  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 $10^3$ 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.
