Modeling of the larval response of green sea urchins to thermal stratification using a random walk approach Rémi M. Daigle ⁎, Anna Metaxas Department of Oceanography, Dalhousie University, 1355 Oxford St., Halifax, Nova Scotia, Canada B3H 4R2 abstract article info Article history: Received 15 February 2012 Received in revised form 28 August 2012 Accepted 5 September 2012 Available online 30 October 2012 Keywords: Bio-physical model Larval behavior Larval dispersal Random walk model Thermocline Vertical migration Larval transport in the ocean can be affected by their vertical position in the water column. In biophysical models that are often used to predict larval horizontal dispersal, generally larval vertical positions are either ignored or incorporated as static parameters. Here, we evaluate the ability of one dimensional random walk based model to predict larval vertical distribution of Strongylocentrotus droebachiensis in response to thermal stratification. Vertical swimming velocities were recorded at various temperatures and used to parameterize the model. Data from a previous laboratory study on the effects of thermal stratification on larval vertical distribution of S. droebachiensis were compared to the model results to evaluate the predictive ability of the model. The model predicts general trends in vertical distribution fairly well, but has a systematic bias which can be explained by un-quantified larval behaviors at the boundaries of the experimental water column. Overall, our behavioral model successfully reproduces the mechanism which regulates larval vertical distribution in response to thermal structure. Collectively, the findings suggest that simple behavioral models parameterized using simple lab exper- iments can prove useful in estimating the vertical distributions of invertebrate larvae in the laboratory and likely in the ocean. Such models can then be linked to bio-physical models to more accurately predict larval dispersal. © 2012 Elsevier B.V. All rights reserved. 1. Introduction For larval marine benthic invertebrates, horizontal swimming speeds are generally considered to have a negligible effect on larval transport since they are much smaller than the velocity of the prevailing currents (Largier, 2003). However, larvae are able to alter their vertical position behaviorally, and even weak swimmers, such as gastropods and bivalves, display vertical migration (Lloyd et al., in press). This vertical migration can be in response to numerous biological and phys- ical cues such as salinity, temperature, turbulence, predators and food (Boudreau et al., 1992; Fuchs et al., 2007; Gallager et al., 1996; Metaxas and Burdett-Coutts, 2006; Metaxas and Young, 1998; Sameoto and Metaxas, 2008a; Young, 1995). By vertically migrating, the dispers- al pattern of larvae can be altered since different water layers can flow in different directions. Consequently, determining the relative impor- tance of these cues, as well as the mechanism and timing of the response, is important in making predictions of larval dispersal. While it is possible to quantify realized dispersal using geochemical tracers or genetics, bio-physical modeling is the only method currently used to predict trajectories of larval dispersal (Cowen and Sponaugle, 2009; Levin, 2006). Bio-physical models are either general circulation models or advection–diffusion models used to quantify the effects of the physical properties of the ocean (e.g. general circulation patterns, tides, wind-driven circulation) on larval dispersal (Metaxas and Saunders, 2009). Ideally, these studies should incorporate the best available biological parameters, such as pelagic larval duration, mortal- ity and vertical migration, which, are often unknown or inaccurately quantified. Currently, most bio-physical models do not incorporate vertical migration (Metaxas and Saunders, 2009) except in a handful of studies, where it affected the larval dispersal potential across a number of species (Banas et al., 2009; Dekshenieks et al., 1996; DiBacco et al., 2001; North et al., 2008). An early attempt using the shrimp Penaus latisulcatus did not model swimming behavior, but rather evaluated the effect of actual vertical position on dispersal (Rothlisberg et al., 1983). In that study, an ontogenetic shift in diel vertical migration resulted in offshore dispersal of younger larvae, and onshore transport of older ones. However, the framework used by Rothlisberg et al. (1983) fixed larvae to a certain water layer at any given time, and the lack of simulated swimming precluded any interaction with vertical advection. Similarly, Banas et al. (2009) showed that diel and tidal vertical migration affected the larval dispersal of Carcinus maenas. However, the role of larval swimming was less important than seasonal differences in hydrodynamics in explaining the difference in dispersal between spring and summer spawnings. Other studies have shown that the larval dispersal of Crassostrea virginica can be affected by vertical distributions, which were in turn modulated by salinity gradients and temperature (Dekshenieks et al., 1996; North et al., 2008). However, in Journal of Experimental Marine Biology and Ecology 438 (2012) 14–23 Abbreviations: ZCM, the center of larval mass; SL, simulated larvae; MPA, Marine Protected Areas; PDF, probability distribution functions. ⁎ Corresponding author. Tel.: +1 902 494 3675; fax: +1 902 494 3877. E-mail address: daigleremi@gmail.com (R.M. Daigle). 0022-0981/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jembe.2012.09.004 Contents lists available at SciVerse ScienceDirect Journal of Experimental Marine Biology and Ecology journal homepage: www.elsevier.com/locate/jembe