Introduction to Models Landscape Ecology

What are models?

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

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.

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.

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

Flock Size Consumption

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.

Questions/Comments

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

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.

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

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

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.

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

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

IBMs for larval/ juvenile fish and yellow perch have been developed ◦ Fulford et al. 2006, Letcher et al 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

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

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

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

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

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)

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

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

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

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 Next fish/ next day Bioenergetics Submodel

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

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

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

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

Net Logo….

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

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

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

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

Building a model… What does it take?

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

Building a model Conceptual Model

b) Conceptual Model of Microcosm

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

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

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

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

Random Discharge

Weighted Discharge

Sensitivity Local Spread Distance and p (weighted models only) 10-km 20-km 30-km Model Null Random Discharge Weighted Discharge Specificity Local Spread Distance and p (weighted models only) 10-km 20-km 30-km Model Null Random Discharge Weighted Discharge Kappa Local Spread Distance and p (weighted models only) 10-km 20-km 30-km Model Null Random Discharge Weighted Discharge

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

Building a model Experimentation and Prediction

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 Next fish/ next day Bioenergetics Submodel

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

Conditions and Scenarios STATIC DYNAMIC

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