Variation in egg spawning among subpopulations of sea urchins Strongylocentrotus droebachiensis: a theoretical approach

Variation in zygote production, by determining the initial size of the larv alpool, can aff ect the population dynamics of marine invertebrates with a planktonic larval stage. In this paper, we model temporal and spatial patte rns in egg spawning of the sea urchin Strongylocentrotus droebachiensis in the shallow subtidal zone along the Atlantic coast of Nova Scotia. In this region, population outbreaks of sea urchins have caused major transitions f rom kelp beds to barrens (areas devoid of fleshy macroalgae). We define 3 c ommunity states and associated subpopulations of sea urchins: (1) the estab lished kelp bed state, where sea urchins are in low density and small; (2) the transition state, with sea urchins in kelp beds, newly created (transit ional) barrens, and grazing fronts (dense aggregations of large sea urchins along the edges of kelp beds); and (3) the barrens state after fronts have dispersed and intermediate densities of moderately sized sea urchins remai n in post-transitional barrens. Using data from the literature and unpublis hed sources, we parameterize mathematical models to predict egg spawning fo r each subpopulation, both on an areal basis and for the entire coast. The predicted number of eggs spawned per m(2) is 1 order of magnitude higher in grazing fronts (7.1 x 10(7)) than in transitional and post-transitional ba rrens (5.8 x 10(6) and 4.4 x 10(6), respectively), and 4 to 6 times higher in barrens than in established kelp beds (1.0 x 10(6)). Differences among s ubpopulations in the number of eggs spawned are directly related to differe nces in adult density, female gonad output, and body size. The total number of eggs spawned (all subpopulations combined) on a coastal scale increases similar to6-fold from the established kelp bed state (5.6 x 10(14)) to the late transition state (3.1 x 10(15)) and then drops slightly in the barren s state (2.4 x 10(15)). During most of the transition state, sea urchins in barrens spawn the greatest number of eggs. Based on published values, we e stimate that fertilization rates are highest in grazing fronts (62 %), inte rmediate in transitional and post-transitional barrens (36 and 43 %,respect ively) and lowest in kelp beds (15 %), resulting in up to 2 orders of magni tude differences in the number of zygotes produced in these subpopulations 14.4 x 10(7), 2.1 x 10(6), 1.9 x 10(6), and 1.5 x 10(5)). Total zygote prod uction tall subpopulations combined) on a coastal scale increases similar t o 16-fold from the established kelp bed state (8.1 x 10(13)) to the late tr ansition state (1.3 x 10(15)) and then drops slightly in the barrens state (1.1 x 10(15)). During most of the transition state, sea urchins in barrens contribute the greatest number of zygotes to the total zygote pool, with t hose in grazing fronts contributing up to 44 % of all zygotes. Sensitivity analysis and evaluation of model assumptions indicate that our predictions should be correct in a relative sense (i.e. comparing among subpopulations) , although absolute numbers may be overestimated. A disparity between tempo ral patterns of estimated zygote production and observed settlement rates o f S, droebachiensis in the shallow subtidal zone suggests that zygote produ ction interacts with other factors to determine settlement rates of this sp ecies.