Individual-Based Modeling in Ocean Ecology:Where Behavior, Physiology and Physics MeetHal BatchelderOregon State University

Supported by NSF and NOAA within the U.S. GLOBECNortheast Pacific Program

IBM Outline Introduction to i-state distribution and i-state configuration models How they differ Why IBMs 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

ConsiderationsTake Home Messages Challenges and Opportunities

Individual Based Modeling

Ecosystem ModelFranks et al., 1986

Vitals:380 lbs, 71; SOME BIOMASS

Vitals:380 lbs, 71; Vitals:~380 lbs, MORE BIOMASS

=?Vitals:380 lbs, 71; Vitals:~380 lbs,

=?Vitals:380 lbs, 71; one mouth; Vitals:~380 lbs, 40 mouths; Regularly puts foot in mouth (figuratively)Actually able to put foot in mouth

Euphausia pacifica life stagesN2MetanaupliusAdultCalyptopi

Individual SizeImpacts preferred prey type (abundance/size)Impacts growth rateImpacts mortality when size-dependentImpacts behaviorImpacts internal pools (lipid reserves)

Euphausia pacifica life stagesN2MetanaupliusAdultCalyptopi~3.2 g ind-1~7 g ind-1~4000 g ind-1Stage-specific CW

Euphausia pacifica life stagesN2MetanaupliusAdultCalyptopi~3.2 g ind-1~7 g ind-1~4000 g ind-1Stage-specific CW1250 indiv.571 indiv.1 indiv.

Allometric Relationships are ImportantRobin Ross (1982)

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

Euphausia pacifica life stagesN2MetanaupliusAdultCalyptopi~3.2 g ind-1~7 g ind-1~4000 g ind-1Stage-specific CW1250 indiv.571 indiv.1 indiv.R=633.6 ug C d-1G=425 ug C d-1R=529.2 ug C d-1G=519.6 ug C d-1R=122.9 ug C d-1G=26 ug C d-1

R (ug C d-1) = f(Weight, Prey, Temp)Bioenergetics of an Individual Process

A Stage Progression ModelE. pacifica Belehradek function for time to stage as function of temperature

Basic Form is: Di = ai (T + b)c

Di is the time (days) from egg to stage i

ai 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: Di = [ai (T + b)c] / [1 e-kP]

Interindividual variation in lipid weight of C5 stage of Calanus pacificusLaboratory 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)

2.52.8Hakanson (1984, Limnol.Oceanog.)

i-state Distribution Models fundamental tools of demographic theoryproduce differential or difference equations examples:NPZ+ modelsLotka-Volterra predator-prey modelsMcKendrick-von Foerster equationsSuppose: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.

Suppose: Only indiv body size and life-stage are important to dynamicsThen: Could model population using n life-stages, each having mn wt classes.What if: There are many more dimensions important to dynamics?Within Stage WeightLife Stage

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)

Individual SizeImpacts preferred prey type (abundance/size)Impacts growth rateImpacts mortality when size-dependentImpacts behaviorSome early classic examples

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 SensitivityInterspecific Effects Relative Size

i-state configuration models (aka Individual Based Models)Each individual has a vector of characteristics associated with itExamples are:Body size (weight, length)AgeReproductive ConditionNutritional (structural or physiological) ConditionBehaviorLocation= Defines Present Environment

Conditions in which i-state distribution models are insufficient and i-state configuration models (IBMs) are necessary:Complicated i-states Many elements in i-state configuration vector; numerical solutions as distribution difficultSmall populationsDemographic analysis of endangered speciesViability of small populationsLocal spatial interactions importantSpatial heterogeneity of the environmentLocal interaction of individualsSize- or individual-specific behaviors

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

Costs Involved in IBM ApproachDifficult to implement feedback from IBM (Lagrangian) to underlying Eulerian model, esp. across multiple trophic levelsConsumption (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 ParticlesDifficult 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 dependence4)Extensive Computation PenaltyBiological/biochemical processes for individuals are many and complex5)Increased knowledge about the system (this might be a good thing)

Design of Marine Protected AreasThe NW Atlantic Scallop Example

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

Transport patterns

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

No Closed RegionsClosed Regions10 Year Scallop Simulation w/ 1 spawning per year; 40 day larval drift; individual surviving scallops plotted (red are oldest individuals)

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

Transport patternsFrom C. Grant Law (unpubl.)

QuestionsHow 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.)

Management HistoryNE side of Georges BankNE side of Nantucket shoals Head of Hudson CanyonPre-Closure DistributionFrom C. Grant Law (unpubl.)

