How an Internal Evolutionary Mechanism may produce 'Complexity' ©2002 John Latter ([email protected]) Click here to join the mailing list

 (There is an error in the mathemathics - a corrected, and necessarily expanded version, will be uploaded when time permits - instead of "Consider an organism, 'x'," the analogy should begin  (apparently) with "Consider an organism, represented by the fibonacci number 'x',")

"If, as Gould and Lewontin suggested, organisms should be analyzed as 'integrated wholes' [1] then one possibility for an internal mechanism is to initially presume that there is a center to that integration:  specifically, an apex to the homeostatic hierarchy in the form of a localized area of equilibrium such as that described for the indirect homeostatic mechanism [2] on which the following is based" [3]

At first glance an homeostatic mechanism seems a contradiction in terms insofar as homeostasis can be used in the context of "staying the same" and "variation about a mean". By using a mathematical analogy, however, some first thoughts will hopefully show how a homeostatic mechanism could produce 'complexity':

Consider an organism, 'x', whose localized area is in a state of absolute equilibrium. Generations pass, the internal mechanism is triggered, and a 'mutation' is generated so that equilibrium is restored in the offspring; 'x' is now 'x+1'. More time passes, mutations are gained and lost, but overall the process is accumulative and 'x' has become 'x+n'. [I hope my maths stetches to this!:]  When the ratio of 'x' to 'x+n' approaches phi (the 'Golden Number': {square root of 5 minus 1}/2) the situation becomes untenable and 'x' and 'n' are integrated together ('x':='x' times 'x+n'/'x').The process begins in the localized area and cascades down throughout the genome until absolute equilibrium has been re-established. 'x+n' is now 'y' and the cycle can begin again.

Mathematically the above should produce the externally perceived 'complexity' of:

[0, 1,] 1, 2, 3, 5, 8, 13, 21, 34, 55, [etc.]

which is the Fibonacc Series. Internally, however, the localized area "stays the same".

If the initial mutation had been 1a, rather than 1, then this could cause branching at that level.

It might be stretching the analogy even further but if the localized area is the apex of the homeostatic hierarchy then there would be 'subsets' within it:

          3 (apex)

2a                 2b

1a    1b          1c   1d

An experiment by Jeffery [4] appears to support the superposition that if, as an example, 2a were the eyes of a cavefish then the negative effect of 'disuse' on the localized area would cause 'degeneration' but substructures within the eye would not, at least initially, be affected ('degeneration' would only reach down to that level which restores equilibrium at the localized area).

I'm sure more reflection will lead to something better than the above. In the meantime, however, any comments (particularly regarding the maths!) would be welcome: email [email protected]

[1] "The Spandrels of San Marco and the Panglossian Paradigm"  [Return to text]
http://www.aaas.org/spp/dser/evolution/history/spandrel.shtml

[2] Model of an Internal Evolutionary Mechanism  [Return to text]
http://members.aol.com/jorolat/TEM.html

[3] Not yet uploaded  [Return to text]

[4] "Blind fish reveal eye growth factors"  [Return to text]
http://www.abc.net.au/science/news/stories/s156871.htm

["How an Internal Evolutionary Mechanism may produce 'Complexity'" was originally posted in the "Where Darwin meets Lamarck?" discussion forum]

"Words frozen in time should be differentiated from those carved in stone" - John Latter

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