# Effective population size of a metapopulation structured on a grid

Scenario

Consider a rectangular metapopulation consisting of $x \cdot y$ demes, where $x$ is the number of deme horizontally and $y$ is the number of demes vertically. The population size per deme is $N$ and the migration rate between any two adjacent demes is $m$.

Assumptions

I welcome any kind of assumptions for the purpose of this post.

Question

Can you help me to calculate an expectation of the effective population size $Ne$ of the whole metapopulation?

• I am not an expert in this area but if the initial population in all the demes is homogeneous then you can consider the entire metapopulation as one unit with x × y × N individuals. If the sex-ratios are skewed then you may expect different dynamics. – WYSIWYG Apr 27 '16 at 8:35
• Mating is not random in the total metapopulation, the $Ne > x \cdot y \cdot N$ even if (as I assumed in the question) all demes have the same size $N$. – Remi.b Apr 27 '16 at 15:24