1 individual-based modeling for salmonid management roland h. lamberson humboldt state university...
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Individual-based Modeling for Salmonid Management
Roland H. LambersonHumboldt State University
http://math.humboldt.edu/~ecomodel/
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Credits
Funding: EPA STAR Grant
• Research collaborators:– Steve Railsback, Lang, Railsback, and Associates
– Bret Harvey, USFS Redwood Sciences Lab
– Software: Steve Jackson, Jackson Scientific Computing
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Presentation Objectives
• inSTREAM our individual-based trout model
• Advantages of IBMs for modeling fish population response to stressors
• Example applications of our stream trout IBM to management research and decision-making
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What is an IBM?
• A model of the environment+
• Models of individual animals– The mechanisms by which the environment affects an individual
– The mechanisms by which individuals interact
– The behaviors individuals use to adapt to their environment and each other
• Population responses that emerge from individual behaviors
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What is an IBM? Demo
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• IBM’s resolve the two fundamental dilemmas of modeling: – Models usually assume many individual organisms can be
described by a single variable like population size or biomass. IBM’s provide for individuals and their differences.
– Most models don’t distinguish between organisms’ locations. IBM’s provide for distinctive interactions with neighboring individuals and the local environment.
Why an Individual-based Model?
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• Complex, cumulative effects can be simulated:– Base flow
– High and low flows: timing and magnitude
– Temperature
– Turbidity
– Losses of individuals (angler harvest, diversion entrainment)
– Food production
– Reproduction, recruitment
– Species interactions: competition, predation
– ...
Advantages of IBMs for Modeling Fish Population Response to Stressors
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• Complex, cumulative effects can be simulated:
• These complex interactions emerge from individual-level mechanisms – instead of having to be foreseen and built into a model
– you just have to model how stressors affect individuals
Advantages of IBMs for Modeling Response to Stressors
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• IBMs are testable in many ways
– They can produce many kinds of predictions that can be tested with many kinds of data
• Habitat selection patterns over space, time, flow ...
• Statistical properties of population (size, abundance)
• Trends in abundance with environmental factors
• etc.
Advantages of IBMs
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• IBMs provide a way out of the complexity - uncertainty dilemma:
– A well-designed IBM is a collection of simple submodels for separate processes at the individual level
– Each submodel can be parameterized and tested with all the information available for its process
– Yet IBMs can simulate complex population level responses
Advantages of IBMs
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Stream Trout Model
• Habitat is modeled as rectangular cells• External hydraulic model simulates how
depth, velocity vary with flow
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Stream Trout Model
• Habitat:– Water depths and
velocities
– Temperature, turbidity
– Food availability
– Daily time step
• Fish:– Habitat selection
(choosing the best cell)
– Feeding and growth
– Mortality
– Spawning & incubation
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Feeding Model
• Drift feeding strategy
– Food intake per fish:
Food concentration velocity capture area.
Capture area:
Reactive distance
Dep
th
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Feeding 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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Growth Model (bioenergetics)
• Growth = Food intake - metabolic costs
– Metabolic costs:• increase with swimming speed
• increase with temperature
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Foraging Model: Growth vs. Velocity, Fish Size, Feeding Strategy
-6%
-5%
-4%
-3%
-2%
-1%
0%
1%
2%
3%
0 20 40 60 80 100
Water velocity, cm/s
Dai
ly g
row
th,
% b
ody
wei
ght Drift feeding, no shelters,
15 cm trout
Drift feeding, withshelters, 15 cm trout
Drift feeding, no shelters,5 cm trout
Drift feeding, withshelters, 5 cm trout
Search feeding, 15 cmtrout
Search feeding, 5 cmtrout
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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 Model: Overall Risks
0 35 7
0 10
5 14
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0
40
80
0.8
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0.95
1
Survival probability
Depth, cm
Velocity, cm/s
Survival For 3 cm Trout
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Survival Model: Overall Risks
0 35 7
0 10
5 14
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40
80
0.8
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0.95
1
Survival probability
Depth, cm
Velocity, cm/s
Survival for 10 cm Trout
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Habitat Selection: Overview
• Habitat selection is critical:– Moving is the primary way fish adapt to changing
conditions
• Our approach assumes fish use behaviors that evolved to maximize fitness
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Habitat Selection Rules
• Move to the cell that offers highest potential “fitness”
– (within the radius that fish are assumed to be familiar with)
– Railsback, S. F., R. H. Lamberson, B. C. Harvey and W. E. Duffy (1999). Movement rules for spatially explicit individual-based models of stream fish. Ecological Modelling 123: 73-89.
