Download Carrying capacity reconsidered

Carrying Capacity Reconsidered
David Price
Cornell University
The concept of carrying capacity has gained broad currency, although some population ecologists are dubious about its value. This paper assesses the utility of the
concept and develops an alternative understanding of population growth. First, carrying capacity is viewed in historical perspective and evidence that is supposed to
support it is criticized. Then the underlying assumptions upon which it rests are
reexamined. Limits to growth are seen to be both multiple and variable. The mechanism that is supposed to regulate population is critically reviewed. And the assumptions of balance in nature and equilibrium in biotic communities are reevaluated.
These assumptions having been found wanting, population growth is reassessed
in relation to environmental variability. The strategies by which different species
cope with variability are described, and the windfall effect, which causes some
populations to grow rapidly and then collapse, is identified. Finally, it is suggested
that carrying capacity may be a self-validating belief and that it has limited relevance to human population growth, which is better understood in other ways.
INTRODUCTION
People who are concerned about overpopulation often talk about carrying capacity. It is hard to make the case that a population of some size
might be dangerously large without saying (or at least implying) that there
is some size at which it would not be dangerously large. The difference
between the two—the limit up to which the size of the population would
be acceptable—is understood to be carrying capacity. Definitions vary, but
all convey the idea that there are environmental constraints that set a maxiPlease address correspondence to David Price, 811 Mitchell Street, Ithaca, NY 14850.
Population and Environment: A Journal of Interdisciplinary Studies
Volume 21, Number 1, September 1999
© 1999 Human Sciences Press, Inc.
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mum to the size a population can safely attain. Scholars such as Ehrlich
and Ehrlich (1990), Catton (1980), and Cohen (1995) use the concept of
carrying capacity in discussions of human population growth, as do popular works such as The Global Ecology Handbook (Corson 1990).
The concept comes from the field of ecology, where carrying capacity
has been an essential topic in introductory texts for more than twenty-five
years. A generation of college students has learned that there are environmental limits to the size populations can attain, and that populations tend
to stabilize at these limits or fluctuate around them. In this way, "carrying
capacity" has become part of the popular vocabulary. It appears in magazines and newspapers, and in the electronic media. It is prominent in political discourse, and people with quite diverse agendas subscribe, in common, to the idea that there is some maximum human population that the
earth can sustain. It is understood to be a legitimate ecological concept,
and its scholarly heritage is thought to give it the scientific seal of approval.
But the idea of carrying capacity is highly problematic. It has long
been criticized as unclear and imprecise (Edwards & Fowle, 1955; Dasmann, 1964). A recent text warns, "The term has acquired so many meanings it is almost useless" (Smith, 1992). Colinvaux (1986) defines it, with
heavy irony, as the limits imposed by a researcher's experimental design.
And two articles, written from the very different perspectives of wildlife
ecology (Dhondt, 1989) and range management (Bartels et al., 1993), both
suggest that it may be time for the term to be abandoned.
ORIGINS OF THE CONCEPT
The term "carrying capacity" was presumably coined by range managers, who were concerned with the use of land for grazing livestock. Bartels et al. (1993, p. 90) trace it back to the 1906 Yearbook of the U.S.
Department of Agriculture, and the 1991 edition of the Random House
Webster's College Dictionary dates it from between 1880 and 1885. The
term proved useful for scholars concerned with domesticated herbivores
(Hadwen and Palmer, 1922), and was soon used in relation to wild herbivores (Leopold, 1933). It was taken up by other wildlife biologists (Errington, 1934) and began to make its way into textbooks.
In 1953, Eugene Odum gave the term a precise mathematical meaning
in the first edition of his influential text, Fundamentals of Ecology, where
he equated it with the constant K in what is known as the "logistic equation." This equation had been proposed, in 1920, by Raymond Pearl and
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his colleague, Lowell J. Reed, as a general model of population growth.
They reasoned that there must be some absolute limit beyond which further population growth would be impossible, and that the rate of population growth, which might accelerate if circumstances were propitious,
would slow down as it approached this limit. They expressed this idea as a
differential equation that is now generally presented in the form:
where N = the population size
t = time
r = rate of population growth
K = an asymptote.
What this says is that the rate of increase of the population per unit
time equals the rate of population growth per capita, times the population
size, times the as-yet-unutilized opportunity for population growth. According to this formula, a growing population will trace a sigmoid curve—
a curve that rises slowly at first, then faster and faster until it reaches an
inflection point, after which it rises more and more slowly until it approximates a horizontal asymptote (Figure 1). Pearl and Reed (1920) felt that
they had made a significant discovery which might be a first approximation, at least, to a general law of population growth.
