The main difficulty with the interaction of Western civilization and nature is with our inability to accurately characterize and value ecosystems. Without properly evaluating the functions of an ecosystem and our interrelations with our immediate surroundings we remain ignorant of the integral importance our biosphere is to our real existence. What is needed today more than ever is a cogent means for showing how and why an ecosystem exists as a means to establish a value for natural areas and biodiversity.

The characterization presented here, though supported with associative observations, has not been specifically tested. This essay is the product of a manual search that included all of the chemical literature, most of the biological literature and much itinerant study. Most of the principals, such as mass balance, are grounded in irrefutable science, and require little investigation to prove, but require much more investigation in the specifics of ecosystems. Though agricultural research provided the majority of factual data, this hypothesis is extended into ecosystems based upon observations such as companion plant relationships and extant phytochemical studies. Mathematics supplied the multidimensional regression used to correlate the mass balance data that alludes to an integrated interrelationship between the species of an ecosystem.

Although an ecosystem is in essence a cooperative interrelation, the characterization presented here is essentially hierarchical. It is presented as such to express the variety of layers that have emanated as a consequence of the necessity for life to persevere in a turbulent environment.. In order, the layers of cooperation within a system that will be used here are; 1). Mineral composition of the substrate. 2). Phytochemical cooperation. 3). Physical adaptation. 4). Chemically communicative animals. 5). Non-chemically communicative animals.

Perpendicular to this hierarchy there is a second hierarchy of magnitude. From the molecular level to the ecosystem itself, each order of magnitude addressing the consequences of its scale of habitat. The difference between these two categories is that one is subjective, the other objective.

Climate is not considered dominant in this characterization, as ecosystems of some variety have colonized every environment on the planet. The ecosystem itself, then, must have universal principals that exist in all environments. This is not to say that the environment does not have a profound effect on the physical manifestation of an ecotype, it does. Climate must be ignored as a property in a characterization of an ecosystem audaciously purported to be universal.

The positive points of this particular model are 1). It remains consistent with the observation that nutrient increases are often accompanied by a reduction in diversity. 2). It preserves the principal of conservation of mass. 3). It is consistent with the evolution of species-species interrelationships. 4). It is independent of environmental conditions. 5). Though this model retains a chemical grounding, it does not preclude the "functionality" claim of current ecosystem science. The strong correlation between the two is a potential source of academic intrigue. Though the focus of this particular model of an ecosystem is upon the terrestrial environment, it can be extended to incorporate marine systems. In marine systems, the limiting factor is light or energy and nutrients are abundant. In the terrestrial system, the opposite is true.

The ecosystem itself is a self-organizing entity that creates its specific form to adapt precisely to the static environmental conditions it resides in. The requirement to adapt at all is a consequence of the necessity of living entities to retain relatively specific complements of nutrients in order to persist. In fact, the mineral substrate is an environmental characteristic and function and should be characterized as such. In the final analysis, however, mineralogical diversity is the most important and most neglected factor in the selection of species that inhabit a microhabitat.

Though moisture, light and temperature are highly influential forces in the final expression of an ecosystem, they are, to some extent ubiquitous. Certainly the quantities of each of these that is available governs the vitality of the ecosystem, yet there is no requirement for a specified quantity of energy, moisture, or atmospheric gasses to the extent that they dominate the interrelationships within an ecosystem. What is absolutely essential for the manifestation and perpetuation of the species that compose an ecosystem are the chemical elements that characterize life.

The first layer of cooperation of an ecosystem is at the mineralogical level. The minerals available to the ecosystem are typically those originally present in the substrate. These minerals are those comprising the bedrock upon which the alluvium that becomes soil, is based. Although this is an environmental condition, minerals are finite and do not cycle back into the system automatically as do air and water. Energy in the form of sunlight is perpetually renewable and is essentially the same as a cyclic resource also. Based upon these conditions the minerals of the earth are unique in their finitude and great extraction difficulty, becoming a governing feature of ecosystem interactions.

