1. Fountain Darter Model Bill Grant Hsiao-Hsuan Wang (Dr. Rose) University of Texas Texas A&M University May 12, 2014

2. Outline (Plan A) I. A bit of modeling philosophy II. 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

3. Outline (Plan A) I. A bit of modeling philosophy II. 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

4. Rosen (1991) in Saltelli et al. (2008) Natural system Natural system Formal system Formal system Entailment EncodingDecoding Modeling

5. Outline (Plan A) I. A bit of modeling philosophy II. 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

6. Model Input Water flow Aquatic Habitat Fountain Darter Population Structure and Dynamics Model Output

7. Egg Larva Juvenile Adult Aquatic vegetation type Water depth Water velocity Water temperature Life cycle HabitatMovement Model Structure

8. 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. 2003 Dec. 2008 Bio-West annual reports Water depth = f (flow) Old Channel 10 - 80 cfs Hardy et al. (2010) Water velocity = f (flow) Old Channel 10 - 80 cfs Hardy et al. (2010) Water temp. = f (hour) Jan. 2003 Dec. 2008 Bio-West annual reports Model Function Life cycleMovementHabitat

9. 1 Initialization 2 Input 2.1 Input vegetation types 2.2 Input water temperatures 2.3 Input water depths and water velocities 3 Submodels 3.1 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

10. Outline (Plan A) I. A bit of modeling philosophy II. 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

11. Available Data Driving Variables (Input) Data Process Data (Functional Relationships for Model Equations) Evaluation (of Output) Data Aquatic Vegetation Data mapping of vegetation types plant growth = f (temp.) plant biomass = f (% veg. cover) (2014) plant growth rate and dispersal = f (substrate, depth, velocity) Fountain Darter Data density = 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) S UseS of Data in Model

12. ELJA Depth Velocity Recr. & DO Mort. = f Temp. Food Cover/Pred. f (veg.) Veg. Flow f (flow) Movement = f (veg., flow) Veg. = f ( flow, veg. restoration, recreation, substrate, light) SubstrateLight Veg. restorationRecreation Hypothesized Relationships Model Input Water Flow Aquatic Habitat Fountain Darter Dynamics Model Output

13. Outline (Plan A) I. A bit of modeling philosophy II. 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

14. Predicting the future? (Embracing uncertainty) “Oye filósofo ¿va a llover por la noche?” “Te digo mañana.” (El Filósofo de Guemes) Natural system Natural system Formal system Formal system Entailment EncodingDecoding

15. Estimated parameters Estimated parameters Uncertainty and sensitivity analysis Model Input data Inference Saltelli et al. (2008) Estimation Parametric bootstrap version of uncertainty and sensitivity analyses

16. Estimated parameters Estimated parameters Model Loop on boot- replica of the input data Inference Chatfield (1993) in Saltelli et al. (2008) Estimation Bootstrapping of the modeling process (Structural uncertainty) Model identification Bootstrap of the Modeling process

17. Bayesian model averaging Data Prior of model(s) Prior of parameters Inference Posterior of model(s) Posterior of parameters Sampling Saltelli et al. (2008)

18. The End