While their paper was in press, however, they became aware that a
little-known Belgian mathematician named Pierre-Francois Verhulst had
published the same idea in 1838. Whatever disappointment they may have
felt at not being the first to formulate this "law" must have been offset by a
belief that independent discovery supported its validity. Giving due credit
to Verhulst, Pearl went on to present the model, with refinements and additional evidence—sometimes with Reed as co-author and sometimes without—in a range of different venues. He was forceful and enthusiastic, and
he promoted the idea tirelessly for the rest of his life (Kingsland 1995).
Soon, both the logistic equation and the term carrying capacity were
appearing in ecological texts, although they were often separated from
each other by many pages (Dhondt, 1989). Then Odum brought the two
ideas together, using the term carrying capacity to name the constant that
the logistic curve of population growth tended to approximate. The alliterative label for the neat mathematical concept assured its popularity, and
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FIGURE 1. Carrying capacity as an asymptote to a logistic curve.
carrying capacity, often illustrated with Pearl's original examples, became a
required part of any scholarly discussion of population biology.
THE GROWTH OF POPULATIONS
The logistic model of carrying capacity involves two ideas: that the
environment establishes a constant limit to the growth of populations, and
that populations grow until they stabilize at this limit.1 Pearl and his followers addressed the second idea. They sought to validate the logistic
equation by showing that the growth of populations does, in fact, describe
a sigmoid curve. Pearl cited in evidence earlier work done by Tor Carlson
(1913), a Swedish scientist who had studied the growth of yeast in laboratory cultures. Pearl and Reed conducted their own experiments with fruit
flies (Pearl 1925). And G. F. Cause, a young Russian whose teacher had
studied with Pearl, became an inspired experimentalist, working with yeast
and protozoa (1934, 1935). All found population growth that convincingly
approximated logistic curves—and graphs of their observations with fitted
curves have been reproduced in textbooks that deal with the growth of
population for the rest of the twentieth century.
But the evidence that some populations grow in a way that approxi-
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mates the logistic curve hardly supports the contention that the logistic
curve is a general law of growth, or even a first approximation to such a
law. Pearl seemed to lose his faculty for skepticism, once he had committed himself to promoting the logistic equation (Kingsland 1995). He extrapolated from his laboratory experiments in a way that their design did not
warrant. He saw partial sigmoid curves in data that could easily be interpreted in other ways (see many of the examples in Pearl 1925). And he did
not understand that the curve traced by Carlson's yeast does not even represent the growth of a live population; it represents increase in the mass of
the material that Carlson was able to remove by centrifuge—which consisted of both live cells and dead ones.
Outside the laboratory, it has been nearly impossible to find examples
of logistic growth. The one example that sometimes appears in textbooks
involves the sheep population of Tasmania during the nineteenth century
(Figure 2). But as Davidson (1938, p. 345) explained in his original report,
the tendency of the curve to level out did not come about by natural
means. Rather, a relatively constant population resulted from the actions of
sheep farmers, who learned that the quality of their pastures was diminished by overgrazing, and in the long term it was better not to overstock
them.
Commonly, natural populations fluctuate. Some vary with no apparent
regularity, while others, such as lemmings, wax and wane cyclically. Some,
such as locusts, are prone to occasional outbreaks in which population
skyrockets and then plummets. Populations of many species grow wildly in
response to unusually benign conditions, and then collapse. Some populations can even seem stable over considerable periods, but seldom if ever
does a natural population rise sharply and then stabilize in the form of
sigmoid curve.
LIMITS TO GROWTH
Concern with whether the growth of populations describes logistic
curves has diverted attention from a more important issue: whether the
environment does, in fact, set constant limits to growth. One needs to ask
the nature of the factors that might constrain growth, how they constrain
growth, and whether there is any good reason to suppose they are constant.
Verhulst says that a population finds its limit in "the extent and fertility
of the country." "The growth of population must have a limit," he explains,
"be it only in the amount of land necessary to shelter that population." He
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FIGURE 2. Growth of the sheep population in Tasmania, fitted with a
logistic curve (after Davidson, 1938, p. 344).
admits that a nation might increase its subsistence base by importing food,
although he would still expect growth to cease "well before the entire surface of the country were covered with towns." But, he argues, "Any formula that would attempt to represent the law of population" must suppose
some maximum size that the population can approach but never attain
(Verhulst 1838, p. 113-15).2 Pearl and Reed describe the limiting conditions in similar terms. "In any restricted area," they write, "a time must
eventually come when population will press so closely upon subsistence
that its rate of increase per unit of time must be reduced to the vanishing
point." If the course of growth is given graphic expression, they add, the
curve will approximate an asymptote that represents "the maximum number of people which can be supported on the given fixed area" (1920, p.
