Wave propagations in the secondary forest succession

Xiaojie Hou
Mathematics, University of Cincinnati

(April 5, 2007 10:30 AM - 11:30 AM)

Wave propagations in the secondary forest succession

Abstract

The secondary forest succession is caused by the interaction between pioneer and climax tree species. Such interaction is modeled by a reaction diffusion system. The succession can be described by traveling wave solution connecting the initial and final stages of the succession.

Under some mild conditions, we show the existence, uniqueness and stability of the traveling wave solutions and their asymptotics in the model system. We use method of positive invariant region, method of super and lower-solutions, sliding domain method, asymptotic analysis as well as spectral analysis in the proofs.

The implications of the results are very interesting: the existence of the traveling wave solution implies that the succession is wave-like; the wave has certain particular shape and maintains its speed during the propagation. The asymptotics of the traveling wave solutions reveal that the rate the pioneer tree species leaving the site is proportional to that of the climax tree species entering the site in the final stage of the succession. The uniqueness the wave solution shows that the same wave can also be observed at another time and location. The stability of the traveling wave solution in the weighted Banach spaces tells us that the succession is delicate, in the sense that any big disturbance can disrupt the process.

Another interesting finding is the failure of the K-Selection due to the Allee effect in the climax tree species.