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Habitat Selection: Fitness Measure
• Fish move to cell offering highest fitness
• Key elements of fitness are:– Future survival– Attaining reproductive size
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Habitat Selection: SummaryHow a Fish Rates A Potential Destination Cell
• Considers:– Potential growth in cell (function of habitat, competition)
– Mortality risks in cell (function of habitat)
– Its own size and condition
• Probability of surviving for 90 days in the cell?– Assuming today’s conditions persist for the 90 days
• How close to reproductive size after 90 d in the cell?
• Rating = Survival probability fraction of reproductive size
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• Many realistic behaviors emerge:
– Normal conditions: territory-like spacing
– Short-term risk: fish ignore food and avoid the risk
– Hungry fish take more chances to get food (and often get eaten)
– Conditions like temperature, food availability, fish density affect habitat choice
Habitat Selection
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• The “pattern-oriented” analysis approach:
– Test specific processes of an IBM by whether it reproduces a wide range of behaviors that emerge from the process
– Test a complete IBM by whether it reproduces a wide range of observed population-level patterns
– Railsback, S. F. (2001). Getting “results”: the pattern-oriented approach to analyzing natural systems with individual-based models. Natural Resource Modeling 14: 465-474.
Analyzing Individual-based Models
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• Validation:– Individual level
• Railsback, S. F. and B. C. Harvey (2002). Analysis of habitat selection rules using an individual-based model. Ecology 83: 1817-1830.
– Population level• Railsback, S. F., B. C. Harvey, R. H. Lamberson, D. E. Lee, N. J. Claasen and
S. Yoshihara (2002). Population-level analysis and validation of an individual-based cutthroat trout model. Natural Resource Modeling 15: 83-110.
Pattern-Oriented Analysis of inStream
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Validation of Habitat Selection Rules: Six Patterns (a)
• Feeding hierarchies
• Movement to channel margin during high flow
• Juveniles respond to competing species by using less optimal habitat (higher velocities)
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Validation of Habitat Selection Rules: Six Patterns (b)
• Juveniles respond to predatory fish by using shallower, faster habitat
• Use of higher velocities in warmer seasons
• Habitat shift in response to reduced food
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Expected Reproductive Maturity vs. Habitat Suitability Criteria as Indicators of Habitat Quality
• PHABSIM habitat suitability criteria (HSC)
– Basis: Empirical observations of fish
• Expected Reproductive Maturity (EM)
– Basis: Mechanistic models of feeding, mortality risks, fitness
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60 70 80 90 100
Velocity, cm/s
Su
itab
ility
Reactive distance
Dep
th
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EM vs. HSC Indicators of Habitat Quality
• HSC
Habitat rating varies only with fish life stage:
fry, juvenile, adult, spawning
(occasionally: season)
• EM
Habitat rating varies with:Fish sizeFish conditionTemperature & seasonFood availabilityCover for hiding, feedingOther factors affecting
growth or survival
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EM as an Indicator of Habitat Quality
Base Scenario: 15 cm Trout
Depth, cm
Vel
ocity
, cm
/s
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 50 100 150 200
020
4060
80
• Adult trout – drift feeding
– using velocity shelter
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EM as an Indicator of Habitat Quality:With vs. Without Velocity Shelters for Drift Feeding
No Velocity Shelter Scenario
Depth, cm
Vel
ocity
, cm
/s
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 50 100 150 200
020
4060
80
Base Scenario: 15 cm Trout
Depth, cm
Vel
ocity
, cm
/s
0.1
0.2
0.3
0.4
0.5
0.6
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0 50 100 150 200
020
4060
80
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EM as an Indicator of Habitat Quality: Without vs. With Hiding Cover
Base Scenario: 15 cm Trout
Depth, cm
Vel
ocity
, cm
/s
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 50 100 150 200
020
4060
80
High Hiding Cover Scenario
Depth, cm
Vel
ocity
, cm
/s
0.1
