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Individual and Population Level Analysis and Validation of an Individual-based Trout Model
Roland H. Lamberson
Humboldt State University
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Individual and Population Level Analysis and Validation of an Individual-based Trout Model
• Collaborators:
– Steve RailsbackLang, Railsback, and Associates
– Bret HarveyUS Forest Service, Redwood Sciences Laboratory
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Individual and Population Level Analysis and Validation of an Individual-based Trout Model
http://math.humboldt.edu/~simsys/
•Products & publications:
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Individual and Population Level Analysis and Validation of an Individual-based Trout Model
• Our Approach to Validation• Validation Experiments
– Individual behavior– Population level behavior
• Results• Conclusions
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Individual-based Trout Model
• Growth potential and mortality risk vary with:– Space (cell)
• Depth, velocity, feeding & hiding cover, food availability
– Fish• Length, weight, condition
– Competition: Size-based hierarchy• Food consumed by larger fish in a cell
is not available to smaller fish
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Individual-based Trout Model
• Movement (Habitat Selection)
– Movement is the most important mechanism available to stream fish for adapting to changing conditions
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Individual-based Trout Model
• Movement Rules
– Move to maximize fitness – Examine all habitat nearby each day– Move if fitness can be improved– Move to site with highest fitness measure
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Individual-based Trout Model
• Fitness measure
– Expected Maturity (EM)• Probability of survival to fixed time horizon
(usually 90 days)
Times
• Expected fraction of mature size at next spawning
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Habitat Selection
• Do 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)
– Habitat conditions like temperature, food availability affect habitat choice
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Validating Individual Behavior
• Habitat Selection– Hierarchical feeding
– Response to high flows
– Response to interspecific competition
– Response to predatory fish
– Variation in velocity preference with season
– Changes is habitat use with food availability and energy reserves
• Railsback and Harvey, (2002) Ecology
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Validating Individual Behavior
• We compared 3 alternative theories:
– EM: Our “expected survival and growth to maturity over a future time horizon” theory
– MG: Fish select habitat to maximize today’s growth
– MS: Fish select habitat to maximize today’s survival probability (minimize risk)
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Validating Individual Behavior
• Hierarchical Feeding
– A consistent preference for specific feeding sites
– Dominant fish displace others from preferred sites
– Sub-dominant fish occupy preferred sites when dominant fish are removed
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Validating Individual Behavior
• Hierarchical Feeding• Simulation:
– 10 adult trout in a small habitat – Five time steps to equilibrate– Largest fish are successively removed
• Results: – Works for EM, MG (via food competition)– EM and MG result in different habitat preferences
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Validating Individual Behavior
• Habitat Selection– Maximize Survival
– No hierarchical feeding
– All fish use cell with
highest daily survival
probability
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Validating Individual Behavior
• Habitat Selection– Maximize Growth
– Hierarchical feeding: – Clear preference for
cell providing highest growth rate
– Competition for food initially excludes most fish from the optimal cell
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Validating Individual Behavior
• Habitat Selection– Expected Maturity
– Hierarchical feeding occurs
Risks in the preferred cell are
much lower: mean survival
times of 6900 days, vs. 180 days
in cell that maximizes growth
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Validating Individual Behavior
• Response to High Flows
– At flood flows, trout move to quieter water on the stream margin
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Validating Individual Behavior
• Response to High Flows– Simulation: Flow rises from 0.6 to 5 m/s, then recedes
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Validating Individual Behavior
• Response to High Flows• Results:
– Works for EM, MG, MS– Moving to stream margin maximizes both growth
and survival
– (This experiment had no power to resolve the 3 competing fitness measures)
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Validating Individual Behavior
• Variation in Velocity Preference with Season
– Adult trout use lower velocities in winter than in summer
• Simulation: Four temperature scenarios
5, 10, 15, 20º C
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Validating Individual Behavior
• Variation in Velocity Preference with Season– Metabolism increases
with temperature
Metabolism affects future starvation risk
Only EM considers futurestarvation
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25
30
35
40
45
50
0 5 10 15 20
Temperature
Mea
n ve
loci
ty, c
m/s
MG
MS
EM
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Validating Individual Behavior
• Response to reduced food availability
– When food availability (or energy reserves) are reduced, trout take more risks to get more food
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Validating Individual Behavior
• Response to reduced food availability• Simulation:
– Five adult trout in a small habitat– After 5 days, food availability was reduced by 2/3
• Results: – MG fish were already at the cell with highest intake– MS fish are not concerned with food– ...
