The CO2 level is controlled by the combined activity of all organisms and so we would expect the same to be true of oxygen. The role of enzymes would be to ensure that oxygen is maintained at the equilibrium level. When organisms sequester carbon or modify the sequestered carbon they also affect the oxygen level. If carbon is stored as carbohydrate the ratio of carbon to oxygen (C/O) is 1/1. When stored as bicarbonate or carbonate the ratio is 1/3. As coal is almost all carbon the ratio is over 1/ million. If this does not give nature enough degrees of freedom to juggle optimum levels of CO2, oxygen, and ocean pH then she has more degrees of freedom via the decomposition of water and storing the hydrogen in the bicarbonate ion or hydrocarbons or even allowing the hydrogen to escape into outer space. To determine the number of degrees of freedom actually needed is not easy because all the mineral cycles are linked together and there are about forty elements used to build most organisms. However it would not be that difficult to model the movement of the major eight elements to infer how oxygen is maintained at a constant level. If one enzyme can successfully maintain CO2 then perhaps only one is needed for oxygen. Is this enzyme(s) in denitrifying bacteria, nitrogen fixing bacteria, bacteria that convert cellulose to peat or is it somewhere else. To my way of thinking six or less enzymes would give ample control. While it is possible to paint a picture using three primary colours what is to stop nature using a broader palette if one is available?
It has been thought that ocean pH can drop quickly because volcanoes or fossil fuel combustion can rapidly release enormous quantities of CO2 into the atmosphere, but the raising of ocean pH is slow because the weathering of minerals is a slow process. In other words the ocean becomes acidified by CO2 moving from the atmosphere into the ocean but the ocean becomes alkaline by the movement of bicarbonate ions from land into the sea. This logic ignores the action of algae which have the potential to rapidly elevate ocean pH. When algae die and sink, or is it sink and die, they take carbohydrates and hydrocarbons to the bottom, they have extracted CO2 from the upper layer of the ocean raising the pH. If ocean photosynthesis is around 90 Gt (carbon) and if 15% to 20% of this, sinks to the deep ocean, then around 16 Gt of carbon can sink annually. Now, depending on how much of this carbon is being respired, there is the possibility for a very rapid rise in pH. Nature therefore has a fairly powerful weapon in manipulating ocean pH. Unfortunately we know very little about what factors affect the ecosystems responsible for the respiration of ooze on the seabed. The history of the last 50 years has seen ocean pH fall. It would seem that nature has not dramatically reduced ooze respiration at this stage.
Ocean pH is mostly affected by seven general classes of reaction. ONE
Solution of CO2 into ocean water
CO2 + OH- ----> HCO3- pH moves down
Formation of carbonate skeletons
2HCO3- + Ca++ ----> CO2 + CaCO3 + H2O pH moves down
HCO3- ----> OH- + CO2 The gas is used in photosynthesis and ends up as ooze on the sea floor. pH moves up.
Of the seven reaction styles controlling ocean pH only reaction ONE is not under the control of the DNA in living systems. The rate of reaction TWO is at the mercy of the DNA of reef communities. Reaction THREE is under the supervision of the many ocean algal communities.
CaO + CO2 ----> CaCO3 pH moves up
FeO + CO2 ----> FeCO3
MgO + CO2 ----> CaCO3
Here micro-organisms in rocks, using CO2 oxidise minerals such as feldspar. Traditionally this reaction has been considered as chemical weathering but now we know better. It was not connected with ocean pH. However any reduction in atmospheric CO2 will ultimately affect the balance of CO2 in the ocean. In addition reaction FOUR is followed by reaction FIVE. FIVE
CaCO3 + CO2 ----> Ca++ + 2HCO3- pH moves up
Similarly for the other carbonates. Here micro-organisms attack carbonate and send the calcium and bicarbonate ions into the ground water and off to the ocean. Reactions FOUR and FIVE are not the result of any civic duty that micro-organisms have toward balancing ocean pH, these reactions constitute their energy supply. However, if the reactions are catalysed by enzymes that are rate sensitive to CO2 then we have more evidence in the vindication of GAIA theory. So we need to set up an experiment to see if reactions FOUR, FIVE and similar reactions accelerate with higher CO2 levels.SIX
CO2 + CaSiO3 ----> CaCO3 + SiO2 pH moves up
Similarly for other silicates. Micro-organisms attack silicates.
