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Ecology 302: Introduction.

(Ricklefs, Chapter 1; Levins, “Strategy of Model Building” (pp. 421-

423; 430-431); Borges, “Exactitude in Science”.)

“Imagine that we are living on an intricately patterned carpet. … Some parts of the pattern appear to be random, like an abstract ex-pressionist painting; other parts are rigidly geometrical. A portion of the carpet may seem totally irregular, but when the same portion is viewed in a larger context, it becomes part of a subtle symmetry.

“The task of describing this pattern is made difficult by the fact that the carpet is protected by a thick plastic sheet with a translu-cence that varies from place to place. In certain places we can see through the sheet and perceive the pattern; in others the sheet is opaque. The plastic sheet also varies in hardness. Here and there we can scrape it down so that the pattern is more clearly visible. In other places the sheet resists all efforts to make it less opaque. … No one knows how thick the plastic sheet is. At no place has any-one scraped deep enough to reach the carpet's surface, if there is one. “

--- Martin Gardner, as quoted by Arthur Winfree, The Geometry of

Biological Time, p. xiv

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Key Points.

• Definition of Ecology.

• Levels of ecological organization range from local

populations to the biosphere.

• All theories are models.

• Models can be falsified in two ways.

• Separation of time scales permits model simplifica-

tion.

• Complex systems:

o can respond to external inputs in unexpected ways.

o Complex systems often inherently variable making

it difficult to distinguish external “forcings” from

“natural variability.”

• Interesting questions.

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I. Ecology

A. Study of how organisms interact with each other and their

environment.

1. Nature of the interactions.

2. The consequences

a. Patterns in time and space that result.

b. Response to exogenous inputs.

3. Interplay between ecology and evolution.

B. Ecological systems can be studied at different levels.

1. Populations. Generally of organisms belonging to the same

or a small number of species.

2. Communities. Assemblages of coexisting species – often re-

lated taxonomically or by ecological role.

3. Ecosystems. All species in a particular place.

4. Biosphere. The global biota.

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Figure 1. Ecological levels.

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C. What we measure depends on the level.

1. Population ecologists study

a. Changing population numbers.

b. Behavioral, developmental, physiological, etc. response

to environmental change (biotic or abiotic).

c. Selective consequences of such change.

2. Community ecologists place greater emphasis on species.

a. Who lives with whom.

b. Functionally similar communities in different locales.

3. Ecosystem ecologists emphasize flows of energy and mate-

rials.

D. Levels overlap.

E. Plant population/community ecology, by virtue of its empha-

sis on water and gas exchange, connects more readily with

ecosystem ecology than its animal-focused counterparts.

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II. Science as the Modeler’s Art.

Figure 2. Science as the modeler’s art. Mechanistic assumptions and

simplifying approximations inform the construction of a model that

generates predictions. Falsification results when observation contra-

dicts prediction (red slashes) or when new observations indicate as-

sumptions or simplifications to be untenable (blue slashes).

.

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A. Models are simplified representations of reality.

1. Mathematical, pictorial or verbal.

2. Reduce real world complexity to “the essentials.”

B. All theories are models, and they must be falsifiable.

C. Mechanistic assumptions => testable predictions.

D. Model falsification results if

1. Observation ≠ prediction.

2. Assumptions and / or simplifying approximations turn out

to be wrong or inappropriate.

3. Distinguishing between these alternatives can be challeng-

ing

E. Model acceptance results when repeated attempts at falsifi-

cation fail.

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F. Remarks:

1. Models can be falsified but never be proved.

a. Revising a model’s assumptions in light of new infor-

mation ≠ confirming its predictions.

b. What results is a new model, nothing more.

2. Models reduce real-world

complexity to “managea-

ble” approximation.

3. Simplification essential if

model to be useful.

4. Abundant computing pow-

er a blessing / curse of mo-

dernity.

a. “All-but-the-kitchen-

sink” computer simula-

tions replace systems

that aren’t understood

with models that can’t

be understood – certain-

ly not mathematically.

Figure 3. Computer perfor-

mance (a) and feasible model

complexity (b). (McGuffie and

Henderson-Sellers 2005).

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b. All one can do is to perform numerical experiments.

c. Inescapable imprecision increases with the addition of

each new variable / parameter.

d. “Adjustable” parameters a Faustian temptation - espe-

cially when system time scales long.

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G. Gardner’s carpet reminds us that science at best a sequence

of successive approximations to reality.

1. One hopes that the approximations converge.

2. Even when they do, the result is not necessarily correct

a. Like the dinosaurs of Jurassic Park, scientists often “move

in herds.”

b. E.g., 19th

century geological estimates of the age of the

earth.

