[Paleopsych] Fwd: Universal Footprint: Power Laws
HowlBloom at aol.com
HowlBloom at aol.com
Tue Oct 11 05:52:20 UTC 2005
Fascinating. But you have me hooked. What in the world could the answer be
to the following question: "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?"
And why are periglacial environments, environments poor to the naked eye,
richer than tropical environments, which seem very, very rich?
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?
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.
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?
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?
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?
And why does the gaudy display of excess show up so often in a cosmos that
we think obeys strict laws of frugality?
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?
A lot of questions, Val, but you've provided food for a lot of thought.
Howard
In a message dated 10/10/2005 7:31:47 PM Eastern Standard Time,
kendulf at shaw.ca writes:
Dear Howard,
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) Bioenergetics and Growth, (mine is a Hafner
reprint). An utterly timeless, brilliant work if there ever was one! 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) 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!
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, please see “Primary rules of
reproductive fitness” pp.2-13 of my 1978 “Life Strategies…” book. Some of the
insights in the essay presented as new are actually discussed in D’Arcy Thompsons
(1917) On Growth and Form. 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.
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
Deer of the World (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 Arctic, 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! The
further north, the larger the antlers!
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 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(antler mass in grams) = f
(weight in kg)1.35 . 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 luxury conditions.
Note luxury! I a moment you will see why! Antler mass is determined in above
deer from small to large by y(antler mass in grams) = 2.6 (wtKg) 1.50. Horn
mass in wild sheep happens to be y=2.32 (wtKg)1.49. And increase in relative
brain volume from Australopithecus gracilis to Homo sapiens is y(cm3 of brain)
= 1.56 (wtkg)1.575. 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.
I have written enough! Cheers, Val Geist
----- Original Message -----
From: _HowlBloom at aol.com_ (mailto:HowlBloom at aol.com)
To: _paleopsych at paleopsych.org_ (mailto:paleopsych at paleopsych.org)
Sent: Friday, October 07, 2005 12:26 PM
Subject: [Paleopsych] Fwd: Universal Footprint: Power Laws
In a message dated 10/7/2005 3:13:06 PM Eastern Standard Time, Howl Bloom
writes:
All thanks, Jim. I just gave a presentation related to this subject to an
international quantum physics conference in Moscow--Quantum Informatics 2005.
I wish I'd seen the article before giving the talk. It would have come in
handy.
Meanwhile I tracked down a copy of the full article. It's downloadable for
free at
_http://www.pasteur.fr/recherche/unites/neubiomol/ARTICLES/Gisiger2001.pdf_
(http://www.pasteur.fr/recherche/unites/neubiomol/ARTICLES/Gisiger2001.pdf)
Better yet, enclosed is a file with the full article and with another
article that relates. I may not have the time to read these, so if you digest
anything interesting from them and get the time, please jot me an email and give
me your summary of what these articles are getting at.
Since Eshel Ben-Jacob has been trying to point out for years why such
concepts as scale-free power laws and fractals fail to get at the creative twists
evolution comes up with as it moves from one level of emergence to another,
anything in these pieces that indicates how newness enters the repetition of
the old would be of particular interest.
Again, all thanks. Onward--Howard
In a message dated 10/5/2005 5:12:27 PM Eastern Standard Time,
JBJbrody at cs.com writes:
_Biological Reviews_
(http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#) (2001), 76: 161-209 Cambridge University Press
doi:10.1017/S1464793101005607 Published Online 17May2001 *This article is
available in a PDF that may contain more than one articles. Therefore the PDF
file's first page may not match this article's first page.
_Login_
(http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#)
_Subscribe to journal_
(http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#)
_Email abstract_
(http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#)
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bridge.org/action/displayAbstract?fromPage=online&aid=74595#)
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Review Article
Scale invariance in biology: coincidence or footprint of a universal
mechanism?