2KAlSi3O8 + 3H2O ----> Al2Si2O5(OH)4 + 2K+ + 2OH- + 4SiO2 pH moves up
This and similar reactions probably involve micro-organisms, the ions flowing in ground water to the sea.
Obviously, if Gaia is any sort of reasonable theory, these reactions will be under enzymatic control and like rubisco they will be rate-sensitive to CO2. However do not necessarily expect all of them to be ramped up by CO2, some may be negatively geared. I personally would anticipate a positive gearing but who knows?
WATER VAPOR AND CLOUDS
The greatest unknown factor in any climate model has to be cloud cover. Clouds have enormous control of our weather. The problem is that we are quite ignorant about cloud formation. To what extent is cloud formation biologically controlled? What are bacteria doing in clouds? What is their energy supply? Do they consume dimethyl sulphide or is it just a site for condensation of ice or water?
It has been suggested from time to time that mankind could terraform Mars, so that humanity could slip across to the red planet when the Earth became too hot. The idea is to genetically engineer a few bugs; zip them over to Mars; spread them around; wait a few thousand years and presto: one planet ready for habitation. Contrast this with our Earth, terraformed for the perfect climate, over a period of 4.5 billion years using around 50 million species. Perhaps the complexity of terraforming a planet has been underestimated. Perhaps also, it has been forgotten that Mars does not have a large magnetic field and is not able to retain much of an atmosphere.
REPRODUCTION AND THE BEGINNING OF LIFE
A possible stumbling block to our understanding of the origin of life arises from the imprecise definition of the word reproduction. Most of us would think of reproduction as a discrete process that either occurs or does not. However this concept robs us of the chance to think laterally. Growth is more or less the same concept as reproduction. When a yeast cell buds it appears to be just extra growth. We announce that reproduction has occurred when the bud separates from its parent and becomes autonomous. So a nanometre of space is the only difference between growth and reproduction.
The first 'organisms' did not need to reproduce they only needed to be able to grow. They did not even need to be complete organisms. This is how I see the beginning of life. Chemical compound A is able to grow by combining with source compounds R, S and T from the environment. In the process it releases compounds U and V. Chemical B is able to grow by absorbing U,V and X from the environment and releasing R, S and T. So we can see that growth of species A helps species B and vice versa. This logic overcomes two mental hurdles: How did such complicated things as cells arise and how did early life solve all of its own problems by itself. Obviously cells did not need to develop until after most cellular processes had already developed and early life did not have to solve its own problems but just contribute to the environment in some small way. This is the same way that human society works. Each of us makes a small contribution and in return we enjoy the effort of other peoples' labour.
Question to see if you are awake. In the above scenario, when does growth stop?
Sexual recombination of genes is the source of most diversity but mutation is also a source of new variations upon which natural selection directs evolutionary change. Plant biologists use x-rays and teratogenic chemicals to deliberately increase the rate of mutation. The process is very hit and miss. A much more efficient process involves the splicing in of desirable genes. If man can do it, then nature probably discovered it first. The idea that point mutation is the chief source of new genes might not be correct. While point mutation is a source of new variants, jumping genes offer a much faster method of producing functional new genes. Junk DNA offers a storehouse of ready-made prototypes for jumping genes to use.
THE UNSEEN THEORY
Why was Gaia not embraced for so long? Lovelock saw Gaia on cue. The question is why was he alone and more obviously why was mainstream science so slow to catch on? Personally, I think the problem lies within our language. In my mind I had the idea that competition and cooperation were two equally valid processes that were mutually exclusive. I no longer think this way. In a system, all the parts must cooperate together, that is, each part must do its job. It is not possible to have a system where the parts do not cooperate. So cooperation is the very heart of systems.
