Gaia Hypothesis page one (of three)

THE GAIA HYPOTHESIS: EVIDENCE, MECHANISM AND IMPLICATIONS

Along with water vapour, carbon dioxide is the principal greenhouse gas in the atmosphere. At the current level of 0.039% it keeps the Earth's atmosphere at an average temperature of around 15 degrees Celsius. Without any carbon dioxide (CO₂) the atmospheric temperature would be less than -10 degrees Celsius. Although the albedo of the Earth has an effect on temperature, the albedo is greatly influenced by the carbon dioxide level.

The carbon dioxide content of the atmosphere is measured in gigatonnes of carbon. The weight of the oxygen in the CO₂ molecule is ignored. Currently (2010) the atmosphere contains around 810 gigatonnes of carbon. Alternatively, the carbon dioxide content can be stated as the partial pressure that CO₂ exerts. For the purpose of the mathematical treatment, the partial pressure in kPa is used instead of gigatonnes.

David Schwartzman has argued that Gaia is not a fully fledged theory – perhaps he is right. I have never thought that a theory needed much in the way of evidence to be called a theory. To my mind a theory must have a certain amount of logic and at least some evidence. As the evidence rolls in then the theory slowly gains more acceptance. In the very early stages of plate
tectonics, evidence was pretty sketchy, but the theory inspired people to look for more. Similarly, Gaia has provided a great impetus to investigate the Earth's systems. Gaia, however, desperately needs a logical basis and a means of exerting selection pressure.
Well not any more!

In what follows, the Earth is not considered to be an organism. This is probably not an important point. Keeping living things in one box and the non-living in another box just makes it more convenient for me to explain my views.

One of these views explains that homeostasis is not the main principle of this theory. The main principle of Gaia is modification of the planet so that the living systems can evolve and gain more control and sophistication. The life on this planet is just following the laws of thermodynamics and probability and this usually leads to more species and more sophistication but not always. Before you spill your coffee, yes there is a scientific definition of sophistication.

Another view explains that just about all fluxes of elements cycling through the crust, ocean, atmosphere are controlled by reactions taking place in living things, to the extent that in most, if not all cases, we really can ignore any chemistry that is not occurring inside or beside a living organism. As an example, it is estimated by Schwartzman and Volk that the rate of oxidation of rock minerals is accelerated 1800 times by the living systems.
Perhaps I should not have done it, but I did! I have taken the name 'Gaia' and applied it to a measurement of the Earth. According to my back of the envelope calculations the Gaia of the Earth is around 50 kPa^-1years ^-1.
Abstract.
The rubisco enzyme is one of the main regulators in maintaining the carbon dioxide content of the atmosphere at a constant level. This enzyme does not set the equilibrium CO₂ concentration but it works to maintain the equilibrium. The actual equilibrium CO₂ level is set by the balance between the net sequestering activities of ecosystems and the release of CO₂ by volcanoes and other geological processes.

Disturbances to the CO₂ concentration allow us to measure of the Gaia of the planet. The Gaia of the whole Earth is around 50 inverse kilopascal years (50 kPa^-1years ^-1which we can call 50 Lovelocks). In simple terms this means that the Earth in its present condition is, each year, sequestering 1 Gt of carbon. This important concept will allow us to measure how fast we are degrading the planet because we will be able to see this number fall in the coming years.

The Theory of Evolution and the Gaia Hypothesis can be combined together into one theory. Where the essential driving force of evolution depends on the concepts of competition and adaptation to the environment, the expanded theory has additional mechanisms - cooperation between organisms and modification of the environment. Instead of natural selection choosing suitable adaptations as the only selection criteria, a second selection process is at work. We can call this process selection by environmental punishment.

Life on this planet is perched near the top of an energy dome (inverted potential well). Disturbances to CO₂ levels can perturb this balance. This dome is the consequence of the albedo of ice and the fact that ice has a positive feedback to its own formation.
The recurring episodes of ice and interglacial periods over the last 2.6 million years can be explained as the manipulation of day length. The benefit of changes to the rotational speed of the Earth is the boosting of the Earth's magnetic field.

Coral and other limestone forming organisms have developed a method of harnessing energy from the heat of the Earth. The coral never uses any of this energy. Indeed, the energy is not made available until millions of years after the coral has died. The energy is supplied to nanobes and bacteria living in rocks. This coral-bacteria arrangement constitutes a massive CO₂ pressure regulator. A hypothetical enzyme, hardrockco, may control the metabolism of these bacteria.

A second hypothetical enzyme, softrockco, in soil carbonate bacteria also assists in controlling atmospheric carbon dioxide.
The Gaian systems of feedback are completely overwhelmed by the activities of mankind. The assumption is being made that modern industrial society should be able to cope with CO₂ levels at two or three times pre-industrial levels. It is more than probable that six or seven billion people, will not be fed by a ravaged planet.

Every organism on this planet that has been present for a long time has totally transformed the planet.

