[Paleopsych] Fwd: Universal Footprint: Power Laws

HowlBloom at aol.com HowlBloom at aol.com
Fri Oct 7 19:26:27 UTC 2005

In a message dated 10/7/2005 3:13:06 PM Eastern Standard Time, Howl Bloom  

All thanks, Jim.  I just gave a presentation related to this subject  to an 
international quantum physics conference in Moscow--Quantum Informatics  2005.  
I wish I'd seen the article before giving the talk.  It would  have come in 
Meanwhile I tracked down a copy of the full article.  It's  downloadable for 
free at 
Better yet, enclosed is a file with the full article and with another  
article that relates.  I may not have the time to read these, so if you  digest 
anything interesting from them and get the time, please jot me an email  and give 
me your summary of what these articles are getting at.
Since Eshel Ben-Jacob has been trying to point out for years why such  
concepts as scale-free power laws and fractals fail to get at the creative  twists 
evolution comes up with as it moves from one level of emergence to  another, 
anything in these pieces that indicates how newness enters the  repetition of 
the old would be of particular interest.
Again, all thanks.  Onward--Howard
In a message dated 10/5/2005 5:12:27 PM Eastern Standard Time,  
JBJbrody at cs.com writes:

_Biological  Reviews_ 
(http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#)  (2001), 76: 161-209 Cambridge University Press  
doi:10.1017/S1464793101005607 Published Online 17May2001 *This article is  
available in a PDF that may contain more than one articles. Therefore the  PDF 
file's first page may not match this article's first page. 
_Subscribe  to journal_ 
_Email  abstract_ (http://journals.cambridge.org/acti
_Save  citation_ 
_Content  alerts_ 

Review Article

Scale invariance in biology:  coincidence or footprint of a universal 

T.  GISIGER a1 _p1_ 
a1 Groupe de Physique des Particules, Université de Montréal, C.P. 6128,  
succ. centre-ville, Montréal, Québec, Canada, H3C 3J7 (e-mail: 
_gisiger at pasteur.fr_ (mailto:gisiger at pasteur.fr) )


In  this article, we present a self-contained review of recent work on 
complex  biological systems which exhibit no characteristic scale. This property can 
 manifest itself with fractals (spatial scale invariance), flicker noise or  
1/f-noise where f denotes the frequency of a signal (temporal scale  
invariance) and power laws (scale invariance in the size and duration of  events in the 
dynamics of the system). A hypothesis recently put forward to  explain these 
scale-free phenomomena is criticality, a notion introduced by  physicists 
while studying phase transitions in materials, where systems  spontaneously 
arrange themselves in an unstable manner similar, for  instance, to a row of 
dominoes. Here, we review in a critical manner work  which investigates to what 
extent this idea can be generalized to biology.  More precisely, we start with a 
brief introduction to the concepts of  absence of characteristic scale 
(power-law distributions, fractals and 1/f-  noise) and of critical phenomena. We then 
review typical mathematical models  exhibiting such properties: edge of chaos, 
cellular automata and  self-organized critical models. These notions are then 
brought together to  see to what extent they can account for the scale 
invariance observed in  ecology, evolution of species, type III epidemics and some 
aspects of the  central nervous system. This article also discusses how the 
notion of scale  invariance can give important insights into the workings of 
biological  systems.

(Received October 4 1999)
(Revised July 14  2000)
(Accepted July 24 2000)

Key Words: Scale invariance;  complex systems; models; criticality; fractals; 
chaos; ecology; evolution;  epidemics; neurobiology. 


p1 Present  address: Unité de Neurobiologie Moléculaire, Institut Pasteur, 25 
rue du Dr  Roux, 75724 Paris, Cedex 15, France. 