The minerals comprising a habitat occur in finite quantities that are rarely, if ever, well proportioned to support life without some modification. Modification, however, requires an investment in energy and specialized information amongst the gene pool. In addition, the mineral composition immediately available from the soil in any given spot is not a uniform constant. Life mitigates the vicissitudes of the earth by accumulating what is optimally essential and allowing unusable or superfluous elements to erode away.

In the mitigation of mineralogy, life employs species diversity such that a combination of species occurs that can match the average composition of a given substrate. No single species must carry the burden of assimilating the full wild compliment of minerals emanating from the substrate. Instead, there is a wide array of nutrient specialists and a communicative arrangement that assists in the coordination of individual species creating life from rock.

The hypothesis that a mass balance is established between the soil and life through the use of biological diversity was tested utilizing a computer programmed with a multidimensional regression technique. A series of tree species with the typical mineral composition published¹ was used as one database. A published series of marshland and aquatic species mineral compositions was used for another database², and values for food stuffs yielded the mineral compositions of a third set of data³. I am currently collecting local "wild" plant and insect species and obtaining mineral analysis of these from a local University Extension service. Several tests were run on this mineral data.1). A test for how the number of species affects the precision of the fit. The remainder in such a limited system would be lost to erosion as those minerals could not be "fixed" by any combination of extant species. Among trees for instance, a local minimum was obtained for systems consisting of four species, but erosion was still fairly high, 40%. With 20 species in the same test, erosion was reduced to 1%, a factor of 40. 2). A test for the number of different three to five member combinations of plant species that can match the substrate mineralogy. In any system, the variation of the mineralogy of microhabitats, the impact of environment and the presence of competition all combine to require a multiplicity of systems that can readily recombine in different linear combinations to satisfy substrate variations in order to maintain the potential of the biomass. 3). A test for how a given set of species' would vary in population if the substrate or soil were drastically altered, though using actual substrate parameters⁴. This test yielded the expected result that Oaks, among others, are keystone species, possessing a very average mineral composition. Their population changes the least from one substrate to another amongst a given array of other tree species. 4). Analysis for how the addition of various decomposition products such as composts of various types, could be matched with agricultural species in order for erosion to be minimized. This test's results showed strong agreement with empirically observed companion plant combinations. It also shed some light on the roll of insects in the management of the mineral mass balance of an ecosystem. Broccoli and raspberries on deciduous leaf compost were the offending combination. However, the habitat of choice of parasitic wasps is brambles, such as raspberries. The main insect pests of members of the Brassica family are caterpillars, which are the host of choice for these parasitic wasps. The mineral exchange may be occurring not through the soil, but through the air here. Many human cultures have grasses as a primary staple in our diets, indicating the potential for a boron deficiency. Strangely, of the 50 species I've had tested to date, the species Echinacea Purpuria, a close relative, medicinally comparable to the popular Echinacea Angustifolia, has the highest Boron content. Does this have anything to do with its medicinal potency? Does boron play a role in the production of sesquiterpenes or echinacin?

The conclusion drawn from this form of mathematical modeling is that species diversity, in addition to allowing for adaptation to environmental conditions, is necessary for cooperation between the species of an ecosystem to minimize the Gibbs energy potentials that arise due to the consequence of the disparity between substrate mineral composition and individual species' optimal requirements. The number of species in an ecosystem is a reflection of the level of precision that system must maintain, through the use of micro-ecosystems that approximate the substrate, in order to out pace the rate of erosion, yet without over-accumulating nutrients. Finally, this level of complexity suggests that phytochemical production may function in the communication of mineral information between species, such that coordination is optimized.

Beyond the realm of plants there exists the world of animals, the preponderance of which are arthropods. Preliminary mineral analyses of insects are revealing more clearly that the role insects play in the ecosystemic management of minerals. Higher concentrations of phosphorus, sulfur, zinc and sodium with lower concentrations of boron, iron and aluminum.