Competition by contrast, can be part of a functioning system, but it is not essential. Competition helps systems to evolve and become better at what they do, but all competition occurs within the context of cooperation. In sport the players obey the rules, or the game makes no sense. In business, firms and individuals obey the laws, or chaos and anarchy soon result. There is no such thing as competition without the framework of cooperation. Competition is like curry in curried chicken it is not a meal in itself.
The differential equations I and II constitute a model. The main purpose of this model is pedagogical. We can use a basketball as a model of the Earth. With such a crude model and a lamp, we can explain the concepts of night and day but not much else. These equations are the simplest model that can be devised to explain the real function of the rubisco enzyme.
Life has a vice-like grip on this planet. It achieved a foothold in what we would consider searing conditions. It has over the last four billion years evolved an unknown number of strategies to improve the conditions for its own benefit. Life is not set to relinquish this planet no matter what our self-serving technology throws at it. We live on a terraformed satellite of the Sun, an engineered system with multiple redundancies built in. We humans, however, fail to appreciate this engineering marvel or the probable consequences of our actions.
Most of the engineering is the handiwork of the microbes. Multicellular organisms are the new arrivals. Animals and plants are, as Lovelock describes, "the icing on the cake". If our disturbance to the atmosphere and climate is to have dire consequences then it will be the icing that slides off the cake. The microbes are resilient. The multicellular flora and fauna will bear the brunt of the changes. The Gaia of the Earth will fall. This fall will gain momentum. Higher atmospheric temperatures will subject temperate and rainforests to so much fire that they deteriorate extensively. The exposed soil will be subject to erosion slowing the re-growth of the forest. The oceans are just as vulnerable and most of the coral is doomed. Warming oceans will dump more CO2 into the atmosphere making the greenhouse effect more pronounced. Most coral will die. The ice sheets will melt reducing the Earth’s albedo and flooding coastal regions. All tropical and temperate forests will burn. The Gulf Stream, Kuroshio and Humboldt currents may shut down. Methane hydrates will release methane into the atmosphere.
Gaia checkmates Technology: end of contest.
Of immediate concern is the bleaching and death of the coral reefs due to the warming of the oceans. We face the possibility that 400 million years of evolution can be set back for thousands of years by a century of fossil fuel combustion. The damage may last millions of years if the ocean pH falls too far. Realistically, how are we going to remove 200 Gt of carbon from the atmosphere? It is most likely that we will not be able to stop the western Antarctic ice sheet from melting. We may possibly be able to save the eastern sheet but that depends on the oceans continuing to sink CO2, and on our reducing CO2 emissions from 8 Gt down to 0.4 Gt.
If we fail to limit CO2 emissions to 0.4 Gt within twenty years then cascading collapses of ecosystems will accelerate. Food production will fall, law and order will evaporate. The gossamer blanket of security that we know as civilisation will become but a distant memory.
77 Pine Avenue
REARRANGING THE EQUATION
ln R - ln (D- A*P*R) = D*t + K3
R/(D-A*P*R) = exp(D*t + K3)
R = D(exp(D*t + K3) –A*P*R*exp(D*t + K3)
R(1 + A*P* exp(D*t + K3))= D exp(D*t + K3)
R = D exp(D*t + K3)/(1+A*P* exp(D*t + K3))
R = D/[ exp(-D*t + K4) + A*P]
ADAPTING THE MODEL TO THE EARTH AND THE DERIVAION OF EQUATION dR/dt= R*A*δC
In the mathematical model there is no sequestration and there are no emissions from volcanoes. Not withstanding these limitations it is possible to derive this important equation.
At target level dR/dt= 0
0 = R(AC-AoO-Resp)
If C increases by δC then
dR/dt= R(A(C+δC) - AoO - Resp)
Subtracting the first equation from the second gives
So the power of plant mass to increase is dependent on the product of three quantities: the amount of plant mass; the fertility of the Earth and the imbalance of CO2 in the atmosphere. The equation is only true for small changes in C. How small is small? The deviation must be small enough so as not to upset the climate as this would affect species distribution and change the value of A. The deviation in C is currently around 0.01 kPa (100 ppm). This is a giant deviation, which will cause all ice to melt and utterly decimate a large number of habitats. I would estimate that in order to maintain the established species, we should not have allowed C to deviate more than 0.003 kPa. We are now in uncharted waters and this equation does not help us a great deal, because the magnitude of A is falling daily, as species disappear or become limited in their range.
