Lagrangian Descriptions of Marine Larval Dispersion David A. Siegel Brian P. Kinlan Brian Gaylord Steven D. Gaines Institute for Computational Earth System Science & Marine Science Institute University of California, Santa Barbara

Talk Outline Develop a Lagrangian model for larval dispersal driven by ocean circulations Use this to construct a dispersal kernel & compare with current understandings Assess role of time on recruitment patterns for nearshore communities

Life History of Nearshore Organisms

Coastal flows are highly variable... Libe Washburn [UCSB]

and in a Lagrangian frame… Ed Dever & Clint Winant [SIO]

Larval Transport Planktonic larvae are planktonic  follow currents Determinants of larval transport are … –Time in the plankton Duration of pre-competency & settlement time scales –Coastal circulation characteristics Mean & time varying velocity field –Larval behavior [during latter development stages] Changing depth distribution & possible settlement cues

Larval Transport Planktonic larvae are planktonic  follow currents Determinants of larval transport are … –Time in the plankton Duration of pre-competency & settlement time scales –Coastal circulation characteristics Mean & time varying velocity field –Larval behavior [during latter development stages] Changing depth distribution & possible settlement cues

Dispersal vs. Time in Plankton From Siegel et al (MEPS 260:83-96) r 2 = 0.802, p<0.001 n=32 Planktonic Larval Duration (days) Genetic Dispersal Scale (km)

Modeling Larval Transport Provide a metric for source-to-destination exchanges among nearshore populations Incorporate important oceanographic & organism life history characteristics Constrain using easily obtained observations Useful for modeling spatial population dynamics Siegel et al. [2003; MEPS 260: 83-96]

Dispersal Kernels Dispersal kernels define settling probability as function of distance for a given time scale Units are [settlers / km / total settlers] Distance alongshore [km] K(x) X=0

Modeling of Dispersal Kernels Model trajectories of many individual larvae Correlated random walk -> Markov chain Based on realistic velocity statistics –Simple ocean with constant circulation statistics –“CODE-like” scenario following Davis (1985) Ensemble averaging location of “settled larvae” provides the dispersion kernel

Example Trajectories Flow Statistics : U = 5 cm/s,  u = 15 cm/s &  L = f(y) (0.5 to 3 d) PLD = 0 to 5 days 6 to 8 weeks

Dispersion Kernels PLD = 0 to 5 days 6 to 8 weeks K(x) defines along shore settling probability distribution 5000 trajectories are summed to determine K(x)

A Gaussian form for K(x) holds for nearly all flow/settling protocols: Mean currents regulate offset (x d ) RMS flow drives spread (  d ) & amplitude (K o ) Kernel Modeling Results  K(x)Kexp (xx) 2 o d 2 d    2 []

Kernel Modeling Results D d = f(T M U+T M σ u ) K o = f(1/(T M  u )) “amplitude” x d = f(T M U) “offset”  d = f(T M  u 2 ) “spread” “dispersion scale”

Model Validation? Genetic Dispersion Scale (km) Modeled Dispersion Scale, D d (km)

Conclusions & Possibilities Simulations of Lagrangian particle dispersion are consistent with biological larval dispersal metrics Scaling collapses model results well & is consistent with classical diffusion theory Useful for spatial population dynamic modeling Dispersal kernels can be easily configured for arbitrary environments  K(x,y,  )

Implied Issue of Time... Idealized kernels calculated use many individual particle trajectories (N=5000) Represents ensemble mean conditions The implied time to construct this mean estimate is ~20 years!! –Assumes larval releases are daily & a decorrelation time scale of 3 days

An actual recruitment pulse may be a small sampling of the kernel (N = 10?, or less!!) –(300 releases / year) * (10% survival) / (3 day  L ) Example - intermediate disperser (N = 100) Time, continued... A discrete K(x) suggests that connections among sites are stochastic & intermittent N=5000

Data Courtesy - PISCO [UCSB] Invertebrate Settlement Time Series – Ellwood, CA

Interpreting Settlement Time Series Stochastic, quasi-random time series No correlation of settling among species Few settlement events for each species Events are short (  2 days)

A Stirred, Not Mixed Ocean! Short-time larval transport is driven by coastal stirring rather than mixing Quasi-random sampling of K(x) leads to stochasticity in settlement time series Larval dispersal needs to be modeled using discrete (or “spiky”) kernels

Implications of Stirring Makes observations/assessments difficult Hard to relate larval sources to settlement Local stock-recruitment relationships will be noisy Limits applicability of smooth dispersal kernels Evolution/genetics/biogeography? Probably Annual management of a fishery? No!!

Flow, Fish and Fishing Dave Siegel, Chris Costello, Steve Gaines, Bruce Kendall & Bob Warner [UCSB] Ray Hilborn [UW] Steve Polasky [UMn] Kraig Winters [SIO/UCSD] A Biocomplexity in the Environment Project

The Flow, Fish & Fishing Idea Larval transport is stochastic driven by stirring Fish stocks, yields & their assessment are directly affected by this stochastic signal Management must account for this uncertainty The key is assessing the flows & values of information in this complex dynamical system

Flow, Fish & Fishing…

Summary Lagrangian estimation of larval dispersal kernels –Physical oceanography & organism life history –General applicability  challenge to oceanographers Kernels provide many insights –Larval transport is stochastic –Both local & non-local transports are important –Leads to uncertainty in stock-recruitment relationships

Thank You!!

Where do drifter beach? CCS Drifter Beachings from inshore stations o = release site & + = beaching Data from Ed Dever & Clint Winant (SIO)

Drifter Model Validation?? PLD = 2 d U = 15 cm/s  u = 15 cm/s PLD = 7 d U = 5 cm/s  u = 15 cm/s

Dispersion Modeling Choose a velocity field Mean flow - U = 0, 5 & 10 cm/s & V = 0 RMS fluctuation -  u = 5, 10, 15 & 20 cm/s Alternatives - CODE (Davis, 1985)  varies from 0.5 to 3 d from on- to off-shore Choose a Planktonic Larval Duration (PLD) Many macroalgae 0 to 5 days Some inverts & fish2 to 3 weeks Many others1 to 3 months

Mathematically... xxtuU i t1 i t i t  

Modeling Fluctuating Velocity Here, spatial homogeneity in velocity statistics is assumed uu tt i t1 i t   1 2    RN u

Example F3 Questions What sets the scales of fish stocks & harvest? larval settlement, habitat, natural & fishing mortality, fluid stirring scales, adult migration, regulation, bathymetry, ?? Given the sources of uncertainty, how can we best manage resources? What are optimal instruments? What is the value of information? How do fishermen adapt & learn?

Drifter tracks from E. Dever & C. Winant - CCS/SIO A Lagrangian View ≈ ?

Steve Ralston [NMFS] Stock / Recruitment in Rockfish

Extreme Variation in Dispersal n=90 Average Alongshore Dispersal Distance (Genetic Estimates) Kinlan & Gaines (2003) Ecology 84(8):

Dispersal Differs Among Taxonomic Groups

Inhomogeneous case – ‘CODE-like’ flow Distance Offshore (km) Alongshore velcoity (cm/s) Crossshore velcoity (cm/s) Davis, 1985