The low boron concentration of the American Bird Grasshopper suggests that this species thrives in early succession habitats, or grasslands⁵, where the important mineral boron is not as bioaccumulated as in a forest⁶ for example. This insect appears in summer when there is plenty of sunlight and the root activity of plants is high. As the insect assimilates plant matter, many nutrients of use to plants are eliminated through the grasshopper, allowing for reassimilation by remaining species, possibly feeding a large complement of microorganisms. If the grasshopper is keying in on chemical stress signals by its food, it is strengthening those plants and myofauna in direct proximity that are less stressed. The better-adapted species can then advance and become established.

In animals, boron occurs in high levels in things like teeth and bone, which insects do not have. The legitimacy of higher animals thus lies in our superior mineral storage capacity. Insects, serve in an ecosystem as fine tuning mechanisms specifically moving mineral nutrients from spot to spot, guided, hypothetically, by chemical signals which they receive via their antennae⁶.

Phytochemicals are produced in nature predominantly by enzymes, which typically require metal cofactors for optimum activity. This automatically implicates metals, or minerals in the production of phytochemicals. If a substrate is low in a particular mineral nutrient and required by a given species, it will produce phytochemicals in aberrant concentrations, signaling to other species that evolved in the same demesne that this species is stressed and vulnerable to displacement.

This chemical organization is one possible reason that foreign species introduced to an ecosystem will not be as susceptible to predation, disease, or competition. Without chemical clues to the inadequacy of a species in the adaptation to a substrate, there is little activity stimulated for their removal. In past natural history, the introduction of a new species was beneficial, since in the long run the increase in diversity led to an increase in the viability of the common habitat.

Diversity on the other hand does regulate itself. Too much diversity can result in the excessive retention of nutrients, which either causes a lot of shade or fuel for periodic fires and eventual species loss and transformation, or else, there is a microbial increase that can produce conditions necessary for disease. Too little diversity results in larger numbers of nutrient loss related catastrophes and a finite potential for colonization by visitors, which then become members of the balanced set.

Over great lengths of time, and many environmental disturbances, a set of species will occupy a substrate, or habitat, that maximizes the biotic potential to survive catastrophe. This is a balance of species diversity, total phytomass, genetic potential (succession) and strategy. These species may be unique to the habitat, members of a wide array of ecosystems, or visitors that just happen to satisfy an unused section of the mineralogical spectrum (opportunists).

Humans, birds, and a few other species are long distance travelers, which are not necessarily territorial. In those cases where species interact with a large number of ecosystems, it becomes more efficient to forego learning or adapting to the chemical signals of ecosystemic stability. Instead, we form more generalized associations between observed phenomenon and the effect of our participation. The species in this category have highly developed cerebral cortexes suited to making these extra-ecosystemic, non-olfactory associations. The benefit of species such as us is that we serve to introduce inappropriate species into extant ecosystems, insuring that diversity, especially with regards to succession, is maintained. Obviously, we have carried this role a bit too far, proving that, ecologically nature is (or was) still evolving the long-term survival strategy. At this point, there seems to be a limitation strategy required to moderate the role of humanity which does not appear to exist, excepting our own intelligence. In our inattentive exaggeration of the diversification process, we have reduced the ecological importance of species such as birds, which has resulted in a drastic reduction of avian populations, furthering global ecosystem instability.

In addition, the interactive compliment must also adapt to environmental forces on the physical scale of wind, rain, and desiccation, while simultaneously engaging the mineralogy at the molecular level. To accomplish this, diversity of scale is also employed. The high precision of specialization that occurs at the microbial level is justified at the animal level with an active capacity for preservation of these hard won minerals allowing them to be made available after reductive events. In addition to this is soil itself that serves as microbial habitat and a second storage mechanism for nutrients, complexed with the humates and fulvates released by the action of microorganisms on plant and animal matter. The depth of the soil in an ecosystem is an indication of the level of storage biologically required to mitigate long range environmental forces.

