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<DIV><FONT size=2>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT face="Times New Roman"
size=3>Dear Howard,</FONT></P>
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"urn:schemas-microsoft-com:office:office" /><o:p><FONT face="Times New Roman"
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<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT face="Times New Roman"
size=3>The essay on power functions struck a cord within for a number of
reasons. (a) Biologists are – finally – waking up to utility of power functions,
which, since the 1920’s have been one of the major tools of the agricultural
discipline of Animal Science. These scientists – totally innocent of biology –
developed great mastery in the study of body growth and production in
agricultural animals. Their goals were strictly utilitarian (how to produce
bigger haunches in cattle and sheep, or longer bodies in pigs so as to get
longer slabs of beacon etc. because that’s where the money led), however, when I
took Animal Science in the late 1950’s I became quickly aware of the
applicability of both, their insights and methods, in the study of evolution and
ecology of large mammals. That included anthropology, us, as I shall illustrate
for the fun of it, below. And then there is the Bible of Animal Science, the
genial summary work of Samuel Brody (1945) <I
style="mso-bidi-font-style: normal">Bioenergetics and Growth</I>, (mine is a
Hafner reprint). An utterly timeless, brilliant work if there ever was one!<SPAN
style="mso-spacerun: yes"> </SPAN>So, that’s my first source of happiness!
(b) Might I raise the hope that, finally, after decades of working with power
functions - in splendid isolation - I just might be able to discuss insights
about human biology and evolution using power functions? The closest I ever got
was explaining to colleagues how to use their hand calculator to pull logs and
anti-logs! So, the essay raised my hopes - and there is nothing like hope! And
that’s my second source of happiness. (c)<SPAN style="mso-spacerun: yes">
</SPAN>In over 40 years of reading and reviewing papers I have caught only one
out and out fraud! And this gentleman had the gift of creatively misusing power
functions. The paper I got was based on the second half of a PhD Thesis for
which Harvard had awarded him a doctorate. He had bamboozled four eminent
scientists into signing off that piece of fraud. By one of those co incidents I
was just working on something very similar to him and became suspicious because
his theoretical predictions fitted his data too well, and the raw data in that
are never looked that good. I managed to recreate all his calculations and
discovered that he had misused his own data, had falsely attributed data to
existing authors (whom I called on the phone), that he had invented not only
data – his own and under the names of reputable scholars, but that he had
created fictitious references as well. Then a buddy in mathematics looked at
some of his mathematical discussions and declared them as invalid on multiple
counts. I returned with my friend a stinging review promising we would expose
him next time. The fellow had a most undistinguished career in several degree
mills subsequently and the only other paper of his I subsequently refereed was
OK, but mediocre. I refused to read the published first half of his thesis, but
some buddies who did shook their head and wondered out loud that there is
something eerie about that paper! Yes indeed! However, I kept my mouth shut and
a fraud was able to acquire a university position. So much for
happiness!</FONT></P>
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<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT face="Times New Roman"
size=3>Power functions are absolutely basic to understanding life processes, and
they do a sterling job of relieving the theory of evolution of unnecessary ad
hoc explanations. If you have it handy,<SPAN style="mso-spacerun: yes">
</SPAN>please see “<I style="mso-bidi-font-style: normal">Primary rules of
reproductive fitness</I>” pp.2-13 of my 1978 “<I
style="mso-bidi-font-style: normal">Life Strategies</I>…” book. Some of the
insights in the essay presented as new are actually discussed in D’Arcy
Thompsons (1917) <I style="mso-bidi-font-style: normal">On Growth and Form</I>.
To my embarrassment I discovered that his book by a zoologist is known better in
Architecture and the Design disciplines than among current zoologists. Thompson
uses real mathematics, where as current life scientists focus on statistics. It
is he who discusses that globular cells merely take advantage of the fee
shape-forming energy of surface tension and that it costs real energy for a cell
to deviate from this shape. In principle life scavenges free energy from physics
and chemistry to function as cheaply as possible, for power functions drive home
mercilessly just how costly it is to live and how supremely important to life is
the law of least effort, or Zipf’s (1949) Law. </FONT></P>
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<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT face="Times New Roman"
size=3>Thje beauty of power functions is that they state rules with precision
and that such are essential to comparisons. Let’s look at an amusing example
that suddenly becomes relevant to understanding humans. As I detailed in my 1998
<I style="mso-bidi-font-style: normal">Deer of the World</I> (next most
important magnum opus) the deer family is marvelously rich in examples essential
to the understanding of evolutionary processes in large mammals, humans
included. They show several times a pattern of speciation from the Tropics to
the <st1:place>Arctic</st1:place>, that among primates only the human lineage
followed. In several deer lineages there is a progressive increase in antler –
those spectacular organs beloved by trophy hunters. There is a steady, but
step-wise, increase in size and complexity from equator to pole!<SPAN
style="mso-spacerun: yes"> </SPAN>The further north, the larger the
antlers!</FONT></P>
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<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT face="Times New Roman"
size=3>However, antlers do not increase in proportion to body mass (weight in Kg
raised to the power of 1), nor to metabolic mass (weight in Kg raised to the
power of<SPAN style="mso-spacerun: yes"> </SPAN>0.75), rather, antler
growth follows a positive power function, which, between species is 1.35. So, to
compare the relative antler mass of small and large deer one generates for each
species y<SUB>(antler mass in grams)</SUB> = f (weight in kg)<SUP>1.35 </SUP>.
