Ergebnis für URL: http://alexei.nfshost.com/PopEcol/lec1/model.html1.2. Models as analytical tools
Population ecology is the most formalized area in biology.
Model is a tool and should never be considered an ultimate goal in ecological
studies.
Model and reality are linked together by two procedures: abstraction and
interpretation:
[mod_sys.gif]
Abstraction means generalization: taking the most important components of real
systems and ignoring less important components. Importance is evaluated by the
relative effect of system components on its dynamics. For example, if we found
that parasitism rate in insect pest is always below 5%, then parasitoids can be
excluded from the model.
Interpretation means that model components (parameters, variables) and model
behavior can be related to components, characteristics, and behavior of real
systems. If model parameters have no interpretation, then they cannot be measured
in real systems.
Most field ecologists are not good at abstraction. If they build a model they
often try to incorporate every detail. Most mathematicians are not good at
interpretation of their models. Usually they think of clean models and dirty
reality. However, both abstraction and interpretation are necessary for
successful modeling. Thus, close collaboration between ecologists and
mathematicians is very important.
Models are always wrong ... but many of them are useful.
How it may happen that the wrong model can give a correct answer? In the same way
as old maps, which assumed a flat earth and used wrong distance relations, where
useful for travelers in the past.
Modeling strategy:
1. Select optimal level of complexity
2. Never plan model development for more than 1 year
3. Avoid the temptation to incorporate all available information into the model
4. Follow specific objectives, don't try to make a universal model
5. If possible, incorporate already existing models
System properties and model properties
1.
Many system properties are not represented in the model.
Example: age structure is not represented in both exponential and
logistic models.
2.
Some model properties cannot be found in real systems.
Example: solutions of differential equations are always smooth,
while trajectories of real systems are always noisy.
Example of a wrong question: Does this population have an equilibrium density?
The stable equilibrium is a state to which all trajectories of the system
converge infinitely close with increasing time. The model (e.g. the differential
equation) may have an equilibrium density, but real populations don't have it
because:
1. Population density cannot be measured with infinite accuracy.
2. Weather fluctuations always add noise to system's dynamics.
3. Time series are never long enough to talk about limits and convergence.
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[4]Alexei Sharov 1/12/96
References
1. http://alexei.nfshost.com/PopEcol/lec1/whatis.html
2. http://alexei.nfshost.com/PopEcol/lec1/popsyst.html
3. http://alexei.nfshost.com/PopEcol/lec1/struct.html
4. http://alexei.nfshost.com/~sharov/alexei.html
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Errormessages are in German, sorry ;-)