Fountain Darter Model

Bill GrantHsiao-Hsuan Wang

(Dr. Rose)University of Texas

Texas A&M UniversityMay 12, 2014

Outline (Plan A)I. A bit of modeling philosophyII. The current model

• Model input / output• Model structure• Model function• Model programming

III. The future model• Available data• UseS of data in model• Hypothesized relationships

IV. Predicting the future? (Embracing uncertainty)• Parametric uncertainty• Structural uncertainty

Outline (Plan A)I. A bit of modeling philosophyII. The current model

• Model input / output• Model structure• Model function• Model programming

III. The future model• Available data• UseS of data in model• Hypothesized relationships

IV. Predicting the future? (Embracing uncertainty)• Parametric uncertainty• Structural uncertainty

Rosen (1991) in Saltelli et al. (2008)

Naturalsystem

Formalsystem

Entailment

Entailment

EncodingDecoding

Modeling

Outline (Plan A)I. A bit of modeling philosophyII. The current model

• Model input / output• Model structure• Model function• Model programming

III. The future model• Available data• UseS of data in model• Hypothesized relationships

IV. Predicting the future? (Embracing uncertainty)• Parametric uncertainty• Structural uncertainty

Model Input

Water flow

Aquatic Habitat

Fountain DarterPopulation Structure and Dynamics

Model Output

Veg. type

Time

Egg

Larv

a

Juve

nile

Adul

t Aquatic vegetation typeWater depth

Water velocity

Water temperature

Life cycle HabitatMovement

Model Structure

Egg laying = f (month)Schenck and Whiteside (1977)

Egg mort. = f (temp.)Larva mort. = f (temp.)Juvenile mort. = f (temp.)Adult mort. = f (temp.)

Picher and Hart (1982)Brandt et al. (1993)Bonner et al. (1998)

Density-dependent mort. = f (# veg. patches)

Movement= f (veg. type)

Stay in habitat patch with vegetation

Move toward habitat patch with vegetation

Aquatic veg. type = f (season)Jan. 2003Dec. 2008

Bio-West annual reports

Water depth = f (flow)Old Channel

10 - 80 cfsHardy et al. (2010)

Water velocity = f (flow)Old Channel

10 - 80 cfsHardy et al. (2010)

Water temp. = f (hour)Jan. 2003Dec. 2008

Bio-West annual reports

Model Function

Life cycle Movement Habitat

1 Initialization

2 Input2.1 Input vegetation types

2.2 Input water temperatures

2.3 Input water depths and water velocities

3 Submodels3.1 Adjust vegetation types (seasonally)

3.2 Adjust water depths and water velocities (daily)

3.3 Adjust water temperatures (hourly)

3.4 Adjust fountain darter ages and developmental stages (daily)

3.7 Calculate fountain darter egg laying (recruitment) (daily)

3.5 Calculate fountain darter mortalities (daily)

3.6 Calculate fountain darter movements (hourly)

3.8 Update aggregated (output) variables (hourly)

Model Programming

Outline (Plan A)I. A bit of modeling philosophyII. The current model

• Model input / output• Model structure• Model function• Model programming

III. The future model• Available data• UseS of data in model• Hypothesized relationships

IV. Predicting the future? (Embracing uncertainty)• Parametric uncertainty• Structural uncertainty

Available Data

Driving Variables (Input) Data

Process Data (Functional Relationships for Model Equations)

Evaluation (of Output) Data

Aquatic Vegetation Datamapping of vegetation typesplant growth = f (temp.)plant biomass = f (% veg. cover)

(2014) plant growth rate and dispersal= f (substrate, depth, velocity)

Fountain Darter Datadensity = f (veg. type)

(Drop nets)Size class distribution

(Dip nets)

mortality = f (temp.)fecundity = f (habitat quality)predation = f (veg. density)movement = f (habitat

preference, dispersal)

(2014)

UseS of Data in Model

E L J A

Depth

VelocityRecr. &

DOMort. = f

Temp.

FoodCover/Pred.

f (veg.)

Veg.

Flow

f (flow)

Movement = f (veg., flow)

Veg. =

f ( flow, veg. restoration, recreation, substrate, light)

Substrate Light

Veg. restoration Recreation

Hypothesized Relationships

Model Input

Water Flow

Aquatic Habitat

Fountain DarterDynamics

Model Output

Outline (Plan A)I. A bit of modeling philosophyII. The current model

• Model input / output• Model structure• Model function• Model programming

III. The future model• Available data• UseS of data in model• Hypothesized relationships

IV. Predicting the future? (Embracing uncertainty)• Parametric uncertainty• Structural uncertainty

Predicting the future?(Embracing uncertainty)

“Oye filósofo ¿va a llover por la noche?”“Te digo mañana.”

(El Filósofo de Guemes)

Naturalsystem

Formalsystem

Entailment

Entailment

EncodingDecoding

Estimated parameters

Uncertainty and sensitivity

analysis

Model Input data

Inference

Saltelli et al. (2008)

Estimation

Parametric bootstrap version of uncertainty and sensitivity analyses

Estimated parameters

ModelLoop on boot-replica of the

input data

Inference

Chatfield (1993) in Saltelli et al. (2008)

Estimation

Bootstrapping of the modeling process (Structural uncertainty)

Modelidentification

Bootstrap of theModeling process

Bayesian model averaging

Data

Prior of model(s)

Prior of parameters

Inference

Posterior of model(s)

Posterior of parameters

Sampling

Saltelli et al. (2008)

The End