Population Dynamics in a Stirred, not Mixed, Ocean Bruce Kendall, David Siegel, Christopher Costello, Stephen Gaines, Ray Hilborn, Robert Warner, Kraig Winters

How do organisms disperse? Many spatial population models have assumed some sort of diffusive spread Based on “random walk” model of movement Each individual’s movement is independent Results in smooth (typically Gaussian) distribution of dispersers across space Mostly tested in terrestrial organisms

But the ocean is turbulent! At “small enough” space-time scales, movement of organisms being advected in the ocean is NOT a random walk NOT independent among individuals What are the relevant space-time scales? What are the implications for fisheries modeling?

Narrowing the scope Emphasis on nearshore species with: relatively sessile adults planktonic larval dispersal Competency window (CW) defines range of ages over which larvae can successfully settle red abalone (CW = 7-20 d) kelp bass (CW = d) Focus on the larval dispersal phase Movement dominated by fluid dynamics

A model larva? Drifters are buoys designed to float at or just below surface Released at multiple sites/times Tracked by satellites Gives good indication of surface flow

Drifters released off of central California

What the physical oceanographers say On average, flows become decorrelated on a temporal scale of about 3 days on a spatial scale of km Relatively few drifters return to shore in a given time window

Biological implications All larvae released within ~3 days and 10 km will settle at about the same place Only about 10 “statistically independent” larval releases per month from a given site Spatial scale of “site” is about 10 km Each bolus of larvae has small chance of settling in CW

Two more timescales Length of competency window Determines probability that a given group of larvae reach shore at appropriate time Mean time in plankton Determines amount of dispersion among independent larval groups

Threads of Connectivity?? Distance ->

Modeling stochastic dispersal 300 d breeding season CW = d 10% settlement rate

A simple metapopulation model Discrete in space and time Recruits mature in one year No age structure of adults Constant per-capita survival and larval production Recruitment success of settlers declines with adult density at settlement site

Stochastic recruitment generates spatial variability

Stochastic dispersal increases mean adult density

Stochastic dispersal increases mean harvest

Harvest magnifies spatial variability in adult density Heather Berkley et al.: “Fishing in a stirred ocean: Sustainable harvest can increase spatial variation in fish populations” Thursday 10:50 AM Oral session 102: Modeling II

The answers? What are the relevant space-time scales for turbulent dispersal? Larvae dispersing within 3 days and 10 km should tend to travel (and settle) together What are the implications for fisheries modeling? Stochastic recruitment creates spatial variability Variability + density dependence = “nonlinear averaging” – increasing mean density Deterministic models may be misleading!

Some future directions Fluid dynamic simulations to confirm time and space scales Some more biology – e.g., size and age structure of adults Evaluate various management strategies – quotas, MPAs, spatial mgmt, etc. What is “value of information” in a stochastic and uncertain world?

Acknowledgements Heather Berkley Marc Conte Elizabeth Madin Satoshi Mitarai Robin Pelc Crow White

Stock-Recruit relationship