lokta volterra and atmospheric CO2

Our planet’s atmospheric carbon dioxide levels have varied substantially in the last 500 million years, and we are currently living in an era (The Quarternary Era[1]) of extremely low atmospheric CO2 levels (Figure 1).[2]  The highest atmospheric CO2 levels existed during the Cambrian Era (see Figure 1), and were about 16 times higher than the present and the flourishing of plants during the next era (the Ordovician) elicited a sharp drop in CO2 levels (but nevertheless 13 times higher than presently) which may have caused an ice age.  This fact suggests that earth’s temperatures are not dictated by the absolute concentration of atmospheric CO2 levels, but by the rate of change of those CO2 levels.

[1] The Quarternary Era denotes the most recent period in the Cenozoic era, following the Tertiary period and comprising the Pleistocene and Holocene epochs (and thus including the present).

[2] Diagram also represented in the text Gant C (2021) An Earthly Chance, which involves more background support.

In Figure 2, over the last million years or so, a vastly shorter time period compared to the Graph in Figure 1 (1,000,000 years relative to 600 million years), temperature and CO2 levels are shown to be related, and this serves as the theoretical basis for the “greenhouse gas” model of Climate Change (see Figure 2).[1]  Besides the fact that these time periods are extremely truncated so that extensive time periods in earth’s history are not represented, the temperature variations were estimated based on the Antarctic’s warmer coastline data, while inland the Antarctic temperatures which are perpetually freezing and never come close to rising above zero degrees Fahrenheit, are not represented.  This deceitful bit of data ensures NASA of funding as it substantiates absurd Climate Change propaganda that suggests that the earth’s temperatures are rising so rapidly, that very soon the Antarctic ice will melt and swamp the coastlines of the world.

Figure 2 – Carbon dioxide levels match Antarctic temperature variations closely over the last 800,000 years, which is historically an extremely small time period.  https://earthobservatory.nasa.gov/features/CarbonCycle/page4.php.  However, these temperatures were taken on the coastal areas of Antarctica, which is far warmer than the interior of Antarctica, where 99+% of Antarctic ice exists and where yearly temperatures are always far below freezing.  The ice in Antarctica is accumulating all the time, not melting.  The NASA attempt to misrepresent this fact, by presenting the data on coastal regions only, is used as a political manipulation to suggest that rising CO2 may warm Antarctica soon and cause the miles thick ice sheets to melt, which could raise ocean levels by 200 to 300 feet and swamp coastal cities.  This is completely false and is merely NASA’s attempt to bolster Climate Change fake propaganda and get political support for NASA funding.

The question that almost never gets asked is; When atmospheric carbon dioxide levels fall, where does the carbon go?  The answer is alluded to when the IPCC (the Intergovernmental Panel on Climate Change) studied this issue and discovered that approximately a third of the excess atmospheric carbon currently measured does not come from the burning of fossil fuels at all, but instead is derived from the ground through modern agricultural practices such as tilling of the earth’s agricultural soils.  The historical declines of atmospheric CO2 (Figure 2), a factoid which undermines much of the Climate Change panic-propaganda, occurs via sequestration of carbon into plants, the soils of the earth and the oceans (causing increases in carbonic acid).  As atmospheric CO2 falls, the earth cools, ice ages may occur, organic plant material decays, and gradually much later, CO2 re-enters the atmosphere to support plant growth and begin a new cycle of global warming. In other words, this NASA graph above represents only a half of the true cycle, and the complete representation is properly graphed (Figure 3 below)[1] as a classical predator prey relationship and mathematically represented below as the Lokta-Voltera differential equations.[2]

As you can see in Figure 3, the graphing of a classical predator/prey relationship, as the rabbit population increases, it causes a corresponding increase in the population of the predators (lynx), which then decreases the population of the rabbits, and which then decreases the population of the predators, and the cycle begins all over again. 

The same graph can be used for any two variables in such a relationship, such as atmospheric CO2 levels (the prey) versus concentrations of CO2 in the soil (the predator).  In other words, atmospheric CO2 increases and warms the atmosphere which “feeds” plant growth, plants grow in abundance, which drives more and more carbon into the soils, which uses up atmospheric CO2, and which then drives atmospheric CO2 down, which then causes a “die off” of plants, so that the temperature cools as there is less of an insulating effect of atmospheric CO2, and soil organic material decays enough to release CO2 back into the atmosphere and the cycle begins anew.

