Overdispersed spatial models arise when dealing with entities that are in competition for resources.  For instance, oak trees in a forest,
cells in tissue, or molecules in space will tend to be more evenly spaced then a simple Poisson point process would predict.  This can be 
introduced into the model by adding a repulsive factor to the density that penalizes points that are too close together.

One type of Markov chain for approximately sampling from this process is the spatial birth and death process introduced by Preston.  
In this talk I will introduce a new type of move to these birth and death processes, a swap move where points can be born and die 
simultaneously.  These new moves are very easy to add and can dramatically speed up chains for these repulsive processes.

In addition, I will show how these new moves can be used with the perfect simulation protocol of dominated coupling from the past to 
create an algorithm that generates samples that are drawn exactly from the stationary distribution of the chain.