1. Introduction to Models Landscape Ecology

2. What are models?

3. What is a model? How is it different from a theory? Hypothesis?

4. Theory, hypothesis, model? Theory  (theoria – a looking at, contemplation, speculation) ◦ A formulation of apparent relationships or underlying principles of certain observed phenomena which has been verified to some degree. Hypothesis:  (hypotithenai – to place under) ◦ an unproved theroy, proposition, supposition ◦ Tentatively accepted to explain certain facts or to provide basis for further investigation.

5. Theory, hypothesis, model? Model  (modus – the way in which things are done) ◦ A stylized representation or a generalized description used in analyzing or explaining something. ◦ Models are tools for the evaluation of hypotheses.

6. Example: Hypothesis: ◦ Birds forage more efficiently in flocks than individually

7. Flock Size Consumption

8. Example: Hypothesis: ◦ Birds forage more efficiently in flocks than individually Models: ◦ Consumption proportional to flock size. ◦ Consumption saturates as flock size increases. ◦ Consumption increases and then decreases with increaseing flock size.

9. Questions/Comments

10. Why use models? Most basic… Help test scientific hypotheses ◦ Clarify verbal descriptions of nature and of mechanisms. ◦ Help define process ◦ No model is fully correct  So comparing models may aid in helping understand process. ◦ Aid in analyzing data ◦ Can’t experiment ◦ Insights into dynamics ◦ Prediction

11. Model as a scientific tool Need to validate assumptions Model needs validation ◦ Compare to data?  If model is inconsistent with some data…  Do we reject the model? ◦ All models are wrong…  The question is…  Which models are most consistent and which ones meet the challenges of new experiments and new data. ◦ Comparison of multiple models.

12. “The validation of a model is not that it is ‘true’ but that it generates good testable hypotheses relevant to important problems.”

13. Types of models Deterministic ◦ Same inputs… same outputs Stochastic ◦ Includes probabilities  How to do this?  Random number based on some distribution.

14. Types of models Scientific (Mechanistic/process based) ◦ Begins with a description of how nature might work and proceeds from this description to a set of predictions relating the independent and dependent variables. Statistical (empirical) ◦ Forgoes any attempt to explain why. ◦ Simply describes the relationship.

16. Develop a predictive model of how turbidity type/ intensity affects growth and survival of age-0 yellow perch Obj 1: Develop an IBM framework that models daily ingestion and bioenergetics Obj 2: Integrate laboratory results to explicitly include the influence of turbidity on growth and mortality

17. Individual Based Models (IBM) Uses a distribution of traits to model natural variance in a population, not just a mean µ Attempts to recreate and predict complex phenomena based on simple rules

18. IBMs for larval/ juvenile fish and yellow perch have been developed ◦ Fulford et al. 2006, Letcher et al. 1996 Modifications of these models to explicitly include: ◦ Different turbidity types and intensities ◦ Prey switching due to ontogenetic shift ◦ Temporal changes in turbidity type and intensity ◦ Laboratory feeding rate data for daily ingestion Modification of Existing Models

19. Initial Larval Condition

20. –Initial lengths from random distribution: n=10,000 µ= 5.3 sd=0.3 –Individual weights calculated as: Weight = 0.519*Length^3.293

21. Initial Larval Condition Ingestion Submodel Total Ingestion (µg/d)

22. Initial Larval Condition Ingestion Submodel Replaces traditional foraging submodel Calculated from laboratory results Turbidity types/ intensities and developmental stage Total Ingestion (µg/d)

23. Initial Larval Condition Ingestion Submodel Daily Growth Rate (µg/d) Bioenergetics Submodel Total Ingestion (µg/d)

24. Initial Larval Condition Daily Growth = (Total Ingestion*Assimilation Efficiency) - TC - Modifiers include temperature and individual size Ingestion Submodel Daily Growth Rate (µg/d) Bioenergetics Submodel Total Ingestion (µg/d)

25. Initial Larval Condition Ingestion Submodel Starvation Threshold Reached? Set to 53% of previous maximum mass Ingestion Submodel Daily Growth Rate (µg/d) Bioenergetics Submodel Total Ingestion (µg/d) YES Individual Dead X

26. Initial Larval Condition Ingestion Submodel Starvation Threshold Reached? Daily Growth Rate (µg/d) Total Ingestion (µg/d) YES Individual Dead X NO Bioenergetics Submodel