Retrieved February 16, 2005, from  the World Wide Web  
http://www.sciencenews.org/articles/20050212/bob9.asp  Week of Feb. 12, 2005; Vol. 167, No. 7 ,  p. 
106 Life on the Scales Simple mathematical relationships underpin much of  
biology and ecology  Erica  Klarreich  A mouse lives just a few  years, while an 
elephant can make it to age 70. In a sense, however, both  animals fit in the 
same amount of life experience. In its brief life, a mouse  squeezes in, on 
average, as many heartbeats and breaths as an elephant does.  Compared with 
those of an elephant, many aspects of a mouse's life—such as the  rate at which 
its cells burn energy, the speed at which its muscles twitch, its  gestation 
time, and the age at which it reaches maturity—are sped up by the same  factor as 
its life span is. It's as if in designing a mouse, someone had simply  
pressed the fast-forward button on an elephant's life. This pattern relating  life's 
speed to its length also holds for a sparrow, a gazelle, and a  person—
virtually any of the birds and mammals, in fact. Small animals live fast  and die 
young, while big animals plod through much longer lives.  "It appears as if 
we've been gifted with  just so much life," says Brian Enquist, an ecologist at 
the  University of  Arizona in  Tucson. "You can spend it all at  once or slowly 
dribble it out over a long time."  a5850_1358.jpg Dean MacAdam  Scientists 
have long known that most  biological rates appear to bear a simple mathematical 
relationship to an  animal's size: They are proportional to the animal's mass 
raised to a power  that is a multiple of 1/4. These relationships are known 
as quarter-power  scaling laws. For instance, an animal's metabolic rate 
appears to be  proportional to mass to the 3/4 power, and its heart rate is 
proportional to  mass to the –1/4 power.  The  reasons behind these laws were a 
mystery until 8 years ago, when Enquist,  together with ecologist James Brown of the 
 University of New  Mexico in Albuquerque and physicist Geoffrey West of  Los 
Alamos (N.M.) National Laboratory proposed a model to  explain quarter-power 
scaling in mammals (SN: 10/16/99, p. 249). They and their  collaborators have 
since extended the model to encompass plants, birds, fish and  other 
creatures. In 2001, Brown, West, and several of their colleagues distilled  their model 
to a single formula, which they call the master equation, that  predicts a 
species' metabolic rate in terms of its body size and  temperature.  "They have 
identified  the basic rate at which life proceeds," says Michael Kaspari, an 
ecologist at  the University of  Oklahoma in  Norman.  In the July 2004 
Ecology, Brown, West,  and their colleagues proposed that their equation can shed 
light not just on  individual animals' life processes but on every biological 
scale, from  subcellular molecules to global ecosystems. In recent months, the 
investigators  have applied their equation to a host of phenomena, from the 
mutation rate in  cellular DNA to Earth's carbon cycle.  Carlos Martinez del Rio, 
an ecologist at the  University of  Wyoming in  Laramie, hails the team's work 
as a  major step forward. "I think they have provided us with a unified 
theory for  ecology," he says.  The biological  clock  In 1883, German physiologist 
 Max Rubner proposed that an animal's metabolic rate is proportional to its 
mass  raised to the 2/3 power. This idea was rooted in simple geometry. If one 
animal  is, say, twice as big as another animal in each linear dimension, then 
its total  volume, or mass, is 23 times as large, but its skin surface is 
only 22 times as  large. Since an animal must dissipate metabolic heat through 
its skin, Rubner  reasoned that its metabolic rate should be proportional to its 
skin surface,  which works out to mass to the 2/3 power.  a5850_2473.jpg Dean 
MacAdam  In 1932, however, animal scientist Max Kleiber of the University of  
California, Davis looked at a broad range of data and concluded that the 
correct  exponent is 3/4, not 2/3. In subsequent decades, biologists have found 
that the  3/4-power law appears to hold sway from microbes to whales, creatures 
of sizes  ranging over a mind-boggling 21 orders of magnitude.  For most of 
the past 70 years,  ecologists had no explanation for the 3/4 exponent. "One 
colleague told me in  the early '90s that he took 3/4-scaling as 'given by God,'" 
Brown recalls.  The beginnings of an explanation came in  1997, when Brown, 
West, and Enquist described metabolic scaling in mammals and  birds in terms of 
the geometry of their circulatory systems. It turns out, West  says, that 
Rubner was on the right track in comparing surface area with volume,  but that an 
animal's metabolic rate is determined not by how efficiently it  dissipates 
heat through its skin but by how efficiently it delivers fuel to its  cells.  
Rubner should have  considered an animal's "effective surface area," which 
consists of all the inner  surfaces across which energy and nutrients pass from 
blood vessels to cells,  says West. These surfaces fill the animal's entire 
