Seeking Realistic Behavior from Virtual Fish

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Seeking Realistic Behavior from Virtual Fish

• California Individual Based, Instream, Fish
  Population Simulator
• Roland Lamberson
• Steve Railsback
• Bret Harvey
• Steve Jackson
• http//math.humboldt.edu/simsys/

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Overview

• Philosophy and objectives
• Basic model structure
• Some details of the fish and habitat models
• Movement models
• State variables and fitness
• Rules that work and some that dont

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Objectives of the Model

• Evaluate the individual-based modeling approach
  for management applications
• Predicting the individual and cumulative impacts
  of timber harvests
• Water diversions
• Habitat Alterations

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Individual-based Models

• Track each individual in the population spatially
  and temporally
• Allow individuals to be different
• Allow for differing environmental impacts on
  individuals that are similar

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Individual-Based ModelDesign Philosophy

• Build simple mechanistic representations of key
  processes affecting survival and reproduction
• Avoid hardwiring in behaviors like
  territoriality, specific feeding strategies,
  habitat shifts with age
• Let animals choose behaviors that maximize some
  estimate of fitness

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Individual-Based ModelDesign Philosophy

• Include environmental and biological processes if
  and only if they have important effects on
• Habitat selection
• Feeding and growth
• Survival
• Spawning and redd incubation

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Individual-Based ModelDesign Philosophy

• Develop a simple model for each process
• Based on salmonid literature
• Test and validate model processes by whether they
  produce
• Realistic individual behavior
• Realistic population behavior

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Individual-Based ModelDesign Philosophy

• Models of individual fish are easier to build
  from available information
• its easy to observe and model what individuals
  do
• IBMs predict meaningful and measurable
  outcomes
• Fish abundance
• Fish growth size
• Habitat use

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California Individual Based, Instream, Fish
Population Simulator

• Three Parts
• Hydraulic Model (Habitat)
• Demographic Model (Fish)
• Movement Model (Connects fish with habitat)

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California Individual Based, Instream, Fish
Population Simulator
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California Individual Based, Instream, Fish
Population Simulator

• Habitat is modeled as rectangular cells
• External hydraulic model simulates variation of
  depth and velocity with flow

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California Individual Based, Instream, Fish
Population Simulator

• External Driving Variables
• Stream flow
• Water temperature
• Turbidity
• Food availability

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Habitat Model

• Depth, velocity, hiding cover, and velocity
  shelter
• Temperature
• Food availability
• One day time step

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Hydraulic Model

• PHABSIM or RHABSIM
• Parameterized on stream cross sections
• Computes depths and velocities based on flow
  rates

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Hydraulic Model

• Flow affects
• Food availability
• Ability of fish to feed
• Mortality risks
• Temperature affects
• Mortality risks
• Energetics
• Spawning

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Demographic Model

• Simulates
• Spawning, egg incubation
• Growth, based on food intake and energy expended
• Mortality

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Demographic Model

• Mortality
• Starvation
• Spawning
• Temperature
• Velocity
• Stranding
• Terrestrial predation
• Aquatic predation
• Demonic intrusion

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Demographic Model

• Mortality risks vary with habitat
• Depth
• Water velocity
• Cover
• Turbidity
• Temperature
• Fish size

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Demographic Model

• Food intake varies with habitat
• Food supply
• Water velocity
• Turbidity
• Temperature
• Competition largest fish feeds first

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Stream Trout Demonstration

• Simulation Flow rises from 0.6 to 5 m/s, then
  recedes

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Demographic Model

• Feeding and Growth
• Simulate drift feeding and search for benthic
  food
• Energy costs of feeding depend on feeding
  strategy and availability of velocity shelters
• Assume that fish choose the most energetically
  profitable feeding strategy

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Feeding Model

• Drift feeding strategy
• Food intake per fish
• Food Concentration ? velocity ? capture area.
• Capture area

Depth
Reactive distance
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Feeding Model

• Search feeding strategy
• Food Intake per fish
• Benthic production rate ? Search area ? Velocity
  factor
• Velocity factor reduces intake as water velocity
  in cell approaches fishs maximum sustainable
  swim speed

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Growth Model (bioenergetics)

• Growth is a function of
• food intake - metabolic costs
• Metabolic costs
• increase with swimming speed
• increase with temperature

