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On the Atlantic coast of Nova Scotia, transitions between alternative states of the subti- dal ecosystem, kelp beds and sea urchin barrens, occur on a decadal scale. To explore the process of urchin aggregation within kelp beds that leads to the shift to barrens, we developed a coupled map lattice model to simulate the spatial dynamics of kelp and green sea urchin Strongylocentrotus droe- bachiensis abundance over time. Our simulations show that the following factors can cause sea urchins to form grazing aggregations that create gaps in a kelp bed: (1) random movement by >60% of sea urchins residing in the bed, (2) moderate to high levels of spatial variability in sea urchin recruitment (30 to 90 (urchins m -2 ) 2 ), (3) localized aggregation of sea urchins (150 urchins m -2 ) amid a moderate to high background density of sea urchins within the kelp bed (>10 urchins m -2 ), with or without a chemotactic response of sea urchins to kelp, and (4) removal of kelp from areas >20 m 2 (to simulate physical or biological disturbance, or harvesting). Gaps formed at random locations within the spatial domain and expanded and coalesced to form barrens in which sea urchins were randomly distributed. Sea urchins formed circular fronts around gaps in the kelp bed. The rate of advance of fronts (and increase in gap size) was linearly related to the density of sea urchins at the front. The duration of the transition to the barrens state decreased with increases in (1) the proportion (Pm) of sea urchins moving (from >6 yr for Pm = 0.8 to 5 yr for 30 (urchins m -2 ) 2 to <3 yr for 90 (urchins m -2 ) 2 ). Our findings support observa- tions of gap formation within kelp beds that resulted in widespread destructive grazing on this coast in the late 1960s. Our model provides a predictive tool for the design of monitoring programs and field experiments to explore the underlying mechanisms of an ecosystem phase shift that has major ecological consequences.

Spatial dynamics, ecological thresholds and phase shifts: modelling grazer aggregation and gap formation in kelp beds