T. GISIGER a1 _p1_
(http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=74595#p1)
a1 Groupe de Physique des Particules, Université de Montréal, C.P. 6128,
succ. centre-ville, Montréal, Québec, Canada, H3C 3J7 (e-mail:
_gisiger at pasteur.fr_ (mailto:gisiger at pasteur.fr) )
Abstract
In this article, we present a self-contained review of recent work on
complex biological systems which exhibit no characteristic scale. This property
can manifest itself with fractals (spatial scale invariance), flicker noise or
1/f-noise where f denotes the frequency of a signal (temporal scale
invariance) and power laws (scale invariance in the size and duration of events in the
dynamics of the system). A hypothesis recently put forward to explain these
scale-free phenomomena is criticality, a notion introduced by physicists
while studying phase transitions in materials, where systems spontaneously
arrange themselves in an unstable manner similar, for instance, to a row of
dominoes. Here, we review in a critical manner work which investigates to what
extent this idea can be generalized to biology. More precisely, we start with a
brief introduction to the concepts of absence of characteristic scale
(power-law distributions, fractals and 1/f- noise) and of critical phenomena. We then
review typical mathematical models exhibiting such properties: edge of
chaos, cellular automata and self-organized critical models. These notions are
then brought together to see to what extent they can account for the scale
invariance observed in ecology, evolution of species, type III epidemics and some
aspects of the central nervous system. This article also discusses how the
notion of scale invariance can give important insights into the workings of
biological systems.
(Received October 4 1999)
(Revised July 14 2000)
(Accepted July 24 2000)
Key Words: Scale invariance; complex systems; models; criticality; fractals;
chaos; ecology; evolution; epidemics; neurobiology.
Correspondence:
p1 Present address: Unité de Neurobiologie Moléculaire, Institut Pasteur, 25
rue du Dr Roux, 75724 Paris, Cedex 15, France.
Retrieved February 16, 2005, from the World Wide Web
http://www.sciencenews.org/articles/20050212/bob9.asp Week of Feb. 12, 2005; Vol. 167, No. 7 , p.
106 Life on the Scales Simple mathematical relationships underpin much of
biology and ecology Erica Klarreich A mouse lives just a few years, while an
elephant can make it to age 70. In a sense, however, both animals fit in the
same amount of life experience. In its brief life, a mouse squeezes in, on
average, as many heartbeats and breaths as an elephant does. Compared with
those of an elephant, many aspects of a mouse's life—such as the rate at which
its cells burn energy, the speed at which its muscles twitch, its gestation
time, and the age at which it reaches maturity—are sped up by the same factor
as its life span is. It's as if in designing a mouse, someone had simply
pressed the fast-forward button on an elephant's life. This pattern relating
life's speed to its length also holds for a sparrow, a gazelle, and a person—
virtually any of the birds and mammals, in fact. Small animals live fast and die
young, while big animals plod through much longer lives. "It appears as if
we've been gifted with just so much life," says Brian Enquist, an ecologist at
the University of Arizona in Tucson. "You can spend it all at once or
slowly dribble it out over a long time." a5850_1358.jpg Dean MacAdam Scientists
have long known that most biological rates appear to bear a simple
mathematical relationship to an animal's size: They are proportional to the animal's
mass raised to a power that is a multiple of 1/4. These relationships are
known as quarter-power scaling laws. For instance, an animal's metabolic rate
appears to be proportional to mass to the 3/4 power, and its heart rate is
proportional to mass to the –1/4 power. The reasons behind these laws were a
mystery until 8 years ago, when Enquist, together with ecologist James Brown of
the University of New Mexico in Albuquerque and physicist Geoffrey West of
Los Alamos (N.M.) National Laboratory proposed a model to explain
quarter-power scaling in mammals (SN: 10/16/99, p. 249). They and their collaborators
have since extended the model to encompass plants, birds, fish and other
creatures. In 2001, Brown, West, and several of their colleagues distilled their
model to a single formula, which they call the master equation, that predicts a
species' metabolic rate in terms of its body size and temperature. "They
have identified the basic rate at which life proceeds," says Michael Kaspari, an
ecologist at the University of Oklahoma in Norman. In the July 2004
Ecology, Brown, West, and their colleagues proposed that their equation can shed
light not just on individual animals' life processes but on every biological
scale, from subcellular molecules to global ecosystems. In recent months, the
investigators have applied their equation to a host of phenomena, from the
mutation rate in cellular DNA to Earth's carbon cycle. Carlos Martinez del
Rio, an ecologist at the University of Wyoming in Laramie, hails the team's
work as a major step forward. "I think they have provided us with a unified
theory for ecology," he says. The biological clock In 1883, German
physiologist Max Rubner proposed that an animal's metabolic rate is proportional to
its mass raised to the 2/3 power. This idea was rooted in simple geometry. If
one animal is, say, twice as big as another animal in each linear dimension,
then its total volume, or mass, is 23 times as large, but its skin surface is
only 22 times as large. Since an animal must dissipate metabolic heat
through its skin, Rubner reasoned that its metabolic rate should be proportional to
its skin surface, which works out to mass to the 2/3 power. a5850_2473.jpg
Dean MacAdam In 1932, however, animal scientist Max Kleiber of the
University of California, Davis looked at a broad range of data and concluded that
the correct exponent is 3/4, not 2/3. In subsequent decades, biologists have
found that the 3/4-power law appears to hold sway from microbes to whales,
creatures of sizes ranging over a mind-boggling 21 orders of magnitude. For most
of the past 70 years, ecologists had no explanation for the 3/4 exponent.
