1. Individual-Based Modeling in Ocean Ecology: Where Behavior, Physiology and Physics Meet Hal Batchelder Oregon State University Supported by NSF and NOAA within the U.S. GLOBEC Northeast Pacific Program

2. IBM Outline Introduction to i-state distribution and i-state configuration models How they differ Why IBM’s Advantages and Disadvantages Eulerian-Lagrangian Coupled Approaches and Details Examples Design of Marine Protected Areas for Scallops Nearshore retention (copepods in EBC upwelling regions; ADR) DVM of dinoflagellates using a cell N quota model Connectivity and Retention through Lagrangian Approaches Considerations Take Home Messages Challenges and Opportunities

3. Individual Based Modeling

4. Ecosystem Model Franks et al., 1986 N ZP

5. Vitals: 380 lbs, 7’1”; SOME BIOMASS

6. Vitals: 380 lbs, 7’1”; Vitals: ~380 lbs, MORE BIOMASS

7. = ? Vitals: 380 lbs, 7’1”; Vitals: ~380 lbs,

8. = ? Vitals: 380 lbs, 7’1”; one mouth; Vitals: ~380 lbs, 40 mouths; Regularly puts foot in mouth (figuratively) Actually able to put foot in mouth

9. Euphausia pacifica life stages N2Metanauplius Adult Calyptopi

10. Individual Size Impacts preferred prey type (abundance/size) Impacts growth rate Impacts mortality when size-dependent Impacts behavior Impacts internal pools (lipid reserves)

11. Euphausia pacifica life stages N2Metanauplius Adult Calyptopi ~3.2 μg ind -1 ~7 μg ind -1 ~4000 μg ind -1 Stage-specific CW

12. Euphausia pacifica life stages N2Metanauplius Adult Calyptopi ~3.2 μg ind -1 ~7 μg ind -1 ~4000 μg ind -1 Stage-specific CW 1250 indiv. 571 indiv. 1 indiv.

13. Allometric Relationships are Important Robin Ross (1982)

14. Allometric Relationships are Important (here it is weight specific relation) Robin Ross (1982)

15. Euphausia pacifica life stages N2Metanauplius Adult Calyptopi ~3.2 μg ind -1 ~7 μg ind -1 ~4000 μg ind -1 Stage-specific CW 1250 indiv. 571 indiv. 1 indiv. ΣR=633.6 ug C d -1 ΣG=425 ug C d -1 ΣR=529.2 ug C d -1 ΣG=519.6 ug C d -1 ΣR=122.9 ug C d -1 ΣG=26 ug C d -1

16. Body Size Prey Temperature R (ug C d -1 ) = f(Weight, Prey, Temp) Bioenergetics of an Individual Process

17. A Stage Progression Model E. pacifica Belehradek function for time to stage as function of temperature Basic Form is: D i = a i (T + b) c D i is the time (days) from egg to stage i a i is a stage specific constant b is a stage-independent shift in temperature c is assumed to be -2.05 (commonly observed from experiments; determines the curvature) Data from Ross (1982) and Feinberg et al. (2006) What if low food conditions delay development? Revised Form is: D i = [a i (T + b) c ] / [1 – e -kP ]

18. Interindividual variation in lipid weight of C 5 stage of Calanus pacificus Laboratory reared individuals (range of hi to low food) varied by a factor of ca. 2.5; lipid content in field collected individuals even more variable (ca. 2.8) 2.5 2.8 Hakanson (1984, Limnol.Oceanog.)

19. i-state Distribution Models fundamental tools of demographic theory produce differential or difference equations examples: NPZ+ models Lotka-Volterra predator-prey models McKendrick-von Foerster equations Suppose: One population; two important dimensions control dynamics: individual age and individual size; given the assumption that all individuals experience the same environment (global mixing), then all individuals with the same i-state will have the same dynamics and can be treated collectively.

