1. Fishing in a stirred ocean: sustainable harvest can increase spatial variation in fish populations Heather Berkley Bruce Kendall David Siegel

2. How do marine larvae disperse? In a turbulent ocean, stirring (rather than mixing) means that: Dispersal is NOT diffusive Individual larval releases are NOT independent Traditional Gaussian dispersal does NOT accurately describe larval dispersal and settlement data

3. Drifters: Example of Larvae Dispersing? Buoys float near surface Released at multiple sites/times Tracked by satellites for 40 days Give good indication of surface flow http://www-ccs.ucsd.edu/research/sbcsmb/drifters/

4. Drifters released off central California coast http://www-ccs.ucsd.edu/research/sbcsmb/drifters/makeDepTable.cgi

5. Implications for Larval Dispersal Physical oceanographers say: Flows become decorrelated on a temporal scale of about 3 days on a spatial scale of 10-50 km So, larvae released in a region within a few days tend to travel together Annual recruitment may be a small sampling of a Gaussian dispersal kernel E.g. From 100 independent releases, 10% may make it back to shore within competency window

6. “Spiky” vs. “Smooth” Recruitment This “spiky” recruitment better fits empirical larval settlement data Connections among sites are stochastic and intermittent In this model we can compare both the “spiky” and “smooth” dispersal kernels

8. Our Fisheries Model Single species, near shore fishery Linear coastline Sessile adults Dispersal only in larval stage Rockfish Urchin Abalone Homogeneous ocean with realistic ocean velocity statistics

9. # of adults at x in time t+1 # of adults harvested Natural mortality of un-harvested adults Fecundity Larval survival Larval dispersal Fraction of settlers that recruit at x # of larvae that successfully recruit to location x from everywhere An integro-difference model describing coastal fish population dynamics:

10. 4 Fishing Policies Implemented 4 fishing policies Each controlled by 1 parameter: h Definition of h differs between policies

11. Constant Effort Same fraction of adults is harvested (h) at all locations Fishing Policy #1

13. Constant Escapement Escapement level same for each location: (1 – h) (virgin K) Fishing Policy #2

15. Constant Total Allowable Catch TAC set for the whole region: (h) (virgin K) (size of domain) effort concentrated on locations with most fish Fishing Policy #3

17. Constant Local Harvest TAC set for the whole region, divided equally among all locations Fishing Policy #4

19. Post-settlement Density Dependence When adults are near carrying capacity, recruitment at a location will be lower As harvest reduces adult density, the effect of density dependence on recruitment decreases and individual recruitment “spikes” become larger Harvest Adults Density Dependence Recruitment

20. Parameters Ran model for 50 years Domain size: 2000 km broken into 5km sections Absorbing Boundaries Post-Settlement Density Dependence (Ricker) Calculated spatial variance Graphs show means of 50 simulations at each harvest fraction (h)

27. Maximum Yield “Optimal” harvest fraction (where yield is the highest) also maximizes the spatial variance in adults and recruitment Maximum recruitment also occurs in this region (due to decreased density dependence effect)

28. Summary For all 4 harvest policies: Variance in Recruitment increases with harvest due to decrease in density dependence Combination of variance in Recruitment and Escapement determines variance in Adults Spatial pattern of harvest determines how variance in escapement changes with increased fishing

29. Conclusions All fishing policies showed: Increasing the harvest increases the spatial variance in fish densities until severe over harvest/extinction (does NOT spatially homogenize) Maximum yield occurs at peak spatial variance Therefore, spatial variation is important and needs to be considered in fisheries models and management decisions

31. Next Steps Redo with pre-dispersal density dependence Add optimal harvest level for each policy to graphs Add optimal harvest strategy: Constant Escapement set at each location

32. Thanks! Bruce Kendall, Dave Siegel, Chris Costello, Crow White, Steve Gaines, Bob Warner, Ray Hilborn, Steve Polasky, Kraig Winters, Erik Fields Flow, Fish, & Fishing A Biocomplexity in the Environment Project

33. Post-settlement Density Dependence, c=0.015

35. Constant Effort See max Recruitment with intermediate harvest because it decreases the density dependence and recruitment spikes increase Variance in Escapement and Adults increases at first because of bigger recruitment spikes No extinction until 100% harvest No extinction (due to definition of h)

36. Pre-settlement Density Dependence

38. Constant Escapement Variance in Escapement always decreases because there are fewer places where adult population is less than the escapement level Variance in Adults and Recruitment eventually decreases because escapement is low enough to make everything look the same

39. Constant TAC Similar shape to Constant Escapement except: sharper drop-off due to extinction Dip in Adult variance: first dominated by the high variance in escapement then by increase in recruitment later Range of h over which extinction occurs is very narrow

40. Constant Local Harvest Variance in Adults and Escapement are the same because harvest is the same at each location Extinction around same place as Constant TAC policy