Resource Load Carrying Capacity and Kphase Technology
by Peter Hartley (1993)
This is from FOCUS, Vol. 4, No. 2.
For copies contact: Carrying Capacity Network
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Society today must face the question of whether it can sustain opportunity and freedom and quality of life generally. Engineers, who design the means by which society provides for its needs, must have an especially clear grasp of the question, set forth if possible in terms readily assimilable to engineering considerations.
Many serious difficulties confront our world, and we hear predictions of disaster. But the future is not an inevitability; it is a choice. We do not face disaster unless we make disastrous choices. Engineers bear a special responsibility to inform society regarding the practical implications of its choices. Therefore, we who educate engineers bear a special responsibility to ensure that engineering students develop a meaningful basis for judging the practical implications of social tendencies and choices.
Society has valued industrial technology because society has perceived industry as offering choices. At the same time, industry has created problems we can no longer avoid. The list is familiar: acid rain, toxic waste, greenhouse effect, resource exhaustion, etc. Some people insist that to maintain the benefits of industry, we must continue designing and using technology in the same outmoded and increasingly dangerous way. Those who believe instead that the future is a choice know we can fully understand our alternatives only through more realistic engineering analysis creating the basis for a new engineering that offers genuine technical and social alternatives responsive to actual needs.
Resource issues have perhaps the broadest practical implications of any we face, as citizens or as engineers. Traditional industrial technology has always depended on sheer volume of resources to overwhelm problems, and engineers have always been trained to think along those lines. In the face of limits becoming obvious today, the old industrial paradigm of unlimited growth is unsustainable, since it requires unlimited drawdowns of limited planetary resource storages, and unlimited environmental capacity to absorb externalities. Engineering conceived in terms of that paradigm is likewise unsustainable. What we need is an entirely new paradigm for the way we design industrial technology, and that paradigm is sustainability. To achieve sustainability, we need sustainable engineering.
How should we conceive of sustainable engineering? What does it mean, and what kinds of technologies does it imply? To answer these questions, we need a resource oriented variation of a concept that ecologists refer to as "carrying capacity." When properly modified, the idea of carrying capacity enables us to formulate a very clear generalized definition of sustainability. 
The term "carrying capacity" originated in an entirely new population biology, and ordinarily it is defined in terms of the population being carried by the resources of an environment. We must instead conceive of it in terms of the resources that carry the population and the consumption of (impact on) those resources by the population. To understand resource use (resource load) carrying capacity, we have to keep in mind several terms:
R= Resource(s), or environment
N = Population (number of individuals) consuming R
C = Per capita rate of R consumption or use by individuals of population N; i.e., per capita rate of impact on R
L = C x N = Load on R = Resource Load or Ecological Load or Environmental Load
Using N for population comes from the word "Natality" as used in population biology. Using R for resources seems obvious, but note that we are using R both in limited and in very general senses. Depending on our focus, R can mean a particular substance, such as oil or coal, or a particular living species, such as codfish or deer or pine trees, or several resources considered together, such as all marine species. R can also refer to entire ecosystems or geographical areas, such as the Yellowstone ecosystem or the continent of Antarctica. More abstractly, R can refer to environmental processes and ecological interactions. R might refer to a desirable condition, such as the condition of having atmospheric CO2 concentration remain below a certain point, or the condition of having water in an aquifer at a certain purity. We can even have R refer to the environment—the ecosphere of earth—as a whole. Whatever the resource, we should keep in mind that to grasp the full significance of resource load carrying capacity, we must regard C not just as per capita rate of consumption by N, but ultimately as per capita rate of impact on R.
For example, the important resource issue when we eat grain is not the grain we consume, but the land we consume, both in terms of the natural habitat that farming takes from other creatures, and in terms of the enormous topsoil loss that our farming methods cause. With that in mind, we need one more term:
KL = The resource load carrying capacity (resource use carrying capacity or impact carrying capacity) for a given resource R. KL is the load L that represents the maximum consumption or use (impact) of a given kind that R can withstand without irreversibly declining or losing suitability for that use, and without such use causing the irreversible decline of any other R.
The supremely important feature of this concept, originated by William R. Catton, Jr., is its emphasis on the characteristics and requirements of R.  Emphasizing the well-being of R implies that engineering must regard the human relationship to nature as subject to usufructuary constraint. Usufruct is a legal term for the right of limited use and enjoyment of something without damaging that thing in anyway. An example is the old riparian principle of water rights, which gave dwellers along a river usufructuary access to its water—they could use the water in limited ways, as long as they did not diminish the river. 
Alternatively, it is possible to view KL as the maximum sustainable yield that R can provide indefinitely. However, the idea of yield places emphasis back on what we can take from R which is exactly the old-paradigm emphasis that created the environmental difficulties we face. The old-paradigm emphasis will not tend to promote ways of sustaining R, and if we are to achieve sustainability, engineering must emphasize finding ways to sustain R. The fundamental requirement of sustainability is sustaining R; viewing KL as first of all a load or burden on R rather than as a yield or benefit to humans will improve our chances of engineering ways to sustain both R and humans.