body, like linens stuffed  into a laundry machine.  The idea,  West says, is that 
a space-filling surface scales as if it were a volume, not an  area. If you 
double each of the dimensions of your laundry machine, he observes,  then the 
amount of linens you can fit into it scales up by 23, not 22. Thus, an  animal's 
effective surface area scales as if it were a three-dimensional, not a  
two-dimensional, structure.  This  creates a challenge for the network of blood 
vessels that must supply all these  surfaces. In general, a network has one more 
dimension than the surfaces it  supplies, since the network's tubes add one 
linear dimension. But an animal's  circulatory system isn't four dimensional, so 
its supply can't keep up with the  effective surfaces' demands. Consequently, 
the animal has to compensate by  scaling back its metabolism according to a 
3/4 exponent.  Though the original 1997 model applied  only to mammals and 
birds, researchers have refined it to encompass plants,  crustaceans, fish, and 
other organisms. The key to analyzing many of these  organisms was to add a new 
parameter: temperature.  Mammals and birds maintain body  temperatures between 
about 36°C and 40°C, regardless of their environment. By  contrast, creatures 
such as fish, which align their body temperatures with those  of their 
environments, are often considerably colder. Temperature has a direct  effect on 
metabolism—the hotter a cell, the faster its chemical reactions  run.  In 2001, 
after James Gillooly,  a specialist in body temperature, joined Brown at the  
University of New  Mexico, the researchers and their collaborators  presented 
their master equation, which incorporates the effects of size and  temperature. 
An organism's metabolism, they proposed, is proportional to its  mass to the 
3/4 power times a function in which body temperature appears in the  exponent. 
The team found that its equation accurately predicted the metabolic  rates of 
more than 250 species of microbes, plants, and animals. These species  
inhabit many different habitats, including marine, freshwater, temperate, and  
tropical ecosystems.  The equation  gave the researchers a way to compare organisms 
with different body  temperatures—a person and a crab, or a lizard and a 
sycamore tree— and thereby  enabled the team not just to confirm previously known 
scaling laws but also to  discover new ones. For instance, in 2002, Gillooly 
and his colleagues found that  hatching times for eggs in birds, fish, 
amphibians, and plankton follow a  scaling law with a 1/4 exponent.  When the 
researchers filter out the effects of body temperature, most  species adhere closely 
to quarter-power laws for a wide range of properties,  including not only life 
span but also population growth rates. The team is now  applying its master 
equation to more life processes—such as cancer growth rates  and the amount of 
time animals sleep.  "We've found that despite the incredible diversity of 
life, from a tomato  plant to an amoeba to a salmon, once you correct for size and 
temperature, many  of these rates and times are remarkably similar," says 
Gillooly.  A single equation predicts so much, the  researchers contend, because 
metabolism sets the pace for myriad biological  processes. An animal with a 
high metabolic rate processes energy quickly, so it  can pump its heart quickly, 
grow quickly, and reach maturity quickly.  Unfortunately, that animal also 
ages and  dies quickly, since the biochemical reactions involved in metabolism 
produce  harmful by-products called free radicals, which gradually degrade 
cells.  "Metabolic rate is, in our view, the  fundamental biological rate," 
Gillooly says. There is a universal biological  clock, he says, "but it ticks in 
units of energy, not units of time."  Scaling up  The researchers propose that 
their  framework can illuminate not just properties of individual species, such 
as  hours of sleep and hatching times, but also the structure of entire 
communities  and ecosystems. Enquist, West, and Karl Niklas of  Cornell  University 
have been looking for  scaling relationships in plant communities, where they 
have uncovered previously  unnoticed patterns.  a5850_3175.jpg  REGULAR ON  
AVERAGE. Newly discovered scaling laws have revealed an unexpected relationship  
between the spacing of trees and their trunk diameters in a mature forest.  
PhotoDisc  The researchers have  found, for instance, that in a mature forest, 
the average distance between trees  of the same mass follows a quarter-power 
scaling law, as does trunk diameter.  These two scaling laws are proportional 
to each other, so that on average, the  distance between trees of the same mass 
is simply proportional to the diameter  of their trunks.  "When you walk in  
a forest, it looks random, but it's actually quite regular on average," West  
says. "People have been measuring size and density of trees for 100 years, but 
 no one had noticed these simple relationships."  The researchers have also 
discovered  that the number of trees of a given mass in a forest follows the 