280).
Both Verhulst and Pearl and Reed take as their unit of analysis the
population of a nation state, and both discern two kinds of limiting factor
that might impose a ceiling on growth: space and food. Verhulst expects
growth to be constrained by available food, including imports, while Pearl
and Reed expect it to be constrained by the amount of food that can be
produced in a limited space—the agricultural lands of the nation under
study. To model these conditions in his experiments with fruit flies, Pearl
restricted their living space, while providing an abundant supply of food.
That the productivity of agricultural lands might actually diminish was a
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possibility he rejected out of hand. "The world's farmers are always producing more food," he said (Pearl 1925, p. 32).
The assumption that food is the limiting factor goes back to the observation, popularized by Malthus (1798), that means of subsistence do not
grow as fast as population. But when other species are taken into account
it becomes clear that constraints can be of many different kinds. The limiting factor can be space, as with barnacles that have plenty of food but a
restricted surface on which to attach themselves. For some species, the
availability of places to hide from predators may be a constraint. For other
species, the availability of nesting materials may be decisive. In arid regions, the population of many species may be constrained by the availability of water. In sum, a number of qualitatively different factors may limit
the growth of population.
With no restrictions on the kind of parameters that can serve as constraints, it is possible to imagine something that would limit the growth of
any population of any species. No population can be expected to grow
forever, and it is easy to posit obstacles that would prevent it from doing
so. But it is not sufficient to imagine a limit that seems obvious and convincing; it is necessary to show that the growth of the population is actually
affected by this limit. As Verhulst observed, space might constrain the
growth of a nation's population, but unless the population grows until the
land is entirely covered with towns, something else must be the operative
factor. With natural populations, however, it is often difficult to figure out
what the constraint might be, much less demonstrate its role in the regulation of population.
DENSITY-DEPENDENT
REGULATION
In 1933, Nicholson gave the theory of logistic growth a greater degree
of sophistication by proposing a means by which the size of natural populations might be regulated. He accepted Pearl's fruit-fly experiments as
demonstrating that populations "reach a state of stationary balance under
constant environmental conditions" (Nicholson, 1933, p. 133), and argued
that this balance must be achieved through the operation of mechanisms
that are sensitive to population density. He contended that competition
among the members of a population increases as density increases, letting
a relatively sparse population grow faster but making a relatively dense
population grow more slowly. In essence, Nicholson espoused the logistic
model and proposed density-dependent feedback involving intraspecific
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competition as the means by which populations tend to stabilize at environmental limits. Nicholson's ideas were sharpened by Smith (1935) and
were used persuasively by Lack in a seminal study of bird populations that
appeared in 1954.
In another book published that same year, however, Andrewartha and
Birch (1954) rejected the assumption that natural populations necessarily
attain some sort of balance and contested the utility of a distinction between density-dependent and density-independent environmental factors.
They contended that Nicholson and his followers failed to appreciate the
spatial variability of the environment, pointing out that for any given species some places are more propitious than others, with local populations
based in these patches expanding into marginal territory when conditions
are favorable, shrinking back when conditions are hostile, sometimes going
extinct, and sometimes recolonizing patches where other local populations
have been wiped out. Through a proper appreciation for the patchiness of
the environment, they argued, it was possible to understand how species
might persist even though their populations fluctuated.
Andrewartha and Birch supported their case with meticulously gathered empirical data, while Nicholson, who was primarily a theorist, presented little data in support of his ideas. But patchiness is not as exciting an
explanation as feedback, and the model developed by Andrewartha and
Birch has never had as many adherents as density-dependent regulation.
Today, most population ecologists subscribe to density dependence, although it is still hard to demonstrate convincingly. Proponents continue to
claim that without regulation, "populations would show a random walk
through time and would eventually go extinct" (Sinclair, 1989, p. 203).
This is not a problem, however, for those who regard the extinction of local
populations as a normal occurrence and believe that species persist because catastrophes do not usually affect all local populations at the same time.
Occasionally, of course, whole species do go extinct, as the theory of
natural selection requires and the fossil record shows. So the issue comes
down to a question of timing. Do populations go extinct at a rate that
would be expected if they were responding randomly, or do they persist
longer—suggesting regulation? Murdoch and Walde devised a method intended to explore this question, and their results seemed to show "that
many populations in nature are indeed regulated." But then they found that
"as many as a third of simulated populations that are varying purely at
random" also appeared to be regulated for a "distressingly" long period of
time (1989, p. 122-23). So the hegemony of density-dependent regulation
is not assured.