There is a distinction between the terms "Gaia" and "fertility". Gaia refers the the Earth's ability to manipulate CO₂ and fertility refers to the ability of plants to grow quickly. For the Gaia to be a large number, the Earth has to be fertile and the ecosystems that are responsible for sequestration have to be active and ready to to their job. Sometimes the terms are used interchangeably.

We need to realise that a complex system such as the Earth can manipulate equilibriums to solve problems. The Earth will manipulate any degree of freedom that is available to it, if benefits will accrue. In other words life has triumphed over the Second Law of Thermodynamics because life is a feedback system where the probabilities of outcomes change as the feedbacks roll in. This is not to imply that life violates the Second Law of Thermodynamics. The Earth-Sun system is undergoing increasing entropy. The Second Law does not preclude the chance formation of complex molecules but it does state that the purely chance formation of a protein is close to zero. Life defeats the Second Law because the Second Law can not deal with feedbacks.

The mathematical analysis that follows has two stages of development:

• The initial stage where there is no sequestration by plants and the carbon is stored in protoplasm. Here the enzyme and the initial conditions set the equilibrium level of CO₂. The intention is just to demonstrate that rubisco is a feedback regulator.
• The second stage where the equilibrium level of CO₂ is determined by the plants and animals sequestering carbon in various forms, each with a different half-life. Here the model is applied to the real world.

INTRODUCTION
In order to understand the Earth and its history we need a basic grasp of the enormity of time and the cumulative effects of small changes.
A million does not sound like a large number, but a million seconds is a little under two weeks of time, so it would take a person at least a month to count up to 1 million, if they stopped to sleep and eat. However, a million years of Earth history, is a mere blip of time. In this blip, a mountain range growing at 1 mm per year will reach a height of 1 kilometre.
In only 100 million years continents can break up and move half way across the globe and a coral reef at a depth of 5 metres, laying down 1cm of coral per year will reach the surface in only 500 years. Some time in the last 5 million years our ape ancestors made the transition from ape to human. Seemingly small changes given enough time totally transform this planet and we have to realise that most of these changes are the result of living processes.
THE GAIA OF THE EARTH
Imagine that you are introduced to woman at a party, a shy mousy girl that attracts little attention. After several hours she removes her wig, spectacles and coat, to reveal a gold lame-clad diva with the voice of Maria Callas. The transformation would be most entertaining. I have had a very similar experience. I invented a mathematical concept as an aid to describing a phenomenon in nature - plants grow faster as carbon dioxide levels rise. This mousy little number that I conjured up, originally had form as a small decimal fraction in a simple computer program. It had no units and it represented in my mind some kind of affinity of the rubisco enzyme for carbon dioxide molecules. My intuition perceived it to be some type of chemical affinity that would ultimately be measured in a laboratory. A year or more later, miss mouse disrobed to reveal that she also represented the Gaia of the Earth. So miss mouse started out as 'A' the affinity factor of the rubisco enzyme for the carbon dioxide molecule and she transformed herself into 'Gaia' the fertility of the planet.

Scientists do not believe in absolute proof. Einstein is often quoted as saying something to the effect "a thousand experiments cannot prove me right but one experiment can prove me wrong". There are no absolutes in science, just a growing body of theories with varying degrees of evidence to support them. I am proposing that the rubisco enzyme is excellent proof that the Gaia Hypothesis is a sound scientific theory. James Lovelock, will one day stand beside Darwin, Wallace, and Hutton, as one of the architects of the theories explaining our planet's evolution.
The Gaia Hypothesis was initially conceived by James Lovelock in 1965 and appeared in print in 1972. While many scientists are prepared to acknowledge the appealing nature of the hypothesis, no convincing mechanism for its operation has been forthcoming - until now. The hypothesis proposes that living things have, over the last four billion years, created: our atmosphere, our climate, the salinity of the ocean, and almost any other characteristic of our planet that we can conceive.

Not since the time of Galileo, has a theory so rankled the hackles of the establishment, only this time the establishment is the scientific mainstream and not the cardinals of the Roman Catholic Church. Why has the scientific establishment so openly opposed Gaia? The simple answer is that proponents of Gaia, have never described a mechanism for this theory. Without a mechanism, Gaia, appears to conflict with the workings of Darwinian Evolution. It just does not appear to follow conventional logic.

Darwinian evolution is explained in terms of natural selection: organisms competing for resources and successful organisms passing on the superior traits to the next generation. There does not appear to be any place for cooperation between organisms. From the Gaian supporter's viewpoint, the evidence for Gaia is all around us. How is it possible for a planet to stay relatively stable in temperature and salinity for millions of years without some controlling mechanism? This is the very heart of the puzzle that is our Earth. The Earth is a system, and no system can survive for more than a brief interval without some amount of negative feedback.

All systems need negative feedbacks. The two concepts: system and negative feedback loop, are synonymous; one does not exist without the other. As a nine year-old I once challenged myself to see how far I could walk down the street with my eyes closed before I bumped into something. To my chagrin, with arms outstretched, I made five paces before my forehead collided the the sharp edge of a brick wall. Not that I perceived myself as a system and the exercise was nothing other than a personal challenge, but systems do not survive without feedback.