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Foraging Model

• Food intake varies between drift and search
  feeding strategies
• Relative advantages depend on flow, fish size,
  habitat
• Food intake can be limited by competition (food
  consumed by bigger fish)
• Each fish picks the feeding strategy offering
  highest growth
• Preferred strategy can vary among cells

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Foraging Model Growth vs. Velocity, Fish Size,
Feeding Strategy
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Survival Model

• Survival probabilities
• Vary with habitat
• Depend on fish size, condition
• Include
• Poor condition (starvation)
• Terrestrial predation
• Aquatic predation
• High temperature
• High velocity (exhaustion)
• Stranding (low depth)

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Survival Predation Risks

• Terrestrial predation risk
• Represents birds, otters, etc.
• Increases with depth and velocity
• Increases with fish size
• Increases with distance to hiding cover
• Decreases with turbidity

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Survival Predation Risks

• Fish Predation Risks
• Increases with depth
• Decreases with fish size
• Decreases with temperature
• Decreases with turbidity

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Survival Model Overall Risks
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Survival Model Overall Risks
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Survival Model Overall Risks
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Movement Models(Habitat Selection)

• Departure Rules
• Destination Rules
• Fitness Measures

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Previous Models

• Movement Models
• Departure Rules
• Search for new habitat when current fitness less
  than average over previous days
• Clark and Rose 97 Van Winkle 98

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Previous Models

• Movement Models
• Destination Rules
• Pick direction
• Examine accessible sites
• Choose one with fewest bigger fish
• Clark Rose 1997

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Previous Models

• Movement Models
• Destination Rules
• Limited random walk
• Stop when depth and velocity acceptable
• Early version of Van Winkle 1996

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Previous Models

• Movement Models
• Fitness Rules
• Maximize Growth (Clark Rose)
• Minimize
• mortality risk/growth or
• mortality risk/(C growth)
• (Van Winkle et al 1996)

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Previous Models
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Realistic Behaviorfrom Virtual Fish

• Move to maximize fitness
• If in poor condition seek areas of high food
  intake even if high risk
• If short-term high risk, seek shelter
• If not mature take more risks

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The State Variable Approach

• Move to maximize fitness
• Decisions directly link current choices to future
  fitness

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The State Variable Approach

• Dynamic programming approach doesnt work
• Give animals ability to predict future condition
  in each cell same as current

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California Individual Based, Instream, Fish
Population Simulator

• Move to maximize fitness Departure and
  Destination Rules
• Examine all habitat nearby each day
• Move if fitness can be improved
• Move to site with highest fitness measure

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Movement to maximize survival to some time horizon

• Non-starvation survival probability
• PtT (T days to time horizon)
• where Pt is the daily survival probability
• Pt product of survivals for each potential
  cause of death

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Movement to maximize survival to some time horizon

• From todays food intake and energy reserves,
  fish predict their size and condition at end
  time horizon
• Starvation survival probability
• St e(aKb)/1 e(aKb)
• K is condition factor
• fraction of normal weight for length

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California Individual Based, Instream, Fish
Population Simulator
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Expected Reproductive Maturity (EM)

• Expected probability of survival to T
• Multiplied by
• Fraction of mature size expected at T

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State Variables Fitness

• EM allows fish to use their knowledge of their
  current state (age, size, condition,) and their
  surroundings and project into the future while
  making habitat selection and feeding strategy
  decisions

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Building Individual-based Models

• Very early in the project Identify the traits
  of model individuals that are key for explaining
  population responses What are the most
  important ways individuals adapt to each other
  and their environment?

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Building Individual-based Models

• Very early in the project Determine whether
  there is existing, tested theory for modeling the
  key individual traitsThere probably isnt

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Building Individual-based Models

• Make development and testing of theory for the
  key traits a primary goal of the entire program
• IBM design analysis
• Software
• Field studies

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Building Individual-based Models

• Building the agent-based model is only the first
  stepAn IBM is like a real population you have
  to design and conduct controlled experiments on
  it to understand it and learn from it

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Validating the Model"Analysis of Habitat
Selection Rules Using an Individual-based Model
", Railsback and Harvey. Ecology
(2002)Population Level Analysis and Validation
of an Individual-based Cutthroat Trout Model,
Railsback, Harvey, and Lamberson Natural
Resource Modeling (2002)
http//math.humboldt.edu/simsys/