The idea of yield is in any case dangerously compatible with an exclusively instrumental view of natural resources, because it focuses too exclusively on a single resource or type of use. In Crossing the Next Meridian, Charles F. Wilkinson recounts an engineer's enthusiasm for transferring Montana water to San Diego by pipeline from the Yellowstone River, without building a dam. Since there would be no dam to silt up, yield could be sustained forever, as long as the river flows; yet diverting enough flow to make such use feasible would probably make it unsustainable in our sense. As Wilkinson says: "The Yellowstone River must sustain much more than just the extraction of water for commodity purposes. Fish and wildlife. The falls in the world's first national park. The magic of Paradise Valley,…The ranching, farming, mining, and recreation economy from Gardiner to Livingston and even farther …"  This is why my above definition of KL ends with a qualification involving all affected resources. Sustainability requires an ecologically conceived usufructuary view that focuses on maintaining undamaged resources in an undamaged environmental context.
With such qualifications in mind, we can now use a CN diagram to represent visually the meaning of KL in relation to L.  The CN diagram in Figure 1 shows KL represented by a circle of a given area, next to coordinates for C and N. Since it shows no values for C or N, Figure 1 indicates a condition of L = 0 and KL therefore unaffected by any L.
Figure 2 represents a situation with some load L, indicated by a rectangle with area equal to the product C x N. Here L < KL, so in this case the per capita rate of consumption or use (per capita rate of impact on R) represented by C can go on indefinitely as long as the population level represented by N does not increase. The small shaded L-circle has the same area as the L-rectangle; the unshaded blank portion of the large KL-circle represents the KL margin left for additional L before the onset of permanent damage to R and permanent KL reduction. The condition L < KL defines sustainability.
Figure 3 shows L = KL. Under that condition, there can be no additional L without permanent damage to R (I arbitrarily assume that "permanent damage" means any adverse effect from which R cannot recover in less than a human lifetime). As long as L never exceeds KL, we can assume that if L declines, the previously affected portion of KL will regenerate. That is, if , then KL – L -> KL as L -> 0. This makes the condition L = KL seem technically acceptable, although actually it is precarious. The idea of maximum sustainable yield is predicated on the acceptability of L = KL, which is exactly why maximum sustainable yield is a dangerous concept; it encourages seeing L = KL as an acceptable goal rather than as a prelude to the permanent decline of R.
Figure 4 shows L > KL. Note that the overload makes KL shrink; the blackened part of the circle represents permanently lost KL that cannot regenerate. To exceed KL is to reduce it. Here it is important to remember that KL does not represent the quantity or supply of the resource; KL is a quantity of load. KL is simply the load that represents the absolute maximum stress or impact that a resource R can withstand indefinitely, whether by direct use (cutting timber) or by pollution (chlorofluorocarbons in the ozone layer), or by other stress. KL may be diminishing even if for the moment we seem to have plenty of R as such left. For example, consumption of tree seedlings by cattle might seriously reduce the KL of a forest even if plenty of mature trees remain for the time being. It is obvious that in the long run, the forest R of mature trees must decline under such conditions, as KL for such trees declines. Evidently, certain kinds of analysis might require using the symbol R to mean some crucial parameter of resource viability rather than mere quantity of the resource as such.
Note that once we make L > KL, we cannot save the remaining KL just by removing the initial overload L KL, because that overload triggers a deviation-accelerating feedback process; what was before the precariously acceptable maximum L of Figure 3 now begins to overload the reduced fully loaded KL left by the initial overload shown in figure 4.
The only way to keep from entirely losing an overloaded KL to runaway overload acceleration is to stop overload feedback by making L permanently smaller than it had been in Figure 3 before the initial overload. Reduced KL indicates a condition of permanent resource shrinkage called range compression.  It means either that everyone using R will have to use less, or that some people will have to stop using R entirely, if we want to have any R left at all. Obviously, Figure 4 represents a condition of unsustainability in resource use.
The only remedy is prevention—sustainable engineering's first priority must be to maintain sustainability, and as stated above, Figure 2 in effect provides a definition of the term: sustainability is a condition such that L < KL. This is the new paradigm, and it gives us a simple, clear goal, easy to visualize. Of course, reality is never so conveniently simple. We have become so dependent on an inherently unsustainable old-paradigm technology that changing to new paradigm engineering will take considerable effort and ingenuity. The old paradigm has made us more and more dependent on nonrenewable resources, whereas sustainability requires renewable resources, since quite obviously KL for nonrenewable resources is zero. Any consumption of a nonrenewable resource causes an irreversible decline in the resource. This is why responsible engineers should urge that society ought to regard nonrenewable resources as only a temporary bridge to a future based entirely on sustainable technologies that use renewable resources exclusively. Further, engineers should be the first to point out that all along we have depended on renewables to an extent that the industrial system does not take into account. That is, we continue to depend on natural life-support systems that make life on earth possible for us as well as for other creatures, and those systems consist of interactions among renewable species. Yet technologies based on nonrenewables inevitably erode our natural support systems.
Sustainability requires limiting both C and N. Limiting human N is a very tough problem: world N of humans is over five billion now; six billion by the year 2000 seems inevitable, and eight billion by 2025 is projected. The present world human N is reducing KL nearly everywhere, and we can reasonably assume that even if we could reduce the average per capita impact C, world KL would continue to decline. Very likely, the earth already has more humans than the natural environment can withstand indefinitely. That is, humans have very likely begun to exceed the earth's carrying capacity at any level of C, which means that stopping N growth is not enough. We have got to reduce world N significantly.
Yet we cannot define the problem simply in terms of a numerical target; from both ethical and political standpoints, we must consider not only how many humans the earth can sustain, but how equitably the means for well-being are distributed among them. Defining a world N that would be sustainable in the aggregate is only half of the sustainable population issue; people do not live as a total world aggregate, but in specific places and conditions. A materially sustainable world population aggregate of which some were comfortable and some were barely surviving would be undesirable and probably unstable. Even if the poorest were reasonably comfortable, allowing a few rich to command lavish excess would foster chronic dissatisfactions unlikely to be politically sustainable in the long run.