"One colleague told me in the early '90s that he took 3/4-scaling as 'given by
God,'" Brown recalls. The beginnings of an explanation came in 1997, when
Brown, West, and Enquist described metabolic scaling in mammals and birds in
terms of the geometry of their circulatory systems. It turns out, West says,
that Rubner was on the right track in comparing surface area with volume, but
that an animal's metabolic rate is determined not by how efficiently it
dissipates heat through its skin but by how efficiently it delivers fuel to its
cells. Rubner should have considered an animal's "effective surface area,"
which consists of all the inner surfaces across which energy and nutrients pass
from blood vessels to cells, says West. These surfaces fill the animal's
entire body, like linens stuffed into a laundry machine. The idea, West says,
is that a space-filling surface scales as if it were a volume, not an area. If
you double each of the dimensions of your laundry machine, he observes, then
the amount of linens you can fit into it scales up by 23, not 22. Thus, an
animal's effective surface area scales as if it were a three-dimensional, not
a two-dimensional, structure. This creates a challenge for the network of
blood vessels that must supply all these surfaces. In general, a network has
one more dimension than the surfaces it supplies, since the network's tubes add
one linear dimension. But an animal's circulatory system isn't four
dimensional, so its supply can't keep up with the effective surfaces' demands.
Consequently, the animal has to compensate by scaling back its metabolism according
to a 3/4 exponent. Though the original 1997 model applied only to mammals
and birds, researchers have refined it to encompass plants, crustaceans, fish,
and other organisms. The key to analyzing many of these organisms was to add
a new parameter: temperature. Mammals and birds maintain body temperatures
between about 36°C and 40°C, regardless of their environment. By contrast,
creatures such as fish, which align their body temperatures with those of their
environments, are often considerably colder. Temperature has a direct effect
on metabolism—the hotter a cell, the faster its chemical reactions run. In
2001, after James Gillooly, a specialist in body temperature, joined Brown at
the University of New Mexico, the researchers and their collaborators
presented their master equation, which incorporates the effects of size and
temperature. An organism's metabolism, they proposed, is proportional to its mass
to the 3/4 power times a function in which body temperature appears in the
exponent. The team found that its equation accurately predicted the metabolic
rates of more than 250 species of microbes, plants, and animals. These species
inhabit many different habitats, including marine, freshwater, temperate,
and tropical ecosystems. The equation gave the researchers a way to compare
organisms with different body temperatures—a person and a crab, or a lizard and
a sycamore tree— and thereby enabled the team not just to confirm previously
known scaling laws but also to discover new ones. For instance, in 2002,
Gillooly and his colleagues found that hatching times for eggs in birds, fish,
amphibians, and plankton follow a scaling law with a 1/4 exponent. When the
researchers filter out the effects of body temperature, most species adhere
closely to quarter-power laws for a wide range of properties, including not
only life span but also population growth rates. The team is now applying its
master equation to more life processes—such as cancer growth rates and the
amount of time animals sleep. "We've found that despite the incredible
diversity of life, from a tomato plant to an amoeba to a salmon, once you correct for
size and temperature, many of these rates and times are remarkably similar,"
says Gillooly. A single equation predicts so much, the researchers contend,
because metabolism sets the pace for myriad biological processes. An animal
with a high metabolic rate processes energy quickly, so it can pump its heart
