individual and population level analysis and validation of an individual-based trout model

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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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• Collaborators:

– Steve RailsbackLang, Railsback, and Associates

– Bret HarveyUS Forest Service, Redwood Sciences Laboratory

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http://math.humboldt.edu/~simsys/

•Products & publications:

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• Our Approach to Validation• Validation Experiments

– Individual behavior– Population level behavior

• Results• Conclusions

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Individual-based Trout Model

• Spatially Explicit with One Day Time Step

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• 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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• Movement (Habitat Selection)

– Movement is the most important mechanism available to stream fish for adapting to changing conditions

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• 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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• 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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• 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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• 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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• 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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• Habitat Selection– Maximize Survival

– No hierarchical feeding

– All fish use cell with

highest daily survival

probability

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• 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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• 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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• Response to High Flows

– At flood flows, trout move to quieter water on the stream margin

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• Response to High Flows– Simulation: Flow rises from 0.6 to 5 m/s, then recedes

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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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 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 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 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 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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• 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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• 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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• 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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– 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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– Fall mean weight of age 0 trout is related to

• Time of emergence

• Size-dependent mortality

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– 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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– 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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– 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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• 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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• 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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• 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

individual and population level analysis and validation of an individual-based trout model

Documents

equilibratelargest fish

larger fish

riskhungry fish

adult trout

habitat use

small habitat

sizebased hierarchyfood

population level analysis