This cycling process can be represented by Lotka–Volterra equations[1], which are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of such biological systems. The variables change through time according to the pair of differential equations:

x represents the numerical representation of the prey (for example, rabbits, or the concentration of atmospheric CO2);  y represents the numerical representation of some predator (for example, foxes, or the concentration of sequestered soil CO2);                   t represents time; α, β, γ, δ are positive real parameters describing the interaction of the two variables that can modeled over time to accurately describe such systems (see Figure 4 below). Phase I (see Figure 4 below) describes the release of carbon into the atmosphere as would occur from the tilling of soils (source of approximately 33% of atmospheric carbon) or from combustion of wood, coal, natural gas and oil.  As atmospheric CO2 escalates, temperature increases[1] and these conditions stimulate plants to accelerate photosynthesis and sequester carbon into the ground, plant material (including wood), soil supportive microbes, earthworms, etc. (Phase II).  In Phase III, atmospheric CO2 lowers as the carbon becomes increasingly locked up into plant material (e.g., trees and agricultural products) and the soils, micro-organisms and lifeforms that support their growth.  Some carbon is sequestered into coal, oil, shale and natural gas underground, as well as the oceans.  The lowering of CO2 inhibits plant growth and temperatures drop significantly which has often initiated an ice age in Earth’s past.  In Phase IV, the die-off of plant material and decaying organic matter in the soils proceeds to release CO2 and methane into the atmosphere, the earth heats up, and the cycle begins anew (Phase I).

Many factors can affect this cyclic variation of carbon during earth’s history, including the availability of water, solar cycles, volcanic activity, temperature variations and other factors, but this cycling of carbon and temperature variations appear to be a factor in earth’s history to affect climate.  Currently, Phase II has been interrupted and the concern is that Phase I is continuing without interruption (see Figure 5).

The Lokta-Volterra equations have been applied to climate modeling.[1]  The assumptions at the time of that and other publications did not account for the marked thinning of topsoils around the world, and thus Phase II (Figure V) was considered to be endlessly viable, e.g., that the agricultural topsoils were not being destroyed on planet earth and were able to sequester CO2 in large quantities.  

An article by Arsenault in Scientific American[2] suggests that within 30 to 60 years, the agricultural topsoils on planet earth will be destroyed completely and there will not be anywhere left to sequester CO2.  In 30 to 60 years, the cyclicity of carbon movement between the ground and the atmosphere may be completely interrupted and Phase II will no longer exist (Figure 5).  Consider quotes from this Scientific American article:

“ROME (Thomson Reuters Foundation) – Generating three centimeters of topsoil takes 1,000 years, and if current rates of degradation continue all of the world’s top soil could be gone within 60 years, a senior UN official said on Friday.”

“About a third of the world’s soil has already been degraded,[1] Maria-Helena Semedo of the Food and Agriculture Organization (FAO) told a forum marking World Soil Day” (this quote in 2014, about 8 years ago).

“The causes of soil destruction include chemical-heavy farming techniques, deforestation which increases erosion, and global warming. The earth under our feet is too often ignored by policymakers, experts said.”

“Soils are the basis of life,” said Semedo, FAO’s deputy director general of natural resources. “Ninety five percent of our food comes from the soil.”

“Unless new approaches are adopted, the global amount of arable and productive land per person in 2050 will be only a quarter of the level in 1960, the FAO reported, due to growing populations and soil degradation.”

“Soils play a key role in absorbing carbon (emphasis mine) and filtering water, the FAO reported. Soil destruction creates a vicious cycle, in which less carbon is stored, the world gets hotter, and the land is further degraded.”

“We are losing 30 soccer fields of soil every minute, mostly due to intensive farming,” Volkert Engelsman, an activist with the International Federation of Organic Agriculture Movements told the forum at the FAO’s headquarters in Rome.”

“Organic (farming) may not be the only solution but it’s the single best (option) I can think of.”

Of course, organic farming is but the first step towards regenerative agriculture, which in terms of humanity’s survival on planet earth, now has two important outcomes.

