Identifying critical regions in small-worldmarine metapopulationsJames R. Watsona,1,2, David A. Siegela,b, Bruce E. Kendallc, Satoshi Mitaraid, Andrew Rassweillere, and Steven D. GainescaEarth Research Institute,bDepartment of Geography,cBren School of Environmental Science and Management, andeMarine Science Institut e, Universityof California, Santa Barbara, CA 93106; anddMarine Biophysics Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha Onna-son, Okinawa904-0412, JapanAUTHOR SUMMARYIt can be difficult to mitigate the impactsof disturbances in nearshore marine sys-tems. This is mainly because nearshoremarine species occupy separate but con-nected subpopulations, with stress placedat one location, be it from overfishing oran oil spill, potentially being detrimentalto stock levels at many other locations(1, 2). Understanding how this connec-tivity affects the whole metapopulation iscrucial to our management of these sys-tems. Here, we use detailed and realisticsimulations of connectivity to identify thelocation of the most critical nearshoresites where protection from perturbationmaximally reduces the risk of stock col-lapse. Specifically, using spatially explicitpopulation modeling, we explore thestructure of subpopulation connectivityfor a range of nearshore species in theSouthern California region. We find thatthese species live in small worlds, meaningthat they are well connected by a small setof well-connected “hub” subpopulations.Using a metric from network theory, ei-genvector centrality, we identify the loca-tion of these key hub subpopulations.These key sites are precisely those thatshould be protected from perturbation ifpreventing stock collapse is the goal.Many adult nearshore marine specieshave restricted home ranges (i.e., on theorder of 0.1–10 km) and rarely move be-yond these limits. For example, kelp bass(Paralabrax clathratus) and sheephead(Semicossyphus pulcher), two species fromthe US West Coast, have adult homeranges of around 100 m. In contrast,newly spawned larvae travel much greaterdistances (i.e., ∼100 km), primarily drift-ing on ocean currents. As a direct conse-quence of this larval dispersal stage,nearshore marine species exist in a spa-tially complex system of connected subpopulations. Typically,connectivity has been estimated using simple statistics of oceancurrents and geographic distance. This approach has beenused extensively to gauge criteria for the persistence of meta-populations and in the design of protected areas, but it ignoresseveral important factors. For instance, theoretical studies haveshown that heterogeneity, asymmetry, and temporal variability inconnectivity are key properties that affect the persistence ofnearshore metapopulations. To a large degree, these propertiesare not captured by standard modeling methods; thus, we are stilllimited in our understanding of connectivity in many systems.Author contributions: J.R.W., D.A.S., B.E.K., S.M. , A.R., and S.D.G. designed research;J.R.W., S.M., and A.R. performed research; J.R.W. analyzed data; and J.R.W., D.A.S., B.E.K.,S.M., A.R., and S.D.G. wrote the paper.The authors declare no conflict of interest.This article is a PNAS Direct Submission.1Present address: Atmospheri c and Oceanic Sciences Program, Princeton University,Princeton, NJ 08544.2To whom correspondence should be addressed. E-mail: [email protected] full research article on page E907 of www.pnas.org.Cite this Author Summary as: PNAS 10.1073/pnas.1111461108. 0.50.60.70.80.9Kelp bass critical subpopulations34oN -120oW 118oW%Fraction of coast removedKelp bass removalFraction of virgin biomass0.20.40.60.8100.2 0.4 0.6 0.8 10CentralityHabitatRandomGreedyoKelp bass Lagrangian PDF119oW117oW121oW34oN -SourcesMainlandS.IslN. Isl197631N. IslS.IslMainland135Kelp bass potential connectivity6397135Destinations118oW120oW162MainlandNorth Islands (63-96)South Islands (97-135)ABCDFig. P1. (A) Example of a Lagrangian PDF for kelp bass. Lagrangian particles are released fromthe purple subpopulation during the kelp bass spawning period and are transported with oceanvelocities, generated by a regional ocean model, for a given pelagic duration. Given thesetime constraints, Lagrangian PDF s quantify the probability of a Lagrangian particle reachingother locations (color scaling). (B) Potential connectivity of kelp bass. Potential connectivityis the probability of larval transport between a source ( y axis) and a destination (x axi s)subpopulation. The numbering of axes relates to the subpopulation labels in A.(C) Noderemoval curves for kelp bass. Metapopulation biomass is expressed as a fraction of the virginbiomass (y axis) and declines as subpopulations are removed (x axis) following ( i)eigenvectorcentrality (red), (ii) the area of suitable habitat (green), (iii) randomly (100 realizations areshown in light blue, and the mean over 2,000 realizations is shown in dark blue), and (iv)usinga greedy algorithm (black circles). (D) Spatial distribution of key kelp bass subpopulations,covering ∼ 13% of the coast. Colors are the fractional drop in metapopulation biomass whenthat subpopulation was removed.www.pnas.org/cgi/doi/10.1073/pnas.1111461108 PNAS|October 25, 2011|vol. 108|no. 43|17583–17584ECOLOGYSUSTAINABILITYSCIENCEPNAS PLUSTo capture these complexities we combined ocean circulationsimulations with realistic metapopulation modeling (3). Over thepast decade, simulation approaches to quantifying patterns oflarval dispersal, and the connectivity between subpopulations,have grown in prominence. Our goal was to use ocean circulationsimulations to explore how nearshore metapopulations respondto local perturbations, such as overfishing at a particular place,and to identify specific nearshore regions that are fundamentalfor metapopulation robustness (i.e., the ability to withstandperturbation). We focused our attention on the dynamics ofseveral commonly fished species in the Southern CaliforniaBight: kelp bass (P. clathratus), kelp rockfish (Sebastes atrovirens),ocean whitefish (Caulolatilus princeps), red sea urchin (Strong-ylocentrotus franciscanus), opaleye (Girella nigricans), Californiahalibut (Paralichthys californicus), and California sheepsheadwrasse (S. pulcher), which have a broad range of life-historycharacteristics. These species were used as part of a recent ma-rine protected area planning program in the Southern Californiaregion, and our methods use the numerical models developed forthis