quickly, grow quickly, and reach maturity quickly. Unfortunately, that
animal also ages and dies quickly, since the biochemical reactions involved in
metabolism produce harmful by-products called free radicals, which gradually
degrade cells. "Metabolic rate is, in our view, the fundamental biological
rate," Gillooly says. There is a universal biological clock, he says, "but it
ticks in units of energy, not units of time." Scaling up The researchers
propose that their framework can illuminate not just properties of individual
species, such as hours of sleep and hatching times, but also the structure of
entire communities and ecosystems. Enquist, West, and Karl Niklas of Cornell
University have been looking for scaling relationships in plant communities,
where they have uncovered previously unnoticed patterns. a5850_3175.jpg
REGULAR ON AVERAGE. Newly discovered scaling laws have revealed an unexpected
relationship between the spacing of trees and their trunk diameters in a
mature forest. PhotoDisc The researchers have found, for instance, that in a
mature forest, the average distance between trees of the same mass follows a
quarter-power scaling law, as does trunk diameter. These two scaling laws are
proportional to each other, so that on average, the distance between trees of
the same mass is simply proportional to the diameter of their trunks. "When
you walk in a forest, it looks random, but it's actually quite regular on
average," West says. "People have been measuring size and density of trees for
100 years, but no one had noticed these simple relationships." The
researchers have also discovered that the number of trees of a given mass in a forest
follows the same scaling law governing the number of branches of a given size
on an individual tree. "The forest as a whole behaves as if it is a very
large tree," West says. Gillooly, Brown, and their New Mexico colleague Andrew
Allen have now used these scaling laws to estimate the amount of carbon that
is stored and released by different plant ecosystems. Quantifying the role
of plants in the carbon cycle is critical to understanding global warming,
which is caused in large part by carbon dioxide released to the atmosphere when
animals metabolize food or machines burn fossil fuels. Plants, by contrast,
pull carbon dioxide out of the air for use in photosynthesis. Because of this
trait, some ecologists have proposed planting more forests as one strategy
for counteracting global warming. In a paper in an upcoming Functional
Ecology, the researchers estimate carbon turnover and storage in ecosystems such
as oceanic phytoplankton, grasslands, and old-growth forests. To do this, they
apply their scaling laws to the mass distribution of plants and the
metabolic rate of individual plants. The model predicts, for example, how much stored
carbon is lost when a forest is cut down to make way for farmlands or
development. Martinez del Rio cautions that ecologists making practical
conservation decisions need more-detailed information than the scaling laws generally
give. "The scaling laws are useful, but they're a blunt tool, not a
scalpel," he says. Scaling down The team's master equation may resolve a
longstanding controversy in evolutionary biology: Why do the fossil record and genetic
data often give different estimates of when certain species diverged?
Geneticists calculate when two species branched apart in the phylogenetic tree by
looking at how much their DNA differs and then estimating how long it would
have taken for that many mutations to occur. For instance, genetic data put
the divergence of rats and mice at 41 million years ago. Fossils, however, put
it at just 12.5 million years ago. The problem is that there is no
universal clock that determines the rate of genetic mutations in all organisms,
Gillooly and his colleagues say. They propose in the Jan. 4 Proceedings of the
National Academy of Sciences that, instead, the mutation clock—like so many
other life processes—ticks in proportion to metabolic rate rather than to time.