What is seldom appreciated is that the parties to the controversy favor
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different answers largely because they ask different questions. Nicholson
and his camp want to know, "How is a population regulated?" while Andrewartha and Birch want to know, "Why does a population fluctuate?" It
is often possible to ask both questions about the same population, because
any population that has not yet gone extinct may be seen as regulated, and
any population that is not absolutely stable may be seen as fluctuating. But
the questions grow out of different assumptions, and the assumptions determine the way they are answered.
The two schools of thought have been referred to as biotic and abiotic
(e.g. Tamarin, 1978) because proponents of density-dependent regulation
commonly point to biotic limiting factors such as predators, parasites, and
competition for food and other resources, while their adversaries are more
concerned with the effects of abiotic factors such as changes in the weather.
These labels are misleading, however, for the essential difference is not in
the nature of the environmental constraints, but in the way they affect population. Proponents of feedback believe constraints to the growth of population are constant, while partisans of patchiness believe they are variable.
BALANCE AND EQUILIBRIUM IN THE BIOTIC ENVIRONMENT
Density-dependence requires a constant constraint because feedback
regulates a dependent variable in accordance with an independent variable.
A thermostat, for example, regulates the temperature of some medium, such
as a room, in accordance with the temperature to which it is set. Similarly, in
the density-dependent view, population is regulated in accordance with an
environmental limit. This limit is thought of as relatively constant, for otherwise there would be nothing to which the dependent variable could adjust. If
a thermostat were randomly reset at frequent intervals, it could not regulate
temperature, and if an environmental limit were not constant, it could not
regulate population. Therefore, Nicholson was at pains to defend his faith in
the balance of nature, and more recently Sinclair has stated that "the logical
necessity for density dependence is a mathematical result of the premise that
there is an equilibrium" (Sinclair, 1989, p. 201).
The idea of balance in nature is deeply rooted in the Western religious
and philosophical tradition. Egerton (1973) finds evidence of it from the
pre-Socratic philosophers onward, although the "earliest explicit account"
appears in the 1600s, and the term "balance of nature" is credited to Linnaeus (1749). The idea is grounded in "providential ecology"—a view of
the earth as created whole, perfect, and unchanging. But such a view is
inconsistent with a modern understanding of the geological record, and
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Egerton (1973) affirms that most biologists no longer speak of "the balance
of nature" except for rhetorical purposes.
A more sophisticated view holds that long-established biotic communities tend toward equilibrium through the coevolution of their member
species. The argument for this position is that any population (no matter
what the species) participates in a biotic community consisting of populations of other species with which it is interdependent. All species in such a
community are subject to natural selection, and as the constituent species
adapt to their environment, they adapt to each other. Predators adapt to
their prey, prey adapt to predators, parasites adapt to hosts, hosts adapt to
parasites, and co-competitors adapt to each other. Ehrlich and Raven
(1964) are responsible for calling attention to this process of stepwise mutual adaptation between interacting species and naming it coevolution.
As a consequence of coevolution, the biotic context of a given species
can come to limit the growth of its population. If, for example, the population of a particular small animal grows and remains large for a sufficiently
long time, this presents an opportunity which predators and parasites can
adapt to exploit, and a threat which prey can adapt to defend against—
thus constraining the growth of the population under consideration (see
Pimentel, 1988, for examples). Insofar as all the species in a biotic community are linked in a complex network of interactions, coevolution moves
the community toward an impasse in which constituent populations tend
toward stability. Biotic communities may not be in a state of perfect equilibrium, but coevolution pushes them in this direction. And in long-established communities, where equilibrium is approximated, relatively constant populations of some species may act to limit the populations of other
species, in much the way that Nicholson envisioned.
For those who favor density-dependent regulation, the persistence of
many interacting species is evidence of equilibrium. It is a mistake, however, to assume that all populations are regulated in accordance with constant environmental limits. The degree of equilibrium in biotic communities presumably depends on how long they have been established; the
tendency toward equilibrium does not mean that all constituent species are
in a state of balance; and outside factors can interfere with the tendency
toward equilibrium. Indeed, while the biotic environment may tend to
move in the direction of equilibrium, the abiotic environment remains subject to random fluctuations.
