[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
writes:
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
handy.
Meanwhile I tracked down a copy of the full article. It's downloadable for
free at
_http://www.pasteur.fr/recherche/unites/neubiomol/ARTICLES/Gisiger2001.pdf_
(http://www.pasteur.fr/recherche/unites/neubiomol/ARTICLES/Gisiger2001.pdf)
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.
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Review Article
Scale invariance in biology: coincidence or footprint of a universal
mechanism?
T. GISIGER a1 _p1_
(http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#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) )
Abstract
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.
Correspondence:
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 |
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----------
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
www.howardbloom.net
www.bigbangtango.net
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:
www.paleopsych.org
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
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