Within the human body feedback control loops maintain: body temperature, blood glucose, blood pH, blood volume etc. If evolution can build these loops into animals for their individual benefit why is it not possible for control loops to be built into organisms so that they control the planet?
The opponents of Gaia are asking us to believe that all the animals and plants are not wired together - they all act independently and selfishly. Somehow, for four billion years without coordination, the planet has just been lucky, it has neither permanently frosted over nor cooked itself with runaway greenhouse. Not withstanding the evidence that the Earth has had some huge ice-ages, we are expected to believe that CO₂ levels have just accidentally fluctuated so that the Earth is not too hot or too cold. To imagine such luck is equivalent expecting the glucose level of a diabetic to remain adequate without any inputs of insulin or dietary control. The glacial cycles over the last 2.6 million years should not be considered as too cold. Uncomfortable for humans but not cold enough to cause any mass extinctions. As postulated earlier, these cold periods are necessary to boost the magnetic field.

Various flavours of the hypothesis have been described from Influential Gaia - the weakest form, up to Optimising Gaia - the all singing, all dancing variety. I will attempt to explain the logic behind this Optimising Gaia. To test the logic I have written a simple computer program, which simulates organisms and feedback to the environment. The program is designed to see if selfish genes will win out over genes that enhance the environment. Unlike some models where benefits to the environment come at no cost to the individual, in my program the environmental genes use up valuable energy and the individual has less energy available for reproduction or leaf manufacture. It is interesting to watch the program run. With lots of selfish genes in the community, populations stay small, because the environment is infertile, then the unselfish genes begin to kick in, and the environment begins to improve. Despite the fact that the individuals that possess these environmental genes are at a distinct disadvantage, their numbers swell.
It sounds incredible - too good to be true you might think. But consider our own society. Why do most citizens choose to be honest, if self-interest is such a motivating factor? You might offer the answer that people have conscious thought and are consciously aware of the benefits of cooperation and they are also consciously aware of the functions of police and the judicial system. Your argument is totally valid. What I'm suggesting is: cooperation in the animal and plant kingdom does not require any form of conscious thought, cooperation is merely behaviour that helps the environment become more fertile.
THE THERMOSTAT OF THE EARTH: RUBISCO
This story begins in 1985 when a colleague and I attended a rainforest field study 50km west of Wauchope, NSW. The workshop was led by Alex Floyd who was at the time employed by NSW Parks and Wildlife. At the conclusion of the workshop, in the course of some idle conversation a group of us were having, Alex Floyd remarked to us:
"..You want to be pretty sure of what you are doing if you think you can improve upon nature."
The remark struck home to me. I took it to be an instance of supreme understatement. Here was a scientist who had spent forty years studying plants in rainforests and other habitats, passing on to me some of the distilled essence of a life's work. This idea completely dominated my mind for a couple of days: it was so contrary to my way of thinking. I had, to that day, believed what most of western culture believes. Over my lifetime I had adopted the assumption that industrial society equated to progress. Here in one sentence my belief system had been seriously challenged.

It was a new paradigm for me. I had always been impressed by nature. However this was something quite different. The view that nature was, if not perfect, then at least so adapted in an evolutionary sense that we, mankind, were unlikely to be able to improve upon it. I was prepared to seriously consider that nature, after four billion years of trial and error, had evolved a somewhat complex and effective set of interactions.

Some years later, in the late 1980's I became aware of James Lovelock's Gaia Hypothesis. While the scientific community, seemed to be duly sceptical I was quite receptive to Gaia. I thought little more about this until the 23rd July 1998 when I picked up a magazine lying on a desk at work. The next day I was at home sick with a virus and I was able to read some of the articles in the magazine. In an article on the work of Dr. Dean Price at Royal Society for Biological Sciences, titled, "Its not easy being green", mention was made of the rubisco enzyme, ribulose 1-5 biphosphate carboxylase\oxygenase. This enzyme is the most abundant enzyme on the Earth. Apparently this enzyme, upon which almost all, modern life depends, is flawed. Nature has entrusted rubisco with the job of being a switch controlling the rate of photosynthesis. Rubisco's flaw is that it has trouble distinguishing between oxygen and carbon dioxide. It spends approximately 75% of its time reacting with CO₂ doing the correct thing. The rest of the time this confused evolutionary boofhead of a molecule spends reacting with oxygen, doing the opposite of what it is supposed to do. The tone of the article did not imply the condescending nature of the words I have just used. The article dispassionately stated that it has been a conundrum for the previous twenty years why rubisco is so inefficient when all other enzymes are orders of magnitude more efficient. Not content to be just slow and clumsy, rubisco actually plays the saboteur, by initiating a process called photorespiration in which the plant goes on to waste energy that it had previously captured.

How can nature be so stupid? We marvel at the incredible complexity and efficiency of the human body and yet plants deliberately waste around one quarter of all the energy they catch. To put the situation into perspective, it's like building a motorcar, with precision engineering all through the motor and transmission and then deliberately making a hole in the fuel tank so that one quarter of all the fuel spills out onto the roadway.

