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The stochastic nature of larval connectivity among nearshore marine populations D. A. Siegel* †‡ , S. Mitarai*, C. J. Costello* § , S. D. Gaines* , B. E. Kendall* § , R. R. Warner* , and K. B. Winters *Institute for Computational Earth System Science, Departments of Geography and Ecology, Evolution, and Marine Biology, and § Donald Bren School of Environmental Science and Management, University of California, Santa Barbara, CA 93106; and Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093 Communicated by Jane Lubchenco, Oregon State University, Corvallis, OR, April 17, 2008 (received for review April 4, 2006) Many nearshore fish and invertebrate populations are overex- ploited even when apparently coherent management structures are in place. One potential cause of mismanagement may be a poor understanding and accounting of stochasticity, particularly for stock recruitment. Many of the fishes and invertebrates that comprise nearshore fisheries are relatively sedentary as adults but have an obligate larval pelagic stage that is dispersed by ocean currents. Here, we demonstrate that larval connectivity is inher- ently an intermittent and heterogeneous process on annual time scales. This stochasticity arises from the advection of pelagic larvae by chaotic coastal circulations. This result departs from typical assumptions where larvae simply diffuse from one site to another or where complex connectivity patterns are created by transport within spatially complicated environments. We derive a statistical model for the expected variability in larval settlement patterns and demonstrate how larval connectivity varies as a function of dif- ferent biological and physical processes. The stochastic nature of larval connectivity creates an unavoidable uncertainty in the as- sessment of fish recruitment and the resulting forecasts of sus- tainable yields. coastal oceanography fisheries marine ecology N earshore ecosystems host a wide variety of marine organ- isms and are among the most productive environments on Earth. Yet many species harvested from these ecosystems are overfished (1–3), a problem that is especially acute for those invertebrates and fishes with a relatively sedentary adult life stage. One potential cause of overfishing is mismanagement because of a poor understanding and accounting of stochasticity in these systems (4, 5). Stochasticity caused by climate variations has long been known to influence the dynamics of ocean ecosystems and the fisheries they support (6). Climate variation affects rates of fecundity and recruitment by altering water temperature, coastal circulation patterns, or the availability of spawning grounds (7, 8); such effects can be understood and, given sufficient data, may be predictable. Here, we introduce a mechanism that generates stochasticity in spatial and temporal patterns of larval transport on annual time scales. This stochas- ticity is inherently unpredictable because of the chaotic nature of coastal circulations and the relatively short larval time scales. Many harvested fish and invertebrates from nearshore eco- systems have a life cycle that includes a pelagic larval stage that can last up to months and a localized benthic adult stage (9, 10). These relatively sedentary adults release hundreds to millions of larvae that are advected and dispersed by ocean currents as they develop competency to settle (9–13). Spawning releases can occur continuously over months or in a few short events. Biotic factors, such as active swimming and vertical migration, also contribute to movement patterns (12, 14, 15). A small fraction of the larvae settle at suitable sites, and an even smaller fraction recruit to adult stages where they can reach reproductive age and contribute to fishery yields. Larval transport therefore plays a key role in the structuring and dynamics of nearshore popula- tions. Although many larval transport models exist based on classical advection–diffusion dynamics (9–13, 16, 17), the dy- namics of larval transport on annual time scales remains poorly understood. Conceptually, larval transport should be stochastic consider- ing the relevant time scales. Characteristic time scales for the trajectories of surface water parcels (the Lagrangian decorrela- tion time) are 2–5 days in the coastal ocean (13, 17–19). Therefore, a single subpopulation continually spawning larvae over a 90-day season will have only 30 statistically independent larval releases (assuming a Lagrangian time of 3 days), of which only a small fraction will successfully return to nearshore set- tlement environments (13). This means that connectivity of nearshore populations, even in the absence of temporal climate fluctuations or bathymetric complexity, will be an intermittent and spatially heterogeneous process driven by the turbulent transport of larvae by coastal circulations. This process leads to spatiotemporal variability in recruitment and larval connectivity that is inherently unpredictable on the annual time scales required for fishery management. This source of uncertainty has not been considered in previous larval connectivity models of nearshore marine populations (9–12, 16). A Bio-Physical Model of Larval Connectivity To illustrate the stochastic nature of larval transport, we imple- mented a bio-physical model of larval connectivity patterned after the central California coastline (ref. 20; see Methods). The model domain is 256 km (along-shelf) by 288 km (cross-shelf) and is unstructured in the alongshore direction. The flow is forced by a time-varying wind field and a mean alongshore pressure gradient, both derived from observations. The bio- physical model reproduces dispersion statistics found in surface drifter observations (17–18, 20). As a base case, we modeled larval transport for a settlement competency window between 20 and 40 days, which roughly typifies many nearshore fishes (9, 21). Larvae were released daily for 90 days from sites spaced every 2 km apart within 10 km of the coastline and were advected by the simulated currents. Biological sources of larval mortality are not included. Example trajectories [Fig. 1 and see supporting information (SI) Movie S1] show the advection of larvae, roughly along lines of constant sea level following the jets formed between the eddy features, and those patterns evolved rapidly. Importantly, eddies swept newly released larvae together into ‘‘packets,’’ which stayed together through their pelagic life stage. Author contributions: D.A.S., S.M., C.J.C., S.D.G., B.E.K., R.R.W., and K.B.W. designed research; D.A.S., S.M., and B.E.K. performed research; D.A.S., S.M., C.J.C., B.E.K., and K.B.W. contributed new reagents/analytic tools; D.A.S., S.M., and C.J.C. analyzed data; and D.A.S., S.M., C.J.C., S.D.G., B.E.K., and R.R.W. wrote the paper. The authors declare no conflict of interest. Freely available online through the PNAS open access option. To whom correspondence should be addressed. E-mail: [email protected]. This article contains supporting information online at www.pnas.org/cgi/content/full/ 0802544105/DCSupplemental. © 2008 by The National Academy of Sciences of the USA 8974 – 8979 PNAS July 1, 2008 vol. 105 no. 26 www.pnas.orgcgidoi10.1073pnas.0802544105 Downloaded by guest on February 3, 2021

