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Introduction to Models

This overview delves into the roles of models in landscape ecology, specifically focusing on their definitions, differences from theories, and types. It explains hypotheses as unproven propositions that guide scientific inquiry. Models serve as representations to analyze and explain ecological phenomena, helping in hypothesis testing and data evaluation. This article highlights how models, whether deterministic or stochastic, contribute to understanding complex ecological processes, providing insights into dynamics and predicting outcomes in scenarios like fish growth in varying turbidity conditions.

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Introduction to Models

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  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.

  15. 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

  16. 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

  17. 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

  18. Initial Larval Condition

  19. 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

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

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

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

  23. 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

  24. 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

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

  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? NO Update Individual’s Mass/ Length Next fish/ next day Modified from Fulford et al 2006, Letcher et al. 1996

  28. 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

  29. 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

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

  31. Types of models • Analytical • Numeric solution • Simulation • No numeric solution, requires computers

  32. Net Logo….

  33. Types of models • Dynamic • Change through time • Static • Constant relationships

  34. Spatial models • When is a spatial model needed? • Distance or arrangement is important.

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

  36. 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

  37. Building a model… • What does it take?

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

  39. Building a model • Conceptual Model

  40. b) Conceptual Model of Microcosm

  41. Building a model • What type of model? • What is the expected use of the model? • Data availability?

  42. Building a model • Model development • So many types of models….

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

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

  45. Random Discharge

  46. Weighted Discharge

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