0. 2
0.3
0.4
0.5 0.6
0.7
0.8
0.9
0 50 100 150 200
020
4060
80
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EM as an Indicator of Habitat Quality: 15° vs. 5° Temperature
Base Scenario: 15 cm Trout
Depth, cm
Vel
ocity
, cm
/s
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 50 100 150 200
020
4060
80
Low Temperature Scenario: 5C
Depth, cm
Vel
ocity
, cm
/s
0 .1 0.2
0.3
0.4
0.5
0.6
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0.9
0 50 100 150 200
020
4060
80
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EM as an Indicator of Habitat Quality: Low vs. High Turbidity
Base Scenario: 15 cm Trout
Depth, cm
Vel
ocity
, cm
/s
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 50 100 150 200
020
4060
80
Turbidity Scenario: 30 NTUs
Depth, cm
Vel
ocity
, cm
/s
0.1
0.1
0.2
0.2
0.3
0.3
0.4
0 50 100 150 200
020
4060
80
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Example Use of IBM for Management Research: Effect of Habitat Complexity on Population Dynamics
• Observed pattern: When deep pools are eliminated, a lower abundance of large trout results:– Bisson & Sedell (1984) observed fewer pools & fewer large trout in clearcuts
• Simulation experiment: – Simulate populations over 5 years with, without
pool habitat in the model
– Railsback, S. F., B. C. Harvey, R. H. Lamberson, D. E. Lee, N. J. Claasen and S. Yoshihara (2002). Population-level analysis and validation of an individual-based cutthroat trout model. Natural Resource Modeling 15: 83-110.
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Effect of Habitat Complexity on Population Dynamics
• Simulation results (1):– Abundance of all age classes was lower when pools were
removed
– Impact was greatest on oldest age class
– Terrestrial predation caused the lower abundance - pools provide shelter from terrestrial predators
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Effect of Habitat Complexity on Population Dynamics
• Simulation results (2):– Size of age 0 and 1 trout increased when pools were
removed -
– Why??
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Effect of Habitat Complexity on Population Dynamics
• Simulation results (2):– Size of age 0 and 1 trout increased when pools were
removed -
• Abundance decreased, so there was less competition for food
• Age 1 trout were forced to use faster, shallower habitat where predation risk is higher BUT food intake and growth is higher
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Example IBM Application: Effects of Instream Flow Magnitude & Variability
• How does the amount and timing of flow affect trout abundance and growth?
• Site: Little Jones Creek (3rd order coastal stream in N. California)
• Scenarios: hypothetical hydropower reservoir – Constant flow vs. Natural monthly mean flow
• Simulations: 10 years, 5 replicates per scenario
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Example IBM Application: Effects of Instream Flow Magnitude & Variability
0
5
10
15
20
25
30
0% 20% 40% 60% 80% 100%
Flow, % of natural
Mea
n n
um
ber
of
age
2+ t
rou
t Constant flow
Natural monthly
No hydro
0
5
10
15
20
0% 20% 40% 60% 80% 100%
Flow, % of natural
Mea
n l
eng
th (
cm)
age
2+ t
rou
t
• How does the amount and timing of flow affect trout abundance and growth?
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Example Application: Effects of Turbidity
• Turbidity decreases feeding ability, but decreases predation risk
What are the population-level consequences?
• Site: Little Jones Creek
• Five turbidity scenarios: – Turbidity = x Q– Five values of x: very clear to very turbid streams
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Example Application: Effects of Turbidity
• Result: Interactions between turbidity and food availability are strong
Scenario
Num
ber
of A
ge 2
+ F
ish
1 2 3 4 5
010
20
30
40
50
Scenario
Num
ber
of A
ge 2
+ F
ish
1 2 3 4 5
40
50
60
70
80
90
Low food availability
High food availability
Turbidity Turbidity
Tro
ut a
bund
ance
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Example Use of IBM for Management Research:Habitat Selection vs. Habitat Quality
• Theory to be tested: The habitat that animals use most often is the best habitat
– This assumption is the basis for many management models
– It is widely questioned but very difficult to test in the field
• “Relations between habitat quality and habitat selection in a virtual trout population.” Railsback, S. F., H. B. Stauffer, and B. C. Harvey. (to appear in Ecological Applications.)