Sustainability implies that no group should be allowed to maintain excessive R consumption—that seems clear. In contrast, the desirability of ensuring a reasonable level of C for everyone on earth also seems clear; yet achieving material security for everyone might well cause a disastrous acceleration of population growth, unless fundamental changes in cultural attitudes take place at the same time. The crucial question is: can we suppose that ensuring a reasonable level of C for everyone will in itself encourage reproductive discipline? Many people think so. The influential "demographic transition" theory assumes that impoverished populations exhibit high fertility due to ignorance and despair, whereas populations that have undergone a "demographic transition" enabling comfortable C inevitably reduce fertility in order to maintain prosperity. On that basis, subsidizing third-world national economies to promote gross economic growth for job creation seems advisable. Unfortunately, the "demographic transition" theory is simply false, as Virginia D. Abernethy has amply demonstrated.  Present cultural norms typically encourage people to have as many children as they can afford.
Instead of subsidies to national economies, Abernethy suggests small loans for locally conceived and controlled projects in third-world countries—especially projects that provide local economic opportunities for women. Ensuring that people everywhere can readily obtain family planning assistance is essential, of course. Yet it is ridiculous for the United States to suppose that it can rescue the world, because the United States has not been able to rescue itself. The most important contribution the United States can make is to transform itself into a sustainable society with a stable population that has achieved a reliable state of L < KL .
In any case, advanced industrial countries are not very well equipped to guide others toward sustainability, because advanced industrial countries all adhere to the old paradigm, basing their existence on the manifestly unsustainable goal of everincreasing consumption. Since we are proposing a goal of limited consumption, what level of C should we recommend as standard? To determine that, we need to have some idea of how large the world population N reasonably ought to be. At the 1993 Carrying Capacity Network conference, Dr. David Pimentel suggested that two billion would be an optimum human population for the planet. Sustainable engineering ought to develop some estimate of what worldwide level of C might be sustainable for that population. Then at least we could propose that as a first step toward sustainability, industrial countries ought to make sure they are within that per capita consumption limit.
One thing is certain: we have reached the point where the larger world N gets, the lower we have to set world C to avoid KL decline. But the old paradigm regards progress as increasing C without limit, because the old paradigm identifies progress with the growth imperative. The old paradigm is incapable of setting limits, because it aims at the exact opposite. The whole meaning of old-fashioned, old-paradigm progress is: ALL YOU CAN CONSUME.
To address this, we need a scheme for thinking clearly about variations of C. Accordingly, we will think of consumption in terms of three levels.  The lowest level is the Minimum Daily Requirement (MDR) or bare survival level of consumption, which we will refer to as CMDR. The next level is the Recommended Daily Allowance (RDA) or ample subsistence level of consumption, providing the means for robust good health and confidence about the future. We will refer to this as CRDA. The next level is not so much a level as a tendency or aim, the old paradigm aim already mentioned, which defines progress as All You Can Consume, without limit; we can call this unlimited consumption. Since it aims to exceed any level whatever, and since it already exceeds the reasonable level CRDA, we can also call it excessive consumption. However, at any given time it is at some definite level, which we will call CAYCC. The excess equals the difference CAYCC – CRDA. Understanding the sequence CMDR < CRDA < CAYCC is absolutely essential for understanding the present condition of the human species and the challenge now facing engineers who design technology.
Those who think that industrial countries should help the third world raise its C level ought to consider that the existing CAYCC – CRDA excess that members of industrialized populations enjoy consumes resources from the third world that would help the world's CMDR people attain CRDA. Yet the CAYCC system—which is simply our still dominant old-paradigm industrial system—operates to maximize the difference CAYCC – CRDA for people in that system, who strive to place themselves as far above CRDA as they can.
Ruled by our outmoded industrial paradigm, we continue to assume that the more rapidly we consume our resources, the more secure we will be. Everyone wants economic growth. Everyone wants economic output this year to exceed last year's by some percentage. Lately we have had about 3% economic growth in the United States, but most people would like to see that percentage increase. When anything grows with a percentage increase per unit time, we have a compound interest effect that results in exponential growth. Though there may be temporary exceptions due to efficiency improvements, in general we can assume that resource consumption increases directly with economic output. Figure 5 shows exponential growth in terms of resource load L as a function of time t, thus: L=L0ert, with L0 as the initial value of L, r as the specific growth rate, and e as the base of natural logarithms.  Fortunately, we can replace r with the percentage growth rate with which we ordinarily express economic growth: if a g% growth rate is such that g / 100 << 1, we can use g / 100 instead of r in the expression. This gives us the more readily useful L=L0e(g/100)t.
We can regard the exponential growth curve as a dynamic representation of the old industrial paradigm. The curve's full significance may not be immediately apparent; Albert A. Bartlett has shown that doubling time T2 provides the best way to appreciate the full devastating import of exponential growth.  Doubling time is the time required for an exponentially growing quantity to double. When dealing with growth rates typical of most public policy issues, we can apply the Rule of 70, T2 = 70/g, valid for g% growth rates when g/ 100 << 1.  Thus a growth rate of 3%/year implies T2 = 70/3, a doubling time of 23 years. Assuming that resource consumption and associated environmental impacts increase in step with economic output, 3% economic growth means that in 23 years we will be consuming resources (and polluting) twice as fast as we are now, and in 46 years we will use resources four times as fast. If oldparadigm efforts boost growth to 4%, T2 = 70/4 tells us we will consume resources at twice our present rate in only 17.5 years, and will quadruple our rate of resource destruction in only 35 years. Figure 6 illustrates exponential doubling times for L.