Alex Floyd's words bounced around inside my head. "This cannot be right" (the actual words were somewhat more pithy), I said to myself. There must be some logical reason for the enzyme behaving the way that it does. A possible explanation, I thought, might be that rubisco controls the gaseous composition of the atmosphere. Anyone who understands equilibrium chemistry is familiar with the concept of a balance between forward and backward reactions. It occurred to me that the backward reaction, when the idiotic molecule is doing the wrong thing, is a means by which rubisco stops the atmospheric CO₂ concentration from dropping too low. As CO₂ concentration drops, the forward reaction slows down and the interfering reaction with oxygen takes up proportionately more time. In electronic or cybernetic terms we have a textbook case of feedback control. It was here, in the very genesis of the idea that I made a mistake. I could see that rubisco was controlling plants to stabilise the atmosphere and so I assumed that rubisco set the equilibrium level of CO₂. Fortunately this mistake was no impediment to my progress.

I set to work at my computer. After several hours of writing code and some debugging I was finished. The output showed rapid convergence to a stable level of carbon dioxide. I was elated. It was a simple computer model with some fiddle factors but it worked just fine. Had I discovered something important or had I just juggled the numbers and fooled myself? Over the next few months I was unable to raise much enthusiasm for my ideas – none in fact. Computer programs are not the conventional or accepted means of proving basic science. Never the less, I had much to understand, even from a simple computer simulation.

After eight months I realised that I needed more credibility. My proof was inside a very simple computer program. I had to convert the simulation into a mathematical form, if the hypothesis was ever to be seriously considered. This was a task I was reluctant to begin, as I was unsure if my mathematical skill would prove adequate. Fortunately the mathematics turned out to be relatively straightforward. The real challenge was provided when attempting to give physical interpretations to, and understand the relationships between the constants and variables.
Before I attempted the mathematics, other questions held my curiosity. Why did the rubisco molecule control carbon dioxide levels but not oxygen levels? This was a great source of intrigue. For every molecule of CO₂ removed from the atmosphere one molecule of oxygen is released. Animal respiration has the same rate of exchange of the two gases. In the computer program if the initial CO₂ levels are made low then the program quickly restores them to equilibrium levels. Yet if the initial oxygen levels are made low then the program quickly brings CO₂ to a different equilibrium level but makes no noticeable attempt to adjust oxygen levels. Indeed, with a little thought we realise that if CO₂ is adjusted then the oxygen levels have to be content with what is left over. But at the same time the program teaches us that oxygen is in control of carbon dioxide. This seems like a contradiction so examine the table below. The figures for CO₂ and O₂ are arbitrarily chosen and represent mass in the atmosphere e.g. gigatonnes.
Table 1

Affinity for CO2 (A)	Affinity for O2 (Ao)	A/Ao	Initial CO2	Initial O2	Equilibrium CO2	Equilibrium O2
0.64	0.18	3,555	1,000	1,000,000	328	1,000,672
0.64	0.18	3,555	100	1,000,000	328	999,772
0.64	0.18	3,555	1,000	800,000	272	800,727
0.64	0.18	3,555	100	800,000	272	799,828
0.64	0.18	3,555	1,000	600,000	216	600,784
0.64	0.18	3,555	100	600,000	216	599,884
0.50	0.18	2,777	1,000	1,000,000	420	1,000,580

With A set at .64 (no units needed at this stage) the computer program loops around until the CO₂ level is constant at 328. This 328 equilibrium is also dependent on the level of oxygen. If we change either the affinity of the enzyme, or the level of oxygen, a new CO₂ equilibrium will establish. The computer program is very simple, around twenty lines of code.
Here is a huge conundrum: if plants produce the oxygen in the atmosphere why don't they control the oxygen levels? If plants don't control oxygen levels, what does? In the past, oxygen was thought to be determined by a 'natural' balance between photosynthesis and the weathering of rock minerals. However David Schwartzman and Tyler Volk have shown that the weathering of minerals accelerates 1800 times if micro-organisms are present. So we must conclude that the rate of weathering of minerals is controlled by life. We must not under estimate the importance of this conclusion as it has transferred a whole arm of the carbon cycle into biological control. As you read on I hope to persuade you that nothing is left to chance or 'natural balance'. Every aspect of the Earth is under strict control. In many cases this control is achieved by large enzymes that have a multiple-substrate active site.

In rubisco the site reacts with carbon dioxide or oxygen. In the enzyme, nitrogenase, the enzyme reacts with nitrogen, carbon dioxide, oxygen and several other molecules, but the actual site of each reaction is still unclear. Oxygen attacks the iron-sulphur cofactor of nitrogenase to achieve an irreversible inhibition.

When I initially began to model the behaviour of the rubisco enzyme I made the assumption that the enzyme sets the equilibrium of CO₂. But this is not the case. The role of the enzyme is to maintain CO₂ at the equilibrium level. The actual equilibrium is set by the rate of sequestration of the entire plant community of the Earth. As an analogy, consider an air conditioning thermostat. The equilibrium temperature is set by the person who turns the dial and the thermostat slavishly works to maintain the room at the chosen temperature.

