Evolution and Mathematics: Advice Needed

Jorolat jorolat at aol.com
Mon Apr 2 13:55:03 EST 2001

The matrix I need help with has 20 entries and because I can't include a gif
here it can be seen at this url: 


Below is a copy of the info I've put on the page, hopefully it will be
interesting for someone to look at it and give me advice!  

"Cytochrome C is a protein about 100 amino acids long thats occurs in organisms
ranging from bacteria to man. The matrix below is obtained by comparing the
number of differences there are in this amino acid sequence for a number of
different organisms." 

(matrix appears here) 

"Mathematically I need to know: 

Finding the average value for bacteria (dark green) seems an obvious case of
adding the values up and dividing by 20. To find the average value for birds
(light blue) do I add up
the values and divide by 9? Is this mathematically valid?. If so what do I do
about the values for mammals (white) where organisms are compared against one
another? Do I include the zeroes and divide by nine or exclude them and divide
by 6? 

Biologically I need to know: 

The average value for bacteria (as I'm currently calculating it) is about 65,
that of
yeasts 42, flowers 43, insects 25, fish 16, reptiles 10, and mammals either 4
or 6. 

I'm looking for a general trend rather than mathematical exactness and for this
exercise I've included the lamprey with the other fish and the snapping turtle
with birds. How great a heresy is this? (after all, it's only a small

The reason I'm doing this exercise is because the values for the groups, after
factorizing, are (bacteria first, and very approximately cos I don't have the
results to hand): 

13, 8.2. 8.1, 5.2, 3.4, 2, 0.8 (note how similar yeasts and plants are) 

This may be an occurence of the fibonacci series which is potentially
significant for a project I am working on (the possible existence of a testable
internal evolutionary mechanism) and could explain, as an example, why the
proto-whale evolved into the whale rather than devolving to any earlier
evolutionary stage. 

The matrix is taken from M. Denton's book "Evolution: A Theory In Crisis"
(Secker & Warburg, London) and originally appears in "Dayhoff: Atlas of Protein
Sequence and Structure". It is interesting to note that Denton emphatically
states the matrix doesn't support evolution because there isn't any linear
relationship between the groups. 

While I'm at it, as long as a reference is given, is it ok to reprint a single
table from
a book without seeking permissions?. 

I would be very grateful for help in any of the above areas!" 



Model of an Internal Evolutionary Mechanism (based on an extension to
homeostasis) linking Stationary Phase Mutations to The Baldwin Effect: 

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