27. Initial Larval Condition Ingestion Submodel Starvation Threshold Reached? Daily Growth Rate (µg/d) Total Ingestion (µg/d) YES Individual Dead X NO Eaten? Predation Submodel YES Bioenergetics Submodel

28. Initial Larval Condition Ingestion Submodel Starvation Threshold Reached? Daily Growth Rate (µg/d) Total Ingestion (µg/d) YES Individual Dead X NO Eaten? Predation Submodel YES NO Update Individual’s Mass/ Length Modified from Fulford et al 2006, Letcher et al. 1996 Next fish/ next day Bioenergetics Submodel

29. Model Construction Each model run starts with 10,000 individuals ◦ Several runs per “condition” Simulation of 120 days post-hatch Switch in feeding regime at 30 mm to simulate ontogenetic shift ◦ Inclusion of larger benthic prey types ◦ Larval vs. Juvenile feeding rates

30. Initial Model Comparisons “Static” conditions No variance in intensity or type over the 120 days Low and High conditions for both turbidity types –Low ~ 5ntu –High ~ 100ntu –Comparison of absolute impact of each type and intensity

31. Large differences in growth between type and intensity High algae Low algae High sediment Low sediment

32. Types of models Analytical ◦ Numeric solution Simulation ◦ No numeric solution, requires computers

34. Net Logo….

35. Types of models Dynamic ◦ Change through time Static ◦ Constant relationships

36. Spatial models When is a spatial model needed? ◦ Distance or arrangement is important.

37. Spatial models Spatial pattern is in independent variable. ◦ Examples? Predicting spatial variation through time. ◦ Examples? Processes or biotic interactions generate pattern. ◦ Examples

38. Assignment Landscape ecological models… Next three lectures will cover Neutral models and dispersal. Find two papers: ◦ One with a neutral model ◦ One with a model of dispersal Describe: ◦ Primary question/objective ◦ Model type ◦ Data needs ◦ Validation

39. Building a model… What does it take?

40. Building a model Defining the problem – ◦ Not trivial ◦ Most crucial step in research.  Like to just go and observe/measure

41. Building a model Conceptual Model

42. b) Conceptual Model of Microcosm

43. Building a model What type of model? ◦ What is the expected use of the model? ◦ Data availability?

44. Building a model Model development ◦ So many types of models….

45. Building a model Computer Implementation ◦ Are there existing packages? ◦ Developing your own code…

46. Building a model Parameter Estimation ◦ Data from literature. ◦ Change value of parameters and see how model output fits empirical data.

48. Random Discharge

49. Weighted Discharge

50. Sensitivity Local Spread Distance and p (weighted models only) 10-km 20-km 30-km Model0.250.5 0.250.5 0.250.5 Null0.190 0.512 0.703 Random Discharge0.371 0.638 0.710 Weighted Discharge0.3480.357 0.4340.444 0.4760.499 Specificity Local Spread Distance and p (weighted models only) 10-km 20-km 30-km Model0.250.5 0.250.5 0.250.5 Null0.845 0.528 0.299 Random Discharge0.605 0.332 0.213 Weighted Discharge0.739 0.6140.613 0.495 Kappa Local Spread Distance and p (weighted models only) 10-km 20-km 30-km Model0.250.5 0.250.5 0.250.5 Null0.031 0.043 0.006 Random Discharge-0.022 -0.028 -0.080 Weighted Discharge0.0800.089 0.0450.054 -0.028-0.006

51. Building a model Model Evaluation ◦ Does it agree with empirical data?  If not… is it a bad model? Multiple model comparisons…

52. Building a model Experimentation and Prediction

53. Initial Larval Condition Ingestion Submodel Starvation Threshold Reached? Daily Growth Rate (µg/d) Total Ingestion (µg/d) YES Individual Dead X NO Eaten? Predation Submodel YES NO Update Individual’s Mass/ Length Modified from Fulford et al 2006, Letcher et al. 1996 Next fish/ next day Bioenergetics Submodel

54. Model Construction Each model run starts with 10,000 individuals ◦ Several runs per “condition” Simulation of 120 days post-hatch Switch in feeding regime at 30 mm to simulate ontogenetic shift ◦ Inclusion of larger benthic prey types ◦ Larval vs. Juvenile feeding rates

55. Conditions and Scenarios STATIC DYNAMIC

57. Tuesday Neutral Models… Bring your models! ◦ Assignment will be email today.