The DNA of small, hot organisms should mutate faster than that of large, cold
organisms, the researchers argue. An organism with a revved-up metabolism
generates more mutation-causing free radicals, they observe, and it also
produces offspring faster, so a mutation becomes lodged in the population more
quickly. When the researchers use their master equation to correct for the
effects of size and temperature, the genetic estimates of divergence times—
including those of rats and mice—line up well with the fossil record, says Allen,
one of the paper's coauthors. The team plans to use its metabolic framework
to investigate why the tropics are so much more diverse than temperate zones
are and why there are so many more small species than large ones. Most
evolutionary biologists have tended to approach biodiversity questions in terms
of historical events, such as landmasses separating, Kaspari says. The idea
that size and temperature are the driving forces behind biodiversity is
radical, he says. "I think if it holds up, it's going to rewrite our
evolutionary-biology books," he says. Enthusiasm and skepticism While the
metabolic-scaling theory has roused much enthusiasm, it has its limitations. Researchers
agree, for instance, that while the theory produces good predictions when viewed
on a scale from microbes to whales, the theory is rife with exceptions when
it's applied to animals that are relatively close in temperature and size. For
example, large animals generally have longer life spans than small animals,
but small dogs live longer than large ones. a5850_4238.jpg Dean MacAdam
Brown points out that the metabolic-scaling law may be useful by calling
attention to such exceptions. "If you didn't have a general theory, you wouldn't
know that big dogs are something interesting to look at," he observes. Many
questions of particular interest to ecologists concern organisms that are close
in size. Metabolic theory may not explain, for example, why certain species
coexist or why particular species invade a given ecosystem, says John Harte,
an ecologist at the University of California, Berkeley. Some scientists
question the very underpinnings of the team's model. Raul Suarez, a comparative
physiologist at the University of California, Santa Barbara disputes the
model's starting assumption that an animal's metabolic rate is determined by
how efficiently it can transport resources from blood vessels to cells. Suarez
argues that other factors are equally important, or even more so. For
instance, whether the animal is resting or active determines which organs are using
the most energy at a given time.
"Metabolic scaling is a many-splendored thing," he says. Suarez' concern is
valid, agrees Kaspari. However, he says, the master equation's accurate
predictions about a huge range of phenomena are strong evidence in its favor.
Ecologists, physiologists, and other biologists appear to be unanimous on one
point: The team's model has sparked a renaissance for biological-scaling
theory. "West and Brown deserve a great deal of credit for rekindling the interest
of the scientific community in this phenomenon of metabolic scaling," Suarez
says. "Their ideas have stimulated a great deal of discussion and debate,
and that's a good thing." If you have a comment on this article that you would
like considered for publication in Science News, send it to
editors at sciencenews.org. Please include your name and location. To subscribe to Science News
(print), go to https://www.kable.com/pub/scnw/ subServices.asp. To sign up
for the free weekly e-LETTER from Science News, go to
http://www.sciencenews.org/pages/subscribe_form.asp. References: Brown, J.H., J.F. Gillooly, A.P.
Allen, V.M. Savage, and G.B. West. 2004. Toward a metabolic theory of
ecology. Ecology 85(July):1771-1789. Abstract. Gillooly, J.F., A.P. Allen, G.B.
West, and J.H. Brown. 2005. The rate of DNA evolution: Effects of body size and
temperature on the molecular clock. Proceedings of the National Academy of
Sciences 102(Jan. 4):140-145. Abstract available at
http://www.pnas.org/cgi/content/abstract/102/1/140. Gillooly, J.F. . . . G.B. West . . . and J.H.
Brown. 2002. Effects of size and temperature on developmental time. Nature
417(May 2):70-73. Abstract available at http://dx.doi.org/10.1038/417070a.
Gillooly, J.F., J.H. Brown, G.B. West, et al. 2001. Effects of size and
temperature on metabolic rate. Science 293(Sept. 21):2248-2251. Available at
http://www.sciencemag.org/cgi/content/full/293/5538/2248. Savage, V.M., J.F. Gillooly,
J.H. Brown, G.B. West, and E.L. Charnov. 2004. Effects of body size and
temperature on population growth. American Naturalist 163(March):429-441.
Available at http://www.journals.uchicago.edu/AN/
journal/issues/v163n3/20308/20308.html. Suarez, R.K., C.A. Darveau, and J.J. Childress. 2004. Metabolic
scaling: A many-splendoured thing. Comparative Biochemistry and Physiology, Part B
139(November):531-541. Abstract available at
http://dx.doi.org/10.1016/j.cbpc.2004.05.001. West, G.B., J.H. Brown, and B.J. Enquist. 1997. A general
model for the origin of allometric scaling models in biology. Science 276(April
4):122-126. Available at
http://www.sciencemag.org/cgi/content/full/276/5309/122. Further Readings: Savage, V.M., J.F. Gillooly, . . . A.P. Allen . . .
and J.H. Brown. 2004. The predominance of quarter-power scaling in biology.