You may wonder why it required eleven years to change my mind from a model which had a fixed thermostat to a model where the thermostat has an adjustable dial. To explain: Originally I thought that the only way to change the temperature of the Earth was to change the efficiency of the rubisco enzyme. If plants with an efficient rubisco enzyme survived at the expense of plants containing a less efficient enzyme, then plants would grow faster, sequester more carbon, and the Earth would become colder. That's what I thought and I don't know why I would take so long to see the superior system that nature has devised. It's not as if I was not getting any hints. In the computer models where sequestration was implemented from a very early stage, the equilibrium level was telling me that it was affected by just about every variable in the program.
In retrospect, I can see the reason for my wayward thinking. At that stage I was using a faulty assumption about sequestration. I hadn't delineated the different forms of sequestration each with a different half-life. I was attempting to balance the atmosphere by adjusting the input of carbon into storage without realising that nature had another degree of freedom up its sleeve – control of the rate at which carbon comes out of storage.

In January of 1999 I decided to write a computer model to see if a hypothetical enzyme in denitrifying bacteria could control oxygen levels. After some weeks of programming I had constructed a model that produced a surprising result. The model simulated the production of nitrogen gas from nitrates by denitrifying bacteria. I had only expected to control oxygen, but the enzyme (ron) managed to control nitrogen simultaneously. Could one enzyme control two gases? My model was really too simple and I did not know much about the nitrogen cycle. I thought it best to learn more and build a bigger model later on. This bigger model incorporates four enzymes, air, ocean, bicarbonate ions, volcanoes, a subducton zone and lots more. Even though this larger model has a moderate amount of sophistication it is only a sketchy description of how our Earth coordinates itself.

With these modifications to Gaia, the theory has a chance of recruiting more mainstream scientists. Now we have some predictions to test. We can search for softrockco and hardrockco. The enzymes provide reasonable theoretical framework for keeping the partial pressures of atmospheric nitrogen, oxygen and carbon dioxide at fairly constant levels over long periods. The gaseous composition of the atmosphere has evolved in response to the living things present on the Earth, but the enzymes ensure that if the species are not changing then the gaseous composition will not change.
Below is a model of the rubisco enzyme from Sector Image Gallery University of Ottawa

The central dot represents the competing gas locus where either carbon dioxide or oxygen combines with the enzyme.




THE CARBON CYCLE AND SEQUESTRATION

There are many types of sequestered carbon each with a different lifetime. The carbon in a dead leaf of a tropical rainforest is back into the atmosphere within a period of several weeks. The trunk of a tree may exist for 500 years before fungal and bacterial breakdown return the carbon to the atmosphere. Bicarbonate ions in the ocean keep carbon out of the atmosphere for millions of years and so does coal, petroleum and limestone. Carbon trading is a total nonsense because there are no carbon sinks that are reliable and economic for us to use. Unless carbon emissions drop below 0.4 Gt then the atmosphere is going to get hotter and hotter, until lack of food brings the human population down to just a few million, maybe even less. Renewable energy is the best and safest option.

Graphic not uploadinng at present
The data on the carbon cycle is under continuous review. This graphic is somewhat dated as the atmosphere now contains around 810 Gt of carbon and emissions from industry are around 7.5 Gt. Missing from the graphic is the largest store of carbon which is contained in the limestone and dolomite rocks.

Many people are unaware of the huge imbalance in the carbon cycle that combustion of fossil fuel has made. The current emissions of CO₂ are far beyond the ability of ecosystems to cope - about fourteen times their ability. Just because marine photosynthesis is around 100 Gt per year, some people mistakenly believe that man's activities are minimal compared to the fluxes in the carbon cycle. Such a view is naive.


Total rate of removal of CO₂ from the atmosphere due to the photosynthetic activity of all terrestrial plants is around 5.5 Gt of carbon per year. Terrestrial animals return 5.5 Gt to the atmosphere during respiration. Deforestation releases 2.2Gt, and around 5.5Gt dissolves into the ocean ( ocean pH is falling rapidly). This leaves approximately 3.9 Gt each year to be stored as a build-up in the atmosphere. The numbers vary depending on how recently they have been updated.

At the beginning of the industrial revolution (circa 1830 AD) the atmosphere contained around 588 Gt of carbon as CO₂. Today the figure is around 810Gt.
THE LOGIC OF GAIA
The whole logic of Gaia is based on an initial movement away from the objective. The most beneficial move may be a move sideways or backwards. This move will be best if it results in the best outcome. A fox could start digging as soon as he arrives at the chicken coop. The clever thing to do, however, is to check out the entire fence looking for an easy point of entry. According to the old logic mammals should not have replaced reptiles because they have the disadvantage of enormous food requirements. But we can see that the disadvantage of a high calorific input is offset by the more flexible lifestyle. The same situation confronts consumers in our modern society . We can rent a house or we can go to the bank and get a loan. In the short term, renting is the easier option, but in the long term buying your own home is the better option. This logic is not that hard to understand - in some cases the best option is the more expensive option.

