1.2. Models as analytical toolsPopulation 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:
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.
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: