Modelling Cystoseira S.L.-Turf Competition Via a Space-Implicit Model with Border Dynamics

Abstract

This paper presents a model of competition between the arborescent canopy-forming algae \emph{Cystoseira s.l.}, and the smaller size algae forming \emph{turf} on rocky bottoms. The two algal assemblages are both grazed by sea urchins. The model is \emph{a 3-species space implicit food web}. Its distinctive feature is the inclusion of \emph{community border effects} in interactions, as only the individuals laying along the canopy border of \emph{Cystoseira s.l.} forests take part in recruitment and competition with algal turfs, and undergo grazing by sea urchins. Also the endogenous recruitment of turf yields a rate depending on the number of border individuals. These \emph{border effects} are taken into account in the same way \emph{herd behavior} is treated in the mathematical ecology of animal species. Some important features of the phase space of the system are investigated, focusing on the capacity of this model to mimic the transitions among ecologically different states of the rocky bottom (co-existence of canopy and turf, survival of the turf only, pure barren). 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 could be of help in describing real ecological processes of canopy degradation and recovery, and possibly managing such ecosystems.

Keywords: Trophic webs, Pack behaviour, Cystoseira, Inter-algal competition, Environmental bio-indicators