In the Amazonian rainforest region, the Hylaea of Alexander Von Humboldt⁷, for example, there is so little nutrient influx from the silica-based substrate that there is no soil layer. As a soil component the nutrient base would be rapidly mineralized by microbial action in the hot, humid conditions and washed away. Instead the nutrients are bound up within the immense diversity of living species that comprise this type of rainforest, with a highly active fungal component at the litter layer assimilating all nutrients and conducting them directly to the tree roots to be transported to the canopy. In this system the physical structure of the forest mitigates all environmental forces. The Hylea has the advantage of a regular large quantity of energy to employ in the coordination of the large diversity of participating species. This implies a large capacity for the production of unique chemicals none of which we understand, but which are obviously communicative and organizational in nature.

The Hylaea is not the typical example, as fertile soil does occur in many ecosystems, which, then, do not require this level of integrity. For the most part the nutrients bound up in the soil layer represent excesses, either temporary or long term. These can be essential minerals, but other than seasonal storage, are plausibly the superfluous minerals that exceed the tolerance or stress levels of the current ecotype. Humate complexes of the soil minerals will persist for many years, remaining available as mineral sources for those species that may require them, as succession or evolution warrants. After a time, though, minerals that go unassimilated will erode or leach away as the humate molecules are metabolized by soil microorganisms. In this respect, the soil acts as a temporal buffer between the evolving ecosystem and the mineral substrate upon which it stands.

Soil then, is a temporary appendage of an ecosystem. If left barren, or without substantial regular additions of biomass, or extractions of complexed minerals by biological entities, the nutrients retained by a soil will erode away and the resident microbiota will be predominantly extirpated. Soil is a manufactured habitat of mineral particulates and cellular microorganisms comprised of diverse communities of cells all functioning to accumulate and retain nutrients. The chemical modifications such as the humates are produced by certain species, while others may utilize highly specific minerals, only to become converted into humates themselves. Even others such as the nitrogen-fixing bacteria assimilate gasses and convert them into forms useable to plants.

Macroscopic life forms are in actuality a more organized form of soil without the physical presence of soil particles. Instead, we utilize a diverse array of cell types in a coordinated fashion to sustain the entire package with what we can glean from soil based ecosystems. Truthfully there are no macroscopic life forms, only microscopic life forms acting in coordinated fashion to present a macroscopic form to the environmental forces.

It can easily be stated that the minerals that make up any substrate other than Hylea are sufficient to reproduce the biota of a particular environment, and have little to say with regard to the purpose of species diversity, i.e. that species diversity is random. This of course is what we assume when we fail to consider the essence of an ecosystem. What certifies that an ecosystem is comprised of a wide range of species functioning to retain an optimized mineral composition is the composition itself.

In most any ecosystem there will be at least three minerals concentrated well above background levels, boron, sulfur and phosphorus. The importance of these minerals is the fact that they are rare in the soil and must be bioaccumulated. Bioaccumulation accounts for the fact of succession, where two varieties of succession must occur, original and crisis. Original succession can take thousands of years as the minerals boron, sulfur and phosphorus are gleaned from the substrate in limited quantities from natural processes, retained biologically and gradually accumulated by a succession of species adapted to perpetuate this process. Members of the animal kingdom such as birds and humans, which typically travel long distances, bring in many of these succession species.

Crisis succession occurs after a physical force, such as a fire, obliterates the biota of an ecosystem. In this situation, species highly adapted for rapid growth, especially of roots and reproductive features, predominate. Their purpose is to recover the minerals stored up within the humates and interstices of the soil before they can be eroded away. As humates do decompose as a function of time, early crisis succession must be rapid, and usually is accomplished well within the time frame of humate decomposition.

The fact that both of these systems are found to exist is a clue that minerals are important to the survival of life. Herbicides such as Glyphosate, which murder all the herbaceous species of an ecosystem are attractive to ecological managers since growth following such an application is usually rapid and vigorous. This vigor is a characteristic of crisis succession and much of the mineral potential is lost anyway. Unless the habitat is left to achieve a late succession stage, subsequent Glyphosate applications may contribute to the eventual erosion of all biotic potential in the soil.

