
Both $K$ (the carrying capacity) and $\nu$ vary spatially (according to altitude) and are calculated from topographical data available from the National Geophysical Data Center.

A manual for the code, which gives further details about the problem we are solving can be found here, also here is a movie of a very early simulation carried out with the code, please click on the image below to view the animation:

In my new role at Newcastle University I investiagting reaction-diffusion models of the spread of Neolithic farmers, from the near-East into Europe. This work is in collaboration with Graeme Sarson, Anvar Shukurov, Richard Boys and Andrew Golightly.

At present I am applying Bayesian statistical methods to the problem of parameter estimation for the model, namely through the use of Markov Chain Monte Carlo MCMC methods.

MCMC inference schemes rely on repeated serial runs of a code, sometimes requiring millions of iterations to obtain convergence.
This is unthinkable with a numerical solution to a two dimensional PDE, such as the FKPP equation, and so we have developed a much faster particle based scheme.
A write up of this method and it's subsequent use in an MCMC scheme are in preparation, and will be detailed here soon, hopefully :-)!