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Validating Individual Behavior
• Response to reduced food availability• Results (continued):
– EM produced movement to new habitat with higher (relative) food intake: the tradeoff between food and risk shifts
– This requires fish to consider future consequences of food intake on starvation risk
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Validating Individual Behavior:Overall Results
PatternMaximize
growthMaximizesurvival
MaximizeEM
1. Hierarchical feeding
2. Response to highflow
3. Response to inter-specific competition
4. Response topredatory fish
5. Seasonal velocitypreference
6. Response toreduced foodavailability
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Population Level Analysis
• Validation Experiments– Self-thinning - a negative power relation between
weight and abundance
– Critical period - density-dependent mortality in young-of-the-year
– Age-specific interannual variability in abundance
– Density dependence in growth
– Fewer large trout when pools eliminated
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Population Level Analysis
• Self-thinning (Elliott 1993)– Mean Weight = k abundance s
– Theory suggests that s = -4/3 • Results from assuming metabolic rate = k weight b
where b = ¾
– Elliott found s to be highly variable but had a 25 year average of -1.33, as predicted
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Population Level Analysis
• Self-thinning (Elliott 1993)– Mean Weight = k abundance s
– Theory suggests that s = -4/3 – Elliott found s to be highly variable but had a
25 year average of -1.33 as predicted– We get s = -1.25 for b = ¾, a bit too low– However, our s is sensitive to b in the right
way
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Population Level Analysis
• Critical survival time (Elliot 1989)– Elliott found intense density-dependent
mortality commencing when trout fry emerge and continuing for from 30 to 70 days
Critical Period
0
0.5
1
1.5
2
2.5
3
3.5
0 50 100 150 200
days after emergence
log
(fry
ab
un
dan
ce)
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Population Level Analysis
• Critical survival time (Elliot 1989)– Elliott found intense density-dependent
mortality commencing when trout fry emerge and continuing for from 30 to 70 days
– In 18 of our 29 simulations we found a critical period, the lengths varied from 30 to 65 days
– However, we found no critical period in years of low age zero abundance (the other 11 cases)
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Population Level Analysis
• Population Variation Over Time (House 1995)– Age 0 abundance varying by a factor of 4– Age 1 least variable age class– Age 2+ most variable
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Population Level Analysis
• Population Variation Over Time (House 1995)– Age 0 abundance varying by a factor of 4– Age 1 least variable age class– Age 2+ most variable– Age 0 abundance variation similar to House– Age 1 more variable than age 2+
• We have more pools - higher survival for adult fish
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Population Level Analysis
• Population Variation Over Time (House 1995)– Weak correlation between peak winter flow and
age 1 abundance the following summer– No correlation between lowest summer flow
and abundance
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Population Level Analysis
• Population Variation Over Time (House 1995)– Weak correlation between peak winter flow and
age 1 abundance the following summer– No correlation between lowest summer flow
and abundance– We found the same though our correlation
between winter flow and age 1 abundance was a little stronger
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Population Level Analysis
• Density Dependence in Growth– Elliott (1994) observed abundance and size of
age 0 trout and concluded abundance had little effect on growth
– Jenkins et al. (1999) observed abundance and growth in natural and controlled streams and concluded abundance had a strong negative effect on size
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Population Level Analysis
• Density Dependence in Growth– Our experiments
demonstrate a negative
relationship
between abundance
of age 0 trout and
their size in fall
(similar to Jenkins), but 0
1
2
3
4
5
6
0 200 400 600 800
Age 0 abundance
Age
0 m
ean
wei
ght,
g
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Population Level Analysis
• Density Dependence in Growth
– But it is not that simple!– We find a weak positive
relationship between
growth rate (grams/day)
and density 0
0.01
0.02
0.03
0.04
0.05
0 500 1000 1500
Age 0 abundance
Age
0 m
ean
grow
th,
g/d
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Population Level Analysis
• Density Dependence in Growth
– How can age 0 size decrease with density when growth rate increases?
0
1
2
3
4
5
6
0 200 400 600 800
Age 0 abundance
Age
0 m
ean
wei
ght,
g
0
0.01
0.02
0.03
0.04
0.05
0 500 1000 1500
Age 0 abundance
Age
0 m
ean
grow
th,
g/d
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Population Level Analysis
• Density Dependence in Growth
– Fall mean weight of age 0 trout is related to
• Time of emergence
• Size-dependent mortality
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Population Level Analysis
• Density Dependence in Growth
– Time of emergence
• Later emergence means less mortality of age zero trout before census and younger thus smaller trout at the time of the census
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Population Level Analysis
• Density Dependence in Growth
– Size-dependent mortality is more important than growth rate in determining average fry weight
• When competition for resources (habitat & food) is greater mortality of age 0 trout is higher and the smaller individuals are the most vulnerable
• The most prevalent form of mortality is starvation and disease due to poor condition
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Population Level Analysis
• Density Dependence in Growth
– Size-dependent mortality is more important than growth rate in determining average fry weight
• The per-fish rate of predation mortality is much lower at high fish density than starvation and disease
• At low density it is just as important as starvation and disease
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Population Level Analysis
• No Pools Produces Few Large Trout (Bisson & Sedell 1984)
– In watersheds with clearcut timber harvests both the pool volume and the abundance of older trout were lower than in comparison control watersheds
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Population Level Analysis
• No Pools Produces Few Large Trout (Bisson & Sedell 1984)– Five year simulation with pools removed resulted in
lower abundance of all age classes especially the older ones
– Terrestrial predation increased because of the shallower water.
– Growth was slower because of the increased energy expenditure in the faster moving water resulting in fewer eggs per spawner.
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Population Level Analysis
• No Pools Produces Few Large Trout (Bisson & Sedell 1984)– 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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Potential Applications
• Instream flow evaluation:– Assessing cumulative effects of changes in:
• flow rate, flow timing, temperature, physical habitat, …
• Evaluating habitat restoration actions:– Assessing benefits of changes in nearshore habitat, wood, in-
stream objects, etc.• What are the benefits of additional cover for hiding vs. feeding?
– Assessing population-level effects of:• Spawning habitat• Stranding
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Potential Applications
• Predicting species interactions: – How does competition among salmonid species/races affect
restoration success?
– What are interactions between salmonids and non-salmonid species (e.g., striped bass)?
• Monitoring & adaptive management framework: – Use model to predict results of management actions
– Design monitoring programs to test predictions and the model
– Use model to understand why observed responses occurred
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Population Level Responses Emerging from Processes Acting
at the Individual Level
• Simple appearing responses at population level may result from complex interactions at the individual level– Density effects on size not explained by food
competition
– Fewer pools resulted in fewer trout and smaller adults but bigger 0 and 1year olds