Bartlett also provides a way to get an ultimate mathematical perspective on the old industrial paradigm. He shows that we can use L = L0ert to obtain an expression for Exponential Exhaustion Time TEE that enables us to calculate the lifetime (exhaustion time) of a nonrenewable resource R under conditions of exponential growth in the load L on that resource, with R0 being the quantity of resource R existing at t = 0. Again, if g/100 << 1, we can use g/100—that is, g%—instead of the specific growth rate r.
For a dramatic example of the perspective on growth that TEE enables, we can suppose that R0 is an impossibly large reserve of any given nonrenewable resource, and see how fast R0 would be exhausted if we increased load L at some definite growth rate. Assume that we have an initial petroleum resource R0 = 6.81 x 1021 barrels, the volume of the entire earth. Set L0 = 3.29 x 109 barrels, which was the United States crude oil production for 1970 in the lower 48 states. In 1970, world oil production was still growing at the historic rate of 7%/ year, so we'll arbitrarily choose g/100 = .07 = r, which gives us a resource life span TEE of only 367 years for a resource initially equal to the volume of the earth! Further, since in this case T2 = 70/7 = 10 years, and since the amount produced in the last doubling time always exceeds the total of the amounts produced in all previous doubling times together, more than half the resource—that is, more than 3.4 x 1021 barrels—would be produced in the last ten years of the 367-year TEE span! This means that suddenly discovering two more earth-volumes of oil at that point would allow less than ten additional years of oil production.
Human resource consumption worldwide is now on an exponential growth curve, and we have got to make it level off before we overload the earth's overall KL. To understand the nature of this problem more clearly, we need to understand the relationship between L and KL dynamically, just as we understand exponential growth dynamically. Because population biology is the ultimate source from which our KL idea derives, we need to examine briefly the population biologist's definition of carrying capacity. Biologists use K to designate that original idea of carrying capacity, so we will use KN specifically to designate that same idea, which is population carrying capacity.
Population carrying capacity KN is the maximum observed population being carried indefinitely in a given environment (habitat) R. KN is therefore the population carrying capacity of that habitat for the species under consideration. In other words, KN is the maximum population that we will find existing indefinitely in the conditions provided by the given environment R. We can picture it as the limit KN that a logistic curve (Verhulst model) approaches asymptotically as population N increases over time under the influence of some density-conditioned limiting factors. Figure 7 shows us the graph.
The logistic curve in Figure 7 is a simplified model of what happens when a species enters a new environment where resources are abundant enough to support N growth without any initial constraint on reproduction.  With no constraint, initial population growth is of course positively exponential, represented in Figure 7 by the curve's r phase, also called an irruption phase. As density-conditioned constraints begin to operate, the curve passes through an inflection point at which r-phase growth changes to K-phase growth, which levels off asymptotically to the carrying capacity limit KN. As stated above, KN is the maximum population that we will find existing indefinitely in the conditions provided by the given habitat R. KN reflects the equilibrium density of a species, because if we set R = habitat area, equilibrium density can be defined as KN/R In nature, KN represents success, a workable adaptation for long term species survival.
One view of KN interprets it as the value of N at which population cannot increase because the number of individuals is so great that access to some particular resource R is saturated and some individuals are too deprived of it to reproduce or even survive; due to insufficient R of some kind, the death rate catches up with the birth rate and N stabilizes at a KN that reflects a general condition of deprivation and misery too great to allow any further N increase. Such conditions do exist; the most notable example is the way Canada lynx populations crash when snowshoe hare populations decline, though even in that instance conditions are miserable only half the time, during the downswing of the cycle. We can use the term Malthusian or Liebig-limited or saturation KN to designate those cases in which KN is due to saturation of access to some R, causing outright material deprivation.  In a Liebig-limited population, most individuals exist at a bare survival CMDR level.
However, KN does not necessarily reflect saturation, but rather may represent behavior that avoids the Malthusian constraint of deprivation. We need not suppose that KN is necessarily determined by the amount (Liebig limit) of some limiting resource. The ecologist Eugene Odum suggests that typically, natural populations limit themselves in a self-regulating manner that serves to protect them from the hardship of extreme material deprivation. The term self-regulating KN can designate that kind of limiting process. This distinction merits emphasis. To exist sustainably on planet earth, the human species obviously must attain some KN one way or another. Just as obviously, we do not want human KN to arrive with a crescendo of desperate Malthusian hardship due to reaching the Liebig limits of indispensable resources. To avoid that, the human species must aim at a self-regulating KN set and maintained by culturally determined behavior norms. Only a self-regulating human KN well short of any Liebig constraints will enable humans to exist indefinitely at a materially sufficient CRDA level. However, we must not imagine that the global population can engage as an aggregate in a process of reaching KN; the actual process can only take place locally, community by self-regulating community. As I said above, a country like the United States might better focus more on enabling its own communities each to achieve self-regulating KN than on trying to stabilize global population.