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Page 1: The stochastic nature of larval connectivity among ...CV set 1 ev evN ev 1/2. [1] If N ev or ev decrease, the settlement pattern will become more stochastic. For the present simulations

The stochastic nature of larval connectivityamong nearshore marine populationsD. A. Siegel*†‡, S. Mitarai*, C. J. Costello*§, S. D. Gaines*¶, B. E. Kendall*§, R. R. Warner*¶, and K. B. Winters�

*Institute for Computational Earth System Science, Departments of †Geography and ¶Ecology, Evolution, and Marine Biology, and §Donald Bren Schoolof Environmental Science and Management, University of California, Santa Barbara, CA 93106; and �Scripps Institution of Oceanography, University ofCalifornia at San Diego, La Jolla, CA 92093

Communicated by Jane Lubchenco, Oregon State University, Corvallis, OR, April 17, 2008 (received for review April 4, 2006)

Many nearshore fish and invertebrate populations are overex-ploited even when apparently coherent management structuresare in place. One potential cause of mismanagement may be a poorunderstanding and accounting of stochasticity, particularly forstock recruitment. Many of the fishes and invertebrates thatcomprise nearshore fisheries are relatively sedentary as adults buthave an obligate larval pelagic stage that is dispersed by oceancurrents. Here, we demonstrate that larval connectivity is inher-ently an intermittent and heterogeneous process on annual timescales. This stochasticity arises from the advection of pelagic larvaeby chaotic coastal circulations. This result departs from typicalassumptions where larvae simply diffuse from one site to anotheror where complex connectivity patterns are created by transportwithin spatially complicated environments. We derive a statisticalmodel for the expected variability in larval settlement patterns anddemonstrate how larval connectivity varies as a function of dif-ferent biological and physical processes. The stochastic nature oflarval connectivity creates an unavoidable uncertainty in the as-sessment of fish recruitment and the resulting forecasts of sus-tainable yields.

coastal oceanography � fisheries � marine ecology

Nearshore ecosystems host a wide variety of marine organ-isms and are among the most productive environments on