20. Suppose: Only indiv body size and life-stage are important to dynamics… Then: Could model population using n life-stages, each having m n wt classes. LS 1 LS 2 LS 3 LS 4 …LS n W1W1 W2W2 W3W3 W4W4 … Wm n What if: There are many more dimensions important to dynamics? Within Stage Weight Life Stage

21. “It is impossible to predict the response of all but the very simplest natural systems from knowledge of current environmental stimuli alone. The problem is that the past of the system affects its response in the present.” Caswell and John (1992, p. 37) System State = f(History,Curr. Envir.) both are required to describe the systems behavior (deterministic) or probability distribution of systems behavior (stochastic)

22. Individual Size Impacts preferred prey type (abundance/size) Impacts growth rate Impacts mortality when size-dependent Impacts behavior Some early classic examples…

23. All figures are from Huston, M., D. DeAngelis, and W. Post. 1988. New computer models unify ecological theory. BioScience 38 (10), 682- 691. Intraspecific Effects - Initial Condition Sensitivity Interspecific Effects – Relative Size

24. i-state configuration models (aka Individual Based Models) Each individual has a vector of characteristics associated with it Examples are: Body size (weight, length) Age Reproductive Condition Nutritional (structural or physiological) Condition Behavior Location = f (history) = Defines Present Environment

25. Conditions in which i-state distribution models are insufficient and i-state configuration models (IBMs) are necessary: 1)Complicated i-states – Many elements in i-state configuration vector; numerical solutions as ‘distribution’ difficult 2)Small populations Demographic analysis of endangered species Viability of small populations 3)Local spatial interactions important Spatial heterogeneity of the environment Local interaction of individuals 4)Size- or individual-specific behaviors ZP

26. Advantages of i-state configuration (IBMs) 1)Biology is often mechanistically explicit. (not hidden in differential equations). 2)Biological-Physical-Chemical Interactions are clearly detailed. 3)Individual is the fundamental biological unit, thus it is natural and intuitive to model at that level, rather than at the population level. 4)Allows explicit inclusion of an individual’s history and behavior. 5)History-Spatial Heterogeneity interactions ‘easily’ handled.

27. Costs Involved in IBM Approach 1)Difficult to implement feedback from IBM (Lagrangian) to underlying Eulerian model, esp. across multiple trophic levels 1)Consumption (depletion) of prey (E) by predators (L) Assume not important (Batchelder & co. 1989,1995) Conversion to concentrations per grid cell (Carlotti & Wolf 1998) 2)Requirement for Large Numbers of Particles Difficult to simulate realistic abundances Each particle may represent one (IBM) or a variable number of identical individuals (Lag. Ens. Method/Superindividuals) 3)Difficult (Impossible?) to simulate density dependence 4)Extensive Computation Penalty Biological/biochemical processes for individuals are many and complex 5)Increased knowledge about the system (this might be a good thing)

28. Design of Marine Protected Areas The NW Atlantic Scallop Example

29. Scallop Larval Drift from Proposed Closed Regions Issues: larval repopulation of source regions, as well as non-closed regions;Long-term effects of marine protected areas

30. Transport patterns

31. Retention effect of circulation over a single 40- day pelagic period within the fall climatology. There is exchange between closed areas 1 and 2. Area 1 is largely self- seeding; Area 2 seeds both areas. Source

32. No Closed Regions Closed Regions 10 Year Scallop Simulation w/ 1 spawning per year; 40 day larval drift; individual surviving scallops plotted (red are oldest individuals)

33. Impacts of Dispersal High Low Population Connectivity Modified from Harrison and Taylor (1997) Single, patchy Population (open) Metapopulation (structured connectance) Separate (closed) From C. Grant Law (unpubl.)

34. Transport patterns From C. Grant Law (unpubl.)

35. Questions  How connected are different populations and does connectivity change with population structure or physical forcing?  Are all populations equally valuable when protected?  Do some regions act primarily as sources and others as sinks?  How often is a given area dependent on recruits from elsewhere?  Under which conditions is a given area self-seeding and how often are those conditions present?  Are there regions of the coast that are particularly robust in terms of self seeding and which also act frequently as a source for remote areas? Modified from C. Grant Law (unpubl.)

36. Management History  NE side of Georges Bank  NE side of Nantucket shoals  Head of Hudson Canyon Pre-Closure Distribution From C. Grant Law (unpubl.)

