Introduction to Models

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. Consumption Flock Size

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 increaseingflock 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. Modification of Existing Models • 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

19. Initial Larval Condition

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

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

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

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

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

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

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

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 Low algae Low sediment High sediment High algae

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