Re: biological laws and rules (long)

	I've just tuned in to the later posts on ecological laws and rules
and noticed that folks are talking about Cohen et al.'s food web laws.  
This seems like very important work because it attempts to specify what 
all ecological systems have in common.  If such properties exist, it 
seems like a basic scientific responsibility for ecologists to discover them.

 	Elaine Ingham's points about these laws are well taken.  Hypotheses are
much more appropriate than laws at this stage.  Even better is rejected
hypotheses!  I've been working on overturning the "laws" of
"scale-invariance" (factions of top, intermediate, basal species and links
between them do not vary with species diversity) in favor of alternative
hypotheses called "constant connectance" and "scale dependence."  These
latter hypotheses appear to be much more accurate and successfully
predicitive than the "laws."  Scale dependence asserts that the fractions
of top and basal species (and links between them) descrease with
increasing diversity while the fractions of intermediate species and links
between them increase.  This December's American Naturalist and early 
next year's Oikos will have more on this assertion.  

	Phil Warren reviewed the constant connectance hypothesis in this
year's April issue of Trends in Ecology & Evolution and it may be as close
to an ecological rule as any in ecology.  Constant connectance asserts that
the mean fraction of all possible links in a food web that are realized is
constant as species diveristy increases.  That is, the number of trophic
links in a web increase as a constant fraction of the square of species
number.  Furthermore, the observed fraction (~0.1, std. dev. ~0.03) is
relatively low compared the the fraction (0.5) expected by chance.  Now
there's a ton of methodological and empirical issues (what's a species?
what's a link? how closely have you looked? etc...) involved in such an
assertion and many (certainly not all) have been looked at in some detail
with a substantial degree of rigor. 

	Folks who know the literature on this might be willing to accept
the following claim:  Constant connectance appears to be the most general,
precise, accurate, and successfully predictive quantitative regularity in
the organization of ecological systems.  So far it applies to hundreds of
webs with 10 to 1000 species.  No bigger webs are yet available.  The
specific value of the constant varies (0.02-0.2) depending on linkage
criteria and which subset of species in a habitat is observed but the
fraction is always much less than 0.5.  The most defensible way to state
it as a rule (a stronger claim than hypothesis) is, "The mean number of
trophic interactions of per species increases with species diversity and
these ecological systems are much more trophically specialized than
expected by chance." 

	Any comments?					-neo

Neo D. Martinez                    email ndmartinez@ucdavis.edu
Research Fellow                    Phone 707-875-2211
Bodega Marine Laboratory                 707-865-0777
University of California, Davis    FAX   707-875-2089