期刊
BULLETIN OF MATHEMATICAL BIOLOGY
卷 81, 期 7, 页码 2290-2322出版社
SPRINGER
DOI: 10.1007/s11538-019-00606-z
关键词
Metastability; Vegetation patterns; Species coexistence; Pattern formation; Reaction-diffusion systems; Semi-arid landscapes
资金
- Maxwell Institute Graduate School in Analysis and its Applications, a Centre for Doctoral Training - UK Engineering and Physical Sciences Research Council [EP/L016508/01]
- Scottish Funding Council
- Heriot-Watt University
- University of Edinburgh
Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction-diffusion model based on the single-species Klausmeier model, to analytically investigate the existence of states in which both species coexist. Ecologically, the study finds that coexistence is supported if there is a small difference in the plant species' average fitness, measured by the ratio of a species' capabilities to convert water into new biomass to its mortality rate. Mathematically, coexistence is not a stable solution of the system, but both spatially uniform and patterned coexistence states occur as metastable states. In this context, a metastable solution in which both species coexist corresponds to a long transient (exceeding 103 years in dimensional parameters) to a stable one-species state. This behaviour is characterised by the small size of a positive eigenvalue which has the same order of magnitude as the average fitness difference between the two species. Two mechanisms causing the occurrence of metastable solutions are established: a spatially uniform unstable equilibrium and a stable one-species pattern which is unstable to the introduction of a competitor. We further discuss effects of asymmetric interspecific competition (e.g. shading) on the metastability property.
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