Prejudice is a real spider web that can tie up the most agile of minds. Despite his explanation of the photoelectric effect helping to launch quantum physics, Albert Einstein is the classic example of a brilliant mind that never came to grips with some aspects quantum mechanics - all because he was convinced that god does not play with dice. There are millions of agile minds that don’t like Gaian theory because they do not understand the logic. Yet Gaia is everywhere we look. It’s a case of seeing but not being receptive to the evidence.
Let’s look at the logic from the point of view of modern traditional science:

Adaptation	Immediate Benefit	Time scale of benefit	Logical/illogical
Energy-rich skin secretion - primitive milk	Minuscule	Immediate (if the newborn knows where to lick)	Logical
Improved camouflage	Minuscule	immediate	Logical
Improved soil condition by feeding soil micro organisms with leaf litter	immediate benefit is negative because of energy investment. Long term benefit is gigantic	a few months or years	Illogical

This is a truly sad state of affairs. Electrons can tunnel through energy barriers and any gambler multiplies risk by potential return to calculate his best bet, but mainstream science is unable to extend these principles to the theory of evolution.

Of course there is no goddess Gaia. Gaia is just a metaphor created by James Lovelock to highlight the fantastic system that nature has evolved to modify the Earth. I like the name Gaia, and Lovelock recounts with some joy, how the name was suggested to him by his neighbour, the novelist, William Golding. But mention the word in the company of many mainstream scientists and blood pressures begin to rise. Many prominent and intelligent people have found Gaia too hard to digest. The idea of some mythical goddess guiding nature to create a nirvana seems a bit far-fetched. And indeed it is.

There is nothing godlike in this system. No great supreme organising being is required. No concerted altruistic foresight of living things is required. Nature just stumbles along creating new life forms as Charles Darwin and Alfred Wallace proposed over a century and a half ago. There is no suggestion that nature does not make mistakes. Indeed she does. Nature makes plenty of 'mistakes' and these 'mistakes' punish nature severely.

A mistake is 'a life form that does not act in the long-term best interest of the planet.' In other words, a selfish plant, animal, bacterium, fungus or whatever.
If one of these selfish organisms does evolve then nature gets punished. The selfish organism creates havoc. The climate deteriorates or the recycling of some nutrient slows or ceases. Things start to get worse. Changing conditions really get Darwinian evolution into top gear. New species arise and old ones die out. If the offending organism has not become controlled then the climate or resource supply continues to deteriorate. Either the offender is controlled or conditions become even worse. Nature being so diverse has the upper hand. Some bug or predator will usually evolve and put the offender in his place. Only the non-selfish will flourish in the long term! In the absence of a controlling predator the climate deteriorates to a mass extinction.

Changing the course of evolution by drastically affecting the environment is not something that happens very often in modern times. Mass extinctions have only occurred five or so times in the last 600 million years but lesser extinction events have occurred on hundreds of occasions. How often major extinctions occurred in the preceding 4 billion years is unknown. If we look carefully at the extremely complex control mechanisms (not yet fully understood) of the rubisco enzyme, then it is difficult to imagine nature developing this degree of sophistication without a lot of trial and error. This leads to the conclusion that in the first billion years of evolution, environmental punishment would have been a regular event.

You should be able to see that the evolution of the planet is only slightly different from Darwin's theory of the evolution of new species. In fact we can explain both Darwin's theory and the Gaian Theory if we make a slight change to the definition of one word and also introduce the concept of environmental punishment.

If we change the definition of the word "adaptation" then Darwin's theory of natural selection will also explain the evolution of the Earth's climate, soil and ocean. So if we redefine an adaptation as "a characteristic that helps an organism to survive and reproduce OR ASSISTS IN THE RECYCLING OF RESOURCES OR MODERATION OF THE CLIMATE " then one theory will explain all.
The two theories work in almost the same way; only the time scale is different. A new adaptation that is directly beneficial to an organism helps it immediately to raise more offspring. An adaptation that benefits the environment may impose a slight energy cost but over the long term both that organism and all other organisms will benefit. Most adaptations incur an energy cost. Think of the huge disadvantage mammals have created for themselves by their warm-blooded adaptation. The extra food that they have to consume compared to a reptile is enormous. Yet the ability to operate at any time in almost any weather more than compensates for the extra food that they must find. In a similar way, an organism that invests energy in improving the environment will in the long term reap a benefit.

This concept that nature (the laws of physics and probability as manipulated by living things) will increase the survival chances of an organism that invests energy in a process that will not, in all probability, provide a tangible benefit for some years, is the mental breakthrough that we need to make. We only have to look around us to see that it is true. When the first flowering plant offered up the first nectar, was there an ant immediately available to use this secretion and increase the distribution efficiency of pollen? Or was there a certain interval when the adaptation had almost no advantage?