It is crucial to understand that the history of the last ten thousand years or so has been the history of more or less deliberate human attempts to evade the establishment of a stabilized KN phase for the human species, which apparently had reached a critical population density in most areas of the world about 10,000 years ago. [l6] At that time, human population density was reaching a point that forced human groups to choose whether to limit population and continue their primal (hunting-gathering) lifestyle in a stable, biologically diverse environment, or develop agriculture and support an endlessly increasing population in an ever more intensely stressed environment. Ecologically, this was a choice between the dependable high biomass/production ratio characterizing natural ecosystems and the precarious high production/biomass ratio that old paradigm agriculture desperately strives to maintain as it inevitably approaches the Liebig limit of the soil.  As we know, the predominating human choice was agriculture and unlimited population growth, generally following the exponential trend N = N0ert typical of agricultural population growth, and inevitably resulting in our familiar human history of periodic f amine and war along with constant political tyranny in most times and places.  The general vehicle of social choice that we call civilization has been incapable of so much as addressing the possibility of a self-regulating KN, and therefore plunges blindly toward some Liebig-limited Malthusian KN at best—that is, if we are even that lucky.
The main purpose of old-paradigm engineering has been to create the technologies enabling us to continue evading any stabilized KN limit on the human population, mainly by using nonrenewable energy sources. We are now beginning to face the ultimate dire consequences of that evasion. We can't duck the problem any more; we must now face the question that our ancestors refused to face for ten thousand years: how can we keep human consumption of resources within ecologically reasonable limits? The buck stops here, with us.
The KN curve gives the idea of carrying capacity a simple mathematical form that we can apply to any similar growth-limiting process. Obviously, we can imagine a similar logistic curve for L growth, thus providing a conception of sustainability formulated in dynamic relation to the exponentially growing human L that we confront in reality. Figure 8 depicts resource load carrying capacity (resource use carrying capacity) KL as the asymptotic limit of an L-growth process subject to increasing constraint as L gets larger.
The logistic L-growth curve in Figure 8 helps us better understand what KL implies, because it provides a way to envision sustainability in dynamic terms as the culmination of a development unfolding in time—a shift of human resource use from r phase to K phase.  We can now see at a glance that K-phase social behavior, necessary for keeping human-caused L permanently below some critical upper limit KL, is the new paradigm, more concisely stated as L < KL. Such behavior is the meaning of sustainability. That social shift requires a shift in our whole approach to engineering, which must now design K-phase rather than r-phase technologies. Therefore, we can regard the logistic L-growth curve as a dynamic representation of the new paradigm. Since this model depicts L as a function of time, we can now think of sustainability as a process in which human society participates through a new engineering suitable for that process.
To understand the basis for our new engineering, we must clearly understand the difference between KN and KL. We need to emphasize that the actual value of KN for a real population is an empirical value arrived at after the fact by observing an existing situation—by counting the steady-state N that develops under given conditions. In effect, KN simply reflects the behavior of N, whereas KL must determine the behavior of L.  Not only does KL refer to load (impact on the resource) rather than to population as such, but KL must be determined in a way entirely different from the way that KN is determined. We cannot find out KL simply by observing L, because doing so means discovering the value of L at which a resource R suffers permanent damage and KL loss as shown in Figure 4, a loss which it is the whole purpose of sustainable engineering to avoid. Many people assume that natural populations are always limited by Malthusian constraints only, so that sheer material deprivation would serve as the only thing keeping any species from exceeding its observed KN. This may indeed be the case with particular species such as the Canada lynx, but as mentioned before, natural populations typically limit themselves in a self-regulating manner that serves to protect them from the hardship of extreme material deprivation. Therefore, we should not assume that a given KN necessarily reflects reaching limits to what the available resources can sustainably provide. That is why we need a different basis, a resource-oriented basis, for indicating the limits to what resources can provide. KL is that basis.
The most crucial thing of all is that KL does not simply reflect the behavior of L; KL reflects the capability of R to carry L. If we think of R as a cow that we milk more and more frequently, then KL is the point beyond which our attempts to get more milk harm the cow permanently—the point at which the cow can withstand no greater milking load. If population N gains access to more resources (more cows, so to speak), it may perhaps establish a higher KN, but there is no way to increase the K, of a given resource. KN can increase or decrease, but the KL of a particular R can only diminish. KL depends on a resource's physiological capabilities, which are limited, just as a cow's physiological capabilities are limited. In fact, we must apply the notion of physiological stress limits not only to particular resources, but to the entire earth, as James Lovelock has shown.  Some grounding in Lovelock's new science of geophysiology ought to be incorporated in every engineering curriculum, and the general idea at least ought to be introduced in all high school science curricula.
The ecologist Eugene Odum suggests that in nature, the existence of a KN for a given species does not typically mean that the species has reached what we are calling the KL limit of its resources to withstand impact, because most species have coevolved with their supporting resource species and have developed behavior patterns that tend to maximize the entire coevolved system for the mutual benefit of all species within it.  Therefore, the maximum L that a typical species puts on its resources is significantly below the KL values for these resources.  Odum implies that in a co-evolved stable relationship between species population N and renewable resource R, the load imposed by N on R goes no higher than a maximum load Lmax < KL, such that there is always a comfortable KL – Lmax , margin that we might call the margin of system quality, as shown in the purely schematic Figure 9. (The reader should understand that in Figure 9, the logistic curve is not intended to represent the dynamics of co-evolution; it is merely an illustrational convenience that accords with our present context.) We can assume that as KL – Lmax goes below some minimum value, the overall quality of the system becomes precarious; this is what we mean by saying that KL – Lmax is the margin of system quality.  Since human society no longer participates in the natural co-evolution process, we cannot expect that any natural human Lmax< KL will develop spontaneously to establish a nonprecarious margin for us. Estimating KL and determining human Lmax in an ecologically responsible fashion will be the critical task for sustainable engineering, which obviously must include a very large component of environmental science.