Having shown that rubisco is a feedback control mechanism it is time to extend the model beyond its original purpose and apply it to the real world. According to the mathematical model, R increases so that CO2 levels fall to the target level. The model is not constructed to deal with continuous emissions of CO2 from volcanoes or the constraint that the Earth has a finite size. But we can easily fix this.
To adapt the model to the real world we can make the following considerations:
- The Earth is almost full of plant matter and any increase in CO2 will result in more carbon being sequestered and very little change in the amount of living plant protoplasm. It is not necessary to have the plants do all the sequestration themselves, the animals can help out.
- Sequestered carbon is any carbon not held in living cells and therefore has no energy overhead in its maintenance. So the respiration of termites does not constitute respiration in this model when it is applied to the real world. The release of CO2 by termites is classified as de-sequestration and grouped with emissions from volcanoes.
- There are many modes of sequestration and each has a different half-life. Animal evolution can change the half-life of a particular mode. For example, the evolution of a new species of termite can change the time that a particular species of xylem remains intact. The growth of grass (the formation of non living xylem in the grass) is sequestration with a half-life of a few weeks because herbivores will soon arrive to consume it. The growth of coral is sequestration with a half-life of several thousand years. These half-lives depend on the species that are present and while it is easy to envision these half-lives changing permanently with the evolution of new species, it is also possible to conceive that these half-lives can vary in a cyclical fashion depending on the climate. When the Earth is cold, animal respiration is much reduced and the half-life of many forms of sequestration is increased.
- The emission of CO2 from volcanoes is de-sequestration because the carbon in the crust was the result of living processes storing carbon.
We can derive the equivalent equation to dR/dt= R*A*δC using the mathematical model adapted to reality.
Assume the earth was in equilibrium before the industrial revolution. The level of sequestration was equal to the release of carbon by de-sequestering processes.
Seq(per year) = R(AC- AoO - Resp)
If man releases some extra CO2 then sequestration is increased
Seq +delta Seq = R(A(C+ δC - AoO - Resp)
Subtract the first equation from the second
delta Seq = R*A*δC
And with a touch more panache!
delta Seq = R*A*dC
ESTIMATING A FOR THE EARTH.
When the Earth is in equilibrium (a difficult concept to define for a system that is continuously evolving and is also programmed to go through cyclical changes) the amount of sequestration is equal to the release of carbon from volcanoes and carbon from de-sequestering activities such as methane released from swamps. If volcanic activity increases and upsets the equilibrium, plant growth will increase. If the Earth is fertile, the extra carbon will quickly be sequestered out of harms way. The Earth is out of equilibrium because of the combustion of fossil fuels since 1830 and forest clearing over the last two thousand years. Measuring the current sequestration rate allows us to measure the value of A.
To measure A we have to measure how much carbon is sequestered each year and substitute this value into delta Seq = R * A(C- .028) where delta Seq is the amount of sequestration that is over and above the amount occurring before the industrial revolution. Currently C is .038 kPa.
From the curve, terrestrial sequestration (in this context sequestration equates to wood and leaf formation) in the northern summer has risen by 0.5ppm i.e. around 1 Gt of carbon when CO2 has risen from .0320kPa to .0380kPa. Most of this extra 1 Gt will be respired and not sequestered. If we guess that 10% is sequestered, then 0 .1 Gt of extra carbon is being removed by the northern forests. If the plankton can match this then the oceans are sequestering an extra 0 .5Gt. Ignore the contribution of the southern terrestrial hemisphere.
delta Seq = 2 * A * (.004) from 1960 ; In 1960 the CO2 level was .004 above equilibrium
delta Seq + .6 = 2 * A *(.01) For 2005 where delta Seq is the rate of sequestration in 1960.
