introduction to models
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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) - PowerPoint PPT PresentationTRANSCRIPT
Introduction to ModelsLandscape 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
Cons
umpt
ion
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 toolNeed to validate assumptionsModel 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 modelsDeterministic
◦Same inputs… same outputs
Stochastic◦Includes probabilities
How to do this? Random number based on some distribution.
Types of modelsScientific (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
µAttempts 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. 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
Initial Larval Condition
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)
YESIndividual
DeadX
Initial Larval Condition
Ingestion Submodel
Starvation Threshold Reached?
Daily Growth Rate (µg/d)
Total Ingestion (µg/d)
YESIndividual
DeadX
NO
Bioenergetics Submodel
Initial Larval Condition
Ingestion Submodel
Starvation Threshold Reached?
Daily Growth Rate (µg/d)
Total Ingestion (µg/d)
YESIndividual
DeadX
NO
Eaten?Predation Submodel
YES
Bioenergetics Submodel
Initial Larval Condition
Ingestion Submodel
Starvation Threshold Reached?
Daily Growth Rate (µg/d)
Total Ingestion (µg/d)
YESIndividual Dead
XNO
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
Model ConstructionEach 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 modelsAnalytical
◦Numeric solution
Simulation◦No numeric solution, requires
computers
Net Logo….
Types of modelsDynamic
◦Change through time
Static◦Constant relationships
Spatial modelsWhen is a spatial model needed?
◦Distance or arrangement is important.
Spatial modelsSpatial pattern is in independent
variable. ◦Examples?
Predicting spatial variation through time. ◦Examples?
Processes or biotic interactions generate pattern.◦Examples
AssignmentLandscape 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 modelDefining the problem –
◦Not trivial◦Most crucial step in research.
Like to just go and observe/measure
Building a modelConceptual Model
b) Conceptual Model of Microcosm
Building a modelWhat type of model?
◦What is the expected use of the model?
◦Data availability?
Building a modelModel development
◦So many types of models….
Building a modelComputer Implementation
◦Are there existing packages?◦Developing your own code…
Building a modelParameter 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 0.25 0.5 0.25 0.5 0.25 0.5Null 0.190 0.512 0.703Random Discharge 0.371 0.638 0.710Weighted Discharge 0.348 0.357 0.434 0.444 0.476 0.499
Specificity Local Spread Distance and p (weighted models only)10-km 20-km 30-km
Model 0.25 0.5 0.25 0.5 0.25 0.5Null 0.845 0.528 0.299Random Discharge 0.605 0.332 0.213Weighted Discharge 0.739 0.739 0.614 0.613 0.495 0.495
Kappa Local Spread Distance and p (weighted models only)10-km 20-km 30-km
Model 0.25 0.5 0.25 0.5 0.25 0.5Null 0.031 0.043 0.006Random Discharge -0.022 -0.028 -0.080Weighted Discharge 0.080 0.089 0.045 0.054 -0.028 -0.006
Building a modelModel Evaluation
◦Does it agree with empirical data? If not… is it a bad model?
Multiple model comparisons…
Building a modelExperimentation and Prediction
Initial Larval Condition
Ingestion Submodel
Starvation Threshold Reached?
Daily Growth Rate (µg/d)
Total Ingestion (µg/d)
YESIndividual Dead
XNO
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
Model ConstructionEach 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 ScenariosST
ATIC
DYNA
MIC
TuesdayNeutral Models…Bring your models!
◦Assignment will be email today.