VARIABILITY OF THE ABIOTIC ENVIRONMENT
Whether the abiotic environment is seen as constant or variable depends on whether one views it from a great distance or up close. From an
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astrophysical perspective, conditions on the surface of the earth have been
remarkably constant during the entire history of life. For billions of years
the sun has been sending out very nearly the same amount of energy (Stix
1991), and this has driven the circulation of earth's atmosphere and hydrosphere, which moderate temperatures and hold them in a range that allows
most of the planet's water to remain liquid, which is necessary for life. In
comparison with the extremes found in the interior of stars and interstellar
space, the temperature on the surface of the earth has remained extraordinarily stable; if this were not so, life could not have evolved.
But stability is a relative concept, and what looks constant in astrophysical perspective looks quite variable to organisms that live within the
earth's ecosystem. In close-up, abiotic features such as temperature and
rainfall are anything but constant. Daily changes, as the earth turns on its
axis, and seasonal changes, as the earth revolves around the sun, are regular and cyclic. Other fluctuations are unpredictable in both frequency and
intensity. There are floods and droughts, unusually harsh winters and exceptionally mild ones. Recorded history documents a "Little Ice Age," and
the geological record gives evidence of big ones. Plate tectonics shows that
tropical continents can drift over the earth's poles. Huge meteorites may
occasionally cause widespread devastation. As a consequence of all these
factors, the earth's abiotic environment fluctuates according to the pattern
known as 1/f noise (see Halley, 1996), as demonstrated by Mandelbrot and
Wallis(1969).
Life is adapted to the middle of the range over which abiotic variables
commonly fluctuate. Natural selection can only favor qualities that maximize the potential for individual organisms to pass on their genes if these
qualities continue to maximize this potential over the course of many generations. And these qualities can only continue to do so if the environmental circumstances to which they confer adaptiveness remain relatively constant. Thus, where temperature is prone to fluctuate over a particular range,
departing more or less from some mean, life adapts to the mean, and its
ability to tolerate departures from the mean diminishes in proportion to
their amplitude.
A large, unpredictable deviation from an abiotic mean that has persisted for a long time can drive many species to extinction. This is what
happened in the great die-offs that punctuate geological history, such as
the one at the end to the Cretaceous period (Stanley, 1987). But smaller,
more regular changes are part of the on-going context of life, and species
develop ways to cope with them. If species did not develop adaptations
that permit some of their members to make it through the winter, or through
the occasional drought or famine, they would not last long at all.
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COPING WITH VARIABILITY
All populations grow when they can and die back when they come
under stress. But within these broad outlines, there are great differences in
the way different species accommodate fluctuations in the supportive capacity of their environments. These differences do not concern the propensity for populations to grow, but rather, the way they die back.
The natural fecundity of all species is well known, having been described, with memorable examples, by Franklin, Malthus, and Darwin (see
Glacken, 1967, p. 624). We must suppose that natural selection has universally favored this propensity, for by leaving more descendants, individuals
of any species maximize the probability that some will survive whatever
catastrophes fate may have in store. Because of natural fecundity, whenever environmental conditions become more favorable, populations grow.
When environmental constraints change for the worse, however, becoming more severe than they have previously been, populations die back.
But populations of different species do so in different ways that reveal different strategies for dealing with variability. One option is to let population
expand when it can, accept massive die-offs when conditions worsen, and
develop means that enable a few representatives to survive until conditions
improve again. A quite different option is to constrain the expansion of
population, so that growth in good times is modest and die-off in hard
times is moderate.
These contrasting strategies correspond to sets of characteristics attributed to what are usually called r- and k-selected species (MacArthur and
Wilson, 1967; Pianka, 1970). These terms were named for parameters of
the logistic equation in the belief that r-selected species are adapted to
conditions of relatively low population density, while k-selected species
are adapted to situations of high population density. But Southwood (1977)
has noted that these two kinds of species are often correlated with different
degrees of environmental variability, and I believe that the characteristics
which distinguish them should be viewed, in many if not all cases, as
strategies for coping with fluctuations rather than adaptations to population
density.3 To make this clear, I prefer to speak of "boom-and-bust" strategies
and "leveling" strategies.4
The boom-and-bust strategy is typical of species whose members have
life spans shorter than or equal to the duration of the usual environmental
fluctuations. Often, they are relatively small organisms, and they have a
large number of offspring. They typically rely on the probability that at
least one or two of their many offspring will manage to pass on their genes,
and do not usually do anything to increase their offspring's chance of sur-
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vival. In some species, adults do not live long after reproducing. A wellknown example of a species with the boom-and-bust strategy is furnished
by the thrips (Thrips imaginis) studied by Davidson and Andrewartha
(1948) (Figure 3). Many other insects, annual plants, and fungi also deal
with spatial patchiness and temporal variability in similar ways.
