Structure, Ecosystems and Stability

Lecture II:  Structure, Ecosystems and Stability

Review

1. Last lecture ended with a brief look at the First and Second Law of Thermodynamics.  The First Law states that energy in a closed system remains constant.  Since the universe is a closed system, this means that the total energy in the universe neither increases nor decreases. 
2. The Second Law states that entropy in a closed system increases with time.  One form of entropy is energy degraded by doing work.  The two laws together entail that degraded energy remains in existence after its work capacity is expended.  This consequence holds for open systems as well - i.e., for systems admitting energy inputs and outputs.
3. The earth's biosphere is an open system comprising all life on earth along with the natural resources that support it.  Energy expended in doing the work that supports life remains somewhere in existence.  Normally it is radiated out into space.  A continuing theme of the present course, however, is that the biosphere currently is unable to rid itself of all entropy it produces, and that this poses danger for many species within it - humanity included.
4. Life on earth also produces entropy in forms other than expended energy.  These also covered by the Second Law.  One alternative form of entropy is that of disorder.  Our discussion of Second Law continues with consideration of relevant kinds of disorder.

Disorder as a form of entropy

1. Thermodynamically speaking, the terms 'order' and 'disorder' apply to the way parts interact within a dynamic system (a system in which work is done).   A system is ordered to the extent that its parts are interdependent (mutually dependent) in their modes of operation.  Conversely, a system is disordered to the extent that its parts operate independently of each other.
2. A useful analogy is the arrangement of cards in a deck.  A deck is maximally ordered when all its cards are arranged sequentially by suit and number.  Cards dealt from such a deck will form a series in which the identity of a given card is maximally dependent on the identities of other cards in the series.  By contrast, the identities of cards dealt from a thoroughly shuffled deck are largely independent from each other in the order of dealing.  This is tantamount to the deck being largely disordered.
3. The same distinction can be made in terms of randomness.  With sufficient shuffling, cards in the deck will be arranged in random sequence.  When the deck is maximally ordered by suit and number, however, its order represents a maximal departure from a random state.
4. These distinctions among arrangements of cards in a deck are only illustrative, and by themselves have no thermodynamic significance.  A deck of cards sitting on a table is not a dynamic system.  An example taken directly from thermodynamics is the arrangement of molecules in a gas within a closed container.  The molecules will move at various velocities, but while the gas remains undisturbed these velocities will be distributed randomly throughout the container.  With respect to velocity, the molecules are in a state of disorderly motion.
5. Now suppose that the container is divided into two separate compartments.  By some means or another, the molecules have been redistributed so that the faster moving half are all in compartment A and the slower in compartment B.  This represents a departure from a purely random arrangement.  It also amounts to a departure from a state of disorder.  As long as this arrangement is maintained, the system is in a highly ordered state.
6. Because of the greater average molecular velocity within compartment A, moreover, it  contains more heat energy than compartment B.  If the heat differential is large enough, work could be accomplished by the flow of energy between the two compartments.  When this heat energy has been expended, of course, the gas in the overall container has returned to a state of general disorder.  This thought experiment illustrates the reciprocity between entropy as expended energy and entropy as disorder and randomness.
7. In general, order can provide energy capable of doing work, and vice versa.  A biological example of the former is the highly ordered structure of sun rays providing energy for photosynthesis.  An example of energy yielding order, on the other hand, is the solar energy that combines water with CO2 to form sugar molecules with highly ordered structures from which other organisms produce ATP (adenosine triphosphate).  ATP, of course, is a chemical many organisms rely on to fuel their metabolisms.  We return to such matters momentarily.
8. In the meanwhile, we should note that the foregoing considerations indicate yet other ways to formulate the Second Law of Thermodynamics.  From before, we have the formulation saying that energy capable of work decreases with time.  To this we may add a formulation saying that things tend to become more disorderly as time progresses.  An equivalent formulation is that things tend to fall apart with the passage of time, which is a colloquial way of saying that randomness increases.  The equivalence of these formulations follows from the fact that randomness, disorder, and degraded energy all constitute entropy in the operation of dynamic systems.  And needless to say, organisms endowed with life are dynamic systems.

Life and ecosystem

1. Life can be characterized in different ways for different purposes.  Our purpose calls for a characterization that illuminates the relation between organism and environment.  A useful characterization was put forward by physicist Erwin Schroedinger in his book What is Life?  To paraphrase, a living organism is a system that maintains itself in a continuing state of order by extracting negentropy from its environment and ridding itself of the resulting entropy.
2. Although any operating system consumes negentropy and discharges entropy, living systems are distinctive in maintaining themselves at higher levels of order than their sources of negentropy.  Consider a rabbit feeding on a carrot as an example.  In nonliving processes, energy flows from higher to lower levels, as when a piece of hot toast melts a dab of butter.  But the rabbit extracts energy from a source less highly structured than itself, which is analogous to the cold butter passing energy to the warm toast instead.
3. In the manner of a rabbit eating a carrot, life typically maintains itself at a high degree of order at the expense of its environment.  As a result of yielding negentropy to its resident organisms, the environment gains entropy more rapidly than it would otherwise.  Life is a catalyst, so to speak, by which the process of gaining entropy is accelerated.  A condition of life continuing is that its environment be able to get rid of the additional entropy that life brings with it.
4. Another distinctive feature of life, on this planet at least, is that it exists in the context of what ecologists call ecosystems.  All organisms are supported by other organisms, as carrots support rabbits and rabbits support eagles.  Organisms rely on inorganic sustenance as well, including water, oxygen, and various minerals.  Briefly defined, an ecosystem is a dynamic system comprised of organisms and their sustaining environment in which every organism either supports or is supported by other organisms in the system.
5. From an engineering perspective, ecosystems are held together by various feedback operations.  Examples can be found in the interactions between prey and predator typical of a stable ecosystem.  When prey is plentiful, predator populations tend to increase more rapidly with succeeding generations.  This is what engineers call positive feedback.  As prey populations decrease from over-predation, on the other hand, predator populations are reduced back to sustainable levels.  This compensating process is called negative feedback.  Positive feedback contributes expansion, while negative feedback brings control.
6. Negative feedback is essential for a stable ecosystem.  A stable ecosystem, broadly characterized, is one in which influences that otherwise would disrupt its structure are countered by feedback adjustments within the system.  When positive feedback goes unchecked by its negative counterpart, however, a system tends toward instability.  An example is the take-over of an ecosystem by invasive species.  Another is the process of global warming, to which we return in the following lecture.

