Introduction to Models

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 lengths from random distribution: n=10,000 µ= 5.3 sd=0.3

– Individual weights calculated as:• Weight = 0.519*Length^3.293


Ingestion Submodel

Total Ingestion (µg/d)


Ingestion Submodel

•Replaces traditional foraging submodel

•Calculated from laboratory results

• Turbidity types/ intensities and developmental stage



Ingestion Submodel

Daily Growth Rate (µg/d)

Bioenergetics Submodel



• Daily Growth = (Total Ingestion*Assimilation Efficiency) - TC• -Modifiers include temperature and individual size

Ingestion Submodel





Ingestion Submodel

Starvation Threshold Reached?

Set to 53% of previous maximum mass

Ingestion Submodel




YESIndividual

DeadX


Ingestion Submodel




YESIndividual

DeadX

NO



Ingestion Submodel




YESIndividual

DeadX

NO

Eaten?Predation Submodel

YES



Ingestion Submodel




YESIndividual Dead

XNO


YES

NO

Update Individual’s Mass/ Length

Modified from Fulford et al 2006, Letcher et al. 1996

Next fish/ next day


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


Ingestion Submodel




YESIndividual Dead

XNO


YES

NO

Update Individual’s Mass/ Length

Modified from Fulford et al 2006, Letcher et al. 1996

Next fish/ next day


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.

Documents

Introduction to Models