.008 A = .02 A - 0.6 by substituting the first equation into the second
8 A = 20 A - 600
12 A = 600
A = 50 /kPa yr
If we substitute this value back into to 1960 equation then delta Seq = 0.4 Gt. So a reasonable estimate is that delta Seq in 1960 was about 0.4 Gt and today it is around 1.0 Gt. Obviously these guesstimates could be in error by 100%: the Earth may only be sequestering half the amount that I have estimated.
THE PROSERPINA PRINCIPLE
Greg Retallack has proposed The Proserpina Principle which as far as I understand says that plants cool the Earth and animals raise the temperature. From my perspective we do not need a new theory that is less powerful and less encompassing than Gaia. But the Proserpina Principle does highlight the fact that animals can raise the temperature of the Earth.
One of the problems that hinders our understanding is the absence of any distinct classes, in any area of knowledge except mathematics. In mathematics within the set of integers there are even numbers, odd numbers and zero. There is no overlap between these three subsets. In science and other studies there are no distinct sets. So while we talk as if there is the set of plants and the set of animals and nothing in between, we are ignoring the fact that the distinction between these two groups is somewhat arbitrary. There is a host of micro-organisms that we cannot decide if they are plant or animal. It would not matter if we became infinitely more fastidious with our definitions there are always organisms that are difficult to classify. So the Proserpina Principle creates problems for itself right from the beginning because at its heart is a murky distinction between two groups.
Retallacks's idea that animals raise the temperature of the Earth posed a problem for me. Is it possible, and if it is true, how does it fit in with the mathematical equations? Firstly, Retallack just mentions animals while the mathematics requires two classes of animal. According to the mathematics which is all done as computer representations of differential equations, there are animals that eat protoplasm and there are animals that bring sequestered carbon out of storage. Of this latter type, should we distinguish between termites that consume carbon that was stored fifty years ago, and bacteria that eat plagioclase, a mineral made from carbon that was stored four hundred million years ago? Then there is the problem that most herbivores actually consume both protoplasm and cellulose – the carbon in protoplasm is part of the variable “R” and the carbon in the cellulose is part of sequestered carbon.
In a stable planet, protoplasm consuming organisms are always at their maximum numbers either limited by food supply or predators. We could be talking about elephants or aphids. Let us consider elephants. The only way we can have greater CO2 output is to have more elephants but the elephant population if it was limited by food supply can not increase without some major shift in the ecosystem. If the elephants changed in some way by doing something new they could change the landscape. If they push over a forest so that the forest is replaced with grassland then the temperature of the atmosphere would rise for a short time. As a general rule the forest had a lot more carbon in storage than the new grassland has, so the CO2 level would rise. Assuming that the nitrogen cycle and other mineral cycles are in good shape, all plants will start growing faster as rubisco is now more efficient and more sequestration will take place. Depending on where the CO2 is sequestered the Earth could end up being hotter or colder.
Now we can consider a mutant variety of termite. If the new termite can decompose wood at double the rate of the old termite, more CO2 is released but the termite quickly runs out of a food supply and no permanent change results. But one possibility remains and this is how the Earth actually improves – this is how the value of A changes from 50.00 to 50.01 making the Earth a more fertile place and more capable of adjusting the atmosphere. It requires the termite to do two things. In addition to bringing carbon out of storage it must also help with one of the other mineral cycles or help with some other aspect of the Earth's fertility. Suppose the termite also assists in improving the habitat of a nitrogen fixing bacteria. If the termite and the bacteria allow larger trees to move into new habitat, habitat that was previously occupied by slower growing species then the value of A will have been increased but the Earth will not necessarily be hotter. If the forest stores more carbon than the scrub did, the Earth should be colder. I say should, because every organism interacts with many others and the cumulative effects of all these changes are too difficult to predict.
