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<DIV>
<DIV>In a message dated 10/7/2005 3:13:06 PM Eastern Standard Time, Howl Bloom
writes:</DIV>
<BLOCKQUOTE
style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue 2px solid"><FONT
style="BACKGROUND-COLOR: transparent" face=Arial color=#000000 size=2><FONT
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<DIV>
<DIV>
<DIV>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.</DIV>
<DIV> </DIV>
<DIV>Meanwhile I tracked down a copy of the full article. It's
downloadable for free at <A
title=http://www.pasteur.fr/recherche/unites/neubiomol/ARTICLES/Gisiger2001.pdf
href="http://www.pasteur.fr/recherche/unites/neubiomol/ARTICLES/Gisiger2001.pdf">http://www.pasteur.fr/recherche/unites/neubiomol/ARTICLES/Gisiger2001.pdf</A></DIV>
<DIV> </DIV>
<DIV>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.</DIV>
<DIV> </DIV>
<DIV>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.</DIV>
<DIV> </DIV>
<DIV>Again, all thanks. Onward--Howard</DIV>
<DIV> </DIV>
<DIV>In a message dated 10/5/2005 5:12:27 PM Eastern Standard Time,
JBJbrody@cs.com writes:</DIV>
<BLOCKQUOTE
style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue 2px solid"><FONT
style="BACKGROUND-COLOR: transparent" face=Arial color=#000000 size=2><FONT
lang=0 face=Arial size=2 FAMILY="SANSSERIF" PTSIZE="10"><A
title=http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#
href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#">Biological
Reviews</A> (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. <BR><A
title=http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#
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alerts</A> <BR><BR>Review Article<BR><BR></FONT><FONT lang=0
style="BACKGROUND-COLOR: #ffffff" face=Arial color=#336699 size=2
FAMILY="SANSSERIF" PTSIZE="10" BACK="#ffffff">Scale invariance in biology:
coincidence or footprint of a universal mechanism?</FONT><FONT lang=0
style="BACKGROUND-COLOR: #ffffff" face=Arial color=#000000 size=2
FAMILY="SANSSERIF" PTSIZE="10" BACK="#ffffff"><BR><BR><B>T.</B>
<B>GISIGER</B> a1 <A
title=http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#p1
href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#p1">p1</A>
<BR>a1 Groupe de Physique des Particules, Université de Montréal, C.P. 6128,
succ. centre-ville, Montréal, Québec, Canada, H3C 3J7 (e-mail: <A
title=mailto:gisiger@pasteur.fr
href="mailto:gisiger@pasteur.fr">gisiger@pasteur.fr</A>)<BR><BR><B>Abstract</B><BR><BR>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.<BR><BR>(Received October 4 1999)<BR>(Revised July 14
2000)<BR>(Accepted July 24 2000)<BR><BR><B>Key Words:</B> Scale invariance;
complex systems; models; criticality; fractals; chaos; ecology; evolution;
epidemics; neurobiology. <BR><BR><B>Correspondence:</B><BR><BR>p1 Present
address: Unité de Neurobiologie Moléculaire, Institut Pasteur, 25 rue du Dr
Roux, 75724 Paris, Cedex 15, France. <BR><BR></FONT></FONT></BLOCKQUOTE></DIV>
<DIV></DIV></DIV></FONT></FONT></BLOCKQUOTE></DIV>
<DIV>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT face="Times New Roman"
size=2>Retrieved <SPAN style="mso-no-proof: yes">February 16, 2005</SPAN>, from
the World Wide Web<SPAN style="mso-spacerun: yes">
</SPAN>http://www.sciencenews.org/articles/20050212/bob9.asp<SPAN
style="mso-spacerun: yes"> </SPAN>Week of Feb. 12, 2005; Vol. 167, No. 7 ,
p. 106 Life on the Scales Simple mathematical relationships underpin much of
biology and ecology<SPAN style="mso-spacerun: yes"> </SPAN>Erica
Klarreich<SPAN style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>"It appears as if we've been gifted with
just so much life," says Brian Enquist, an ecologist at the
<st1:place><st1:PlaceType>University</st1:PlaceType> of
<st1:PlaceName>Arizona</st1:PlaceName></st1:place> in
<st1:City><st1:place>Tucson</st1:place></st1:City>. "You can spend it all at
once or slowly dribble it out over a long time."<SPAN
style="mso-spacerun: yes"> </SPAN>a5850_1358.jpg Dean MacAdam<SPAN
style="mso-spacerun: yes"> </SPAN>Scientists have long known that most
biological rates appear to bear a simple mathematical relationship to an
animal's size: They are<B> 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.</B> <B>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.</B><SPAN style="mso-spacerun: yes"> </SPAN>The
reasons behind these laws were a mystery until 8 years ago, when Enquist,
together with ecologist James Brown of the
<st1:place><st1:PlaceType>University</st1:PlaceType> of <st1:PlaceName>New
Mexico</st1:PlaceName></st1:place> in Albuquerque and physicist Geoffrey West of
<st1:place>Los Alamos</st1:place> (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.<SPAN style="mso-spacerun: yes"> </SPAN>"They have identified
the basic rate at which life proceeds," says Michael Kaspari, an ecologist at
the <st1:place><st1:PlaceType>University</st1:PlaceType> of
<st1:PlaceName>Oklahoma</st1:PlaceName></st1:place> in