same scaling  law governing the number of branches of a given size on an 
individual tree. "The  forest as a whole behaves as if it is a very large tree," West 
says.  Gillooly, Brown, and their  New Mexico colleague Andrew Allen  have 
now used these scaling laws to estimate the amount of carbon that is stored  and 
released by different plant ecosystems.  Quantifying the role of plants in 
the  carbon cycle is critical to understanding global warming, which is caused 
in  large part by carbon dioxide released to the atmosphere when animals 
metabolize  food or machines burn fossil fuels.  Plants, by contrast, pull carbon 
dioxide out of the air for use in  photosynthesis. Because of this trait, some 
ecologists have proposed planting  more forests as one strategy for 
counteracting global warming.  In a paper in an upcoming Functional  Ecology, the 
researchers estimate carbon turnover and storage in ecosystems such  as oceanic 
phytoplankton, grasslands, and old-growth forests. To do this, they  apply their 
scaling laws to the mass distribution of plants and the metabolic  rate of 
individual plants. The model predicts, for example, how much stored  carbon is lost 
when a forest is cut down to make way for farmlands or  development.  
Martinez del  Rio cautions that ecologists making practical  conservation decisions 
need more-detailed information than the scaling laws  generally give. "The 
scaling laws are useful, but they're a blunt tool, not a  scalpel," he says.  
Scaling  down  The team's master equation may  resolve a longstanding controversy 
in evolutionary biology: Why do the fossil  record and genetic data often give 
different estimates of when certain species  diverged?  Geneticists calculate 
 when two species branched apart in the phylogenetic tree by looking at how 
much  their DNA differs and then estimating how long it would have taken for 
that many  mutations to occur. For instance, genetic data put the divergence of 
rats and  mice at 41 million years ago. Fossils, however, put it at just 12.5 
million  years ago.  The problem is that  there is no universal clock that 
determines the rate of genetic mutations in all  organisms, Gillooly and his 
colleagues say. They propose in the Jan. 4  Proceedings of the National Academy of 
Sciences that, instead, the mutation  clock—like so many other life processes—
ticks in proportion to metabolic rate  rather than to time.  The DNA of  
small, hot organisms should mutate faster than that of large, cold organisms,  the 
researchers argue. An organism with a revved-up metabolism generates more  
mutation-causing free radicals, they observe, and it also produces offspring  
faster, so a mutation becomes lodged in the population more quickly.  When the 
researchers use their master  equation to correct for the effects of size and 
temperature, the genetic  estimates of divergence times—including those of rats 
and mice—line up well with  the fossil record, says Allen, one of the paper's 
coauthors.  The team plans to use its metabolic  framework to investigate why 
the tropics are so much more diverse than temperate  zones are and why there 
are so many more small species than large ones.  Most evolutionary biologists 
have tended  to approach biodiversity questions in terms of historical events, 
such as  landmasses separating, Kaspari says. The idea that size and 
temperature are the  driving forces behind biodiversity is radical, he says.  "I think 
if it holds up, it's going to  rewrite our evolutionary-biology books," he 
says.  Enthusiasm and skepticism  While the metabolic-scaling theory has  roused 
much enthusiasm, it has its limitations. Researchers agree, for instance,  
that while the theory produces good predictions when viewed on a scale from  
microbes to whales, the theory is rife with exceptions when it's applied to  
animals that are relatively close in temperature and size. For example, large  
animals generally have longer life spans than small animals, but small dogs live  
longer than large ones.  a5850_4238.jpg Dean MacAdam  Brown points out that 
the metabolic-scaling law may be useful by calling  attention to such 
exceptions. "If you didn't have a general theory, you wouldn't  know that big dogs are 
something interesting to look at," he observes.  Many questions of particular 
interest to  ecologists concern organisms that are close in size. Metabolic 
theory may not  explain, for example, why certain species coexist or why 
particular species  invade a given ecosystem, says John Harte, an ecologist at the  
University of  California,  Berkeley.  Some scientists question the very  
underpinnings of the team's model. Raul Suarez, a comparative physiologist at  the 
University of  California,  Santa Barbara disputes the model's  starting 
assumption that an animal's metabolic rate is determined by how  efficiently it can 
transport resources from blood vessels to cells. Suarez  argues that other 
factors are equally important, or even more so. For instance,  whether the 
animal is resting or active determines which organs are using the  most energy at a 
given time. 
