[Paleopsych] Fwd: Universal Footprint: Power Laws
Val Geist
kendulf at shaw.ca
Wed Oct 12 18:42:01 UTC 2005
Dear Howard,
You asked two questions: 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?
They are good questions, which I think I can answer. In the first, the similarity extends much beyond the fact that both, horns and brains, grow within or from skull bones! Large antlers/horns as well as brains stand, in an odd way, for supreme, highly adaptive all-round ability, for supreme competence and confidence. However, let me start at the real beginning.
Antlers as well as the cerebral cortex (the largest part of the brain) are both tissues of low growth priority. That is, they only grow when the blood stream has supplied all other tissues with their required energy and nutrients. Antlers and brains thus both depend for maximum growth on superabundant food of the highest quality. The brain in addititon to that superlative nutrition requires hard, but diverse exercise in order to grow. It’s like a muscle: no exercise, no growth! The broader the range of abilities mastered the larger the brain! Brain size is not related to excellence in a task, but in many tasks. Therefore, very large brains can only occur together with an athletic body and large body size. And that is the very picture of our wild, ice age ancestors from the upper Paleolithic in the cold, but productive periglacial zones. (It also applies to Neanderthal). The average Cro-magnid, athetic, six-foot plus, and with a brain 20% larger than moderns was a superior human specimen to Val Geist on every count!
As to antlers, they also grow only if there is lots and lots of excellent food. However, here is the rub! In deer societies the females occupy the most secure ground and graze the daylights out of it. For females and young the primary goal is security from predators, and they will gladly accept second rate food to achieve that. Consequently, males cannot thrive on the land occupied by the females. If they want to eat well, as they are driven to do as only large males are successful breeders so chosen by females, they must seek superior feeding grounds. However superior feeding areas are insecure. That is, to eat well is associated with much greater danger from predators and, consequently, more males get killed than females. Therefore, the larger the antlers of the male, the better he has succeeded feeding in very dangerous areas while outwitting and outrunning predators. Since antlers are tissues of low growth priority their size is directly related to superior competence of the male – precisely the male the female will choose for mating.
There is no escape from this: to grow into a superior specimen the young male deer must leave the poor feeding grounds of mother where he was born and raised and seek – boldly, cleverly, persistently - the best food in the most insecure, dangerous localities. His antler size proves his success as a hero! The bigger the more heroic and smart his conduct.
That’s within a species.
Big antlers turn on deer fames and big intelligence in human males turns on females. So big antlers and big brains are probably organs of sexual seelction, formed by ladies choice!
Now antler size in deer and brain size in humans progress in size, stepwise from the equator outward towards the poles. Each step away from the Equatorial Forests towards the poles increases the climates seasonality and severity as shown by Savannah, Steppe, Deserts, Temerate zones, Periglacial, Arctic/Alpine. Ungulates and omnivores many times, but Primates only once, bud off discrete “species” or “forms” from the tropic to the Arctic. Note: in this progression of new “forms” each has to del with the consequences of increased seasonality, with increasing extremes in climate, with ever wider fluctuations temporally and geographically – of resource abundance. Food availability and security demands are totally different in spring, than in summer, than in fall, than in winter. The further from the equator, the greater the demand on the diversity of skills and information to be mastered – and brain size keeps pace with that. Another important point: as poulations are limited by the scarce food supplies of winter, they are increasingly overwhelmed by the abundance of foods during the productivity pulse of summer. So, no productivity pulse in tropical moist forests, some pulse in Savannah, good pulse in steppe, better pulse in temperate zones good, large pulse in cold temperate, sharp but tall productivity spike in the Arctic/Alpine. During the productivity spike individuals enjoy freedome from want or luxury. The further north the greter the luxury – except for time! Towards the Arctic the spike becomes shorter and shorter – not enough Time to grow! Summer in the Arctic is very productive, but too short to allow luxurious body growth.
And another factor: in the tropics leaching drains fertility form the land making it nutrient poor except where nutrients are washed into soils deposited by rivers – alluvial soils. In the north glaciatons have liberated fertility from ground up rock. Ergo, our glaciated north is filthy rich in fertility. Filthy rich! Therefore the progression of species adapts each species to incasing seasonal luxury – totally missing in the moist tropics. In the tropics ferocious competition for nutrients drives species into narrow specialization increasing biodiversity. Each species, though is of minimum design and struggling to make ends meet. In the north, one species does what several species do in the tropics, lowering biodiversity. Also, logically, each northern species grows during the productivity pulse and stores fat for the bad times ahead in winter – lacking in tropical forms. Ergo, we are filthy fat and chimps and gorillas are not!