Earth. Yet many species harvested from these ecosystems areoverfished (1–3), a problem that is especially acute for thoseinvertebrates and fishes with a relatively sedentary adult lifestage. One potential cause of overfishing is mismanagementbecause of a poor understanding and accounting of stochasticityin these systems (4, 5). Stochasticity caused by climate variationshas long been known to influence the dynamics of oceanecosystems and the fisheries they support (6). Climate variationaffects rates of fecundity and recruitment by altering watertemperature, coastal circulation patterns, or the availability ofspawning grounds (7, 8); such effects can be understood and,given sufficient data, may be predictable. Here, we introduce amechanism that generates stochasticity in spatial and temporalpatterns of larval transport on annual time scales. This stochas-ticity is inherently unpredictable because of the chaotic nature ofcoastal circulations and the relatively short larval time scales.

Many harvested fish and invertebrates from nearshore eco-systems have a life cycle that includes a pelagic larval stage thatcan last up to months and a localized benthic adult stage (9, 10).These relatively sedentary adults release hundreds to millions oflarvae that are advected and dispersed by ocean currents as theydevelop competency to settle (9–13). Spawning releases canoccur continuously over months or in a few short events. Bioticfactors, such as active swimming and vertical migration, alsocontribute to movement patterns (12, 14, 15). A small fractionof the larvae settle at suitable sites, and an even smaller fractionrecruit to adult stages where they can reach reproductive age andcontribute to fishery yields. Larval transport therefore plays akey role in the structuring and dynamics of nearshore popula-tions. Although many larval transport models exist based on

classical advection–diffusion dynamics (9–13, 16, 17), the dy-namics of larval transport on annual time scales remains poorlyunderstood.

Conceptually, larval transport should be stochastic consider-ing the relevant time scales. Characteristic time scales for thetrajectories of surface water parcels (the Lagrangian decorrela-tion time) are 2–5 days in the coastal ocean (13, 17–19).Therefore, a single subpopulation continually spawning larvaeover a 90-day season will have only �30 statistically independentlarval releases (assuming a Lagrangian time of 3 days), of whichonly a small fraction will successfully return to nearshore set-tlement environments (13). This means that connectivity ofnearshore populations, even in the absence of temporal climatefluctuations or bathymetric complexity, will be an intermittentand spatially heterogeneous process driven by the turbulenttransport of larvae by coastal circulations. This process leads tospatiotemporal variability in recruitment and larval connectivitythat is inherently unpredictable on the annual time scalesrequired for fishery management. This source of uncertainty hasnot been considered in previous larval connectivity models ofnearshore marine populations (9–12, 16).

A Bio-Physical Model of Larval ConnectivityTo illustrate the stochastic nature of larval transport, we imple-mented a bio-physical model of larval connectivity patternedafter the central California coastline (ref. 20; see Methods). Themodel domain is 256 km (along-shelf) by 288 km (cross-shelf)and is unstructured in the alongshore direction. The flow isforced by a time-varying wind field and a mean alongshorepressure gradient, both derived from observations. The bio-physical model reproduces dispersion statistics found in surfacedrifter observations (17–18, 20).

As a base case, we modeled larval transport for a settlementcompetency window between 20 and 40 days, which roughlytypifies many nearshore fishes (9, 21). Larvae were released dailyfor 90 days from sites spaced every 2 km apart within 10 km ofthe coastline and were advected by the simulated currents.Biological sources of larval mortality are not included. Exampletrajectories [Fig. 1 and see supporting information (SI) MovieS1] show the advection of larvae, roughly along lines of constantsea level following the jets formed between the eddy features,and those patterns evolved rapidly. Importantly, eddies sweptnewly released larvae together into ‘‘packets,’’ which stayedtogether through their pelagic life stage.

Author contributions: D.A.S., S.M., C.J.C., S.D.G., B.E.K., R.R.W., and K.B.W. designedresearch; D.A.S., S.M., and B.E.K. performed research; D.A.S., S.M., C.J.C., B.E.K., and K.B.W.contributed new reagents/analytic tools; D.A.S., S.M., and C.J.C. analyzed data; and D.A.S.,S.M., C.J.C., S.D.G., B.E.K., and R.R.W. wrote the paper.