37. Management History  CLII north & south  CLI SW side of Georges Bank  NE side of Nantucket shoals  Head of Hudson Canyon  Poor recruitment in NLS and VBC closed areas Post-Closure Distribution From C. Grant Law (unpubl.)

38. Zooplankton Population Dynamics in 2D The Oregon Upwelling System

39. Age, Size, Number of Organisms Egestion, P Predation T, B, , LStarvation T, B, P,  Respiration T, B,  Physical Exchange B,  Ingestion T, B, , L, P Migration T, B, P Processes and Environmental Variables Influencing Organism Growth and Number T = Temperature; B=Behavior;  =Turbulence; P=Prey; L=Light Bioenergetic Model Spatially-Explicit Model

40. Physical Forcing (light,wind,IC's) 2D or 3D Eulerian Model Eulerian Fields (velocity, temperature light, food, K) IBM with simulated Lagrangian Particles Individual Zooplankton Characteristics (wt,stage,condition, sex, position) Population Characteristics (Demography) and Spatial Distribution Modeling Approach (Eulerian-Lagrangian Coupling)

41. 0.05.010.015.020.025.030.035.0 Density (# m -3 ) 150-200m 100-150m 50-100m 20-50m 10-20m 0-10m Depth Range of Layer Sampled Euphausia pacifica at NH25 (Aug 4, 2000, daytime) Nauplii Calyptopes Furcilia Juveniles Adults Biological Organisms are not Passive Tracers Figure courtesy of J. Keister All Stages are in upper 20 m during Night

42. Magnitude of Diel Vertical Migration by Life Stage Shelf Stations 0 25 50 75 100 Egg Calyptopis F1F2F3F4F6F7 Juvenile Adult Life History Stage Depth (m) Slope Stations 0 25 50 75 100 125 150 175 200 Egg Calyptopis F1F2F3F4F6F7 Juvenile Adult Life History Stage Depth (m) The top of the vertical bar represents the nighttime Average WMD. The bottom of the bar represents the daytime Average WMD. The height of the bar therefore represents the magnitude of DVM. Based on 6 day-night paired MOCNESS From shelf stations and 8 day-night pairs From slope stations. Vance et al. (unpublished)

43. Individual Based Copepod Model (IBM) Bioenergetics based model –dW/dt = Assimilation - Respiration Growth is a function of weight, hunger condition, ambient food Reproduction within C 6 females with weight specific allocation between somatic and reproductive growth Stage-specific, spatially-constant and weight-based mortality Diel Vertical Migration behavior dependent on –light –size (weight) –hunger condition –food resources –proximity to boundaries 10 m during night 160 m during day Batchelder et al. (2002, PiO)

44. Batchelder and Williams (1995) Individual-based modelling of the population dynamics of Metridia lucens in the North Atlantic. ICES J. Mar. Sci., 52, 469-482.

45. Runge, J. A. 1980. Effects of hunger and season on the feeding behavior of Calanus pacificus. Limnol. Oceanogr., 25, 134-145. Batchelder, H. P. 1986. Phytoplankton balance in the oceanic subarctic Pacific: grazing impact of Metridia pacifica. Mar. Ecol. Prog. Ser., 34, 213-225. ~2X starved fed

46. Hunger (H) Light H Size (S) Food (P) Boundary (Ns,Nb) Slows downmig Slows upmig Batchelder et al. (2002, PiO)

47. Physical Model 2d (x-z) Vertical slice Time-dependent, hydrostatic, Boussinesq, Navier-Stokes Finite difference KPP mixing Explicit mixing-length Bottom Boundary Layer 500 < dx (m) < 1500 1.5 m < dz (m) < 3.7 Topography for Newport, OR Initialized w/ April climatology Southward wind-stress forcing of 0.5 dyne/cm 2, either constant or alternating on/off with 5 or 10 day intervals  100 km   200 m  Batchelder et al. (2002, PiO)

48. 2D Upwelling Scenario Simulations N ZP Batchelder et al. (2002, PiO)

