Can anyone recommend a good book or set of articles on the
mathematics/modelling of evolution? In other words, models or
simulations of how many generations, what rate of mutation, how much
predatory pressure or other natural selection factors, etc. must be
present in order for a new species to emerge? I've seen some very
simple models/simulations but I was hoping for a more detailed
explanation or analysis. It would need to be somewhat accessible to a
"lay person" as I don't have any graduate level math skills :(

Thanks much!

There are two branches of activity in the modeling of evolution.
1) The first can be found under the 
 SEARCH TERM: genetic algorithms

It is well illustrated by this 
Introduction to genetic algorithms with interactive Java applets.
http://cs.felk.cvut.cz/~xobitko/ga/

 The genetic algorithms were inspired by biological evolution,
 but evolved into its own field of study, part of AI and numerical
method for finding  a minina of  complex functions.
  Application shows that a system can indeed evolve from 'simple to complex'.

2) The second branch of activity is the application of mathematical
methods and computer models to biological evolution itself. This is
part of theoretical biology, which is merging with the study of
Complex Systems.
 
http://dmoz.org/Science/Math/Applications/Complex_Systems/

Two subcategories are relevant to your question:

    (A)The "Evolution and Dynamics" subcategory deals with models ,
paticularly the exciting 'Tree of Life project' (= TOL project).
Insprect the three TOL links at the bottom of the list:
  Computational infrastructure - Resources for reconstructing the
evolutionary history of all organisms.
  Tree of Life project - Evolution of Life on this Planet 
  Building a Tree of Life for All Species - How living things have
evolved since the origins of life

    (B) The 'artificial life' subcategory 
    http://dmoz.org/Computers/Artificial_Life/
 
is an intermediate field between both branches. It is study of
multi-agent systems which show increases in complexity, just as
biological systems do.
 These studies do not attempt to correlate results with experimental
(paleontological data) facts about the evolution of life on Earth.
..............................

 If you are just entering this field you 'must' start by reading Lotka:

Alfred Lotka, American physicist-philosopher of Ukrainian origin, 

http://users.pandora.be/ronald.rousseau/html/lotka.html
http://scienceworld.wolfram.com/biography/Lotka.html

 is best known for initiating Population Dynamics studies

http://mathworld.wolfram.com/Lotka-VolterraEquations.html
                   Book: Analytical Theory of Biological Populations 

but in his classical book
              Elements of physical biology
 he did much more than that; he founded mathematical biology,
precursor of today's Complex Systems

 Lotka's books are described in more detail on this page:
http://www.amazon.com/exec/obidos/search-handle-url/ref=br_ss_hs/103-5131209-7933403?platform=gurupa&url=index%3Dstripbooks%3Arelevance-above%26dispatch%3Dsearch%26results-process%3Dbin&field-keywords=Alfred+Lotka&Go.x=0&Go.y=0

For the history and relationship of these overlapping fields, see:
http://answers.google.com/answers/threadview?id=524379

More recent books:
http://answers.google.com/answers/threadview?id=524379tp://www.amazon.com/gp/
product/052162570X/103-5131209-7933403?v=glance&n=283155

http://www.amazon.com/gp/product/0262731215/ref=pd_trkn_qp_b_t/103-5131209-7933403?v=glance&n=283155

 Feel free to ask for clarification. When all is clear, rating is appreciated.

Hedgie

---

Clarification of Answer by hedgie-ga on 26 Jan 2006 04:50 PST

Specifically re:

 "new species to emerge?" 

  Term 'speciacion' is used in chemistry in a different meaning,
 in biology it means 'emergence of a new specie, as used here:

Cornell experts find two new species of crane fly have invaded New
York, threatening lawns, golf courses and pastures
http://www.news.cornell.edu/stories/Aug05/crane.flies.invade.ssl.html

Salmon in a US lake split into two separate populations in just 13
generations, or about 60-70 years, researchers have revealed.
http://news.bbc.co.uk/1/hi/sci/tech/979950.stm


THERE ARE TWO BASIC TYPES:
Allopatric speciation happens when a geographical change - a river
changing course for example or a new mountain range - splits a species
in two. Once separated, as happened to antelope squirrels on either
side of the Grand Canyon in the US, the populations evolve
independently, eventually becoming distinct and reproductively
isolated.

Sympatric speciation occurs when new species emerge without
separation, such as the 13 species of Galapagos finch or Africa's
cichlid fish. These species adapt to different opportunities in the
environment, and then cease to interbreed - perhaps due to some
isolating mechanism. Rarely new species can also form through
hybridisation, such as sunflowers.
http://www.newscientist.com/popuparticle.ns?id=in85

MORE SPECIFIC AND SOMEWHAT TECHNICAl: computer models

 Punc equation model:
The program has a genome of 384 "nucleotides" 
A nucleotide in this context is a computer bit, a 0 or a 1.
 These nucleotides are mutated and a new screen form is produced...
http://home.entouch.net/dmd/nonlin.htm

  Sci. American article
The researchers then devised a computer model to test whether this mating regime
could lead to reproductive isolation and subsequent speciation. ...
http://www.sciam.com/ article.cfm?articleID=000214BD-E52F-1EB7-BDC0809EC588EED



SYMPATRIC SPECIATION
1) Kondrashov AS 1983 Multilocus model of sympatric speciation. I. One character.
Theor. Pop. Biol. 24, 121. ... 5) Practical work with computer models ...
http//www.bgu.ac.il/desert_ecology/ Novoplansky/camp%20evolution/syllabi.htm



2)Simulation of Sympatric Speciation. with Penna Ageing Model. K. Luz-Burgoa ...
http://www.sbfisica.org.br/bjp/files/v33_623.pdf

More technical bibliography
http://www.mun.ca/biology/scarr/2900_Speciation.htm

...

Thank you. That was really outstanding.