The leveling strategy, on the other hand, is typical of organisms whose
life spans are likely to last through many environmental ups and downs.
They are usually larger and can reproduce throughout a significant part of
their lives, but have a relatively small number of offspring. Parents in such
species often take steps to insure that their offspring survive to maturity.
This favors longevity beyond the birth of offspring, since the survival of the
parent is crucial to the survival of the progeny. Many birds and mammals
use a leveling strategy (Figure 4).
The crux of the matter is the life stage that has the greatest probability
of surviving hard times, and thus preventing the population, and the species, from dying out. For boom-and-bust strategists, early life stages serve
this function; seeds, spores, eggs, and even cocoons have an ability to
remain viable for a considerable period in a hostile environment that may
wipe out the entire adult population, and they are capable of re-establishing the population when conditions improve. Among leveling strategists,
on the other hand, young adults have a good probability of surviving hard
times that result in widespread infant mortality (see, for example, Caughley
1966), and their ability to have more offspring when conditions improve
enables them to re-establish the population.
The boom-and-bust strategy and the leveling strategy are not the only
ways to deal with environmental variability, and the particular circumstances of different species have resulted in a wide variety of different responses. But these two strategies do form a pair of contrasting approaches
to the problem that have developed in a great number of species, and one
cannot help but suspect that the the different perspectives of population
ecologists who study leveling species (like birds and mammals) and boomand-bust species (like many invertebrates) may affect the controversy between those who believe in density-dependent regulation and those who
do not. Nicholson, himself, was an entomologist, but Lack (1954) made
density dependence central to his understanding of bird populations, while
the dissenting work of Andrewartha and Birch (1954) featured insects.
CARRYING CAPACITY AND THE WINDFALL EFFECT
We must conclude that the concept of carrying capacity is seriously
flawed. Indeed, it may be no more than a self-validating belief. As Kings-
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FIGURE 3. The boorn-and-bust strategy for dealing with environmental
variation as revealed by changes in a thrips population (after Davidson
and Andrewartha, 1948).
land (1995, p. 68) points out, Pearl and Reed "assumed that which had to
be proved," and those who followed after them may have continued the
self deception in ways that became increasingly sophisticated. Carrying
capacity is supposed to be a natural limit that regulates the growth of populations, but its existence is hard to document apart from its presumed
effect. It is all to easy to infer its existence when the expected effect is
observed, while attributing a failure to observe the expected effect to other
causes. Constant populations can be shown to result from constant limits to
growth in laboratory experiments, so it is assumed that constant populations result from constant limits to growth in nature—even when these
limits cannot be demonstrated or the feedback mechanism that is responsible can only be inferred. And incautious generalization from cases that
seem to show density-dependent regulation has led to a widespread belief
that the environment has a constant carrying capacity for all populations.
Pearl and Reed (1920, p. 284-85) helped foster this belief by predicting the future population of the United States on the assumption that
growth up to 1910 defined the first part of a logistic curve. According to
their calculations, American population would level out at about 197 million in the twenty-first century. This prediction has turned out to be grievously wrong, as the population of the United States has already reached
270 million and continues to grow (Figure 5). But the belief that human
population will stabilize at some carrying capacity in excess of its current
size is still widely held.
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FIGURE 4. The leveling strategy for dealing with environmental variation
as revealed by a relative lack of change in the yellowhammer population
of Britain (after O'Connor, 1980). The CBC Index is a measure of
population density derived from the observations of volunteers who
participate in the Common Birds Census conducted by the British Trust
for Ornithology.
This belief is inconsistent with the accumulated observations of both
population ecology and paleontology, which show that many populations
fluctuate and all eventually go extinct. What is needed, in place of the
claim that all populations are regulated in accordance with carrying capacity, is an explanation of why some populations fluctuate more than others.
The distinction between boom-and-bust species and leveling species is a
step in this direction.
But it is also necessary to understand that once in a great while, the
population of a leveling species may grow with a rapidity that is reminiscent of boom-and-bust species. This happens when environmental constraints that have been limiting the population are suddenly eased. If, for
example, a species invades a new habitat or is introduced into one and
finds a vast abundance of resources but no predators or parasites, it will
grow wildly.