49. Day 20 Day 40 Day 80 Size of bubble is proportional to individual weight Recently layed clutches in hi food region Weight loss below mixed layer Starvation Mortality Few Nearshore No-DVM Simulation (PTM forced with Eulerian Concentrations of Prey, Velocities, and Kv) Batchelder et al. (2002, PiO)

50. DVM Simulation (PTM forced with Eulerian Concentrations of Prey, Velocities, and Kv) Day 20 Day 40 Day 80 Size of bubble is proportional to individual weight Middepth aggregation offshore Large Individuals Inshore Nearshore reproduction and retention No reproduction & mortality loss offshore Population nearshore only Batchelder et al. (2002, PiO)

51. Nutrient Quota Based DVM Of Dinoflagellates Ji and Franks (2007, MEPS) diverse vertical patterns of populations (subsurface aggregations, multiple depth aggregations, day-night differences) Nitrogen Quota IBM (internal nutrient status impacts VM) 1D w/ specified vertical nutrient profiles and vertical diffusivity How is the vertical pattern controlled by MLD, internal waves and light intensity? Use average net growth rate as a measure of fitness 9 physiological parameters (Q min, Q max, α [PvI slope], μ max, V m, σ (descent thresh), γ [ascent thresh], λ [resp rate], g 0 [dark N uptake offset]).

52. Ji and Franks (2007, MEPS) MLD and Migration Pattern MLD = 10m For both 10m and 20m MLD, cells are able to balance their need for light and nutrients by occupying the pycnocline/nutricline. No DVM.

53. Ji and Franks (2007, MEPS) Subsurface vs. DVM Higher light level at 10m yields higher net growth rates than at 20m for subsurface individuals. 10m 20m With an imposed photo-/geotaxis DVM (open bars) ANGR distribution is shifted to the left (poorer growth) for 10m MLD, but shifted to the right (improved growth) for 20m MLD. Imposed DVM broadens the distribution of ANGR in both cases, reflecting the more diverse light and nutrient conditions experienced by individual cells.

54. “AN AVERAGE FISH DIES WITHIN ITS FIRST WEEK OF LIFE!” -- Gary Sharp (in writing) An average larvae is a dead larvae… (Gary at a meeting) The average fish is a dead fish… Ji and Franks (2007, MEPS) 10m 20m Applies also to individuals at most LTLs (phytoplankton, zooplankton) – 60-90% of copepod eggs do not survive to hatch

55. Ji and Franks (2007, MEPS) AVM using quota model Asynchronous vertical migrations occur for many more physiological combinations. Bimodal depth distributions day and night. Synchronous (tied to light) diel vertical migrations only occur for a limited physiological parameter space (large growth rate and small difference between quota thresholds for ascending and descending). 20m MLD

56. Ji and Franks (2007, MEPS) Asynchronous vertical migrations have higher ANGR than DVM, esp. when the mixed layer is deep. Since most grazers on dinoflagellates are zooplankton, which generally do not search for prey using vision, there is no negative effect of being near the surface during the day (as there might be for zooplankton susceptible to visual fish predators). 10m 20m

57. Ji and Franks (2007, MEPS) Internal Waves (12 m amplitude) 20m MLD Case 2a Case 2b

58. Allocation of Consumption within the Adult Female 29 params

59. Lagrangian Particle and Individual Based Modeling for Informing Population Connectivity and Retention

60. RCCS ROMS Model Domain: 41 – 45.5N, -126.7 – 123.5E 166 x 258 x 42 gridpoints (~ 1 km) Forward run for 2002 Lagrangian Particle Tracking 50,000 initial locations on shelf (bottom depths < 500m) (Averages ~ 1-2 indiv/km 2 ) 10-100m depth 3D-advected for 15 days (dt=1 hr) New simulation begins every 7 days RCCS ROMS runs provided by Enrique Curchitser (Rutgers)

61. RCCS 19 Jun 2002 start ET = 7 days Strong Upwelling and Alongshore Flow Untangling spaghetti... Retention Indices and Metrics Displacement distance at some elapsed time e-flushing time for a specified control volume (distance) Connectivity Indices and Metrics Transition Probability Matrix Plots Sources and Destinations (Maps) From Batchelder (in prep.)