  1. Excess atmospheric carbon (CO2) can be sequestered into soils, plants and trees thus mitigating global warming and Climate Change.[2] 
  2. Organic farming attempts to eliminate pesticides, herbicides, fungicides, artificial fertilizers, Glyphosate™, etc. to make food less toxic.  Regenerative Agriculture avoids these artificial products since they are simply no longer required at all.  Food becomes more abundant and less toxic, thus improving human longevity and mitigating chronic degenerative disease.[3]

Phase I is Accelerating As Phase II disappears (see Figure 5) and topsoils are no longer capable of sequestering atmospheric carbon at all, the problem of accelerating atmospheric CO2 levels, or Phase I, is complicating matters dramatically, as has been discussed in previous publications by Gant[4] (see Figure 6).  Although the US and Europe have made cosmetic but bold improvements in CO2 emissions, the entire world is utterly blind to such efforts and is accelerating the burning of fossil fuels dramatically (Figure 6), so that the total planetary increases in atmospheric CO2 emissions are in fact accelerating and showing no signs of decreasing.  The largest industry in the world, agriculture, which consumes about 20% of the world’s fossil fuels in order to power up the world’s 40 million tractors and their associated agricultural machinery, is required to feed the world’s 8+ billion inhabitants.  That number is expected to surpass 11 billion by the end of this century, a very optimistic assessment by the United Nations, so the consumption of the world’s only cheap, plentiful, reliable, scalable, portable and thus indispensable fuel[5] will not be expected to diminish anytime soon.  Also, fossil fuels power up the militaries of the world, and what country would be willing to jeopardize their national security by switching to fuels which are more expensive, less available, unreliable, unscalable, non-portable and relatively dispensable?  Answer:  None.  Fossil fuels are indispensable and are thus here to stay for a century or so until they run out.

Thus, Phase I in Figure 5, will accelerate dramatically in the next century or so, even as Phase II is disappearing and is expected to be completely gone in the next several decades.  Atmospheric CO2 will accelerate rapidly in the next century and sequestration into the topsoils of the planet, AKA regenerative agriculture, will potentially cease, which is a lethal outcome for all human and animal life.  Of course, the regenerative agricultural movement and a flourishing lumber industry, despite being ignored or stymied, must be allowed to thrive, if we are to have any hope of avoiding catastrophic murder of all life on planet earth.  Caring for all life and our ecosystems is the full

blossoming of caring for one another,[1] and we are now facing the 11th hour of collectively making that choice which is promoted by all of the world’s major religions and ethics-based philosophies (see quote and diagram – Margaret Meade)[2].  Sequestration of atmospheric carbon into our planetary agricultural soils via regenerative agriculture and into lumber products (Phase II in Figures 4 and 5) is now mandatory as an expression of caring and love.

[1] https://www.artrainer.com/post/12-bible-verses-about-caring-for-one-another


[1] article published in 2014

[2] Gant C (2021) An Earthly Chance.

[3] Ibid.

[4] Ibid.

[5] Epstein A (2014)  The Moral Case for Fossil Fuels, Penguin.

[1] FABIANO MEIRA DE MOURA LUZ (2014) PREY-PREDATOR MODELING OF CO2 ATMOSPHERIC CONCENTRATION LUIS AUGUSTO TREVISAN, Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, Avenida Carlos Cavalcante 4748 Ponta Grossa, Paraná, ZIP 84030-000, Brazil.- Correspondin Author: luisaugustotrevisan@yahoo.com.br Departamento de Física, Universidade Estadual de Ponta Grossa, Avenida Carlos Cavalcante 4748 Ponta Grossa, Paraná, ZIP 84030-000, Brazil

[2] Arsenault, Chris (2014) Only 60 Years of Farming Left If Soil Degradation Continues.  Scientific American.

[1] Due to the natural insulating effect of atmospheric CO2 in the atmosphere.

[1] https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations

[1] From By &lt;a href=&quot;//commons.wikimedia.org/wiki/User:Lamiot&quot; title=&quot;User:Lamiot&quot;&gt;Lamiot&lt;/a&gt; – &lt;span class=&quot;int-own-work&quot; lang=&quot;en&quot;&gt;Own work&lt;/span&gt; based on &lt;a rel=&quot;nofollow&quot; class=&quot;external text&quot; href=&quot;https://books.google.co.in/books?id=FuIv845q3QUC&amp;amp;pg=PA16#v=onepage&amp;amp;q&amp;amp;f=false&quot;&gt;Pilovsky et al.&lt;/a&gt; 2001 (p. 16, figure 1.13), <a href=”https://creativecommons.org/licenses/by-sa/4.0″ title=”Creative Commons Attribution-Share Alike 4.0″>CC BY-SA 4.0</a>, <a href=”https://commons.wikimedia.org/w/index.php?curid=45036611″>Link</a

[2] https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations

[1] Diagram also represented in the text Gant C (2021) An Earthly Chance, which involves more background support.