"Metabolic  scaling is a many-splendored thing," he says.  Suarez' concern is 
valid, agrees  Kaspari. However, he says, the master equation's accurate 
predictions about a  huge range of phenomena are strong evidence in its favor.  
Ecologists, physiologists, and other  biologists appear to be unanimous on one 
point: The team's model has sparked a  renaissance for biological-scaling 
theory.  "West and Brown deserve a great deal of credit for rekindling the  
interest of the scientific community in this phenomenon of metabolic scaling,"  
Suarez says. "Their ideas have stimulated a great deal of discussion and debate,  
and that's a good thing."  If you  have a comment on this article that you 
would like considered for publication in  Science News, send it to 
editors at sciencenews.org. Please include your name and  location.  To subscribe to Science  
News (print), go to https://www.kable.com/pub/scnw/ subServices.asp.  To sign up 
for the free weekly e-LETTER  from Science News, go to  
http://www.sciencenews.org/pages/subscribe_form.asp.  References:  Brown, J.H., J.F. Gillooly, A.P. 
Allen,  V.M. Savage, and G.B. West. 2004. Toward a metabolic theory of 
ecology. Ecology  85(July):1771-1789. Abstract.  Gillooly, J.F., A.P. Allen, G.B. 
West, and J.H. Brown. 2005. The rate of  DNA evolution: Effects of body size and 
temperature on the molecular clock.  Proceedings of the National  Academy of 
Sciences 102(Jan.  4):140-145. Abstract available at  
http://www.pnas.org/cgi/content/abstract/102/1/140.  Gillooly, J.F. . . . G.B. West . . . and  J.H. 
Brown. 2002. Effects of size and temperature on developmental time. Nature  
417(May 2):70-73. Abstract available at http://dx.doi.org/10.1038/417070a.  
Gillooly, J.F., J.H. Brown, G.B. West,  et al. 2001. Effects of size and temperature 
on metabolic rate. Science  293(Sept. 21):2248-2251. Available at  
http://www.sciencemag.org/cgi/content/full/293/5538/2248.  Savage, V.M., J.F. Gillooly, 
J.H. Brown,  G.B. West, and E.L. Charnov. 2004. Effects of body size and 
temperature on  population growth. American Naturalist 163(March):429-441. 
Available at  http://www.journals.uchicago.edu/AN/  
journal/issues/v163n3/20308/20308.html.  Suarez, R.K., C.A. Darveau, and J.J. Childress. 2004. Metabolic 
scaling:  A many-splendoured thing. Comparative Biochemistry and Physiology, Part B  
139(November):531-541. Abstract available at  
http://dx.doi.org/10.1016/j.cbpc.2004.05.001.  West, G.B., J.H. Brown, and B.J.  Enquist. 1997. A general 
model for the origin of allometric scaling models in  biology. Science 276(April 
4):122-126. Available at  
http://www.sciencemag.org/cgi/content/full/276/5309/122.  Further Readings:  Savage, V.M., J.F. Gillooly, . . . A.P.  Allen . . . 
and J.H. Brown. 2004. The predominance of quarter-power scaling in  biology. 
Functional Ecology 18(April):257-282. Abstract available at  
http://dx.doi.org/10.1111/j.0269-8463.2004.00856.x.  Weiss, P. 1999. Built to scale. Science  
News 156(Oct. 16):249-251. References and sources available at  
http://www.sciencenews.org/pages/sn_arc99/10_16_99/bob1ref.htm.  Sources:  Anurag Agrawal 
Ecology and Evolutionary  Biology Cornell University Ithaca, NY 14853  Andrew Allen 
Biology Department  University of New Mexico Albuquerque, NM 87131  James H. 
Brown Biology Department  University of New Mexico Albuquerque, NM 87131  
Steven Buskirk Department of Zoology and  Physiology University of Wyoming 1000 E. 
University Avenue Laramie, WY  82071  Brian Enquist Department of  Ecology 
and Evolutionary Biology University of Arizona Tucson, AZ 85721  James Gillooly 
Biology Department  University of New Mexico Albuquerque, NM 87131  John Harte 
Energy and Resources Group  310 Barrows Hall University of California, 
Berkeley Berkeley, CA 94720  Michael Kaspari Department of Zoology  University of 
Oklahoma Norman, OK 73019  Carlos Martínez del Rio Department of Zoology and 
Physiology University  of Wyoming Laramie, WY 82071  Karl  Niklas Department of 
Plant Biology Cornell University Ithaca, NY 14853  Raul Suarez Department of 
Ecology,  Evolution and Marine Biology University of California, Santa Barbara 
Santa  Barbara, CA 93016  Geoffrey B. West  Theoretical Physics Division Los 
Alamos National Laboratory MS B285 Los Alamos,  NM 87545  From Science News, 
Vol.  167, No. 7, Feb. 12, 2005, p. 106.       Home | Table of Contents | 
Feedback  | Subscribe | Help/About | Archives | Search  Copyright ©2005 Science 
Service. All  rights reserved. 1719 N St., NW, Washington, DC 20036 | 202-785-2255 
|  scinews at sciserv.org                                   Subscribe Subscribe 
to  Science News. Click OR call 1-800-552-4412.  Google Search WWW Search 
Science  News  Free E-mail Alert Science News  e-LETTER.  Click here to find  
resources for enjoying our planet and the universe. Science Mall sells science  
posters, gifts, teaching tools, and collector items. Finally a store for science  
enthusiasts, professionals, and kids alike! Shop at the Science Mall.  
Science News Logo Wear Science News Logo  Wear Copyright Clearance Center  Photo 
Archive Browse a Science News photo collection. 