62. RCCS 19 Jun 2002 start ET = 7 days Strong Upwelling and Alongshore Flow ‘Destination maps’ identify potential of a site to export to other locations. High potential to supply other locations From Batchelder (in prep.)

63. RCCS 19 Jun 2002 start ET = 7 days Strong Upwelling and Alongshore Flow ‘Source maps’ identify potential of other sites to supply propagules to this location. Large number of sites that can supply this location From Batchelder (in prep.)

64. RCCS 19 Jun 2002 start ET = 7 days Strong Upwelling and Alongshore Flow ‘Destination maps’ identify potential of a site to export to other locations. ‘Source maps’ identify potential of other sites to supply propagules to this location. High potential to supply other locations Large number of sites that can supply this location From Batchelder (in prep.)

65. spatial pattern of residence time Longest residence time and greatest variability in inner Heceta Bank Region StdDevMean From Batchelder (in prep.)

66. Considerations 1)Zooplankton and fish behavior has important demographic consequences—how detailed do we need to model the processes involved? Small improvements in condition, growth, or fitness can lead to survival (being in the tail of the distribution). 2)Zooplankton and larval fish can detect and respond to non- physical gradients (e.g., food conc.) creating aggregations (patchiness) due to behavior (rather than physics directly). 3)IBM’s can deal with complex stage, size and history dependent physiology and behavior at process based level—but at the expense of generality? 4)Under what scenarios is it critical to model zooplankton with IBM’s in a Lagrangian framework vs. a stage-structured, age- within-stage-structured, or physiologically structured Eulerian framework? 5)Feedbacks across trophic levels and considerations of density dependence are difficult to model with IBM approaches.

67. Take Home Messages (1) Concentration based (Eulerian) modeling is used in biogeochemical contexts, with model currency being C, N, or energy. –Capable of, but rarely, considers size structure within a population –Computationally efficient; scales to (number of state variables X number of grid points) –Biology is often hidden in non-mechanistic equations –Difficult (impossible?) to consider behavior and history It is rare that individual members of populations can be justifiably aggregated into a single state variable representing abundance (or total biomass). Consequences of aggregation need to be considered: –To lump individuals of various characteristics (as in NPZ+) requires assumption that individuals are identical, and can be modeled as the mean individual. –Ignores nonlinearities in physiology and behavioral complexity. –Ignores the interesting and evolutionarily significant part (interindividual variability) of population dynamics.

68. Take Home Messages (2) Individual-based (Lagrangian) models explicitly consider inter-individual (and potentially interspecies) variation. –Biology is mechanistically explicit –History-behavior-spatial heterogeneity interactions relatively straightforward –Downsides Can be computationally expensive; scales to the number of individuals/populations modeled Difficult to implement feedback to underlying Eulerian state variables and density dependence Requires more knowledge of the fundamental biological/ecological system

69. A simple 3-component NPZ model in an upwelling circulation reveals –Physical forcing induces nearshore phytoplankton bloom –Horizontal offshore extent of the bloom determined largely by biological parameters A Lagrangian zooplankton model within a 2D upwelling circulation revealed the key role that DVM plays in facilitating nearshore retention –Fundamental assumption that individuals reside at times within the deeper layer onshore flow. –Physiological and behavioral interaction with high nearshore phytoplankton fields further enhances demographic retention resulting from DVM. Take Home Messages (3)

70. As revealed by the dinoflagellate IBM case study –Physical setting can interact with physiological demands/constraints to yield diverse outcomes. IBM’s are commonly used to evaluate the efficacy of spatial management options (design of Marine Protected Areas) for marine fisheries Climate change will alter species distributions, change temperatures (altering PLD), and perhaps alter current pathways and intensities. Lagrangian tracking that considers advection-diffusion- reaction processes will inform connectivity in changed ecosystems. Take Home Messages (4)

