Patches of vegetation consist of dense clusters of shrubs, grass, or trees,
often found to be circular characteristic size, defined by the properties of
the vegetation and terrain. Therefore, vegetation patches can be interpreted as
localized structures. Previous findings have shown that such localized
structures can self-replicate in a binary fashion, where a single vegetation
patch elongates and divides into two new patches. Here, we extend these
previous results by considering the more general case, where the plants
interact non-locally, this extension adds an extra level of complexity and
shrinks the gap between the model and real ecosystems, where it is known that
the plant-to-plant competition through roots and above-ground facilitating
interactions have non-local effects, i.e. they extend further away than the
nearest neighbor distance. Through numerical simulations, we show that for a
moderate level of aridity, a transition from a single patch to periodic pattern
occurs. Moreover, for large values of the hydric stress, we predict an opposing
route to the formation of periodic patterns, where a homogeneous cover of
vegetation may decay to spot-like patterns. The evolution of the biomass of
vegetation patches can be used as an indicator of the state of an ecosystem,
this allows to distinguish if a system is in a self-replicating or decaying
dynamics. In an attempt to relate the theoretical predictions to real
ecosystems, we analyze landscapes in Zambia and Mozambique, where vegetation
forms patches of tens of meters in diameter. We show that the properties of the
patches together with their spatial distributions are consistent with the
self-organization hypothesis. We argue that the characteristics of the observed
landscapes may be a consequence of patch self-replication, however, detailed
field and temporal data is fundamental to assess the real state of the
ecosystems.Comment: 38 pages, 12 figures, 1 tabl