In a natural co-evolved system, a stable population KN must imply a spontaneously established Lmax < KL that the population KN places on the resources R that support it, because L > KL causes a permanent decline in R, which eventually would no longer support N at the given KN level. Further, remembering L = C x N, we assume that a nonhuman species increases its L only by increasing N, since the natural physiology of individuals in any natural species sets a natural maximum per capita consumption rate Cmax that does not change. We can assume that from the standpoint of any R supporting a natural species, Cmax – CRDA for that species is negligible. The vaunted capability of industrial humans to indulge in unlimited CAYCC per capita consumption exacerbated the human problem tremendously. Catton points out that a single pre-agricultural human required the earth to supply a bit under 2,600 kcal of energy a day, about the same as a common dolphin required, whereas a single Homo Colossus—Catton's name for the typical old-paradigm industrial human in the U.S. today—requires the equivalent of a sperm whale's supply of over 202,700 kcal per day.  A common dolphin, of course, still requires less than 2,600 kcal per day. Our old-paradigm outlook takes pride in the escalation of the human per capita daily energy requirement, viewing that escalation as an indication of "progress." The new paradigm regards such a disproportionate increase as a sign rather of ineptness, an institutionalized ecological clumsiness guaranteeing the eventual decline of KL for every aspect of the environment.
Evaluating KL for all the various kinds of renewable R will be not only the most critical but the most difficult problem that sustainable engineering faces, especially when we remember that R in its general sense refers not only to resources used directly in the production activities of human society, but to all species in the co-evolved natural environment affected by those activities, and to the systemic interactions among them. KL can only be estimated, which means that sustainable engineering has got to err on the side of caution. Generally, we can be absolutely sure of a KL value only if we exceed it and thereby discover empirically the L at which that R becomes permanently damaged—that is, the L at which range compression sets in. Then, of course, it is too late to do anything but try to reduce L enough to stay below some new, permanently lower KL. Ecosystems cannot force us to refrain from damaging them. Staying below KL is a choice that we can make. KL is really a limit on our behavior.
The new-paradigm engineer's fundamental aim must be to sustain the earth's life-support system, which means that sustainable engineering has to focus on the needs of R and has to regard those needs as superseding demands for production of commodities. Sustainable engineering must not only assume that any given R varies inversely with increasing L, and that for every type of R there is a KL beyond which the ability of R to withstand L diminishes, but also that for every R there is some minimum value Rvital below which R expires and disappears entirely. This was apparently true for e.g. the passenger pigeon, which had existed in a population nine billion strong, and which for a time served humans as a food resource. Apparently, this extremely gregarious animal required interaction in very large flocks to reproduce successfully. When people had reduced its numbers below some vital level, the passenger pigeon became extinct. (When we consider a species as a resource rather than as a consumer of resources, we must designate its population with R rather than with N.)
We can postulate a somewhat higher level, RD, as a danger threshold indicating an exceedingly precarious level of vulnerability to environmental fluctuations that might suddenly reduce a renewable R below Rvital. The whooping crane, considered to be a resource of unique beauty, presently exists at the RD level. Though it has increased above Rvital, its population is still so low that one extra heavy storm might wipe out the species. Just such a catastrophe befell the heath hen, which excessive hunting had reduced to a probable R vital, of 200 individuals. Population then increased to an RD of 2000, but one bad winter reduced it to 50, which apparently was below Rvital because the species then died out.
Above RD, we can postulate a level RK inversely proportional to KL; any reduction below an existing RK would be irreversible in timeframes on the order of a human lifetime or longer, but as long as the resulting new RK remained significantly larger than RD, the reduction might not threaten extinction of the resource. (How large the magnitude RK – RD has to be would vary with the resource species and its ecological setting, but given that we must regard RK itself as precarious, any reduction at all is undesirable.) Above RK we can assume a dependably sustainable minimum Rmin, inversely proportional to Lmax < KL, that would allow reasonably fast rebound to higher values of R when L is reduced. Although making these ideas applicable to specific resources will require considerable work, they immediately provide a clear-cut framework for reasoning about the resource implications of existing or proposed technological applications. This framework, depicted in Figure 10, allows the new-paradigm engineer to conceive of sustainability directly in terms of R: in terms of the resource itself, sustainability is a condition such that R > RK. Maintaining R > RK has got to be the ultimate concern of sustainable engineering.
Of course, since an engineer's practical activities unavoidably create environmental load, as a practical matter sustainable engineering must think in terms of controlling load to ensure that Lmax < KL. From the load standpoint, then, the ultimate guiding idea of sustainable engineering must be to provide usufructuary means for the human species to live in terms of Lmax = CRDA x KN with respect to the R of planet earth, so that earth's quality margin KL – Lmax is always comfortably large enough to ensure that the planet's high environmental quality continues. (Though achieving a stabilized human KN is not strictly an engineering problem, estimating it is now a requirement for giving responsible advice concerning technology.) The meaning of life organized on such a basis must be conceived in relation to the tendency that, according to Odum, seems to characterize natural ecosystems: maximizing the quality of the overall environment for the mutual benefit of all species within it.