Growth in response to an unexpected windfall cannot outlast the resources that provoke it, however. The increase of the population exhausts
the resources that make it possible, and the population crashes. The collapse is more drastic than it would be for a boom-and-bust species because
leveling species are not adapted to die back and rebound. The reimposi-
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FIGURE 5. Population growth of the United States as predicted by Pearl
and Reed in 1920, on the premise that it would follow a logistic course
(solid line), and as determined by census (dots). Pearl and Reed
calculated that an upper asymptote represented by the dashed line would
limit the population to about 197 million.
tion of environmental constraints, which is sudden and profound, affects
mature individuals as well as infants and elderly. Young adults, who might
survive ordinary environmental fluctuations, have no advantage. It is a
matter of chance whether any remain to replenish the population.
The windfall effect has been documented through the introduction of
reindeer on St. Paul Island and St. Matthew Island in the Bering Sea. In
both cases, a deep mat of reindeer moss that had become abundant before
the herds were introduced made possible rapid population growth. But this
population growth depleted the reindeer moss far faster than it could grow
back. When the populations had exceeded what the remaining reindeer
moss could sustain, they collapsed. On St. Paul Island, where limited hunting was allowed, the herd grew from 25 to 2,000 in 37 years, and then fell,
over the next 12 years, to 8 (Scheffer 1951). On St. Matthew Island, where
there was little or no hunting, the population grew from 29 to about 6,000
21
DAVID PRICE
over 19 years, and then fell abruptly to 42. This figure included 41 females
and only one, apparently dysfunctional, male (Klein, 1968) (see Figure 6).
HUMAN POPULATION GROWTH
Homo sapiens is clearly a leveling species, and over the many thousands of years when humans got their living as hunters and gatherers with
a relatively unchanging technology, their population was probably quite
stable—growing very slowly, if at all. But the ability to use energy without
having to channel it through their bodies put a great windfall at the disposal of human beings, who learned to employ energy from many sources
for their own purposes. Among these sources were draft animals, wind,
falling water, and, most significantly, fire. Homo sapiens evolved in the
presence of fire (for fire had already been tamed by Homo erectus), and the
ability to manage fire distinguishes Homo sapiens from all other animals.
Some of the early uses of fire—for cooking, warmth, protection, and eventually ceramics and metallurgy—undoubtedly conveyed adaptive advantages that stimulated population growth. But the great explosion of humanity during the past three hundred years results from the use of fire to unlock
the energy in fossil fuels (Price, 1995).
The energy in fossil fuels derives, originally, from solar energy trapped
by the riotous plant life of Carboniferous swamps, which has been processed in the bowels of the earth for more than three hundred million
years. The energy in fossil fuels is relatively concentrated, and deposits are
relatively easy to exploit. Fossil fuels return a huge amount of energy in
proportion to the labor required to get them out of the ground and process
them into a usable form; they are relatively easy to transport, and the technology of controlled combustion by which they are made to deliver their
energy is relatively simple. The return on investment given by fossil fuels is
so great that commercial energy is extremely cheap. An amount of energy
equal to that used by a person who works all day, burning up 1,000 calories worth of food, can be bought for less than ten cents (Loftness, 1984, p.
2).
This enormous windfall has spurred fantastic growth in human population. Like the thick mat of reindeer moss that accumulated before the
introduction of reindeer to St. Paul and St. Matthew Islands, fossil fuels
accumulated before the evolution of a species that could exploit them. But
once Homo sapiens appeared and developed the appropriate technologies,
fossil fuels could be used to raise and market vast amounts of food, to
22
POPULATION AND ENVIRONMENT
FIGURE 6. The windfall effect, illustrated by the growth and crash of reindeer
populations on St. Matthew and St. Paul Islands (after Scheffer, 1951, and
Klein, 1968).
make clothing and build dwellings for enormous numbers of people,
and to develop measures that reduce infant mortality. The use of fossil
fuels has allowed world population to grow from about five hundred
million, on the eve of the Industrial Revolution, to six billion. This is a
population that cannot be sustained when the windfall that promoted it
is exhausted.
Optimists believe that other sources of energy can be substituted for
fossil fuels before they are all used up. They fail to see what a rare event
the exploitation of fossil fuels has been, and how unlikely it is that humans can develop a similar energy windfall that will extend its effect.
About 75 percent of the world's commercial energy is now furnished by
23
DAVID PRICE
fossil fuels,5 and at current rates of consumption, known reserves of petroleum will be gone in about thirty years, natural gas in fifty years, and coal
in some two hundred years (WRI/IIED, 1990, p. 145).6 It is not probable
that a source of energy capable of supplanting fossil fuels can be developed and commercialized in this time.