Functional Ecology 18(April):257-282. Abstract available at
http://dx.doi.org/10.1111/j.0269-8463.2004.00856.x. Weiss, P. 1999. Built to scale. Science
News 156(Oct. 16):249-251. References and sources available at
http://www.sciencenews.org/pages/sn_arc99/10_16_99/bob1ref.htm. Sources: Anurag Agrawal
Ecology and Evolutionary Biology Cornell University Ithaca, NY 14853 Andrew Allen
Biology Department University of New Mexico Albuquerque, NM 87131 James H.
Brown Biology Department University of New Mexico Albuquerque, NM 87131
Steven Buskirk Department of Zoology and Physiology University of Wyoming 1000 E.
University Avenue Laramie, WY 82071 Brian Enquist Department of Ecology
and Evolutionary Biology University of Arizona Tucson, AZ 85721 James Gillooly
Biology Department University of New Mexico Albuquerque, NM 87131 John
Harte Energy and Resources Group 310 Barrows Hall University of California,
Berkeley Berkeley, CA 94720 Michael Kaspari Department of Zoology University of
Oklahoma Norman, OK 73019 Carlos Martínez del Rio Department of Zoology and
Physiology University of Wyoming Laramie, WY 82071 Karl Niklas Department of
Plant Biology Cornell University Ithaca, NY 14853 Raul Suarez Department of
Ecology, Evolution and Marine Biology University of California, Santa Barbara
Santa Barbara, CA 93016 Geoffrey B. West Theoretical Physics Division Los
Alamos National Laboratory MS B285 Los Alamos, NM 87545 From Science News,
Vol. 167, No. 7, Feb. 12, 2005, p. 106. Home | Table of Contents |
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----------
Howard Bloom
Author of The Lucifer Principle: A Scientific Expedition Into the Forces of
History and Global Brain: The Evolution of Mass Mind From The Big Bang to the
21st Century
Recent Visiting Scholar-Graduate Psychology Department, New York University;
Core Faculty Member, The Graduate Institute
www.howardbloom.net
www.bigbangtango.net
Founder: International Paleopsychology Project; founding board member: Epic
of Evolution Society; founding board member, The Darwin Project; founder: The
Big Bang Tango Media Lab; member: New York Academy of Sciences, American
Association for the Advancement of Science, American Psychological Society, A
cademy of Political Science, Human Behavior and Evolution Society,
International Society for Human Ethology; advisory board member: Institute for
Accelerating Change ; executive editor -- New Paradigm book series.
For information on The International Paleopsychology Project, see:
www.paleopsych.org
for two chapters from
The Lucifer Principle: A Scientific Expedition Into the Forces of History,
see www.howardbloom.net/lucifer
For information on Global Brain: The Evolution of Mass Mind from the Big
Bang to the 21st Century, see www.howardbloom.net
____________________________________
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----------
Howard Bloom
Author of The Lucifer Principle: A Scientific Expedition Into the Forces of
History and Global Brain: The Evolution of Mass Mind From The Big Bang to the
21st Century
Recent Visiting Scholar-Graduate Psychology Department, New York University;
Core Faculty Member, The Graduate Institute
www.howardbloom.net
www.bigbangtango.net
Founder: International Paleopsychology Project; founding board member: Epic
of Evolution Society; founding board member, The Darwin Project; founder: The
Big Bang Tango Media Lab; member: New York Academy of Sciences, American
Association for the Advancement of Science, American Psychological Society,
Academy of Political Science, Human Behavior and Evolution Society, International
Society for Human Ethology; advisory board member: Institute for
Accelerating Change ; executive editor -- New Paradigm book series.
For information on The International Paleopsychology Project, see:
www.paleopsych.org
for two chapters from
The Lucifer Principle: A Scientific Expedition Into the Forces of History,
see www.howardbloom.net/lucifer
For information on Global Brain: The Evolution of Mass Mind from the Big
Bang to the 21st Century, see www.howardbloom.net
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