Functional stability

1. No less important for a stable ecosystem is an orderly exchange of energy with its operating environment.  This is analogous to the energy interchange between environment and organism, save that now we are concerned with the systematic context in which interchanges of that individual sort take place.  (An ecosystem itself is not an organism, contrary to the Gaia hypothesis, but rather a systematic structure in which organisms interact with each other.)
2. Ecosystems are organized by trophic levels (from the Greek word trophe, meaning nourishment).  Figure 4.1 represents successive trophic levels of a typical ecosystem.

   

   Figure 4.1:  Trophic structure of an ecosystem. From Kenneth Sayre, Unearthed: The Economic Roots of our Environmental Crisis. Used with permission.

   Simple ecosystems contain producers, consumers, and decomposers as a bare minimum.  The figure here breaks consumers down into herbivores, carnivores, and omnivores.  (Examples given are for terrestrial ecosystems.  Others could be given for aquatic.)  Our present focus, however, is not on prey/predator relations but on energy flows within ecosystem.
3. 3 Apart from snakes baking in the sun and such like, solar energy enters an ecosystem at the producer level.  Solar energy is shown as a tightly undulating arrow in Figure 4.2. 
   

   Figure 4.2:  Energy flow in an ecosystem. From Kenneth Sayre, Unearthed: The Economic Roots of our Environmental Crisis. Used with permission.

   The solid arrow in the middle shows chemical energy from photosynthesis providing nutrition to higher levels.  Gently undulating arrows at right represent low-grade heat discharged from all trophic levels.  This heat eventually leaves the earth as black-body radiation.

4. Organisms are composed of material structure (formed from organic and inorganic molecules) made available within their containing ecosystems.  Lighter arrows in Figure 4.3 represent material structure moving from lower to upper levels. 

    

   

   Figure 4.3:  Structural transformations in an ecosystem. From Kenneth Sayre, Unearthed: The Economic Roots of our Environmental Crisis. Used with permission.

   Darker arrows represent matter degraded by metabolic activity that descends from upper trophic levels to decomposers.  Examples are dead leaves, rotting tissue, and various forms of excreta.

5. An organism's function in an ecosystem is keyed to its trophic level. Plants produce chemicals for use by higher level organisms, decomposers process minerals for use in photosynthesis, and so forth.  Interactions of this sort are functional relations.  Every organism in an ecosystem exists in functional relations with other organisms, whether on its own or on different trophic levels.
6. Especially critical for the stability of an ecosystem are the functional relations between its top consumers and its other constituents.  Top consumers occupy an ecosystem's uppermost level (Figure 4.1).  This position is due to their function of consuming organisms on lower levels but not being consumed by other organisms in the system.  Ecosystems can be identified by their populations of top consumers, under the convention that a single population plays that role in any given ecosystem.
7. Let us reconsider system stability from the vantage point of the top consumer.  As a rule (not universal), top consumers are functionally related to most other organisms within their respective ecosystems.  These others either serve in trophic pathways conveying nourishment to the top or help dispose of wastes discharged along those pathways.  An ecosystem remains stable as long as it has both pathways available to meet the needs of its top consumers and means to dispose of the resulting wastes.
8. Figure 4.4 provides a simple illustration.

    

   

   Figure 4.4:  Ecosystem stability as a function of alternative nutrient pathways; three cases. From Kenneth Sayre, Unearthed: The Economic Roots of our Environmental Crisis. Used with permission.

   Case (i) shows only a single trophic pathway.  If a single niche on a lower level becomes dysfunctional, the entire system will collapse carrying its top consumers with it.  Case (ii) represents a more complex ecosystem, with 8 pathways serving the top consumers.  If one or two ceased to function, remaining pathways might be adequate to keep the system in place.  Case (iii) is the most stable of all.  Functional support could be disrupted along several pathways without depriving top consumers of adequate support.

9. Figure 4.4 provides insight into the importance of species diversity.  Each node in these diagrams represents a niche occupied by organisms of a particular species.  There are 3 supporting nodes in (i), 14 in (ii), and 22 in (iii).  Given this organization by trophic pathways, an ecosystem generally will be more stable the more species participate in it.  This generalization carries over to the biosphere at large, in which humankind currently occupies the role of top consumer.
10. Although functional connections of this sort now serving the human population may number well into the millions, that number is diminished as additional species go out of existence.  As a matter of biological fact, a high level of diversity among other species was probably required before human beings could make an appearance on earth initially.  It stands to reason that there is some level at which humanity could no longer exist as other species continue to disappear.
11. Loss of species diversity is but one of several respects in which the biosphere is becoming inhospitable to human existence.  Among others are global warming and a pervasive depletion of ozone in the upper atmosphere.  Both of these are manifestations of a biosphere becoming increasingly disordered - a biosphere impacted with entropy it cannot get rid of.  We return to these topics in the following lecture.