some thoughts on the philosophy of modeling stephen h. jenkins department of biology university of...

Some Thoughts on the Philosophy of Modeling

Stephen H. JenkinsDepartment of Biology

University of Nevada, Reno

18 July 2005

Outline

• The good and the bad parts of the big picture

• Where does modeling fit in science?

• Dichotomies in types of models

• Purposes of models

• A concrete example

• The big picture revisited

The bad part of the big picture

The Wall Street Journal, 21 June 2005:

“The Earth currently does seem to be in a warming period, though how warm and for how long no one knows. In particular, no one knows whether this is unusual or merely something that happens periodically for natural reasons. Most global warming alarms are based on computer simulations that are largely speculative and depend on a multitude of debatable assumptions.”

See www.realclimate.org

How does modeling fit in the scientific process?

Laws, Theories, Hypotheses, Facts

Observations and Experiments

Models?

Giere’s View of Models

Model Real WorldHypothesis

Model Fits?

Predictions

reasoning,calculations

Data

observations,experiments

Agree?

Summary of Giere

• A model is a representation of the real world.

• The linked hypothesis is that the model fits the real world in specified ways.

• Scientists use models to represent some aspects of the real world for specific purposes.

(R. N. Giere, 1997, Understanding scientific reasoning; 2004, Philosophy of Science 71:742-752)

Hilborn and Mangel’s View

• “Models are tools for the evaluation of hypotheses.”

• “Most hypotheses could be represented by a number of models.”

• “models … [are] specific version[s] of hypothes[e]s.”

(1997, The ecological detective)

Levins’ View

• “A mathematical model is neither an hypothesis nor a theory.”

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

(1966, American Scientist 54:421-431)

Many Kinds of Models

verbal, conceptual, pictorial, mechanical, scale, analog, theoretical, mathematical, statistical, causal, …

Atmosphere

Oceans

1x

50x

Plants & Soil

GeologicalReservoirs

Fossil fuels 6x

Sediments 100,000x

3x

peat

form

atio

n

respiration

photosynthesis

gas

exch

ange

volcanic activity

sedimentation

burn

ing o

f fos

sil fu

els

burning, cuttingforests

Pictorial and Mathematical Models

Jackson et al. (2000, Bioscience 50:694-706): This pictorial conceptualmodel → a mathematical model.

Pictorial and Mathematical Models 2

Giere: This pictorial map is an abstract representationof the world, like a mathematical model.

Tactical vs. Strategic Models

• Detailed, realistic models of specific systems = tactical models

• General models for understanding basic principles = strategic models

• This dichotomy attributed by May (1973) to Holling (1966)

Tactical vs. Strategic Models 2

• Tactical models sacrifice generality to realism and precision

• Strategic models– sacrifice realism to generality and precision

or– sacrifice precision to realism and generality

(R. Levins, 1966, American Scientist 54:421-431; S. Orzack and E. Sober, 1993, QRB 68:533-546; Levins, 1993, QRB 68:547-555)

Analytical vs. Simulation Models

•1970’s– Schoener, Cohen,

Roughgarden

•1990’s– Basey, Fryxell

[J. M. Basey and S. H. Jenkins, 1995, Influences of predation risk and energy maximization on food selection by beavers (Castor canadensis), Can. J. Zool. 73:2197-2208.]

Analytical vs. Simulation Models

Deterministic vs. Stochastic Models

Simple vs. Complex Models

Are general circulation models simple or complex?

Is Levins’ Fitness Set Model of the Evolution of Niche Breadth Simple or Complex?

M M

M

M

Simple vs. Complex Models

• E. G. Leigh: “Many advances of understanding were brought about by the demands of simplicity.” (1968, Science 160:1326-1327)

• M. Christie: “A ‘perfect’ but very complicated model … provides no satisfying explanation of how the behaviour of the system arises out of the laws that were incorporated into the modelling.” (2000, The ozone layer, Cambridge Univ. Press)

Christie on Computer Models

• “A modern computer model can be sufficiently complex for there to be a danger … that it can become an end in itself.”

• A model may work without being accurate.

• What is an explanation in science?

• Can we acquire too much data?

Interdisciplinary Modelingand Complex Models


Descriptive vs. Mechanistic Models

• Mechanistic models

– DeAngelis

– malaria example

• A role for descriptive models

Models for Understanding or Prediction?

• Caswell’s “model paradox”:

– An exponential model doesn’t fit human population growth, nor does a logistic model.

– How about a model with per capita growth rate an increasing function of population size?