<st1:City><st1:place>Norman</st1:place></st1:City>.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes">
</SPAN>Carlos Martinez del <st1:place>Rio</st1:place>, an ecologist at the
<st1:place><st1:PlaceType>University</st1:PlaceType> of
<st1:PlaceName>Wyoming</st1:PlaceName></st1:place> in
<st1:City><st1:place>Laramie</st1:place></st1:City>, hails the team's work as a
major step forward. "I think they have provided us with a unified theory for
ecology," he says.<SPAN style="mso-spacerun: yes"> </SPAN>The biological
clock<SPAN style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes">
</SPAN>a5850_2473.jpg Dean MacAdam<SPAN style="mso-spacerun: yes">
</SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes"> </SPAN>In 2001, after James Gillooly,
a specialist in body temperature, joined Brown at the
<st1:place><st1:PlaceType>University</st1:PlaceType> of <st1:PlaceName>New
Mexico</st1:PlaceName></st1:place>, 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.<SPAN style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes">
</SPAN>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.<SPAN style="mso-spacerun: yes">
</SPAN>"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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>"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."<SPAN
style="mso-spacerun: yes"> </SPAN>Scaling up<SPAN
style="mso-spacerun: yes"> </SPAN>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
<st1:place><st1:PlaceName>Cornell</st1:PlaceName>
<st1:PlaceType>University</st1:PlaceType></st1:place> have been looking for
scaling relationships in plant communities, where they have uncovered previously
unnoticed patterns.<SPAN style="mso-spacerun: yes">
</SPAN>a5850_3175.jpg<SPAN style="mso-spacerun: yes"> </SPAN>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<SPAN style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes"> </SPAN>"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."<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>Gillooly, Brown, and their
<st1:State><st1:place>New Mexico</st1:place></st1:State> colleague Andrew Allen
have now used these scaling laws to estimate the amount of carbon that is stored
and released by different plant ecosystems.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes">
</SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes"> </SPAN>Martinez del
<st1:place>Rio</st1:place> 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.<SPAN style="mso-spacerun: yes"> </SPAN>Scaling
down<SPAN style="mso-spacerun: yes"> </SPAN>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?<SPAN style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>"I think if it holds up, it's going to
rewrite our evolutionary-biology books," he says.<SPAN
style="mso-spacerun: yes"> </SPAN>Enthusiasm and skepticism<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes">
</SPAN>a5850_4238.jpg Dean MacAdam<SPAN style="mso-spacerun: yes">
</SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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
<st1:place><st1:PlaceType>University</st1:PlaceType> of
<st1:PlaceName>California</st1:PlaceName></st1:place>,
<st1:City><st1:place>Berkeley</st1:place></st1:City>.<SPAN
style="mso-spacerun: yes"> </SPAN>Some scientists question the very
underpinnings of the team's model. Raul Suarez, a comparative physiologist at
the <st1:place><st1:PlaceType>University</st1:PlaceType> of
<st1:PlaceName>California</st1:PlaceName></st1:place>,
<st1:City><st1:place>Santa Barbara</st1:place></st1:City> 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.</FONT></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT size=2><FONT
face="Times New Roman"><SPAN style="mso-spacerun: yes"> </SPAN>"Metabolic
scaling is a many-splendored thing," he says.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>Ecologists, physiologists, and other
biologists appear to be unanimous on one point: The team's model has sparked a
renaissance for biological-scaling theory.<SPAN style="mso-spacerun: yes">
</SPAN>"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."<SPAN style="mso-spacerun: yes"> </SPAN>If you
have a comment on this article that you would like considered for publication in
Science News, send it to editors@sciencenews.org. Please include your name and
location.<SPAN style="mso-spacerun: yes"> </SPAN>To subscribe to Science
News (print), go to https://www.kable.com/pub/scnw/ subServices.asp.<SPAN
style="mso-spacerun: yes"> </SPAN>To sign up for the free weekly e-LETTER
from Science News, go to
http://www.sciencenews.org/pages/subscribe_form.asp.<SPAN
style="mso-spacerun: yes"> </SPAN>References:<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes">
</SPAN>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 <st1:place><st1:PlaceName>National</st1:PlaceName>
<st1:PlaceType>Academy</st1:PlaceType></st1:place> of Sciences 102(Jan.