A more responsible ecological management tool would be to displace unwanted species by initial removal and displacement by more suitably adapted systems. These systems can be engineered based upon the minerals available in the substrate, and the empirical compositions of the favored species. It must be remembered that a species must be communicatively adapted to the ecosystem as well. The realm of phytochemical knowledge is at present non-existent outside of agricultural pests, which is why it is best to use locally adapted species in "engineered" systems for now.

The minerals boron, sulfur and phosphorus are accumulated by living things above background levels, as a consequence of their physiological roles. Boron is necessary for the reproduction of cells and also plays an important role in some forms of metabolic processes. Sulfur is essential to the manufacture of several essential amino acids and is extremely useful in many enzyme processes. Phosphorus is essential to genetics at the cellular level and to energy transport in higher life forms.

All three of these elements are very soluble and susceptible to erosion, and exist in the oceans at higher concentrations than exist in the earth's crust⁸. Over time, living things evolved to cooperate in the retention and accumulation of these elements, leading to the essence of what we intuitively perceive as an "ecosystem". Though we fail to recognize the chemistry of nature we still share strong instincts for accumulating and retaining the products of nature. This misplaced instinct would be more adaptive if we could consciously endeavor to insure that our accumulation processes correlated more closely with the function of species diversity.

The chemistry of mass balance revolves around minimizing the Gibbs energy differential between the elemental concentrations present in the substrate and the requirements of individual species attempting to persist upon the substrate. The goal of a climax ecosystem is the retention of all mineral elements essential to the perpetuation of the extant species. Superfluous elements are allowed to erode away, rare or limiting elements will have mechanisms present for their accumulation.

Minimizing the Gibbs energy differential between the substrate and the biota minimizes not only individual species' stress, but the energy required by the system for incorporating these elements across the differential. The incorporation of minerals invariably occurs across a membrane. The selectivity of a membrane is a function of a cell's energetics. When the differential concentrations of each of the various elements are minimized, the energy required by the organism will be minimized resulting in a more rapid accumulation rate. In most systems, environmental forces are unpredictable so the faster elements are assimilated the lower is their chance of being eroded away and the greater the potential of the ecosystem as a whole to remain intact.

The viability of the individual species' habitat is a function of the concerted accumulation of mineral nutrients. Where a group of species can cooperate to satisfy unique physical niches, yet minimize the chemical stress for their neighbors, relations can evolve. These relations serve the ecosystem as a whole over the long term, and would, by now, be a dominant theme.

The transfer of phytochemicals through the soil, air and moisture could readily serve to communicate mineral relations. In fact, influencing the sprouting of seeds, the attraction or repulsion of insects⁹, birds and animals, the dissolution of minerals from humate complexes¹⁰, and the nurturing, or discouraging of neighboring vegetation¹¹ is accomplished by phytochemical exudates. In some cases the specificity is broad, such as the dissolution of minerals from humates by fulvic acid root exudates. In other cases, the specificity is highly focused, such as in the attraction of insects by plants.

The retention of minerals in cyclic ecosystems is satisfied by three mechanisms. The first is animals and woody species, which store minerals in their physical structures. These are structures that have evolved to resist, in one way or another, environmental stresses. The second is soil, which, through the action of humates, retains minerals in extensive chemical complexes that are bound to soil particles. The third is through fungi and microorganisms, which can achieve rates of assimilation of minerals fast enough to completely eliminate erosion¹².

There are four components to an ecosystem, the soil system or microbial systems, macro-systems (flora and fauna), mass-balance strategy and multiplicity or redundancy. Each of these components serves in the perpetuation of the concerted species that comprise the ecosystem. The broader goal is the optimization of the process of life.