The authors declare no conflict of interest.

Freely available online through the PNAS open access option.

‡To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/cgi/content/full/0802544105/DCSupplemental.

© 2008 by The National Academy of Sciences of the USA

8974–8979 � PNAS � July 1, 2008 � vol. 105 � no. 26 www.pnas.org�cgi�doi�10.1073�pnas.0802544105

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Settlement occurs only if larvae encounter suitable habitatwithin their settlement competency time window (20–40 daysafter release), and all sites within 10 km of the coast are suitablefor settlement. For the base case, 35% of the released larvaesettled successfully. This settlement fraction was considerablygreater than natural survival rates (10, 12, 22), because biologicalmortality was not considered and all sites were assumed to beequally suitable habitats. Even with this extreme abundance ofsettling larvae, the stochastic nature of arriving settlers wasimmediately apparent: larvae settled in infrequent pulses withsource locations that are both nearby and distant to the settle-ment location (Fig. 2). For the base case simulation, settlementpulses lasted from 5 to 30 days and originated from sourcedistances from 0 to �500 km upstream. Sometimes arrival eventsoccured coincident with reversals in the alongshore winds (seeafter day 30 in Fig. 2), which advected surface water parcelsonshore (23). However, onshore Ekman transport is clearly notthe only process by which larval settlement occurs. More fre-quently, successful settlement pulses occur, because eddies ad-vect larvae toward the shore. For the base case, larval settlementcould be characterized with a time scale of 15 days and a spatialscale of 44 km (Fig. 2).

Connectivity matrices illustrate source–destination relation-ships for regional larval transport exchanges (11–12, 20). Thebase case simulation shows that connectivity is spatially heter-ogeneous even for a uniform coastline (Fig. 3a). Some sitesreceived only a few settlers, whereas others received large pulsesfrom a just a few source locations. These connectivity matricesdo not look like those predicted by simple diffusion theory (Fig.3b); rather they are made up of a few ‘‘hot spots’’ with high levelsof connectivity between a few sites. Different realizations (sim-ulated by using different initial random seeds in the windforcing) produced connections that were still spatially hetero-geneous, but the locations and intensities of the hot spotschanged (Fig. 3 c and d). Hot spots also occured on theself-settlement line (the 1:1 line), indicating that eddies can leadto local retention of production (9, 16). Summing over manyspawning seasons (here 30) produced a connectivity pattern thatapproached the diffusion limit (Fig. 3e), although not as smoothas the diffusion model (Fig. 3b).

Modeling Stochastic Larval ConnectivityThese results suggest that larval connectivity can be modeled asa superposition of arriving packets formed by coastal eddies. Theresulting settlement pattern will depend on the total number oflarval packets arriving for the domain, Nev, and the spatial extentfor each settling packet, �ev (normalized by the domain size). Alarge number of events, each providing settlers over relativelylarge spatial scales, will result in a smooth connectivity pattern;whereas fewer, smaller-sized events will result in a patchy patternof connectivity. The spatial coefficient of variation (CV) innumber of settlement packets, CVset, is a useful measure forassessing heterogeneity. If the probability that a given packetlands on a particular site is �ev and each event is independent,then the expected number of packets arriving at a site is �ev Nev.CVset can be calculated by using a multinomial distribution; itturns out that if all sites have the same �ev, then it can beapproximated very closely by using binomial sampling theory, or

CVset � � 1 � �ev

�evNev� 1/2

. [1]

If Nev or �ev decrease, the settlement pattern will become morestochastic. For the present simulations of a straight coastline, �evis set solely by eddies in the flow (�ev � 0.17; Fig. 2). Otherfactors can influence �ev, such as bathymetry. Scale estimates forNev can be derived knowing the number of eddies in the domainthat can advect larvae (parameterized as the larval releaseduration, T, normalized by the eddy time scale, �, multiplied bythe fraction of the coastline corresponding to the size of eacheddy, 1/�ev) and the fraction of possible arriving packets thatcontain settling larvae, fsv, or

Nev � �T /���1/�ev�f sv. [2]