If evolution is to favour an adaptation then that adaptation has to provide some benefit, but the numerical size can be exceedingly small. Imagine that you pour a glass of water gently onto what you think is a perfectly flat surface. Surface tension will keep the water together as a puddle. However a passing vehicle in the street outside or the vibrations of a distant earth tremor will provide enough energy for the water to take advantage of any defects in the smoothness of the surface and it will flow down the valleys that we cannot see. And so with evolution, the benefit of a new adaptation may be infinitesimally small, but like our puddle of water, which will follow gravity, evolution will flow with probability.

This really does create a revolution in our thinking. For the past one hundred and fifty years we have learned to think of nature as the ultimate competitive spirit. We have used terms such as ‘survival of the fittest’, ‘competition for resources’ and ‘selfish genes’ when in actual fact nature is the ultimate in cooperation.

A lion kills a wildebeest, a bacterium kills a human being, might be seen by some people as the brutal actions of hostile beasts. But nothing could be more wrong. Individuals are insignificant in the grand scheme of things. What happens to the Earth in the long term is the only important consequence. If the actions of the life-forms result in the recycling of the nutrients and the maintenance of the climate, then all is well. The processes of birth, death and the creation of greater diversity will continue for millennia to come.
"There is no grand scheme!!!", I hear you call. You're right. The evolution of the planet is the product of the natural interplay of the laws of probability and thermodynamics.

THE LOGICAL ARGUMENT
From a logical point of view Gaia makes sense. Suppose we split Gaia up into components, say: atmospheric temperature control, rainfall manipulation, soil fertility control, and recycling of minerals. We can use the same argument for each component.
The activities of organisms can affect the Earth in three ways
1 the overall effect is beneficial to atmospheric temperature
2 the overall effect is neutral
3 the overall effect is harmful to atmospheric temperature (too hot or too cold)
If proposition three were true, very little life would be able to survive.
Proposition one represents optimising Gaia.
Position two is highly unlikely from a logical standpoint. What would be the probability that of all the billions of organisms, the detrimental effects would be exactly balanced by the beneficial effects?

CLIMATE CONTROL
The Cretaceous is named from the large deposits of chalk that were laid down 135 mya to 65 mya. The atmospheric temperature was five or six degrees above those of today with levels of CO₂ and methane, also higher. During this whole time there was no glacial–interglacial cycle that has suddenly appeared in the last 2.6 million years. Any theory of climate has to be consistent with these facts. So that rules out Milankovitch cycles from being a major influence on climate when greenhouse gases are prominent. Climate is determined by the balance between incoming and outgoing radiation. Our knowledge of the solar constant is quite speculative, but living systems have enormous control of both incoming and outgoing radiation: using clouds, ice, aerosols and greenhouse gases. Climate is easily controlled by changes to the populations that manipulate these influences.

NEW CHEMISTRY
The Rubisco enzyme controls the rate of photosynthesis of plants and therefore it has the role of returning CO₂ to the equilibrium level. If volcanoes raise the CO₂ above equilibrium then all plants begin to grow faster because rubisco reduces the amount of energy wasted in photorespiration. This faster growth allows the plants to sequester more carbon and the CO₂ level falls. The actual equilibrium level is determined by which plants exist. If the majority of plants are long term sequesterers then the equilibrium level will be low and the planet will be cool. If the majority of plants are short term sequesterers then the planet will be warm. This is a slight simplification because animals do have an impact on how fast carbon comes out of storage.

To model the behaviour of the rubisco enzyme a new entity, the affinity factor, was required. The rubisco enzyme reacts more frequently with carbon dioxide so the affinity factor for CO₂ , A, is a bigger number than the affinity factor for oxygen, Ao.

The core of the mathematics rests with the mathematical expression for the rate of photosynthesis. Usually the input that is in least supply determines the rate of a reaction but this is only partly true. Even if the sunlight is very dim, the soil is very dry or the ocean has a shortage of iron, the rubisco enzyme can speed up or slow down, the rate of photosynthesis in response to CO₂ levels. This is because the enzyme allows the plant to stop wasting energy that it has already collected. If CO₂ levels rise, less energy is wasted during photosynthesis. So rubisco behaves like a hand brake, taking about a quarter of the energy that has been captured. The degree of braking depends on the relative pressures of oxygen and carbon dioxide. Imagine a stationary car on a gentle slope with the handbrake lightly applied. If the handbrake is released somewhat, then the car can proceed to roll downhill. Likewise, if a plant is in a situation where its rate of photosynthesis is equal to its rate of respiration, then an increase in the carbon dioxide levels will allow growth to proceed. So higher CO₂ levels can allow all plants to grow faster, even plants that were previously stalled. However if the plant has no way of using its captured energy because some vital mineral is in limited supply then growth will not accelerate.

THE MATHEMATICS
The mathematical model and the computer model that generated table 1 have one small difference. The mathematical model leaves oxygen at a constant level, which never changes. The computer model is slightly more realistic in that a change in the CO₂ level results in a very small change in the oxygen level. Introducing a third differential equation to account for the conversion of CO₂ into oxygen serves no purpose since we are really only interested in observing how the enzyme returns CO₂ to equilibrium levels in the short term of say a few months or years.