The soil microhabitat is sustained primarily by mortality, though symbiotic relations are important. Deciduous plants, annuals, perennial mortalities, insects and animal mortalities supply the predominant caloric foodstuff that support the microorganism population, which then manufactures humates or modifies the chemical environment in some other way. Chemical modification of the environment serves to provide a nutrient buffer zone. Nutrients will be stored in this zone for a given period of time and then become subject to erosion or leaching. All the while, new material will be added to the warehouse, eventually reaching a steady state equilibrium.

The inorganic soil particulates also contribute to this role, the variability of adsorption energetics varies from mineral to mineral, while humate adsorption energies remain relatively constant. Plant root exudates, primarily amino and fulvic acids can solubilize trace elements from humates with substantial specificity¹³. Interstitial sorption of nutrients in clay materials does serve as a significant source of minerals also, though, as humates are borne of microbial activity, they are enhanced in biologically significant minerals, while inorganic sinks have no specificity, and will assimilate heavy metals, toxic metals, and other xenobiotics. The lack of specificity in the inorganic retention mechanisms reduces their value to the long-term stability of a microhabitat.

The quantity of material stored in the organic component of the soil system is a function of the environmental conditions. Typically, a nutrient base enhanced in minerals of importance to life processes will be established by the soil. The rate of erosion, the rate of mineral cycling in the ecosystem and the rate of primary generation of the minerals from the substrate all combine to form the soil's mineral composition. The microorganism is usually very susceptible to environmental factors. The presence of a high level of species diversity is essential to insuring that beneficial microbial transformations occur at the soil level. Many of these transformations are possibly governed by chemical communication between the species comprising the ecosystem and the microorganisms themselves.

Macro-habitats are the perennials, populations of annuals, animals and insects that interact to minimize the Gibbs energy gradients between them and the substrate. This energy, or stress minimization is accomplished by forming (linear) combinations of species such that the combined mineral requirements approach the available mineral composition. The less dependence there is upon buffer systems, the less energy is spent on sustaining the populations of those systems. The turbulence of the environment necessitates the existence of either adequate physical or structural strength within an ecosystem, or a nutrient buffer capacity to re-grow. The potential diversity of the species themselves and the variety of environmental stresses evolve to determine the strategy the system uses.

In any ecosystem, there can be succession, as rare minerals are concentrated and biomass is accumulated over time, leading up to the appropriate conditions for the most environmentally integrated of species to dominate the ecosystem. The potential for unforeseen and abnormally destructive environmental forces exists as a constant variable. The adaptive ecosystem will maintain the genetic potential for succession to occur, simply to insure its own existence. Maintaining adaptive potential requires a mechanism for regularly destroying the climax system, such as a temporary human settlement, forest fire, or pathogen.

The drawback to these systems is that they can eliminate the genetic potential to recover the climax state if they grow out of proportion. Evolution solves this problem by allowing for the obliteration of these climax systems that eventually results in the termination of the maladaptive disruptive entity, or leads to a climax system more resistant to the disruptive force.

Multiplicity is essential to adapt to the wide variety of microenvironments found in an ecosystem. In addition to microenvironments, there is always the potential for environmental change, such as the construction of a beaver dam that diverts a watercourse, or a groundhog burrow that contributes fresh parent soil material. To adapt to the ever-changing environment, an ecosystem must have within its genetic diversity, the capacity to reconfigure the species combinations to "solve" for the new mineralogical fingerprint.

Along with this, there must be a diversity of species combinations solving for the same mineralogical substrate, as one alone will rarely match it exactly. With a number of these systems, a combination of them will extend the precision of the mineralogical fit and further throttle erosion. The number of mini-ecosystems that compose the stable ecosystem will be a reflection of the rate of nutrient influx. The more mini-systems there are the lower the influx rate, or the higher the potential erosion rate. A system high in nutrient influx will then have a low number of different species, unless it is a unique early succession system.

