Interesting examples of models [closed]

Question

I am studying the general use of models in biology in terms of methodology, applications, usefulness etc, and I would really appreciate any recommendations of some specific examples of models from any area in biology. Some examples are the logistic growth model or the Lotka-Volterra prey predator model.

It would be nice if you could shortly explain what the model is used for and why do you think it's an interesting case, and give a reference for further study.

Also any recommendation of books on model development and other meta-model questions in biology is very welcome. Thank you.

Answer 1

Biology is a large field of knowledge! As you give examples drawn from population biology (logistic population growth and Lotka-Voltera models), I will assume you are mainly interested in ecology and evolution.

For analytical models used in ecology and evolution, I highly recommend the book A Biologist's Guide to Mathematical Modeling in Ecology and Evolution by Otto and Day. The book assumes a relatively low level of knowledge in mathematics from the reader and walk the reader through most of the most iconic models in ecology and evolution, their analysis and interpretation. The mathematical tools used in this book include linear algebra, equilibrium analysis, analysis of cyclic behaviour, Markov chain and esp. birth-death processes, diffusion equations, probability theory and stochastic models, approximation theory, class structure models (Leslie matrix and more) and, separation of time scales among others.

For books, mainly theoretical, in population genetics, please have a look at the post Books on population or evolutionary genetics?.

As you talk about the Lotka-Voltera model, you will find an intro to this model in the post What prevents predator overpopulation?.

Answer 2

One nice model to use as a example the Hodgking-Huxley model that describe the current through a nerve fiber given a certain membrane voltage. This model describes the sodium and potassium currents that are the basis of the action potential.

Some characteristics of this model are:

This model explains the membrane currents through the activation of "charged particles" in the membrane that allow the passage of ions (K+ and Na+). It was latter discovered that in the membrane there are Na+ and K+ channels that carry these currents (in the original model there was no evidence of the molecular components of theses channels).

The model can reproduce the action potential of neurons.

The model predicts the existence of "charged particles" in the membrane that must move before the channel open, named gating charges. Since this particle move from one side of the membrane to the other, they generate a small transient current ("gating currents"). These where actually measured 20 years after the proposition of this model.

This is a great model because it described mathematically and physically the behavior of neurons and also predicted several properties that where later fond.

You can read more here:

HH model