Management HistoryCLII north & southCLI SW side of Georges BankNE side of Nantucket shoals Head of Hudson CanyonPoor recruitment in NLS and VBC closed areasPost-Closure DistributionFrom C. Grant Law (unpubl.)

Zooplankton Population Dynamics in 2D

The Oregon Upwelling System

Processes and Environmental Variables Influencing Organism Growth and NumberT = Temperature; B=Behavior; =Turbulence; P=Prey; L=Light

Modeling Approach(Eulerian-Lagrangian Coupling)

0.05.010.015.020.025.030.035.0Density (# m-3)150-200m100-150m50-100m20-50m10-20m0-10mDepth Range of Layer SampledEuphausia pacificaat NH25 (Aug 4, 2000, daytime)NaupliiCalyptopesFurciliaJuvenilesAdultsBiological Organisms are not Passive TracersFigure courtesy of J. KeisterAll Stages are in upper 20 m during Night

Magnitude of Diel Vertical Migration by Life StageBased on 6 day-night paired MOCNESSFrom shelf stations and 8 day-night pairsFrom slope stations.Vance et al. (unpublished)

Individual Based Copepod Model (IBM) Bioenergetics based modeldW/dt = Assimilation - Respiration Growth is a function of weight, hunger condition, ambient foodReproduction within C6 females with weight specific allocation between somatic and reproductive growthStage-specific, spatially-constant and weight-based mortalityDiel Vertical Migration behavior dependent onlightsize (weight)hunger conditionfood resources proximity to boundaries

10 m during night160 m during dayBatchelder et al. (2002, PiO)

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.

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.

Hunger (H)LightHSize (S)Food (P)Boundary(Ns,Nb)Slows downmigSlows upmigBatchelder et al. (2002, PiO)

Physical Model2d (x-z) Vertical sliceTime-dependent, hydrostatic, Boussinesq, Navier-StokesFinite differenceKPP mixingExplicit mixing-length Bottom Boundary Layer500 < dx (m) < 15001.5 m < dz (m) < 3.7Topography for Newport, ORInitialized w/ April climatology

Southward wind-stress forcing of 0.5 dyne/cm2, either constant or alternating on/off with 5 or 10 day intervalsBatchelder et al. (2002, PiO)

2D Upwelling Scenario SimulationsBatchelder et al. (2002, PiO)

Day 20Day 40Day 80Size of bubble is proportional to individual weightRecently layed clutches in hi food regionWeight lossbelowmixed layerStarvation MortalityNo-DVM Simulation(PTM forced with Eulerian Concentrations of Prey, Velocities, and Kv)Batchelder et al. (2002, PiO)

DVM Simulation(PTM forced with Eulerian Concentrations of Prey, Velocities, and Kv)Day 20Day 40Day 80Size of bubble is proportional to individual weightMiddepth aggregation offshoreLarge Individuals InshoreNearshore reproductionand retentionNo reproduction &mortality loss offshorePopulationnearshoreonlyBatchelder et al. (2002, PiO)

Nutrient Quota Based DVMOf DinoflagellatesJi 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 (Qmin, Qmax, [PvI slope], max, Vm, (descent thresh), [ascent thresh], [resp rate], g0 [dark N uptake offset]).

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

Ji and Franks (2007, MEPS)Subsurface vs. DVMHigher light level at 10m yields higher net growth rates than at 20m for subsurface individuals.10m20mWith 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.

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)AVM using quota modelAsynchronous 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

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). 10m20m

Ji and Franks (2007, MEPS)Internal Waves (12 m amplitude)20m MLDCase 2aCase 2b

Allocation of Consumption within the Adult Female29 params

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

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 Tracking50,000 initial locations on shelf(bottom depths < 500m)(Averages ~ 1-2 indiv/km2)10-100m depth3D-advected for 15 days (dt=1 hr)New simulation begins every 7 daysRCCS ROMS runs provided by Enrique Curchitser (Rutgers)

RCCS19 Jun 2002 start

ET = 7 daysStrong Upwelling and Alongshore FlowUntangling 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.)

RCCS19 Jun 2002 start

ET = 7 daysStrong Upwelling and Alongshore FlowDestination maps identify potential of a site to export to other locations.

From Batchelder (in prep.)

RCCS19 Jun 2002 start

ET = 7 daysStrong Upwelling and Alongshore Flow

Source maps identify potential of other sites to supply propagules to this location.From Batchelder (in prep.)

RCCS19 Jun 2002 start

ET = 7 daysStrong Upwelling and Alongshore FlowDestination maps identify potential of a site to export to other locations.Source maps identify potential of other sites to supply propagules to this location.From Batchelder (in prep.)

spatial pattern of residence timeLongest residence time and greatest variability in inner Heceta Bank RegionStdDevMeanFrom Batchelder (in prep.)

ConsiderationsZooplankton and fish behavior has important demographic consequenceshow 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).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).IBMs can deal with complex stage, size and history dependent physiology and behavior at process based levelbut at the expense of generality?Under what scenarios is it critical to model zooplankton with IBMs in a Lagrangian framework vs. a stage-structured, age-within-stage-structured, or physiologically structured Eulerian framework?Feedbacks across trophic levels and considerations of density dependence are difficult to model with IBM approaches.

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 populationComputationally efficient; scales to (number of state variables X number of grid points)Biology is often hidden in non-mechanistic equationsDifficult (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.

Take Home Messages (2)Individual-based (Lagrangian) models explicitly consider inter-individual (and potentially interspecies) variation.Biology is mechanistically explicitHistory-behavior-spatial heterogeneity interactions relatively straightforwardDownsidesCan be computationally expensive; scales to the number of individuals/populations modeledDifficult to implement feedback to underlying Eulerian state variables and density dependenceRequires more knowledge of the fundamental biological/ecological system

A simple 3-component NPZ model in an upwelling circulation revealsPhysical forcing induces nearshore phytoplankton bloomHorizontal 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 retentionFundamental 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)

As revealed by the dinoflagellate IBM case studyPhysical setting can interact with physiological demands/constraints to yield diverse outcomes.

IBMs 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)

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 variabilityNPZ+ often run coupled with physicsHigher 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 effectsEmpirical functional relationships (food-ingestion; food-egg production) are useful for linking species-specific life history models to NPZ+ models

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 variabilitySimple NPZ models cannot represent the diversity of prey typesPrey switching and omnivorousness complicate dynamicsAveraging in space, time and trophic complexity (e.g., through model resolution) may stabilize models, but ignores important ecological processes.Mortalitythe great unknown.

Thanks also to the NCAR ASP Colloquium Organizers.

Conclusions and Lessons Learned (contd)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.

Initial Locations of Individuals that produced eggsDVMPassivePassive, reduced offshore food

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 InteractionsYOY 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.

Additional Capabilities of the Oregon Shelf Forecast ModelUse 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.

Ji and Franks (2007, MEPS)

Ji and Franks (2007, MEPS)

Individual-Based Model (IBM) for a CopepodBioenergetics based model of growth and reproductionEach individual is represented by a state-vectorMortality is stage specific but independent of locationSpecific 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 temperaturepreferred daytime light leveldevelopment stagesexreproductive weightindividual IDweight (ugC)birthdate (days)time of last reproductiontime attained present stageposition (depth, distance offshore)hunger conditionmost recent food level

E. pacifica Juveniles and AdultsReached F7 in 60 daysReach adult (at 12 mm) within ~ 4 monthsThe most fecund adults are ~ 20 mm or about 12 months of ageCapable of living up to 2 years

From North et al. (2006, JMS)

Hydrodynamic model output and particle distributions. (a) Hydrodynamic model output at day 350. Line contours are salinity and shaded contours are suspended sediment concentrations (kgm3, color scale on right). (b) Initial position of 50,000particles randomly distributed throughout the particle-tracking model domain. (c) Particle distribution after 6h when a random displacement model was used to simulate sub-grid scale turbulence in the vertical direction. (d) Particle distribution after 6h when a random walk model was used to simulate sub-grid scale turbulence in the vertical direction. (From North et al. 2006, JMS)

Backward-in-Time-Trajectory (BITT) SimulationsFrom Batchelder (2006)

Hakanson, J. L. 1984. The long and short term feeding condition in field-caught Calanus pacificus, as determined from the lipid content. Limnol. Oceanogr., 29, 794-804.Sources and Sinks (ASLO Results): Larvae were initiated on September 1 throughout the model domain and transported for 40 days in the top 25 meter flow. The distribution of the source and settlement regions were calculated as the percentage of the individuals at a given location that either originated from (settlement) or settled in (source) a given closed area. This can also be thought of as the probability that an adult at a given location originated from the closed area (sink map) and the probability that a larvae from a given region will settle into a given closed area (source map). Younger stages not shown because of Reverse or NO DVM. Reverse DVMs are not stat sig.Carlotti, F., and H.-J. Hirche. 1997. Growth and egg production of female Calanus finmarchicus: an individual-based physiological model and experimental validation. Mar. Ecol. Prog. Ser., 149, 91-104.n34_destinations_sources.jpg; rccs_ret02_n34.jpgn34_destinations_sources.jpg; rccs_ret02_n34.jpgn34_destinations_sources.jpg; rccs_ret02_n34.jpgn34_destinations_sources.jpg; rccs_ret02_n34.jpg