4):140-145. Abstract available at
http://www.pnas.org/cgi/content/abstract/102/1/140.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN style="mso-spacerun: yes">
</SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>Further Readings:<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>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.<SPAN
style="mso-spacerun: yes"> </SPAN>Sources:<SPAN
style="mso-spacerun: yes"> </SPAN>Anurag Agrawal Ecology and Evolutionary
Biology Cornell University Ithaca, NY 14853<SPAN
style="mso-spacerun: yes"> </SPAN>Andrew Allen Biology Department
University of New Mexico Albuquerque, NM 87131<SPAN
style="mso-spacerun: yes"> </SPAN>James H. Brown Biology Department
University of New Mexico Albuquerque, NM 87131<SPAN
style="mso-spacerun: yes"> </SPAN>Steven Buskirk Department of Zoology and
Physiology University of Wyoming 1000 E. University Avenue Laramie, WY
82071<SPAN style="mso-spacerun: yes"> </SPAN>Brian Enquist Department of
Ecology and Evolutionary Biology University of Arizona Tucson, AZ 85721<SPAN
style="mso-spacerun: yes"> </SPAN>James Gillooly Biology Department
University of New Mexico Albuquerque, NM 87131<SPAN
style="mso-spacerun: yes"> </SPAN>John Harte Energy and Resources Group
310 Barrows Hall University of California, Berkeley Berkeley, CA 94720<SPAN
style="mso-spacerun: yes"> </SPAN>Michael Kaspari Department of Zoology
University of Oklahoma Norman, OK 73019<SPAN style="mso-spacerun: yes">
</SPAN>Carlos Martínez del Rio Department of Zoology and Physiology University
of Wyoming Laramie, WY 82071<SPAN style="mso-spacerun: yes"> </SPAN>Karl
Niklas Department of Plant Biology Cornell University Ithaca, NY 14853<SPAN
style="mso-spacerun: yes"> </SPAN>Raul Suarez Department of Ecology,
Evolution and Marine Biology University of California, Santa Barbara Santa
Barbara, CA 93016<SPAN style="mso-spacerun: yes"> </SPAN>Geoffrey B. West
Theoretical Physics Division Los Alamos National Laboratory MS B285 Los Alamos,
NM 87545<SPAN style="mso-spacerun: yes"> </SPAN>From Science News, Vol.
167, No. 7, Feb. 12, 2005, p. 106. <SPAN
style="mso-tab-count: 1"> </SPAN><SPAN
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<DIV> </DIV>
<DIV><FONT lang=0 face=Arial size=2 FAMILY="SANSSERIF"
PTSIZE="10">----------<BR>Howard Bloom<BR>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<BR>Recent Visiting
Scholar-Graduate Psychology Department, New York University; Core Faculty
Member, The Graduate
Institute<BR>www.howardbloom.net<BR>www.bigbangtango.net<BR>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.<BR>For information on The International
Paleopsychology Project, see: www.paleopsych.org<BR>for two chapters from
<BR>The Lucifer Principle: A Scientific Expedition Into the Forces of History,
see www.howardbloom.net/lucifer<BR>For information on Global Brain: The
Evolution of Mass Mind from the Big Bang to the 21st Century, see
www.howardbloom.net<BR></FONT></DIV></FONT></BODY></HTML>