71. Challenges and Opportunities to Coupling Physical Models, Lower Trophic Level (NPZ) Models and Higher Trophic Models (e.g., fish) (1) Need better winds and heat fluxes in coastal regions; coastal regions are cloudy, have nearby hills, larger hi- freq variability NPZ+ often run coupled with physics Higher trophic levels (HTL) are usually run separately from physics-NPZ+, with the coupling being through advection and diffusion of the HTL, the prey available to them and temperature effects Empirical functional relationships (food-ingestion; food- egg production) are useful for linking species-specific life history models to NPZ+ models

72. Challenges and Opportunities to Coupling Physical Models, Lower Trophic Level (NPZ) Models and Higher Trophic Models (e.g., fish) (2) Food type, chemical composition, size distribution and spatio-temporal distribution of food are important sources of variability Simple NPZ models cannot represent the diversity of prey types Prey switching and omnivorousness complicate dynamics Averaging in space, time and trophic complexity (e.g., through model resolution) may stabilize models, but ignores important ecological processes. Mortality—the great unknown.

73. Thanks also to the NCAR ASP Colloquium Organizers.

75. Conclusions and Lessons Learned (cont’d) Advective transport alone can be very misleading. Models should include diffusive effects also. And, in species capable of swimming, even small active movements can dramatically alter transport pathways. Adding vertical diffusion to an advection-only model increases probability of nearshore retention. Adding DVM of only 8-m (cycling between 3-m and 11-m) to an advection or advection-diffusion model increases probability of nearshore retention.

76. Initial Locations of Individuals that produced eggs DVM Passive Passive, reduced offshore food

80. From DeAngelis, D. L., and K. A. Rose. 1992. Which individual-based approach is most appropriate for a given problem? Pp. 67-87 in Individual-Based Models and Approaches in Ecology, DeAngelis and Gross, Editors. Chapman and Hall Publishing. Spatial Arrangement and Local Interactions YOY Bloater (a FW fish) Small differences in individual growth rates can result in large changes in size, and this can be strongly influenced by mortality, esp. if size based.

81. Additional Capabilities of the Oregon Shelf Forecast Model Use Lagrangian approach to examine spatio-temporal connectivity and retention times in shelf environments. Develop regional and seasonal statistics on connectivity scales and retention times. Some preliminary results have been completed for an earlier RCCS simulation using hindcast of 2002. Adding a Lagrangian tracking component to the coupled model will allow satellite or in situ observations that define the presence or intensity of phytoplankton blooms, including HABs, to be forecast in space/time. Assuming an accurate physical model, discrepancies between the forecast and the next data observation are due to production and loss processes not considered in passive tracking. Lagrangian back-tracking of observed HAB shore interactions (toxic shellfish; beach closures) may be able to hindcast probable trajectories of HABs to identify ocean conditions that led to HAB blooms.

82. Ji and Franks (2007, MEPS)

84. Individual-Based Model (IBM) for a Copepod Bioenergetics based model of growth and reproduction Each individual is represented by a state-vector Mortality is stage specific but independent of location Specific diel vertical migration (DVM) behaviors, perhaps dependent on condition, food resources, etc., hypothesized. Growth is a balance of assimilation and respiration, and is a function of " Most recent temperature " preferred daytime light level " development stage " sex " reproductive weight " individual ID " weight (ugC) " birthdate (days) " time of last reproduction " time attained present stage " position (depth, distance offshore) " hunger condition " most recent food level " Individual weight " hunger condition " ambient food

85. E. pacifica Juveniles and Adults Reached F7 in 60 days Reach adult (at 12 mm) within ~ 4 months The most fecund adults are ~ 20 mm or about 12 months of age Capable of living up to 2 years

87. From North et al. (2006, JMS)

88. Hydrodynamic model output and particle distributions. (a) Hydrodynamic model output at day 350. Line contours are salinity and shaded contours are suspended sediment concentrations (kg m− 3, color scale on right). (b) Initial position of 50,000 particles randomly distributed throughout the particle-tracking model domain. (c) Particle distribution after 6 h when a random displacement model was used to simulate sub-grid scale turbulence in the vertical direction. (d) Particle distribution after 6 h when a random walk model was used to simulate sub-grid scale turbulence in the vertical direction. (From North et al. 2006, JMS)

89. Backward-in-Time- Trajectory (BITT) Simulations From Batchelder (2006)