1. Fishing in a stirred ocean: sustainable harvest can increase spatial variation in fish populations Heather Berkley Bruce Kendall, David Siegel, Christopher Costello University of California, Santa Barbara

2. Spatial Fisheries Models Recently, spatially explicit fisheries models have gained popularity Recently, spatially explicit fisheries models have gained popularity –Adding space can make more realistic –Necessary to model effects of MPA’s However, many of these models still emphasize spatial uniformity However, many of these models still emphasize spatial uniformity

3. Uniformity Assumption Intuition suggests that fishing may homogenize the fish density across spatial domain (by taking adults from where they are most abundant) Intuition suggests that fishing may homogenize the fish density across spatial domain (by taking adults from where they are most abundant) If this is true, assuming a uniform domain is ok If this is true, assuming a uniform domain is ok However, if harvesting does NOT homogenize the population, this assumption may be leaving out important information about the fishery and population dynamics However, if harvesting does NOT homogenize the population, this assumption may be leaving out important information about the fishery and population dynamics

4. Our Fisheries Model Single species, nearshore fishery Single species, nearshore fishery Linear coastline Linear coastline Sessile adults Sessile adults Dispersal only in larval stage Dispersal only in larval stage –Rockfish –Urchin –Abalone

5. # 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:

6. # 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:

7. How to model the dispersal kernel? Realistic ocean flows to disperse the larvae Realistic ocean flows to disperse the larvae Didn’t use typical diffusion, which assumes: Didn’t use typical diffusion, which assumes: –Well-mixed –Independence of individuals Because… the ocean is turbulent: Because… the ocean is turbulent: –Stirred not mixed –Individuals do not move independently

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

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

10. Implications for Larval Dispersal Physical oceanographers say: Physical oceanographers say: –Flows at location x become decorrelated on a temporal scale of about 3 days on a temporal scale of about 3 days on a spatial scale of 10-50 km on a spatial scale of 10-50 km So, larvae released in a region within a few days tend to travel together So, larvae released in a region within a few days tend to travel together These groups of larvae settle together at a few locations (NOT evenly distributed along coast) These groups of larvae settle together at a few locations (NOT evenly distributed along coast)

11. Connections among sites are stochastic and intermittent Connections among sites are stochastic and intermittent –Some sites get lots of recruits from x –Others get none This “spiky” recruitment better fits empirical larval settlement data This “spiky” recruitment better fits empirical larval settlement data In this model we can compare both the “spiky” and “smooth” dispersal kernels In this model we can compare both the “spiky” and “smooth” dispersal kernels “Spiky” vs. “Smooth” Recruitment

13. 4 Fishing Policies Implemented 4 fishing policies Implemented 4 fishing policies Each controlled by 1 parameter: Each controlled by 1 parameter: h = Harvest Fraction Definition of h differs between policies Definition of h differs between policies

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

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

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

20. Constant Local Harvest Constant Local Harvest –TAC set for the whole region, divided equally between all locations Fishing Policy #4

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

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

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

31. Conclusions Spatial pattern of fishing policies determines how variance in escapement changes with increased fishing Spatial pattern of fishing policies determines how variance in escapement changes with increased fishing Counter-intuitively, all fishing policies showed: Counter-intuitively, 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 Therefore, spatial variation is important and needs to be considered in fisheries models and management decisions

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