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<DIV>
<DIV>Fascinating. But you have me hooked. What in the world could
the answer be to the following question: "<FONT face="Times New Roman">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! ... Why?"</FONT></DIV>
<DIV><FONT face="Times New Roman"></FONT> </DIV>
<DIV><FONT face="Times New Roman">And why are periglacial environments,
environments poor to the naked eye, richer than tropical environments, which
seem very, very rich?</FONT></DIV>
<DIV><FONT face="Times New Roman"></FONT> </DIV>
<DIV><FONT face="Times New Roman">How does the PERCEPTION of what's trash and
what's treasure, of what's a resource and what's not, feed into the
equation? Seemingly the bigger the brain, the more likely its owner is to
see resources where smaller brained creatures obstacles and emptiness. But
is this true?</FONT></DIV>
<DIV><FONT face="Times New Roman"></FONT> </DIV>
<DIV><FONT face="Times New Roman">Deer presumably inherit the strategies that
tell them what is trash and what is treasure--what is food and what is
not. They don't make discoveries that turn yesterday's waste into
tomorrow's resource, the way human inventors do. And deer don't have the
repository of solutions inventors draw from, then add their discoveries
to--culture.</FONT></DIV>
<DIV><FONT face="Times New Roman"></FONT> </DIV>
<DIV><FONT face="Times New Roman">So why do the same formulae apply in the case
of deer and of humans? Why do deer find the north, with its eight months
of scarcity, richer than the south, with its twelve months of
lushness?</FONT></DIV>
<DIV><FONT face="Times New Roman"></FONT> </DIV>
<DIV><FONT face="Times New Roman">Where does the technology that produces
clothing, shelter, and tools for hunting and harvesting
fit? What analog of this technology is available to the deer?</FONT></DIV>
<DIV><FONT face="Times New Roman"></FONT> </DIV>
<DIV><FONT face="Times New Roman">Are deer antlers useful for anything--for
scraping lichen and moss off of rocks, for example? Or are they simply
what most of us have always thought--gaudy displays of excess evolved to
appeal to the females of the species?</FONT></DIV>
<DIV><FONT face="Times New Roman"></FONT> </DIV>
<DIV><FONT face="Times New Roman">And why does the gaudy display of excess show
up so often in a cosmos that we think obeys strict laws of
frugality?</FONT></DIV>
<DIV><FONT face="Times New Roman"></FONT> </DIV>
<DIV><FONT face="Times New Roman">How does this extravagance fit into the
notions of economy that underlie Paul Werbos' Laplaceian math? And how
does this excess production of new form fit into a universe that many think is
ruled by the form-destroying processes of entropy?</FONT></DIV>
<DIV><FONT face="Times New Roman"></FONT> </DIV>
<DIV><FONT face="Times New Roman">A lot of questions, Val, but you've provided
food for a lot of thought. Howard</FONT></DIV>
<DIV> </DIV>
<DIV>In a message dated 10/10/2005 7:31:47 PM Eastern Standard Time,
kendulf@shaw.ca 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
size=2>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><FONT face="Times New Roman"
size=3>Dear Howard,</FONT></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><o:p><FONT
face="Times New Roman" size=3> </FONT></o:p></P>
<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>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><o:p><FONT
face="Times New Roman" size=3> </FONT></o:p></P>
<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.
</FONT></FONT></FONT><FONT style="BACKGROUND-COLOR: transparent" face=Arial
color=#000000 size=2><FONT size=2><FONT face="Times New Roman" size=3>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></BLOCKQUOTE>
<BLOCKQUOTE
style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue 2px solid">
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><o:p><FONT
face="Times New Roman" size=3> </FONT></o:p></P>
<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>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><o:p><FONT
face="Times New Roman" size=3> </FONT></o:p></P>
<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>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><o:p><FONT
face="Times New Roman" 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>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><o:p><FONT
face="Times New Roman" size=3> </FONT></o:p></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><o:p><FONT
face="Times New Roman" size=3> </FONT></o:p></P>
<P class=MsoNormal style="MARGIN: 0in 0in 0pt"><o:p><FONT
face="Times New Roman" size=3> </FONT></o:p></P></FONT>
<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=mailto:HowlBloom@aol.com
href="mailto:HowlBloom@aol.com">HowlBloom@aol.com</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A
title=mailto: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 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 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.
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title=http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#
href="http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#">Login</A>
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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
style="mso-spacerun: yes"> </SPAN>Home | Table of Contents |
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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>
<P>
<HR>
<P></P>_______________________________________________<BR>paleopsych mailing
list<BR>paleopsych@paleopsych.org<BR>http://lists.paleopsych.org/mailman/listinfo/paleopsych<BR>
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<HR>
<P></P>No virus found in this incoming message.<BR>Checked by AVG
Anti-Virus.<BR>Version: 7.0.344 / Virus Database: 267.11.13/124 - Release
Date:
10/7/2005<BR></BLOCKQUOTE><BR><BR>_______________________________________________<BR>paleopsych
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<DIV></DIV></DIV>
<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>