The survivability fraction, fsv, will be controlled by a variety offactors, including the larval development time course, larvalmortality, late-stage swimming, etc. The normalized spatialsettlement variance can be expressed as

CVset � � �1 � �ev��

Tf sv� 1/2

. [3]

Fig. 1. Model depictions of sea level (color contours in cm) and the trajectories of larvae for days 40 (Left), 60 (Center), and 80 (Right). The number of the releasedlarvae were reduced from the base case simulation, and larvae were released every 8 km and every 2 days (see Methods). The circles show the location of thelarvae, and the white trails behind each show their previous 2-day trajectories. The vertical dashed red line indicates the boundary for the nearshore habitat fromwhich larvae were released and where settlement occurred. Low sea-level features corresponded to cyclones and supported counterclockwise geostrophiccurrents, whereas anticyclones (higher sea level) created clockwise circulations. The simulated larval trajectories followed constant sea level contours as expectedfor a geostrophic flow field. The flow field was modeled to represent conditions found in the central coast of California (CalCOFI line 70) during a typical July(high upwelling conditions). The simulated domain is 256 km in the alongshore direction and 288 km in the cross shore direction (only the inner 200 km are shownin the cross-shore direction). An animated time-lapsed depiction of this flow field and associated larval transport is provided in Movie S1.

Siegel et al. PNAS � July 1, 2008 � vol. 105 � no. 26 � 8975

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Thus, larval settlement patterns will become smoother (CVsetdecreases) as �ev, T, or fsv increase, or as � decreases.

The scaling relationship can be used to develop a packet modelof larval connectivity where Nev-independent, equally sizedsettlement packets are superimposed to model larval connec-tivity (see Fig. 3f for details). The packet-modeled connectivityretains the stochastic character seen in the flow simulations andprovides a method for including transport stochasticity in spatialmodels of nearshore marine populations.

The scaling theory also provides a simple way for evaluatingthe role of biological parameters on connectivity. For the basecase, these parameters (larval release duration, habitat extent,etc.) were chosen to allow for a high degree of successfulsettlement. If the spawning season (T) is shortened, values ofCVset increase, and a more heterogeneous connectivity matrix(fewer hot spots) is observed (Fig. 3g). Factor of two changes inthe spatial scale between adjacent releases or of times betweenreleases have only a moderate role in altering connectivity (datanot shown); however, large reductions in the frequency ordensity of larval releases dramatically increase the stochastic

nature of connectivity (Fig. 3h), because larval releases nowoccur infrequently compared with eddy scales.

Reducing the larval settlement competency time window(shortening the pelagic larval duration and/or the period duringwhich settlement can occur) makes connectivity more regular(Fig. 3i) because more larvae are found in the nearshoreenvironment during their settlement competency window com-pared with the base case (thus increasing fsv). Importantly,different connectivity patterns arise from the same flow field fororganisms with different life histories.

Movement by individual larvae, both ontogenetic verticalmigrations and late-period active swimming toward suitablehabitat, also can shape connectivity patterns (12, 14, 15). On-togenetic descents should affect larval transport by movinglarvae from higher-speed surface flows to deeper, slower flows.When migrating larvae are modeled to descend from the surfaceto 30 m after 5 days, the resulting connectivity matrix (Fig. 3j)shows only moderate changes from the base case. Active swim-ming toward suitable habitat in the later stages of larval devel-opment or preferential cross-shelf transport associated withshoaling internal waves or other phenomena (24, 25) can bemodeled by increasing the offshore extent of where larvae cansettle. Increasing the extent of offshore habitat from 10 to 20 kmonly moderately reduces the stochastic nature of larval connec-tivity (Fig. 3k).

The base case simulated larval transport at the height ofupwelling conditions, which resulted in strong, highly variablecurrents (Fig. 1). In the winter, upwelling-favorable winds arereduced along the California coast (23, 26). The same larvalrelease schedule applied to a typical winter flow field (seeMethods) still showed a stochastic pattern of connectivity, al-though the mean displacement of settling larvae was reducedcompared with the base case (Fig. 3l) because of the reducedcurrents.

