Forest canopy gaps are important for tree regeneration and species diversity. In this talk, I present a method to analyze patterns of forest canopy gaps using Markov chains on a lattice. Three models of disturbance and recovery are studied: a “two state” model with canopy sites and gap sites; a “three state” model with occupied sites, disturbed sites and empty sites; and a “propagating wave” model with sites representing the actual tree height.
[1] It can be proved that in the equilibrium the two state model is equivalent to the Ising model. Numerical results based on local properties show that the Ising model can be rejected for real forest data if spatial heterogeneity of the environment is neglected.
[2] For all three models, the variance of the fraction of area covered by gaps decreases with the size of the area considered. This statistic respects patterns at multiple scales. We quantify the deviation from a power law and see that forest data (BCI, 50 ha plot) is consistent with the Ising model and three state model, but not with the propagating wave model which shows a characteristic spatial scale.