Simple Mathematics of Evolution

[Boballoo]

I am doing some research for a book and I have run into the wall of my own capabilities. If there is such a thing, what would the mathematics of evolution look like? How would it work? What parts of evolution are visible or could be made visible through mathematics? Can it be described to someone who is not a mathematician?

[studiot]

4 hours ago, Boballoo said:

I am doing some research for a book and I have run into the wall of my own capabilities. If there is such a thing, what would the mathematics of evolution look like? How would it work? What parts of evolution are visible or could be made visible through mathematics? Can it be described to someone who is not a mathematician?

Since you have given us no idea of the level of you understanding of Mathematics I will have to give a general answer.

Mathematically, evolution is a dynamical system.

There is substantial math for dynamical systems of all sorts.

Probably the best place to start would be the so callled predator - prey equations, which can include chaotic solutions.

https://mathworld.wolfram.com/Lotka-VolterraEquations.html

[joigus]

I'm not sure, but I suppose you mean biological evolution. The most general theory (I'd say meta-theory) is the one under the name "dynamical systems." It studies everything that changes.

The Volterra model is a good place to start. Two competing species with situation not depending on time in the simplest case. Easy enough to understand, and solutions are intuitively clear.

A good motivational video (centered on another simple model of change) could be:

https://www.youtube.com/watch?v=ovJcsL7vyrk

But you haven't said what your level of maths is. Maybe you can tackle a book technical enough.

 

Edited November 9, 2020 by joigus

[Boballoo]

4 hours ago, studiot said:

Since you have given us no idea of the level of you understanding of Mathematics

Probably the best place to start would be the so called predator - prey equations, which can include chaotic solutions.

https://mathworld.wolfram.com/Lotka-VolterraEquations.html

Thank you for that. That is interesting. I was trying to convey that my math skills are minimal. I am great with concepts and geometry, but the rest of math baffles me. To be honest, I am not sure what I am looking for, but that "predator-prey" info is great! Thanks again. 

1 hour ago, joigus said:

https://www.youtube.com/watch?v=ovJcsL7vyrk

But you haven't said what your level of maths is. Maybe you can tackle a book technical enough.

 

My math skills are minimal. But that video is good. I'll watch it later. Thanks for your help. My math is so bad that I am not sure what I am looking for but that link is a good start.

Edited November 9, 2020 by Boballoo

[delboy]

The book Evolution by Futuyma deals with a lot of the maths of evolution, but it's pretty advanced. Maybe I should say very advanced actually.

[CharonY]

1 hour ago, delboy said:

The book Evolution by Futuyma deals with a lot of the maths of evolution, but it's pretty advanced. Maybe I should say very advanced actually.

It is a great book though. However, the takeway should be that modelling the process of evolution requires multiple mathematical models for various aspects of it. There is no one elegant unified model (which is probably true for any somewhat complex system).

[Arete]

From a conceptual level, an understanding of basic neutral theory is also a good place to start. If you can wrap your brain around the concepts of how stochastic changes occur at the molecular level in populations, it becomes easier to layer on selective evolution, game theory and other increasingly complex models of evolution. 

The seminal paper is Kimura 1968. http://dosequis.colorado.edu/Courses/MethodsLogic/papers/Kimura1968.pdf but this review is probably more accessible. https://onlinelibrary.wiley.com/doi/full/10.1111/evo.13650

[joigus]

1 hour ago, Arete said:

From a conceptual level, an understanding of basic neutral theory is also a good place to start. If you can wrap your brain around the concepts of how stochastic changes occur at the molecular level in populations, it becomes easier to layer on selective evolution, game theory and other increasingly complex models of evolution. 

The seminal paper is Kimura 1968. http://dosequis.colorado.edu/Courses/MethodsLogic/papers/Kimura1968.pdf but this review is probably more accessible. https://onlinelibrary.wiley.com/doi/full/10.1111/evo.13650

Thanks for the references and for adding the genetic perspective, @Arete.

[Boballoo]

 

On 11/9/2020 at 10:08 AM, delboy said:

The book Evolution by Futuyma deals with a lot of the maths of evolution, but it's pretty advanced. Maybe I should say very advanced actually.

That's good. Thank you. I'll see if I can manage it. 

3 hours ago, Arete said:

From a conceptual level, an understanding of basic neutral theory is also a good place to start. If you can wrap your brain around the concepts of how stochastic changes occur at the molecular level in populations, it becomes easier to layer on selective evolution, game theory and other increasingly complex models of evolution. 

The seminal paper is Kimura 1968. http://dosequis.colorado.edu/Courses/MethodsLogic/papers/Kimura1968.pdf but this review is probably more accessible. https://onlinelibrary.wiley.com/doi/full/10.1111/evo.13650

That's interesting. Thank you for the links. 

Edited November 11, 2020 by Boballoo

[OldChemE]

If you can find it somewhere, look for a Scientific American article "Traces of a Distant Past" by Gary Stix et al published in the July 2008 issue.  It traces out human genetic relationships by changes in DNA and uses a mathematical method of estimating times of the changes based on rates of DNA mutation.  It is only a small piece of what you are looking for, but it might prove interesting.