We have shown that alongshore larval connectivity is astochastic process in a spatially unstructured domain. Bathymet-ric variability and regional variations in wind patterns may createpersistent hot spots for larval export and settlement (11, 12, 27).Two realizations of connectivity for a sinuous coastline pat-terned after the Central California coast (see Methods) do notshow consistent settlement patterns (Fig. 3 m and n), suggestingthat moderate undulations of a straight coastline will not nec-essarily focus settlement onto particular topographic features. Itis expected that topography will have a larger role for regionsdominated by concave coastlines, island chains, or enclosed seas(11, 12, 27).

A summary of the processes that help regulate the nature ofconnectivity is given in Table 1. Overall, we expect highlystochastic settlement patterns in organisms with long pelagiclarval durations and short and periodic spawning seasons thatcoincide during periods of maximum upwelling, with little activelarval swimming ability. Other scenarios can be developed byusing the scaling model (Eq. 3 and Table 1).

Implications of Stochastic Larval ConnectivityWe have shown that larval settlement is inherently a stochasticprocess driven by the interaction between coastal circulationsand organism life histories. Thus, recruitment variability will beinherently unpredictable even in the absence of the sources ofspatial and temporal variability that have been commonly stud-ied (6–8). Connectivity among nearshore populations on annualtime scales will not be well modeled by using mean fieldapproaches such as advection/diffusion models, which will makethe management of nearshore fisheries difficult (28). Fisheriesscientists have long tried to explain the sources of recruitmentvariability so that recruitment can be predicted knowing onlyadult population size and environmental factors (6, 7, 12, 28, 29).Our work indicates that local rates of larval settlement will be

Fig. 2. Time series of the ‘‘departure density’’ showing the alongshoresource locations (y axis), settling times (x axis), and density (color) of larvae thatsuccessfully settle anywhere within the model domain (a), the ‘‘arrival den-sity’’ showing the density (color) of arrival locations for settlers (y axis) from allsource locations and settling times (x axis) (b), and the alongshore wind speedfor the base case simulation (negative is upwelling favorable) (c). The circu-lation model was first driven to a quasi-steady state, and larvae were releaseddaily starting on day 0. Larvae could settle within their competency timewindow (20–40 days) if they were within suitable habitat (the inner 10 km).Larval releases stopped at day 90, and settlement was allowed to continueuntil day 130. The periodic interval in the alongshore direction is stretched inb to account for larval source regions that were many periodic distancesupstream from their arrival locations (a feature of using periodic boundaryconditions). Densities were normalized by the total number of settlers. Timeand space scales for settlement were calculated by using the variogram range(39) of the arrival density with time or location held constant. Departure timeand space scales (a) were 12 days and 56 km, whereas the arrival time and spacescales (b) were 15 days and 44 km, respectively (which corresponds to a valueof normalized arrival space scale, �ev, of 0.17; � 44 km/256 km).

8976 � www.pnas.org�cgi�doi�10.1073�pnas.0802544105 Siegel et al.

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largely decoupled from local stocks, suggesting that stochasticlarval connectivity provides an unexplored source of unresolv-able noise in observed stock-recruitment relationships (28, 29).The packet model introduced here provides a way for assessingthe variability in larval connectivity in stock-recruitment models.

The stochastic nature of larval connectivity will influencemany ecological processes. For example, the pulsed nature oflarval transport, even at long distances from a source, can act toalleviate the Allee effects that limit the success of long-distancecolonization (30). Further, the occasional large, isolated pulsesof larval settlement predicted here should enhance the contri-bution of the ‘‘storage effect’’ to species persistence and coex-istence (31). The fact that these pulses are often the result ofsuccessful settlement of packets of larvae that have remainedtogether throughout larval life suggests that these processes maybe the mechanism leading to the ‘‘sweepstakes’’ patterns seen inthe genetic structure of groups of arriving larvae (32). Finally,the long lives and high fecundity that are characteristic of manymarine organisms have long been posited as evolutionary re-

sponses to recruitment variability (33); variability in recruitmentdriven by turbulent coastal circulations may provide a mecha-nism contributing to this variability. Although the present studyidentifies important features of complex nearshore systems,more work is required to understand the interactions amongvariable coastal circulation, organism life cycles, and the man-agement of these important ecosystems and the fisheries theysupport.