MULTIDIMENSIONAL MATHEMATICS MODELING

Extant models of ecosystems utilize species function as the critical nexus for evaluating the importance of biodiversity¹⁴. In this regard, aspects such as seed dispersal, biogeochemical cycles, pollination, physical environment modification and trophic interactions such as parasitism and predation are the focus. Though this view is not incorrect, it does not reach a universal basis set. It is postulated here, that when mathematics are rigorously applied to these same interactions, a correlation will become apparent that associates these same "functions" with mineralogical transfers.

The weakness of functional models is that they legitimize an ecosystem as a function of time, not of place. A model that elucidates the interconnectedness based strictly upon mineralogical phenomenon connects the ecosystem to the major geological components that formed it. The chemistry ties the ecosystem to a place in time, not just to historical events. The professional ecologists have a responsibility to the western ideologies of property, profit and progress. The independent investigator has no such restrictions. Within the framework of western idealism, it is socially forbidden to engage biotic sustainability at the soil level. If we can overcome this anachronistic taboo, the multiple results of a mineralogical species to substrate analysis can serve as the options from which to consider "functionality" aspects.

The interactions within an ecosystem are diverse and highly interrelated. This immediately suggests a multidimensional regression technique. The multidimensional linear regression (MDLR) solves for correlation with a particular observation from a wide range of data types, simultaneously, incorporating interactions within the data itself into the final result.

The concept is simple enough. The equation is a standard linear regression formula, translated into matrix algebra. The equation solves for a set of correlation coefficients, the Beta matrix, which, when multiplied times a particular set of data, yields a "best guess" result.

In a typical use of a multidimensional linear regression technique, for instance, managing a deer herd, a set of pertinent observations of functional variables are made, such as annual acorn drop, surface water or acreage of grassland, for a number of deer populations in various places. The data are set up in one matrix, with the actual deer population counts in the "Y" matrix. The equation is solved and the resulting correlation coefficients can be used to estimate or manage a deer population by observing, or manipulating the variables. Since there is typically an error or remainder when using this technique, the more variables that are accounted for, the better.

The method used for the mineral analysis is not the same as the above typical use. In the mineral analysis, the species become the same as the function variables, and the elements themselves are the same as the place variables. Instead of deer population counts, the Y matrix is comprised of the elemental fingerprint of the substrate (or perhaps the fingerprint of a foreign invasive species that needs a bit of engineered competition). The correlation coefficients produced by the mathematics are used on the species themselves and equal a best "fit" of species that would match the substrate and minimize the Gibbs energy potentials between the available mineral concentrations and that required by the species themselves.

The formula: Beta = (X^t* X)^-1 * (X^t*Y), where X^t is the transfer matrix. To check for accuracy or in the elemental usage, erosion, the equation: X*Beta = Y+erosion is instructive. Frederick Gauss invented this mathematical technique about 1800.

A comprehensive ecosystem characterization would require knowledge of the mineral requirements of all species present, and the substrate composition. A long-term study should actually consider the mineral requirements of the various species during different times and different stages of growth. The statistical likelihood of environmental perturbations and the effect they have on the system may help explain persistent negativity and other unusual phenomenon.

A climax system, unlike that predicted by a functional diversity theory, would tend to evolve toward greater substrate harmonization, and resultantly fewer interactions (assuming there are significant minerals present in the substrate), as fewer interactions are required to minimize Gibbs energy potentials. In a temperate climax forest, for instance, this indeed is what occurs¹⁵. The intrigue is in correlating functionality with mineralogical diversity. Even more interesting is elucidating the extent to which phytochemical production serves to coordinate the integrity of these species combinations.

Preliminary studies, such as companion planting relationships show a strong association between physical manifestation of a species and mineralogical roles. The traditional Native American combination of corn and squash, for instance, matches the mineral composition of red pine needles, a readily available soil amendment. Both the chemistry and the physics are related. Tying the characterization of an ecosystem down to the chemistry makes the connection with the geology. Since there is often a physical manifestation that correlates with the mineralogical relationships, it is not much of a stretch to place phytochemical production within this scenario as well. Humans and birds do not have well manifested senses of smell, but most other species do.

