  A simplified model of clonal plant growth is formulated, motivated by
observations of spatial structures in Posidonia oceanica meadows in the
Mediterranean Sea. Two levels of approximation are considered for the
scale-dependent feedback terms. Both take into account mortality and clonal, or
vegetative, growth as well as competition and facilitation, but the first
version is nonlocal in space while the second is local. Study of the two
versions of the model in the one-dimensional case reveals that both cases
exhibit qualitatively similar behavior (but quantitative differences) and
describe the competition between three spatially extended states, the bare soil
state, the populated state, and a pattern state, and the associated spatially
localized structures. The latter are of two types, holes in the populated state
and vegetation patches on bare ground, and are organized within distinct
snaking bifurcation diagrams. Fronts between the three extended states are
studied and a transition between pushed and pulled fronts identified. Numerical
simulations in one spatial dimension are used to determine front speeds and
confront the predictions from the marginal stability condition for pulled
fronts.
