Importance of Spatial Population Characteristics on the Fertilization Rates of Sea Urchins JEAN-SE ´ BASTIEN LAUZON-GUAY 1, * AND ROBERT E. SCHEIBLING 2 1 Biology Department, University of New Brunswick, Bag Service 45111, Fredericton, New Brunswick E3B 6E1, Canada; and 2 Department of Biology, Dalhousie University, Halifax, Nova Scotia B3H 4J1, Canada Abstract. We show that inclusion of population charac- teristics in coupled advection-diffusion and fertilization- kinetics models results in higher fertilization rates than those previously reported in theoretical studies. We incor- porate parameters related to both individuals and popula- tions by running simulations over a large spatial scale and incorporating sperm contribution from multiple males. We compare predictions for three subpopulations of the sea urchin Strongylocentrotus droebachiensis (those occupying kelp beds, barrens, and grazing fronts) to observations from small-scale experiments, and estimate effects of population size and current velocity in each subpopulation. Model outputs suggest that fertilization rates are low in kelp beds, intermediate in barrens, and high in grazing fronts. In all populations, increasing current velocity has a negative ef- fect on the relationship between fertilization rate and down- stream distance of gametes after release, but no effect on the relationship between fertilization rate and elapsed time since gamete release. Our model output was most sensitive to changes in the number of spawning males and the sperm release rate, suggesting that spawning synchrony and high gonadic index could greatly increase the fertilization suc- cess in sea urchins. Introduction Fertilization success of sea urchins and other free-spawn- ing benthic invertebrates has been the focus of many em- pirical and theoretical studies over the last 25 years. In particular, a seminal paper by Denny and Shibata (1989) provided a mathematical framework for predicting fertiliza- tion rates under field conditions by combining the steady- state solution of the turbulent advection-diffusion equations (Csanady, 1973) with the fertilization kinetics model devel- oped by Vogel et al. (1982). That model, and variations of it, enabled researchers to examine various hypotheses about determinants of fertilization success, including the size and reproductive output of spawning individuals (Babcock et al., 1994; Levitan and Young, 1995; Claereboudt, 1999), the distances between them (Denny and Shibata, 1989; Levitan and Young, 1995; Claereboudt, 1999), and the hydrodynamic environment during spawning (Denny and Shibata, 1989; Young et al., 1992; Levitan and Young, 1995). The original formulation of the model has been progressively modified to approach field conditions, most commonly by incorporating terms for reflection of gametes at the seabed (Claereboudt, 1999) and water surface (Bab- cock et al., 1994), and the blocking effect of polyspermy (Styan, 1998; Millar and Anderson, 2003). Attempts at validating the Denny and Shibata model (and its deriva- tives) by means of small-scale manipulative field experi- ments with sea urchins and sea stars have generally met with limited success (Denny and Shibata, 1989; Levitan and Young, 1995; Metaxas et al., 2002). Early applications of that model indicated that sperm concentration is likely a major limiting factor, resulting in low fertilization rates except at very high population den- sity. Experimental work with sea urchins subsequently con- firmed that even at densities of 144 urchins per square meter, we could expect fertilization rates below 70% (Wahle and Peckham, 1999). Up to this point, most theo- retical (Denny, 1988; Denny and Shibata, 1989; Young et al., 1992; Metaxas et al., 2002; but see Levitan and Young, 1995) and empirical (Pennington, 1985; Levitan, 1991; Received 27 October 2006; accepted 13 February 2007. * To whom correspondence should be addressed, at Department of Biology, Dalhousie University, Halifax, Nova Scotia B3H 4J1, Canada. E-mail: js.lauzon@unb.ca Reference: Biol. Bull. 212: 195–205. (June 2007) © 2007 Marine Biological Laboratory 195