The most promising sources of alternative energy are biomass, hydropower, nuclear fission, and nuclear fusion. But biomass conversion, which
involves growing plants for their energy content, competes for fertile land
with food crops and timber.7 The construction of huge dams for additional
hydropower would flood human settlements and valleys with rich agricultural soils.8 Fission-based nuclear power plants could supply much
more energy than they now do, but new construction is tangled in safety
issues.9 Controlled thermonuclear fusion may or may not be commercially
feasible, environmentally safe, or ready to come on line before petroleum
runs out.10 Other alternative energy sources, such as windmills, geothermal
generators, photovoltaics, and solar-thermal cells, furnish only a tiny part
of current energy needs" and any significant increase would require the
construction of an unimaginably huge infrastructure. The potential of
waves, tides, ocean thermal energy conversion, and geothermal sources is
severely limited by the accidents of geography.
In sum, the worldwide explosion of human population is best accounted for as a windfall effect consequent to the exploitation of fossil
fuels, which release a vast amount of energy with a very modest energy
investment. There is no other energy source that can provide as much energy, as efficiently. And even if some alternative source could provide a
huge new supply of cheap energy, the course of the windfall effect would
not be altered. Population would just grow to a yet higher level, under the
stimulus of the additional energy resource, before exhausting it and collapsing. The earth has no "carrying capacity" for a human population in
excess of its current level, and damage to planet-wide systems resulting
from the maintenance of a population in the billions may negatively affect
the possibility that even a tiny population regulated by density-dependent
mechanisms can survive in the future.
ACKNOWLEDGMENT
Several readers have made useful comments on earlier drafts of this
paper, but I am especially grateful to David Pimentel for his constant encouragement.
24
POPULATION AND ENVIRONMENT
ENDNOTES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
The logistic equation actually implies both that smaller populations grow to this limit
and that larger populations fall to it—or put another way, that populations tend to approximate this limit. But Pearl was primarily interested in growth.
Translation mine.
Parry (1981, p. 262) points out that "there do not appear to have been any studies in
which the selection pressures responsible for the observed life-history characteristics can
be unequivocally attributed to the amount of crowding."
Many authors have lamented the "r- and k-selected" terminology, and Hutchinson
(1978) refers to the reproductive patterns of the two types of species as "prodigal" and
"prudent." This is a step in the right direction, but my usage is more ambitious, with
terms intended to name not just reproductive patterns but adaptations to environmental
variability.
It is not necessary to suppose that k-selected (or leveling) species evolve through
group selection (as MacArthur and Wilson originally thought); it is quite possible for
them to evolve through individual selection, as pointed out by Roughgarden (1971).
Figures from Energy Information Administration 1992, pp. xv-xvi, adjusted to include
biomass as reported in World Resources Institute and International Institute for Environment and Development 1988, 111.
These are reserves known in 1988, depleted at 1988 rates. I have subtracted from the
figures cited to account for time already elapsed.
Biomass energy, which comes from alcohol, wastes, and wood used as fuels, currently
provides about 15 percent of the world's energy (WRI/IIED, 1988, p.111). Greater use
could undoubtedly be made of biomass, but nearly a quarter of the world's population
may already rely on firewood that is being cut faster than it will grow back (Corson,
1990, p. 199).
Hydropower now furnishes about 5.4 percent of the world's energy (figures from Energy
Information Administration 1992, pp. xv-xvi, adjusted to include biomass as reported in
WRI/IIED, 1988, p. 111). Weinberg and Williams (1990, p. 147) calculate that the potential for hydropower may be as much as five times greater.
Nuclear power plants now supply about 5 percent of the world's total energy needs
(figures from Energy Information Administration 1992, pp. xv-xvi, adjusted to include
biomass as reported in WRI/IIED, 1988, p. 111). Fission reactors could produce a great
deal more if fast-breeder reactors were used. But anyone with a fast-breeder reactor can
make nuclear weapons, so there is considerable political pressure to prevent their proliferation.
The "fuel" for fusion reactions would be deuterium, which can be extracted from ordinary water. There is one deuterium atom for every 6,700 atoms of ordinary hydrogen,
and the energy from one percent of the deuterium in the world's oceans would be about
five hundred thousand times as great as all the energy available from fossil fuels. But
current experiments involve the fusion of deuterium with tritium, which must be made
from a rare lithium isotope (Loftness, 1984, p. 52). If a deuterium-only reaction should
be feasible, energy prospects would improve dramatically, but we do not yet know
whether this can be done. Moreover, a global network of fusion reactors would release
an unacceptable amount of heat into the earth's atmosphere.
In the United States, for example, such sources provide only about 0.3 percent of the
commercial energy consumed (Energy Information Administration 1991, p. 111)
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DAVID PRICE
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