In recognizing this, we instantly transcend any previous conception of engineering. If engineering were to conceive of sustainability as no more than the sustainable imposition of human instrumental purposes on a subordinate world, every value apart from those purposes would eventually succumb to their expedient proliferation. Mere human convenience, even if held within reasonable individual limits, might for example easily justify the conversion of all wilderness to pleasant housing sites, destroying forever the quality that we call wilderness. Natural systems have an intrinsic value that we are obligated to sustain apart from any separate interest we may have. This is a further reason why KL cannot be calculated exactly: we cannot quantify the intrinsic value of R. KL is not a Liebig limit; it is a quantifiable way of representing a decision regarding our own behavior. Such a decision must ultimately derive from a non-quantifiable value commitment made not for material advantage, but on principle, out of an ineluctable obligation to all manifestations of value. KL represents a commitment not to maximum convenience for ourselves, but to maximum quality of our world.
Yet the KL limit is in itself a quantitative conception enabling us to contrast in one image the quantifiable difference between unsustainable and sustainable engineering. Note that the r phase of the logistic curve in Figure 8 is analogous to the exponential growth curve in Figure 5. This r phase represents our chosen behavior toward the environment (R) since the beginning of agriculture, despite the danger of unlimited stress on R, and especially since the beginning of industrial technology, which has increased human L at an ever-accelerating pace. The narrowly focused oldparadigm engineering that has designed such technology we might call r-phase engineering, an engineering that thinks strictly in terms of production goals—that is, maximum growth in production as dictated by the old paradigm. Like the initial exponential growth process that represents it in Figure 8, r-phase engineering is inherently unsustainable, since its reason for existence is to design r-phase technology. The supreme archetype of r-phase technology is the automobile, which undoubtedly has done more to increase the magnitude CAYCC – CRDA, and decrease the amount of social benefit per unit of L, than any other form of technology. In keeping with r-phase standards, world automobile use is accelerating. If we continue r-phase engineering and ignore the need to establish KL limits, we will get firsthand experience of one more type of L curve—the crash curve, as shown in Figure 11.
Figure 11 depicts how KL declines as L overshoots KL, because R is permanently damaged and its ability to support L declines permanently. Note that in the irruption phase, R is inversely proportional to L as the increase in L causes an initially reversible decline in R > RK (see Figure 10 also), but in the crash phase, L is directly proportional to R as the decline in L parallels the irreversible decline in R < RK. Thus, due to precipitous range compression (extreme decline of KL and R), L crashes just as rapidly as it had gone up, but now there is no resource foundation for rising again. If KL drops far enough, there may not be enough resource base for human species survival even on a CMDR minimum level. Nor could the exploitation of extraterrestrial R, proposed by some as a remedy for terrestrial resource depletion, make up for the devastation of earth's ecology—especially if crucial geophysiological processes were to fail.
The alternative, of course, is K-phase engineering, which bases the design of technology on the need to keep L below KL, as shown in a simplified way by the K phase of Figure 8. The result is K-phase technology. Since we presently lack adequate KL and Lmax estimates, common sense has to guide our initial efforts in K-phase technology. Obviously, we need to pursue both low-tech and high-tech ways to reduce L and increase the amount of social benefit per unit of L.
Transportation alternatives are crucial, and we are beginning to see interest in possibilities such as solar powered vehicles, which might enable us to decrease fuel consumption while maintaining for the time being a reasonably close approximation to the present dominant lifestyle, thus avoiding socially traumatic precipitous change. Better housing design is a major need, from low-tech features like better solar orientation and low-flow shower heads to high-tech improvements such as thin-film emissivity coatings for superwindows. Further, as the Rocky Mountain Institute points out, many K-phase developments can be enormously profitable.  K-phase engineering is a philosophy of design that aims not only at sustaining R, but at thereby sustaining maximum freedom and opportunity for everyone, avoiding the range compression that diminishes resources today, and thus avoiding the diachronic competition that discounts the future by stealing from our children. 
K-phase production goals must be subordinate to the goal of sustaining the renewable resources on which the possibility of future production depends, because K-phase engineering recognizes that every production increase is an environmental load increase, and the environment has limits to the load it can sustain. Just as our bodies have stress limits, so does the earth. Old fashioned r-phase engineering gives immediate production the benefit of the doubt, and demands proof of existing environmental damage before holding back. But the possible damage has become too enormous. K-phase engineering gives the earth the benefit of the doubt. That's what it really comes down to—a shift in emphasis. That is fully sustainable engineering, our only basis for real choice in deciding what the future will be like.
Peter Hartley, PhD.
Assoc. Professor of Liberal Arts & International Studies Liberal Arts
International Studies Division
Colorado School of Mines Golden, Colorado 80401
Phone: (303) 2733903
FAX: (303) 2733751
1. See William R. Catton, Jr., "Mines and Pitfalls in the Future of Homo Colossus," Mineral and Energy Resources Vol. 25, No. 4, July 1982. This article lays the groundwork that enables my formulation.
2. The definition of KL given above is based on a definition of carrying capacity that Catton suggests on p. 6 of "Mines and Pitfalls in the Future of Homo Colossus": "the amount of use (of a given kind) a particular environment can endure year after year without degradation of its suitability for that use." Catton's crucial innovation here is to make environmental impact rather than population the essential factor in defining carrying capacity, and to make use the variable to be limited.
It is important to note that the concept of load L is exactly equivalent to the concept of scale in ecological economics. See p. 8 of the Introduction by Herman E. Daly and Kenneth N. Townsend in Valuing the Earth Economics, Ecology, Ethics (Cambridge, Mass.: The MIT Press, 1993), edited by Herman E. Daly and Kenneth N. Townsend.