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Habitat Selection vs. Habitat Quality
• “Habitat Selection” = the observed choice of habitat
• DEN is evaluated as observed animal density
DEN= (# animals using a habitat type) / (area of habitat type)
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Habitat Selection vs. Habitat Quality
• “Habitat Quality” or Fitness Potential (FP) = the fitness provided to an animal by a habitat type, in the absence of competition – “Preference”: the habitat a fish selects in absence of competitors
• In our IBM: – We know the FP of each habitat cell because we programmed it
– FP varies among habitat cells with water depth, velocity, feeding shelter, hiding shelter
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Habitat Selection vs. Habitat Quality
• The experiment: – Observe DEN (fish density) in each habitat cell (snapshot)
– Calculate FP for each cell
– Examine: How well does DEN predict FP?(What can you learn about the quality of habitat by observing the habitat that animals use?)
– Three ages of trout examined separately
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What Does Habitat Selection Tell You about
Habitat Quality??Not much!
• Cells with high density usually are fairly high quality
• Many high quality cells have zero fish
• There is no predictive relationship between observed fish density and habitat quality
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Management Research with the IBM: Why is There So Little Relation Between Habitat Selection and Habitat Quality?
• (1) Competition:– Smaller trout don’t use the habitat that is best for
them because they are excluded by larger fish
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Why is There So Little Relation Between Habitat Selection and Habitat Quality?
• (2) Unused and unknown habitat:
– Good habitat for large trout may be vacant because there are not enough trout to use it all
– Trout may not use the best available habitat because it is too far away to know about
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Why is There So Little Relation Between Habitat Selection and Habitat Quality?
• (3) Cells where food is plentiful but hard to catch can support more fish at lower fitness:– Example: Cells with high velocity
– Each fish can catch less food than optimal
– Because each fish gets less of the food, more fish can share the cell
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Why is There So Little Relation Between Habitat Selection and Habitat Quality?
• (4) Cells where food is plentiful but mortality risks are high can support more fish at lower fitness:– Density is high because there is plenty of food but
– Fitness is low because mortality risk are high
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Habitat Selection vs. Habitat Quality
• Conclusions:– Observed patterns of habitat selection by animals
tell us little about how good the habitat is
– But does this mean models based on habitat selection are worthless??
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Are There Problems with Models Based on Habitat Selection?
• A second simulation experiment:– A good habitat selection model can be a useful
predictor of population response over short times• When habitat modifications are small
• And it is a dominant species or life stage
– BUT:• Habitat selection models have fundamental problems
(mainly: neglecting that habitat selection varies over time)
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Conclusions: Key advantages of IBMs for assessing impacts of multiple stressors on fish
• IBMs can be used to address more questions that are difficult to address with other modeling approaches
• IBMs can be more credible than alternatives– More testable – Able to simulate complex responses to many
stressors without high parameter uncertainty
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Conclusions: Potential Limitations of IBMs
• Computation: There is a limit to how many fish / how much habitat we can simulate (overcome with bigger computers, clusters?)
• Models for new groups of fish can be expensive to build
• Expertise: Few biologists are familiar with IBMs (or the mechanistic, individual-based view of ecology)
• Acceptance by managers: IBMs are unfamiliar, not as simplistic as alternative approaches
• We haven’t done anadromy yet (but have put a lot of work into concepts and software)
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Conclusions: Our Status
• Continued evolution, application of the trout model– Diel shifts in habitat & activity: feeding vs. hiding– Sub-daily time steps and fluctuating flows
• Interest in new applications of our salmonid IBMs– Instream flow assessment– Assessment of restoration activities ...– Regional stressor-response applications
• Development of new models (juvenile Colorado pikeminnow)
• Development & publication of theory & software
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Individual-based Modeling for Salmonid Management
http://math.humboldt.edu/~ecomodel/