Zipf's law and cortical areas

doug doug
Thu Aug 3 22:51:53 EST 1995


	 It is commonly thought that the cerebral cortex is composed of 
columns, or modules.  Each module processes some aspect of a receptive 
field, such as orientation or movement direction.  Groups of modules 
form functional areas that display the entire represented field.  The 
features represented can become abstract as one moves away from the 
primary field, and the receptive fields can become larger so that the 
functional areas become smaller.

My question is: what is the relationship between the size of the cortex 
as a whole and the distribution of size of functional areas?  Can it be 
expected to follow Zipf's law*?

This question is prompted by the following.  I study the mustached bat 
auditory cortex, which is quite small (about 13 sq mm).  Despite its 
size, it contains more thandiscrete areas, some of them specialized 
to process biosonar signals.  I have evidence from corticocortical 
connections for a columnar organization in this cortex (i.e., labeled 
patches about 0.5 mm wide).  However, some of the areas are so small 
that they may be composed of as few as 1 column.

I therefore wonder, do the larger cortices of more commonly studied 
animals contain extremely small areas that process some specific signal 
attribute?  If so, the potential for a very large number of areas would 
exist.  

Yet, it is clear that in larger brains there are some areas that are 
large, much larger than any in the mustached bat.  If the size of the  
largest areas scaled with brain and body size, while the size of the 
smallest areas stayed constant at one or a few columns, could 
predictions be made about how many areas are likely to exist as a 
function of brain size? Has this been done?  

I would appreciate an education on these issues, particularly as to how 
or if Zipfs law could apply here.

Doug Fitzpatrick
E-mail or post is fine

*  As I understand it, Zipfs law is a purely empirical observation that 
many things in biological systems scale according to the rule that as 
larger maximum values occur then more and more intermediate and small 
values also arise, to fill in the distribution.  Is this description 
close?  Are there equations with parameters?




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