Howard Bloom
Author of The Lucifer Principle: A  Scientific Expedition Into the Forces of 
History and Global Brain: The Evolution  of Mass Mind From The Big Bang to the 
21st Century
Recent Visiting  Scholar-Graduate Psychology Department, New York University; 
Core Faculty  Member, The Graduate  Institute
Founder:  International Paleopsychology Project; founding board member: Epic 
of Evolution  Society; founding board member, The Darwin Project; founder: The 
Big Bang Tango  Media Lab; member: New York Academy of Sciences, American 
Association for the  Advancement of Science, American Psychological Society, 
Academy of Political  Science, Human Behavior and Evolution Society, International 
Society for Human  Ethology; advisory board member: Institute for 
Accelerating Change ; executive  editor -- New Paradigm book series.
For information on The International  Paleopsychology Project, see: 
for two chapters from  
The Lucifer Principle: A Scientific Expedition Into the Forces of History,  
see www.howardbloom.net/lucifer
For information on Global Brain: The  Evolution of Mass Mind from the Big 
Bang to the 21st Century, see  www.howardbloom.net

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.extropy.org/pipermail/paleopsych/attachments/20051007/15ea3942/attachment.html>
-------------- next part --------------
An embedded message was scrubbed...
From: HowlBloom at aol.com
Subject: Re: Universal Footprint: Power Laws
Date: Fri, 7 Oct 2005 15:13:06 EDT
Size: 951922
URL: <http://lists.extropy.org/pipermail/paleopsych/attachments/20051007/15ea3942/attachment.mht>

More information about the paleopsych mailing list