Modeling canopy-forming vs. turfing algae competition via a space-implicit model with border dynamics

This paper presents a model of competition between arborescent canopy-forming algae (such as Fucales of genus Cystoseira s.l. or Laminariales of genus Laminaria), and the smaller size algae forming turf on rocky bottoms. The two algal assemblages are both grazed by sea urchins. The model is a 3-species space-implicit food web, and its distinctive feature is the inclusion of community border effects in interactions: the individuals laying along the canopy border take part in recruitment and competition with algal turfs, and undergo grazing by sea urchins, much more efficiently than algae in the canopy bulk. Also the endogenous recruitment of turf takes place mostly along the border of the turf area. The prevalence of these edge effects is taken into account by supposing that the processes affected by them involve only border individuals and is described in the same way herd behavior is treated in the mathematical ecology of animals. It is shown that the border effect inclusion does make a difference in terms of phase space structures, hence in the ecological scenarios it predicts. Various features of the phase space of the proposed system are investigated, focusing on the capacity of this model to mimic the transitions among ecologically different states of the rocky bottom (coexistence of canopy and turf, survival of the turf only, bare rocky bottom). The algae and invertebrates involved in the model play an important role in the health of coastal ecosystems and particularly in the conservation of biodiversity-rich habitats of temperate nearshore rocky reefs. Hence, the model presented may contribute to a deeper understanding of ecological processes underlying canopy degradation and recovery, and provide a framework for their management in future applications.