Let us imagine that man evolved and progressed up to about 1700 AD and then became steady in population and technology. He should have made the Earth hotter as a result of forest clearing and the combustion of small amounts of coal. As long as the large forests of the world had not run into a shortage of nitrogen we can envision a warmer balanced Earth that could continue indefinitely. The unseen difference being that the Earth is revving closer to the red line. That is, the Earth would have less spare capacity to deal with a large volcanic eruption.
However it is possible that man could have lowered the temperature of the Earth. If early agriculture had involved the growing of nut trees or any large food-bearing tree as opposed to the production of cereal crops, then we can imagine the Earth becoming slightly colder.
So I would have to disagree with the Proserpina Principle. In my view any organism has the power to heat or cool the Earth. If carbon moves into long-term storage the Earth cools. If carbon moves into short-term storage the Earth warms.
MOVING FROM 'A' AS A MICROSCOPIC VARIABLE TO 'A' AS A MACROSCOPIC VARIABLE.
The equation dR/dt = R(A*C-Ao*O-Resp) originally did not contain the term for respiration. In the computer model the respiration term appeared in the second differential equation. This term was moved into the first equation when solving the equations mathematically as a means to see if a solution was correct. Both arrangements gave the same result, so Resp was left to remain in the first equation. This does not mean that I knew exactly what I was doing. I first considered the respiration term, as animal respiration and I thought of it as a certain fraction of total respiration. This interpretation is wrong. The respiration term returns all CO2 to the atmosphere (when equilibrium is reached) that is not accounted for by photo-respiration So of all the CO2 returning to the atmosphere, about 1/4 is produced by photo-respiration and 3/4 is produced by the respiration term.
While A and Ao have microscopic interpretations, Resp does not.
On a macroscopic scale, A is a family of three numbers. If the Earth is fertile all three are big numbers, the curves are steep and equilibrium is achieved quickly. Conversely, if the Earth is compromised because many species have become extinct, then all three numbers are smaller and the Earth will take longer to adjust CO2.
On a microscopic scale we are interested in the relative size of A*C and Ao*O, because it is this relativity, which sets the efficiency of photosynthesis and thereby directs the atmosphere towards the equilibrium value of CO2. So if we look at A by itself, in a laboratory we are working on a microscopic scale, we are determining the ratio A*C to Ao*O for a particular species of rubisco molecule. When we calculate A for the Earth (we have also calculated the value of Ao as a by-product), we are looking at the macroscopic scale. The value of Resp has a little independence from A and Ao. It can change by itself to some extent because the CO2 level can change.
Imagine a stable fertile planet. All three numbers are large. If a new herbivore evolves, say a beetle that begins to munch on a prolific water weed, then respiration increases (Resp increases to a new bigger value) and CO2 levels will rise. As long as the environment is not harmed then the Value of A remains as it was. The value of Ao has to remain linked to A. The concentration of CO2 will increase so that at the new equilibrium
AC - AoO - Resp = 0
So the new beetle has increased CO2. Photosynthesis has increased by making rubisco work more efficiently. You might think that the animals have control of photosynthesis and you would be correct to some degree. As animals increase, CO2 levels increase, and plants grow faster because they waste less energy in photo-respiration If the animals somehow improve the nitrogen cycle and perhaps some other cycles as well then a positive feedback loop develops. This means that the value of A and Ao will begin to enlarge and the plants can grow faster still. Of course things will soon settle down as there is a limit to how much the animals can increase the mineral cycles. If the animals decrease the fertility (A) or if they reduce the plant mass (R) then photosynthesis decreases and the food supply dwindles. Respiration levels fall because the beetles begin to starve.
The world grain harvest has increased dramatically in the last few decades as a result of high yielding varieties, nitrogenous fertiliser, warmer weather and higher levels of CO2. This trend will soon reverse, as soil erodes, the weather becomes too hot and storms increase in severity and frequency.
You might think that man has increased the Gaia of the planet by making some crops grow faster. This is not necessarily the case because the Gaia of the Earth depends on which crops are growing and what happens to the carbon in these crops. The Gaia measures how fast the CO2 level can be adjusted so if we use our fertiliser to grow faster growing forests, then we have indeed increased the Gaia of the Earth. However if we replace forest with cereal crops with the nett result that there is less opportunity for sequestration then we have reduced the Gaia.