MethodsTime-dependent, 3D flow fields were simulated by using the Regional OceanModeling System (34, 35). The flow fields were patterned after central Cali-fornia Current conditions and satisfied statistical stationarity and homogene-ity in the alongshore direction, whereas the forcings and boundary conditionswere derived from observed conditions. This model provides a numericalsystem capable of addressing the fundamental processes affecting larvaldispersal.

The flow field was modeled after CalCOFI line 70 (offshore of Point Sur,California). The domain size was 256 km in the alongshore direction, and 288km in the cross-shore direction. The bathymetry increased steeply in depth in

Fig. 3. Larval connectivity diagrams for various scenarios. Connectivity diagrams represent the probability density functions (color) of the relationship betweensource (vertical axis) and destination (horizontal axis) locations along a coastline. The connectivity matrices are normalized so that the summed probabilities equalone. The dashed slanted line represents self-settlement (where source and destination locations coincide). The broader extent of the source locations in thediagrams takes advantage of the periodic boundary conditions. (a) The base case simulation shown in Figs. 1 and 2. (b) A diffusion model assuming the samestatistics of the base case simulation. (c) A second realization of base case simulation. (d) A third realization of base case simulation. (e) The average connectivitymatrix summed over 30 spawning seasons. ( f) An instance of the packet model. The three realizations of the base case simulation (a, c, and d) show differentconnectivity patterns illustrating intermittency of larval transport. The diffusion example (b) is constructed from statistics from the base case simulation (a) usinga mean offset of 115 km and a spread of 64 km for a Gaussian kernel (13). The packet model ( f) is implemented by calculating the number of arriving packets(Nev) by using Eq. 2 (with T � 90 d, � � 15 d, �ev � 0.17, and fsv � 1). The value for fsv is chosen because larval mortality was not considered in the base case simulation.Destination locations for the Nev packets were selected randomly from within the domain, and their source locations were also determined randomly selectingfrom the base case Gaussian kernel model (b), which accounts for the downcoast displacement in the packet model results. (g–l) The effects of changes inbiological or physical parameters on connectivity matrices for larval dispersal are shown. The base case simulation (a) was altered by reducing the larval releaseduration (T) from 90 to 30 days (g), increasing the time interval between larval releases (�trel) from once a day to every 4 days (h), changing the larval settlementcompetency window from 20–40 days to 5–10 days (i), mimicking ontogenetic migration by making larvae swim to 30 m depth after 5 days at the surface (j),mimicking active swimming late in the larval competency window by increasing settlement range from 10 to 20 km offshore (k), simulating low upwellingconditions as is found in the winter (climatological January at CalCOFI line 70) (l). (m and n) Two realizations of larval connectivity for a sinuous coastline basedon the central California Coast (see Methods). For the coastal configuration shown, peak to trough variations in coastline sinuosity were 20 km. With theexception of the two other realizations of the base case (c and d), the low upwelling case (l) and the two sinuous coastline cases (m and n), all of the connectivitydiagrams shown were created by using the same flow field.

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the offshore direction and was constant in the alongshore direction. Theminimum depth was set to 20 m at the coast, whereas the maximum depth wasset to 500 m offshore. The domain was discretized by 2-km-resolution gridpoints horizontally; 20 vertical levels were considered with enhanced resolu-tion near the top and bottom boundaries. The eastern boundary was set to afree-slip boundary condition, whereas an open boundary condition (36) wasused on the western boundary. Northern and southern boundary conditionswere periodic to enable alongshore homogeneity of the flow field. After thesimulation fields reached statistically stationary conditions, passive or activeparticles were added to simulate the trajectories of released larvae. Here, amean alongshore pressure gradient was imposed as an external body force,estimated by using January and July mean dynamic height differences be-tween CalCOFI hydrographic sections off Point Arena and Point Conception(lines 60 and 80; ref. 37). Initial fields were generated by using CalCOFI Line 70(Point Sur) hydrography for a climatological July and January (37).