Now lets quickly go through the species progression south top north in the only primate lineage – anthropoids - which was able to achieve this, what has been achieved many, many times by ungulates. Note the rogression inro climatic severity and its ecological repercussions.
1.. primitive tropical moist forest ancestor – with chimp/bonobo adaptations holding the genetic foundations for human evolution.
2.. the Savannah-adapted gracile Australopithecus form, breaking free from territoriality by adapting to the “selfish herd”. Surface forager in the most productive tropical ecosystems. Climbs trees and builds nests for security at night.
3.. The first advance into the dry, seasonal step braking radically with the anthropoid adaptation by (a) being able to survive predators on the ground at night, (b) discovers underground feeding for stored plant foods (tubers, corms, bulbs, roots) which are only accessible through digging sticks which in turn need to be sculptured with stone tools from tough branches covered densely with sharp spines (tools to make tools) (c) begin to tap into the huge protein stores as represented by the ungulate biomass of the steppe. (d) almost certainly: begin to explore the fat and protein rich foods hidden! in the inter-tidal zones along ocean shores – as are steppe plant foods. All this generates additional profound changes away from the chimp ancestor. This is the Homo habilis/erectus form, the first true humans.
4.. With the first major glacitation about 1.9 m y ago, the beginning of the Pleistocene, this new form hardens its steppe adaptations and – bypassing the desert – begins to invade progressively the temperate zones. About a dozen or more major glaciations follow, desiccating Africa merciless and exterminating all human advances north of the Eurasian mountain chains – again and again. Still spread to Europe and Asia persist. This is the 1.5 my progression of our parent species Homo erectus.
5.. Huge penultimate glaciation 225 000 y ago desiccates Africa crisp and our parent species cannot make it and dies out. Two branches of it however transform to supreme desert conditions, a gracile form (us) and a robust form (Neanderthal). Jump in brain size!
6.. Neanderthal first and the gracile form later, invade the herbivore-rich periglacial zones in Eurasia, develop advanced technology and soon culture as we know it. Both are biologically grotesque and fat Ice Age giants within a fauna of grotesque and fat Ice Age giants (its all dreadfully “biologica!”). Superlative luxury body and brain development in both forms till Neanderthal fades away, and the superlatively developed European specimen fade away with the end of the last glaciation, being replaced by a small-brained starvation culture (Mesolithic) followed by agriculture (followed by genetic decay, and loss of brain size etc).
7.. Meanwhile, one late-glacial branch of the graciles branches out into inner Asia and develops even more brain in a process of neotinization. The supremely cold adapted mongoloid people evolve that colonize the Arctic/Alpine and north America, but only with and after mega-faunal extinctions (earlier attempts by ur-caucasoids and Ainu failed!).
So much for the thumb-nail sketch! Note: no other primate went past the horrific barriers of the African dry steppe! In crashing through we became humans.
So, antlers and brains both depend on ecological riches, and such are found increasingly the closer one gets to the fertile soils formed by glacial actions and warm, moist summers. However, the price to pay is acquisition of competence to deal with increasingly more complex ecological demands.
Cheers, Val Geist
----- Original Message -----
From: HowlBloom at aol.com
To: paleopsych at paleopsych.org
Sent: Monday, October 10, 2005 10:52 PM
Subject: Re: [Paleopsych] Fwd: Universal Footprint: Power Laws
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
To: 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
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 (2001), 76: 161-209 Cambridge University Press doi:10.1017/S1464793101005607 Published Online 17May2001 *This article is available in a PDF that may contain more than one articles. Therefore the PDF file's first page may not match this article's first page.
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Review Article
Scale invariance in biology: coincidence or footprint of a universal mechanism?
T. GISIGER a1 p1
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)
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 | Feedback | Subscribe | Help/About | Archives | Search Copyright ©2005 Science Service. All rights reserved. 1719 N St., NW, Washington, DC 20036 | 202-785-2255 | scinews at sciserv.org Subscribe Subscribe to Science News. Click OR call 1-800-552-4412. Google Search WWW Search Science News Free E-mail Alert Science News e-LETTER. Click here to find resources for enjoying our planet and the universe. Science Mall sells science posters, gifts, teaching tools, and collector items. Finally a store for science enthusiasts, professionals, and kids alike! Shop at the Science Mall. Science News Logo Wear Science News Logo Wear Copyright Clearance Center Photo Archive Browse a Science News photo collection.
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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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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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