3. For an exposition of the social and environmental difference between usufructuary and instrumental attitudes toward resources, see Donald Worster, Rivers of Empire: Water, Aridity, and the Growth of the American West (New York: Pantheon Books, 1985). On p. 88, Worster says: "Under the oldest form of the [usufructuary] principle a river was to be regarded as no one’s private property. Those who lived along its banks were granted [a right] to use the flow for 'natural' purposes like drinking, washing, or watering their stock, but it was a usufructuary right only—a right to consume as long as the river was not diminished."
11. Albert A. Bartlett, "Forgotten Fundamentals of the Energy Crisis," American Journal of Physics, Vol. 46, No. 9, September 1978. See also the expanded version in Mineral and Energy Resources, Vol. 22, Nos. 4 and 5, September and November 1979. My notation differs from Bartlett's, but in mathematical form, my expressions are the same as his. A couple of elaborations that might prove useful: and .
More recently, Bartlett has suggested a program of "sustained availability" as an alternative to unsustainable growth; see Bartlett, "Sustained Availability: A Management Program for Nonrenewable Resources," American Journal of Physics, Vol. 54, No. 5, May 1986.
12. If we start with L=L0ert and select the instant when the initial load has doubled, we can substitute 2L0 for L and solve for t=T2, which gives us T2 = ln2/r. The natural log of 2 is slightly more than .69, so if we round off .69 to .70 and substitute g/100 for r, we get T2 .70/ (g/100)=70/g. T2=70/g is the well-known Rule of 70, valid for g% growth rates when g/100 << 1.
13. See Eugene P. Odum, Fundamentals of Ecology (Philadelphia: W.B. Saunders Co., 1971), pp. 179-188, and Robert Leo Smith, Ecology and Field Biology (New York: Harper and Row, 1974), pp. 303-327. See also Smith, Elements of Ecology and Field Biology (New York: Harper and Row, 1977), pp. 201-246.
14. The expression for the logistic population curve (Verhulst model) is N = KN/1+ea-rt, with a = ln (KN-N0 / N0) at t = 0. Again, r is an instantaneous growth coefficient, and as before we can replace it with a percentage growth rate g / 100<<1 for handy calculation. The derivative dN/dt = rN( KN-N / KN ) shows why N increases more and more slowly as N reaches values close to the value of KN. That is, until the curve reaches its inflection point, N is in the r phase and increases faster and faster every instant as it becomes larger. After the inflection point, N is in the K phase and increases more and more slowly every instant as it becomes larger, because in the K phase the fraction KN-N/Kn has become small, and of course continues to get smaller every instant. We can also say that the condition | a | > | rt | defines the r phase, and the condition | a | < | rt | defines the K phase. All this obviously holds true as well for the entirely analogous logistic L curve discussed below.
15. Baron Justus von Liebig (1803-1873) pointed out that the least available nutrient will be the factor that limits biological productivity. That is, decreasing availability of the scarcest nutrient will be the constraint that halts biological increase.
Thomas Robert Malthus (1766-1834), a clergyman and pioneer economist, pointed out that population tends to increase exponentially (faster and faster as long as people obtain enough nourishment), whereas food supplies can only increase arithmetically (only in direct proportion to the amount of land that can be used to produce food). Therefore, eventually too many people will depend on too little land, and some must starve, meaning that unlimited population growth inevitably must lead to deprivation and misery, and that only deprivation and misery can halt population growth if people will not act to stop it otherwise.
16. Jared Diamond, "The Worst Mistake in the History of the Human Race," Discover, May 1987, pp. 6466. See also Mark Nathan Cohen, The Food Crisis in Prehistory (New Haven: Yale University Press, 1977).
19. By analogy with the logistic N curve, the expression for the logistic L curve is L= KL/1+ea-rt, with a = ln(KLL0)/L0 at t=0, and derivative . Once again, we can use g/100<< 1 instead of r. The mathematical behavior of the logistic L curve is exactly the same as the logistic N curve mathematical behavior described in Note 14 above. Figure 8 is adapted from Catton, "Mines and Pitfalls in the Future of Homo Colossus," p. 3.
20. Catton provides the initial foundation that makes it possible to conceive of this difference between KN and KL. My discussion here develops and articulates some important implications of the difference.
24. In practice, a dimensionless parameter would probably be more useful. I suggest defining a parameter called the quality margin ratio . Note that this is identical to the term that in the derivative for the logistic L curve determines how much the load L increases during a given instant of time. Obviously, as L increases, that term shrinks, and approaches zero as L approaches KL asymptotically. When L = 0, that term has a value of 1, indicating a quality of R undiminished by any human L. Low Q.M.R. values that are small compared to 1 indicate that impact on R is approaching the precarious KL level. Also, we can regard Lmax as equivalent to the concept of optimal scale in ecological economics; see Daly and Townsend, pp. 89. We can therefore define a Q.M.R = KL – Lmax /KL that would indicate optimal scale.
29. See "Abating Global Warming—At A Profit," Rocky Mountain Institute Newsletter, Vol V, No. 3, Fall 1989. The Rocky Mountain Institute is an indispensable source of technological information relevant to sustainable engineering. The Institute's address is: Rocky Mountain Institute, Snowmass, CO 81654-9199.
30. The term "diachronic competition" is from Catton, "Mines and Pitfalls in the Future of Homo Colossus," p. 2. It designates the moral essence of the old paradigm. Regarding the ultimate character of our old paradigm behavior, Alfred W. Crosby, Jr. remarks at the end of The Columbian Exchange (Westport, Conn.: Greenwood Press, 1972): "For the sake of present convenience, we loot the future." That is the process of diachronic competition, and that will also be history's judgement of us if we continue our present typical behavior toward the R of planet earth.