Wind forcing was modeled assuming that the wind field varied on spatialscales much larger than the alongshore scale of the simulated domain whileits magnitude decreased toward the shore (26, 38). Each component of thewind vector was modeled as a Markov Chain given the statistics estimatedfrom hourly buoy wind data (National Data Buoy Center stations 46028,46012, and 46042) and the spatial wind observations (26). Further details ofmodel set-up and validation of the physical flow variables using CalCOFIobservations can be found in ref. 20. The sinuous coastline case (Fig. 3 m andn) used the same oceanographic forcings and larval life histories as the basecase but added a sinuous coastline. Coastal undulations were assessed from aFourier analysis of central California coastline locations for spatial scalesranging from 32 to 128 km. The coastline realization was constructed byassuming random phases among the Fourier components, which ensures thatthe alongshore domain is periodic.

The larval release protocol was modeled after typical benthic reef fishfound in California nearshore waters. For the base case simulation, nearshore

habitats (where larvae were released and settled) were all waters shallowerthan 100 m in depth (�10 km inshore). No variations in suitable habitat wereconsidered in the alongshore direction. The base case released larvae everyday for a season (90 days) near the sea surface every 2 km in nearshore habitat.Larvae settled when they were found within the nearshore habitat for the firsttime during their competency time window. For most of the results presentedhere, the settlement competency time window is assumed to be 20–40 days,which is typical of many nearshore fishes (21). This protocol provides anextreme abundance of settling larvae from which the statistics of larvalconnectivity can be assessed.

Simulated larvae were modeled as Lagrangian particles and were advectedby the modeled currents. The effects of subgrid scale advection processesshould have had little influence on the larval connectivity patterns because ofthe low kinetic energy levels at the grid spatial scale (20). Larvae were modeledto stay within the upper 10 m of the domain. In the case of vertical migration,larvae remained near the surface for the first 5 days and then sank to 30 mdepth after which time they remained at 30 m. Statistics for the dispersal ofmodeled surface trajectories (compare length and time scales and eddy dif-fusivities) compare well with similar statistics derived from surface drifterobservations from the California Current (refs. 17–19 and see also ref. 20).

ACKNOWLEDGMENTS. Discussions with Libe Washburn, Steve Polasky, JohnLargier, Brian Kinlan, Ray Hilborn, Brian Gaylord, and Bob Cowen were helpfulin focusing this article as were the detailed comments from the two anony-mous reviewers. This work is supported by National Science Foundation GrantOCE-0308440 as part of the Flow, Fish, and Fishing Biocomplexity in theEnvironment Project. This article is a contribution of the Partnership forInterdisciplinary Studies of Coastal Oceans: A Long-Term Ecological Consor-tium funded by the David and Lucile Packard Foundation and the Gordon andBetty Moore Foundation.

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Table 1. Life history and oceanographic processes regulating the stochastic nature of larval connectivity

Forcing that will lead to stochasticity(increasing CVset; Eq. 3) Magnitude of effect Expected effect

Effect on conceptualmodel (Eq. 3)

Increase upwelling favorable winds Moderate Leads to decreased survivability because larvaeare advected from inshore regions because ofhigher currents

Decreases fsv

Decrease wind field variability Small to moderate? Provides fewer independent flow fieldcirculations

Can decrease � and �ev

Coastline and bathymetric variability Moderate to large? Adds additional length scales in the flow andallows spatial persistence in settlement tooccur

May modify �ev and �

Longer pelagic larval duration Moderate to large Reduces the chance that larvae are in suitablehabitat during their settlement time window

Decreases fsv

Reducing width of larval settlementwindow

Moderate to large Reduces the time that larvae can find suitablehabitat

Decreases fsv

Shortening reproductive season Moderate to large Decreases number of independent releases Decreases TDecreases in the spatial scale or frequency

of larval releasesSmall to moderate Makes releases more sporadic and rare Decreases fsv

Including larval mortality Moderate? Lowers potential for successful settlement Decreases fsv

Reduction of suitable habitat Moderate to large Decreases effective habitat size Decreases fsv

Reduction in the effectiveness of latelarval stage swimming

Moderate to large Decreases effective width of the nearshorehabitat

Decreases fsv

Question marks denote a large degree of uncertainty for some of these relationships.

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