Mathematical Analysis of a Size Structured Tree-Grass Model in Savanna Ecosystems
DOI:
https://doi.org/10.11145/123Abstract
Several continuous competition-based models have been developed to study the possible coexistence of trees and grass in savanna ecosystems according to environmental parameters such as climate or fire regime. In those models fire intensity is a fixed parameter. Here, we model fire intensity through an increasing function of grass biomass and let fire return-time vary accordingto climate types. (For instance, in Africa, in moist savannas fire occurs every 1-2 years, while in dry savannas it is every 3-10 years.) Following [1], we also consider a tree-grass compartmental model that distinguishes small trees (like saplings) that are sensitive to fire from tall trees that are not.On those bases, we model the savanna vegetation dynamics through three state variables (biomass of grass and of the two classes of woody plants) involved in a system of three interrelated, non-linear equations.We carry out a qualitative analysis that highlights three ecological thresholds namely, the destruction ratio of trees due to causes which aredierent of re, the survival ratio of grass after the "predation" of trees andthe survival ratio of trees after fire. These thresholds summarize the dynamics of the system. Finally, we develop a non-standard numerical scheme[2], and show some numerical simulations to illustrate our analytical results.
References
[1] A.C. Staver, S. Archibald and S. Levin, Tree cover in sub-saharanAfrica: Rainfall and re constrain forest and savanna as alternativestable states. Ecology 92 (5) (2011): 1063-1072.
[2] R. Anguelov, Y. Dumont and J.M.-S. Lubuma, On nonstandard finite difference schemes in biosciences. AIP Conf. Proc. 1487 (2012): 212-223.
Downloads
Published
Issue
Section
License
The journal Biomath Communications is an open access journal. All published articles are immeditely available online and the respective DOI link activated. All articles can be access for free and no reader registration of any sort is required. No fees are charged to authors for article submission or processing. Online publications are funded through volunteer work, donations and grants.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