3. Sometimes we get

a. Right answer for the wrong reasons – Lamarck.

b. Wrong answer for the “right” reasons – Lord Kelvin.

4. Nature indifferent to human proclivity. The Scylla and Cha-

rybdis between which one must navigate are

a. Attachment to one’s own ideas.

b. Ideological proclivity – think Lysenkoism / eugenics.

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III. Macroscopic vs. microscopic levels of organization.

A. Classic example is derivation of the gas law,

�� � �� (1)

from a model of molecular collision.

1. Here,

a. P, V, and T are macroscopic (measurable) quantities.

b. Molecular velocities are microscopic (not measurable)

quantities.

2. The molecular model makes certain assumptions – e.g.,

perfectly elastic collisions between molecules – that break

down under certain conditions.

a. In a good model, one can specify à priori when the model

will fail.

b. E.g., High temperature / pressure in the case of Eq 1.

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Figure 4. Science at small and large length scales. A micro-

scopic model generates macroscopic predictions. As in Fig-

ure 1, red and blue slashes indicate model falsification and

need for revision.

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B. Separation of time scales.

1. Time, length scales vary in-

versely: microscopic variables

fast; macroscopic slow.

2. Assume the fast variables in

approximate equilibrium with

the slow and eliminate.

��� � ��∗�� � (3)

3. In ecology:

a. Microscopic: Changing

numbers / activities of

organisms.

b. Macroscopic: Species di-

versity; community / eco-

system stability; large scale / global fluxes of energy and

materials, etc.

4. Alternative to Eq 3 is to treat the slow variables as constants

and study the slow variables.

5. In biology, macro and micro time scales often overlap. Why?

Figure 5. Viewed in the large,

body size and generation time

co-vary allometrically, i.e., ac-

cording to � � ���.

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IV. Consequences of Human Impacts.

Figure 4. Otter-urchin-kelp ecosystem. Protecting sea otters

indirectly promotes the growth of kelp forests because otters

eat sea urchins that graze kelp. Kelp forests also promote fish

larva survival, and therefore indirectly make more fish availa-

ble for species that eat fish. Alas! The otters eat fish too.

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A. The otter-urchin-kelp ecosystem a good example of a

complex system with multiple feedback loops – see text

for details.

B. Gotchas.

1. There may be additional slow variables whose un-

predictable effects not immediately manifest.

2. Absolutely no reason to expect that ecological sys-

tems go to equilibrium.

3. Non-equilibrium systems often manifest

a. Ragged periodicities on multiple time scales;

b. Abrupt shifts from one dynamical regime to an-

other.

4. For such systems,

a. Distinguishing system response to exogenous

inputs from “natural variability” non-trivial.

b. Predicting the long-term behavior a prescription

for embarrassment.

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C. Twelve year experiment

exposing northern tree

communities to increased

��� and �� an example

slow variable feedback.

1. Limitation of ��� fer-

tilization effect by in-

sufficient soil nitrogen

expected, but not ob-

served.

2. Enhanced net primary

productivity sustained

by increased root

growth / microbial ac-

tivity.

3. Initial reductions in

productivity conse-

quent to increased ��

not sustained as ozone-tolerant individuals / species

took up the slack.

Figure 5. Net primary productivi-

ty in the final years of a 12 year

study. Shaded and unshaded bars

compare trees exposed to ele-

vated ��� (top) and ��(bottom)

with controls. From Zak et al.

(2011. Ecology Letters).

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V. Questions.

A. What level of detail is required to understand / predict

the dynamics / behavior of ecological systems?

B. Related: As we add more variables to ecological models,

do their properties converge?

C. Related: To what extent

can populations, com-

munities, etc., be viewed

as “systems”, i.e., with

everything else being

treated as “the envi-

ronment”?

D. Is it useful to think of

ecological systems as

equilibrial subject to ex-

ternal “forcings”?

E. Equivalently: Is “natural variability” intrinsic, induced

from without or both?

Figure 6. System and environ-

ment. How does one distinguish

one from the other?

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F. Related: Is there a “balance of nature”? If yes, to what

does it pertain: species abundances (relative or abso-

lute), species numbers, productivity, fluxes of energy and

materials?

G. Related: To what extent are species interchangeable, and

in what sense?

H. How does one deal with ecological “contingency” beyond

simply documenting it?

I. Contrapuntally: Are there overarching principles compa-

rable to � � �� and universal gravitation about which

ecology can be organized?

Figure 7. Westward expansion of Sturnus vulgarisi following

its introduction into North America in 1890.

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J. How can ecologists minimize contamination of their con-

clusions by ideological / confirmation bias? Or is this not

a problem?