(H. Caswell, 1976, in B. C. Patten, ed., Systems analysisand simulation in ecology, vol. IV.)

dNrN

dt

2dN rNdt

9 (1.00155)0.25 10 tN

9 2095

(2095 )0.25 10

tN

Exponential Model

“Doomsday” Model

Year

0 500 1000 1500 2000

Hum

an

Po

pu

latio

n (

billi

on

s)

0

1

2

3

4

5

6

Actual

Exponential Model

"Doomsday" Model

What Happens in 2095?

9 2095

(2095 )0.25 10

tN

(J. E. Cohen, 1995, How many people can the Earth support? Norton.)

Multiple Meanings of Prediction

• validation of predictive models– multiple regression – weather forecasting

• testing of models for understanding– test pieces of models– test predictions about experiments– test alternative models

• Prediction

• Understanding

– Mechanisms

– Causes

Means and Ends

How Will Global Climate Change Affect the Distribution of Malaria?

• Malaria causes > 1 million deaths/year.– 400-500 million cases/year; 3.1 billion at risk.

• Will climate change cause more people to be at risk of malaria?

• If so, how many?

Two Models of Climate Change and Malaria

• a descriptive, statistical model– Rogers and Randolph, 2000, Science 289:1763-1766.

• A mechanistic, biological model– Martens et al., 1999,Global environmental change

9:S89-S107.

Descriptive Model: Rogers and Randolph

• Compared multiple climate variables inside and just outside the current range of malaria.

• Correlated climatic factors with range limits of malaria.

• Extrapolated to 2050 using models of global climate change, human population growth.

Descriptive Model: Some Methods

• 15 climatic variables for 3000 sites

• Cluster analysis → 6 groups of sites

• Discriminant analysis → 5 variables that maximize distances between groups of sites with and without malaria– min(monthly mean temp)– mean(monthly max temp)– min(monthly ppt)– 2 SVP variables

How well does the descriptive model predict current malaria distribution?

• 20 independent sets of 1000 random points– 500 with malaria, 500 without– different from points used to make model– predicted malaria with maximum likelihood

• Results– 78% correct predictions– 14% false positives– 8% false negatives

Predictions of Descriptive Model for 2050

Mechanistic Model: Martens et al.

• Plasmodium causes malaria and is carried by mosquitoes

– How do temperature and moisture affect parasites and mosquitoes?

• Extrapolate to 2080 using models of global climate change, human population growth.

Overview of Mechanistic Model

R0 = basic reproduction rate of a parasite

= average # secondary infections following first infection in a population

R0 > 1 → infection can spread

What determines R0 for malaria?

1. Number of mosquitoes infected when they bite an infected person.

2. Probability that an infected mosquito lives long enough for parasite to complete incubation.

3. Number of people infected during remaining lifespan of mosquito.

[1] × [2] × [3]

What determines transfer of parasite from a person to mosquitoes?

[1] = biting rate × # mosquitoes/person × avg. duration of infectiousness × probability of transfer

biting rate depends on temperaturemosquito density depends on precipitationother 2 terms independent of climate

Putting the Mechanistic Model Together

• temperature-dependent terms

• moisture-dependent terms

• transfer probabilities

• model uses relative transmission potential instead of basic reproduction rate of parasite

Comparative Results

• Based on their descriptive model, Rogers and Randolph predicted at most 23 million additional people at risk of malaria by 2050.

• Based on their mechanistic model, Martens et al. predicted 90-200 million additional people at risk of malaria in poor countries by 2080 (van Lieshout et al., 2004, Global Environmental Change 14:87-99).

Comparative Weaknesses

• Descriptive model: Sites lacked malaria because of successful control, not unsuitable climate

• Mechanistic model: Premature

Comparative Strengths

• Descriptive model: considers interactions between climate factors

• Mechanistic model: suggests new research

The Perils of Prediction

• Cultural factors and malaria in the future

• Predictions and politics

• Alternative ways to test models

Barton’s Harassment of Mann et al.

1) A list of all financial support for research that these scientists have received, even including "honoraria“.

2) A list of all conditions relating to the scientists' federal and other grants, including whether these grants include stipulations relating to "the dissemination and sharing of research results“.

3) Information as to the location of data archives for "each published study for which you were an author or co-author“, as well as an explanation of "when this information was available to researchers," how the information may have been modified since study publication, and how someone else can attempt to replicate the work.

4) Provision of the "exact computer code" used to generate the "hockey stick" results.

5) A list of any requests the scientists have received for data and information, as well as explanations of how they have responded to such requests "and why“.

6) “A detailed narrative explanation" of errors in the scientists' work and responses to specific questions raised by critics.

7) A detailed account of the scientists' contributions to the work of the IPCC.

some thoughts on the philosophy of modeling stephen h. jenkins department of biology university of...

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