Example of a planet correcting its atmosphere
Supposing a living planet has stable CO2 at 0.00002 kPa and volcanic eruptions raise this level to .00003 kPa. Faster plant growth reduces the level to .000025 kPa in 1000 years. Given enough time the levels would eventually get back 0.00002 kPa. Can we calculate A, Ao and Resp?
In order to calculate this group of numbers we would need to know the pressure of oxygen in kPa, the total carbon mass in living protoplasm and the ratio of time that the rubisco molecule spends reacting with carbon dioxide and oxygen. However without these three measurements we can still satisfy our mathematical curiosity.
Let us assume that this imaginary planet like our Earth, is quite full of plants and there is no room left for any more and that the increased growth will become sequestered carbon in the form of xylem, organic material in soil or ooze on the bottom of the ocean. This means that R will not actually change in size.
So we can't write dR/dt= RAδC because we are not letting R increase in size. But the plants are growing faster and removing carbon from the atmosphere so we can write -dC/dt= PRAδC
Where P is the constant of proportionality, which converts gigatonnes of carbon to partial pressure. i.e. C = P*Carbon content of the atmosphere: having units of kilopascal per gigatonne (kPa/Gt)
C is the partial pressure of carbon dioxide
R is the mass of carbon in living cells
δC is the imbalance in the level of C, (in this example the initial imbalance is .00003 -.00002 = .00001 kPa)
dC/dt=.00002 PRA - PRAC
The solution is given by
C=(1/PRA) *[.00002 PRA - K (exp -PRAt)] and K is a constant of integration that can be determined by the initial conditions
When t=0 C=.00003
C=(1/PRA)(.00002 PRA - K)
.00003 =(1/PRA)(.00002 PRA - K)
K=- .00001 PRA
When t = 1000 years C=.000025
PRA(.000025) = .00002 PRA + .00001 PRA (exp - PRA* 1000)
25= 20 +10 (exp -PRA*1000)
5= 10 (exp -pra*1000)
PRA= .69/1000 = .00069
If we could measure P and R then we would know the value of A. For the Earth R is approx 2 Gt and P is around 0.00005 kPa/ Gt
Using R= 2 and P = 0.00005
A= 6.9 inverse kilopascal years
These calculations assume that during this one thousand years the species distribution did not change.
ONE PROBLEM AFTER ANOTHER
Most people appear to be aware of the threat of climate change. However they have not made the paradigm shift to viewing nature as the supreme technology. The old mentality still exists. They see CO2 as the problem and the obvious solution is to bury it. They do not perceive that CO2 is just the first of a whole armada of problems about to beset us. When the oceans are empty and the soil is gone, feeding the human population is going to be difficult. The animal and other kingdoms run the mineral cycles. Without these organisms the mineral cycles stop. Without the minerals the plants do not grow. Each, can not return because the other is missing. A global catch 22 situation develops. Reducing the diversity puts evolution into reverse. The Earth will become less fertile and less robust.
Biodiversity is not going to be replaced by gene technology. The Earth is a massively parallel evolving computer. Every cell of every individual has the complexity of a supercomputer. The program of this computer has been running and evolving for 4.5 billion years and while it does not have the conscious thought and planning of the human mind it has produced a genome that controls the planet within the laws of physics and chemistry. As a complex system the Earth is subject to chaotic behaviour, a few flaps of a butterfly's wings can totally change the future of the system.
Eventually the Sun will swallow the Earth. For the remaining time that we have, it would be disappointing for the human race to degrade the genome and commit future generations to existence on an impoverished planet, when the alternative has much more to offer: retain the enormous infrastructure of genetic diversity and allow all species to play their part.
KEEPING R CONSTANT
To keep R constant it is possible only four (perhaps less) conditions are necessary
- high rates of reproduction - lots of seed or spores
- reduced access to sunlight from shading by other plants
These conditions should ensure that plants rapidly cover the available habitats and keep younger plants stalled for lack of sunlight.