Estimating larval production of a broadcast spawner: the influence of density, aggregation, and the fertilization Allee effect Carolyn J. Lundquist and Louis W. Botsford Abstract: The effect of fishing on reproduction is typically quantified by computing the effects of changes in the species abundance and age structure on egg production. For broadcast spawners, reproduction also depends on the local spatial dis- tribution of individuals. Broadcast spawners exhibit an Allee effect at low density: a decline in the fertilization of eggs, owing to increased distance between spawners. We present a method for assessing the likely impact of a fishery on broad- cast spawners, based on gamete dispersion dynamics and individual spatial distributions. We use an individual-based model to simulate larval production over a range of uncertainties in dispersion characteristics. We illustrate our method for the red sea urchin, Strongylocentrotus franciscanus, fishery in northern California, USA. The density of red sea urchins varied over space (0.1–1.6m –2 ), and indices of aggregation were highest at low densities. As gamete dispersion distances increased, larval production exhibited a more linear relationship with density. Average larval production in 1996–1998 was 33.8% of production near the inception of the fishery. After accounting for decreases in mean density, the fertilization Al- lee effect accounted for 21.7 ± 4.1% of the decrease in larval production, and 45.2 ± 21.7% if sea urchins were not aggre- gated. Re ´sume ´: On mesure normalement l’effet de la pe ˆche sur la reproduction en calculant les conse ´quences des changements de l’abondance et de la structure en a ˆge sur la production d’œufs. Pour les reproducteurs a ` la vole ´e, la reproduction de ´pend aussi de la re ´partition spatiale locale des individus. A ` faible densite ´, les reproducteurs a ` la vole ´e subissent aussi un effet d’Allee, un de ´clin de la fe ´condation des œufs a ` cause de la distance accrue entre les reproducteurs. Nous pre ´sentons une me ´thode pour e ´valuer l’impact vraisemblable de la pe ˆche sur les reproducteurs a ` la vole ´e base ´e sur la dynamique de la dis- persion des game `tes et les re ´partitions spatiales individuelles. Nous utilisons un mode `le base ´ sur l’individu pour simuler la production larvaire sur une gamme d’incertitudes dans les caracte ´ristiques de la dispersion. Nous illustrons notre me ´thode avec une pe ˆche de l’oursin rouge ge ´ant, Strongylocentrotus franciscanus, dans le nord de la Californie, E ´ .-U. La densite ´ varie en fonction de l’espace (0,1–1,6m –2 ) et les indices de regroupement sont maximaux aux faibles densite ´s. A ` mesure que les distances de dispersion des game `tes augmentent, la production larvaire montre une relation plus line ´aire avec la densite ´. La production larvaire moyenne en 1996–1998 repre ´sentait 33,8 % de la production observe ´e vers le de ´but de la pe ˆche commerciale. Apre `s avoir tenu compte des diminutions de la densite ´ moyenne, l’effet d’Allee sur la fe ´condation ex- plique 21,7 ± 4,1 % du de ´clin de la production larvaire et 45,2 ± 21,7 % lorsque les oursins ne sont pas regroupe ´s. [Traduit par la Re ´daction] Introduction Reduced density due to fishing can impact the population dynamics of fished species in many ways. Fishery models describing stock–recruitment relationships most often as- sume that while density-dependence may be compensatory at high density, it is linear at low density. However, some species exhibit an Allee effect at low levels of abundance, such that recruitment is severely reduced to levels below that which a linear decline would predict (Courchamp et al. 1999). Many mechanisms can lead to Allee effects (see, e.g., Courchamp et al. (1999), but here we are concerned with decreased fertilization efficiency at low spawning densities (reviewed in Levitan (1995)). Such Allee effects are sus- pected to underlie the failure of some benthic invertebrates to recover after fishing pressure is removed (e.g., white ab- alone in southern California, Tegner et al. (1996)). To account for the effect of fishing on reproduction, stock assessment scientists commonly compute the effects of a narrowed age structure and reduced population density on Received 16 October 2009. Accepted 8 May 2010. Published on the NRC Research Press Web site at cjfas.nrc.ca on 21 December 2010. J21471 Paper handled by Associate Editor Marie-Joelle Rochet. C.J. Lundquist. 1 National Institute of Water and Atmospheric Research, Ltd., P.O. Box 11115, Hamilton 3251, New Zealand; Bodega Marine Laboratory, P.O. Box 247, Bodega Bay, CA 94923, USA. L.W. Botsford. Bodega Marine Laboratory, P.O. Box 247, Bodega Bay, CA 94923, USA; Department of Wildlife, Fish, and Conservation Biology, University of California – Davis, Davis, CA 95616, USA. 1 Corresponding author (e-mail: c.lundquist@niwa.co.nz). 30 Can. J. Fish. Aquat. Sci. 68: 30–42 (2011) doi:10.1139/F10-125 Published by NRC Research Press