The competitor of the multidimensional regression, is the all too ubiquitous Linear Programming. The main difference between the two, is that the multidimensional regression offers the perspective of a remainder, and can produce negative as well as positive correlations. In any ecosystem, death and decomposition is in equilibrium with birth and life. Dead and decomposing organic matter contribute to the available nutrient base, via microbial degradation, to the living system. A linear programming technique can optimize the extraction rate, or the contribution rate, but cannot account for both simultaneously. The multidimensional linear regression can. In addition, the remainder is that component of the mineralogy that cannot be accounted for in any cyclic process (at least not linearly, though matter cannot be created nor destroyed so linearity is fairly significant here). The Linear Programming, if it has a remainder, does not correlate with anything but ethically unrealizable profits and other phantasmagoria.

In a system of multiple mini-ecosystems, when one species expires, its nutrient erosion is in equilibrium with assimilation but a wider area is affected. Negative entities yield a smaller erosion area or potential, positive entities have a greater assimilation potential. The negative entities account for soil maintenance, positive for macroscopic species maintenance. Positive entities should tend to have less competition, while negative entities will have a stressful existence. Linear programming does not offer this contrast.

If species diversity and the integrity of an ecosystem is so important to the management of erosion, how can we participate in a way that satisfies both our requirements and the necessity of maintaining the entire planet's ecology? This is the real question, how to adequately manage the planet's ecology in a way that enables the entirety to persist.

Ecosystems are evolved social vehicles optimizing the capacity for life to perpetuate itself. The rate of evolution of an ecosystem is a function of the level of sustainability life has gained over the past four billion years. The introduction of highly foreign species, or genetically engineered species cannot be accomplished in full awareness of their impact by any stretch of the imagination. In my searches of the literature I could not find sufficient quality information to characterize an ecosystem, let alone determine what perturbations would do to one. The information I have put together is far from comprehensive. It is doubtful that comprehensive data exists as plant analyses which include root systems are completely absent from the literature and insect analyses equals two.

The most likely species for introduction, at the least, would have a mineral composition that either has a composition that exactly matches the bedrock (which would constitute a dominant or keystone species) or a composition that fits successfully within a mineralogical niche. To fit a new species into a niche also requires that the species have communicative processes that allow for its ecological management. Monoculture fails on both of these counts.

A serious form of silviculture or agriculture would utilize regression analyses and a wide diversity of species to optimize both the production of biological resources and the retention of the "soil's" mineralogical potential to produce continuously. Forests should consist of a minimum of four intermixed species of trees, and a minimum of 16 species of ground cover in the temperate regions. Agriculture should focus more upon multi-cropping. Arrangements such as wheat, alfalfa and broccoli (just a guess, not a calculated system) for instance, or sunflowers and cantaloupe (a calculated system) could be engineered according to harvest times, specific species and methods. These are also multiple cropping arrangements that minimize risk of market fluctuations as well.

In any multi-cropping production system, the utility of native species (weeds) occurring in the mix is always a potential reality. The use of unobtrusive "weeds" to maintain long-term soil productivity is not an unconscionable thought¹⁸. This is one reason to value local species diversity. The retention or recovery capacity for nutrients in wetland species¹⁶ is a very good reason to get these ecosystems onto the valuable for their utility list. Obnoxious aquatic species such as Coontail (Ceratophyllum Demursum)¹⁷ are high in phosphate and potassium among other things, which would increase a crop's resistance, at least, to the American Bird Grasshopper. The discouraging of pests and the encouragement of useful species is a function of ecosystem stability. The more we learn about the stress factors in our local ecosystems, urban, rural and wilderness, the more we can obtain benefit from them in a sustainable fashion, with minimum input and optimum economy.

End Notes

James A. Erdman, Hansford T. Shacklette and John Keith, "Elemental Composition of Selected Plants and Soils from Major Vegetation-Type Areas in Missouri," U.S. Govt. Printing Office, 1976, V 87 pp. C28-C29.