The mathematics is very similar to that of a simple resistance-capacitance series circuit. The difference here is that the size of the capacitor changes as the capacitor charges up.
It is important to keep in mind that the purpose of this mathematical model is to demonstrate that the rubisco enzyme is a feedback control mechanism. It is not a model of the dynamics of the whole biosphere. Later I will adapt this model to the whole biosphere.
The rate of growth of all plants is given by:
dR/dt = R(A*C-Ao*O-Resp) (Equation 1)
Where:
R = the mass of carbon in all living plant cells in gigatonnes (Gt). (At this stage it does not matter if we choose R to represent the carbon mass of the whole biosphere or just the terrestrial biosphere.)
A = the affinity factor of rubisco for carbon dioxide. The enzyme can only react with one gas at a time at the competing gas locus.
Ao = the affinity factor of rubisco for oxygen
C = CO₂ partial pressure in kPa at sea level
O = Oxygen partial pressure in kPa at sea level
Resp = Respiration variable. It represents the respiration of all living things including plants. This model assumes that sequestered carbon is stored as living protoplasm and is ready to be returned to the atmosphere as soon as animal populations increase, which obviously does not occur in the real world. In a computer model it is easy to make an allowance for sequestered carbon but here I am attempting to keep the mathematics as simple as possible.

From this equation, using dimensional analysis, we can determine the units of the affinity factor.
Kg /s= Kg *A* kPa
giving the units of A as 1/kPa*s
However, years are more convenient than seconds, giving the units of A as inverse kilopascal years.
Now since every molecule of CO₂ extracted from the atmosphere results in the increase in mass of the plant matter, a second differential equation is created.
-dR/dt= d/dt (CARBON DIOXIDE) (Equation 2)
where:
CARBON DIOXIDE is the mass of carbon in CO₂ in the atmosphere in Gt (approximately 810 Gt in 2010 AD)
Fortunately the solution is easy
-R = CARBON DIOXIDE + K1
rearranging for convenience
R= K2- CARBON DIOXIDE (Equation 3)
Now C is proportional to CARBON DIOXIDE
i.e. the partial pressure of CO₂ is proportional to the mass of CO₂ in the atmosphere
(Estimates give 1 part per million of CO₂ representing 2.1 Gt of carbon. To convert ppm to kPa divide by 10 000 and the error is only ~1.14 %. )
C= P* CARBON DIOXIDE (P is a constant of proportionality)
= P*(K2-R) (Equation 4)
Substituting 4 into 1
dR/dt= R* A*P*(K2-R)- R*Ao*O- R* Resp
= R*D-A*P*R^2
Where D=(A*P*K2-Ao*O-Resp)
To solve this equation we separate the variables and then use partial fractions.
The solution is given by.
ln R - ln (D- A*P*R)= D* t + K3
or
R=D/[exp(-D*t+ K4) + A*P] See appendix 1 for this step. (Equation 5)
Substituting 4 into 5 gives us an equation for the atmosphere
C= P*K2- P*D/[exp(-D*t+K4)+ A*P] (Equation 6)

THIS IS THE EQUATION THAT CONTROLS OUR PLANET. It is valid as long as the extra CO₂ has not changed the climate so much that the species distribution has changed significantly. In usual circumstances, with the modern species currently on the Earth, it would take under a thousand years to extract 222 Gt of carbon from the atmosphere, provided there is no fossil fuel combustion.
This equation looks something like the trace on an oscilloscope of the charging or discharging of a resistance and capacitor in series. It just describes the rate at which the partial pressure of CO₂ will return to its equilibrium value if it is ever out of equilibrium. This curve assumes that if CO₂ is out of equilibrium, then the equilibrium will be restored by plants growing faster and storing carbon in more protoplasm. This curve is not directly applicable to the real world because it assumes that there is plenty of room for more plant mass and this is probably not the case. Despite this, the curve gives us a close idea of how the CO₂ levels will change.


 image not available --it looks like a slippery dip, one is steeper than the other.
Figure 1 is an example to illustrate the shape of the curve with different initial conditions. Both curves approach equilibrium from above. The continuous curve is slow to get started because the initial mass of plant matter was set at a very low level. As the mass of the plants goes up in this model the CO₂ level comes down. The dashed curve drops rapidly because the initial mass of plant matter was set quite high.

Figure 2 shows how the sigmoid curve approaches equilibrium from below. There is only one form of the curve possible because we have to set the initial mass of the plants quite high. In this model the only source of carbon into the atmosphere is derived from respiration exceeding photosynthesis. If the initial mass of plants is set low, then there will not be enough carbon to achieve the equilibrium level.
In the mathematical model the equilibrium level (target level) of CO₂ is determined by the ratio of A to Ao and the magnitude of O and Resp. (Don't despair the model is easily adapted to the real world.)
The horizontal axis should be in some units of time but the computer program has no units of time attached to the iteration process. The equation could be used to create a graph with time on the horizontal axis but in order to do this we would have to make some assumptions about how much plant matter exists on the Earth and how fast plants can grow.
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