First of I can readily compare the amount of antler mass produced by species
despite differences in body size. The largest antler mass is found in cursors
(high speed runners) the smallest in forest hiders. However, in high speed
runners, antler mass grows with body mass - within a lineage - even faster than
suggested above. The huge antlers of the Irish elk, 14 feet of spread turn out
to be of exactly the same relative mass as those of his last living relative the
fallow deer. A small fallow deer, scaled up to the size of an irish elk would
have 14 foot of antler spread! Are antlers incresing in size passively with body
size? Yes, but only under <B style="mso-bidi-font-weight: normal"><U>luxury
</U></B>conditions. Note <B
style="mso-bidi-font-weight: normal"><U>luxury</U></B>! I a moment you will see
why! Antler mass is determined in above deer from small to large by
y<SUB>(antler mass in grams)</SUB> = 2.6 (wtKg) <SUP>1.50</SUP>. Horn mass in
wild sheep happens to be y=2.32 (wtKg)<SUP>1.49</SUP>. And increase in relative
brain volume from <I style="mso-bidi-font-style: normal">Australopithecus
gracilis</I> to <I style="mso-bidi-font-style: normal">Homo sapiens</I> is
y(cm<SUP>3</SUP> of brain) = 1.56 (wtkg)<SUP>1.575</SUP>. Cute, isn’t it? The
human brain is (a) disassociated from body growth following positive allometry.
(b) Provided the environment allows individuals a significant vacation from
shortages and want, that is, body growth under luxury conditions, human brains
expand with (lean!) body mass – period! If humans fall below the expected value,
then you have some explaining to do! Smaller than expected brain size will
therefore be a function of poor nutritional environments. (c) Natural luxury
environments are periglacial and North Temperate ones – up to about 60oN, above
and below that conditions deteriorate. That is, up to about 60oN the annual
productivity pulse has a length and height to facilitates maximum growth.
Therefore, periglacial Ice Age giants are brainy, tropical ones are not! That
certainly applies to the huge brains of Neanderthal and Cro-magnids. As we
invaded the cold, but rich periglacial environments, getting a large brain to
deal with the increased diversity of demands (initially due to ever sharper
seasonality) was filling out an already available growth function! Our brains
expanded at he same rate in (exponent about 1.5) evolution as did the antlers of
giant deer and horns of giant sheep! Awesome organs all! Why? There is no ready
explanation. One would need to compare the growth exponents of other organs.
</FONT></P>
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size=3> </FONT></o:p></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT size=3><FONT
face="Times New Roman">I have written enough! Cheers, Val
Geist<o:p></o:p></FONT></FONT></P>
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size=3> </FONT></o:p></P>
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<BLOCKQUOTE
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=HowlBloom@aol.com
href="mailto:HowlBloom@aol.com">HowlBloom@aol.com</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=paleopsych@paleopsych.org
href="mailto:paleopsych@paleopsych.org">paleopsych@paleopsych.org</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Friday, October 07, 2005 12:26
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> [Paleopsych] Fwd: Universal
Footprint: Power Laws</DIV>
<DIV><BR></DIV><FONT id=role_document face=Arial color=#000000 size=3>
<DIV>
<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
face=Arial color=#000000 size=3>
<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 PTSIZE="10" FAMILY="SANSSERIF"><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#
href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#">Login</A>
<BR><A
title=http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#
href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#">Subscribe
to journal</A> <BR><A
title=http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#
href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#">Email
abstract</A> <BR><A
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href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#">Content
alerts</A> <BR><BR>Review Article<BR><BR></FONT><FONT lang=0
style="BACKGROUND-COLOR: #ffffff" face=Arial color=#336699 size=2
PTSIZE="10" FAMILY="SANSSERIF" 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
PTSIZE="10" FAMILY="SANSSERIF" 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
style="mso-spacerun: yes"> </SPAN>Home | Table of Contents |
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<DIV> </DIV>
<DIV><FONT lang=0 face=Arial size=2 PTSIZE="10"
FAMILY="SANSSERIF">----------<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>
<P>
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