1. Introduction
In the late 1960s and early 1970s the discussion about looming limits of the Earth’s carrying capac-
ity due to population and economic growth initiated the widespread development of environmental
awareness e.g. Ehrlich, 1971; Meadows et al., 1972. Exponential growth of the human popula-
tion and economy, and some of their upper limits e.g. food availability, arable land, nonrenewable
resources
were identified.
Other unknown
upper limits causing irreversible changes in climate, or interrupting severely vital natural processes,
were alluded to or predicted. Later, this discussion also highlighted consumption patterns in industri-
alized countries and their technologies as further pressures on Earth’s carrying capacity e.g. Daily
and Ehrlich, 1992, 1996; Srivastava and Ruesink, 1998. Presently, not many people doubt the rapid
decline and deterioration of environmental re- sources e.g. freshwater, fish stocks, biodiversity,
soil, minerals, fossil resources, the overuse of ecological sinks e.g. waste assimilation in air,
water, soil; Brown, 1998, and the fact that such overuse deteriorates and destroys ecosystems and
ultimately living conditions of humans and other species. Undoubtedly, the concept of carrying
capacity has played a significant part in promo- ting public and political awareness and understand-
ing of looming and existing limits to economic activity.
However, as will be demonstrated, attempts to apply the concept of carrying capacity to socio-eco-
nomic sectors such as tourism or the management of natural sites, and to ecosystems have not been
successful. Either the results have been unreliable or the concept of carrying capacity has been
profoundly modified as in applied ecology, human ecology to make it operational.
The political importance of the concept on the one hand and discontent regarding its applications
and modifications on the other motivated this current investigation of carrying capacity. The aim
of the paper is to provide an improved understand- ing of the concept, its history, its aims, its charac-
teristics, and its flaws, and to clarify where and how it can be applied.
As Malthusian thinking is still perceptible in this concept, the study begins with an examination of
Malthus’ treatise on the development of population. This treatise had a major influence on Darwin and,
subsequently, on later biologists, as well as on the incipient science of demography. Both disciplines
— biology and demography — provide the bedrock of the concept of carrying capacity as it is applied
and used in environmental policy and discussion. However, major modifications of the biological and
demographical understanding of the concept of carrying capacity within the fields of applied ecol-
ogy and human ecology have been made. It is argued that the concept is a normative one as soon
as it is applied in fields where human activity is involved. This implies a considerable role for value
judgments and institutional settings in formulating carrying capacity and deducing policies.
2. Malthus and his influence on Darwin and on human demography
The Reverend Thomas Robert Malthus’ 1766 – 1834 An Essay on the Principle of Population
Malthus, 1986, 1st edition of 1798 has undoubt- edly been a long-lasting, broadly discussed and
culturally absorbed contribution to the overall views of the 19th and 20th centuries. His theory
about human population growth can be considered as providing a basis for the concept of carrying
capacity. This is mainly because of Malthus’ great influence on Darwin’s concept of natural selection,
the foundation of modern evolutionary biology and ecology, and finally because of Malthus’ influence
on the incipient science of human demography.
What are the essentials of Malthus’ theory? There are three basic assumptions, the first being that food
was considered to be necessary for the existence of man and to be the sole limiting factor on human
population growth. Secondly, Malthus put major emphasis on the assumption that the human pop-
ulation increases geometrically exponentially, 1, 2, 4, 8, 16, 32… as God gave humans an
unchanging force of sexual passion. However, the idea of exponential growth was deduced by
Malthus from population growth in North Amer- ica and was not observed elsewhere at his
time.
2
Interestingly, in North America immigra- tion largely accounted for the exponential growth,
a point ignored by Malthus. Lastly, he took for granted that food production could only be in-
creased linearly 1, 2, 3, 4, 5… and that this would lead to food shortage given the geometrical
growth of population. These three assumptions form the basis for Malthus’ explication of the
scarcities and misery he observed in England, and for his prediction of everlasting food shortages
and poverty. Hence, he declared, paucity in food and consequent ‘vice and misery’, which he con-
sidered as being always with mankind as biblical texts indicate, to be ‘checks’ to population growth
imposed by the prescribed bounds of nature Bowen, 1954, p. 88ff..
Malthus’ Essay met with an approving audi- ence and only a few suspicious critics see Bowen,
1954, p. 81ff.. The positive reception of his Essay was principally because his general thesis pleased
nearly everybody. Capitalist apologists as well as those who defended the landed interest agreed
with Malthus’ stance that population tends to outrun subsistence. Furthermore, his theory fitted
in with all schools of classical economics which used it for their own ends Worster, 1985, p. 84.
Beside such rather ideologically-based support, it has to be noted that Malthus was, as Bowen puts
it, ‘‘a brilliant publicist… and… a ‘philosopher’ who first saw the importance of the limiting fac-
tors of environment on human material pro- gress.’’ Bowen, 1954, pp. 95 – 96.
3
Finally, it has to be stressed that Malthus’ theory reflects the
overall societal situation and mind of the industri- alizing Victorian England. So, it is not pure inven-
tion to conclude that Malthus’ success is largely due to his excellently presented ideas which
reflected the overall circumstances of his time and concurred even with opinions and judgments of
broad public sectors otherwise opposed to one another. However, not all of Malthus’ approving
readership might have agreed with his ideological standpoint that measures to reduce poverty and
misery are in vain.
Malthus’ great success is in fact astonishing because his very rough, unrealistic assumptions
were not proven by any empirical evidence. De- spite criticism, Malthus initially refused to admit
any restraints on human population growth and institutional influences on reproduction. It is only
in the 2nd edition 1803 of his treatise that he began to admit some existing restraints on popu-
lation growth, namely moral restraints, and insti- tutional influences on these moral restraints. He
did so by suggesting that income equality and common ownership of property would offset any
moral restraint Bowen, 1954, p. 93. Acknow- ledging the influence of institutional settings on
population development made ‘‘his case… explic- itly a political case… and [it] no longer rested on
inexorable demological tendencies’’ Bowen, 1954, p. 93. Furthermore, Malthus only considered
food as a limiting factor, but other constraints also exist e.g. housing, health, energy. Another
critical point which, however, was not stressed in Malthus’ time is the fact that he put humans and
other species on the same level,
4
and that he
bounds. What were unprecedented in Malthus’ argument were the ironclad ratios and his warnings of impending national
apocalypse.’’ Worster, 1985, p. 152. Also, Schumpeter states that all facts and arguments Malthus put forward had already
been developed by many other authors before so that Malthus’ ideas had already been widely accepted in the 1790s Schum-
peter, 1965, p. 706. It is worthwhile to note that geometrical population growth was already discussed in demographical
research of the 17th and 18th century. Thus, Malthus’ assump- tions about population growth were not new see the perusal
of scientific demography from 17th century onwards in Hutchinson, 1979, pp. 5 – 21.
4
Young 1969 p. 129 quotes Malthus as saying: ‘‘... it is not to be supposed that the physical laws to which he [man] is
subjected should be essentially different from those which are observed to prevail in other parts of animated nature.’’
2
Observed patterns of global population growth during the last thousand years indicate that different human populations
have different exponential growth curves. Nevertheless, it is important to note that during the last 1000 years, the periods
in which the global population doubles have become shorter and shorter see Cohen, 1995a, p. 94.
3
It has been claimed Malthus had ideological aims as a publicist. Bowen writes: ‘‘…a brilliant publicist who wished to
attack existing social legislation, and also to attack ‘specula- tions’ upon possible improvement of existing institutions of
government and property’’ Bowen, 1954, pp. 95 – 96. Worster notes, that ‘‘[t]here was nothing new in the idea that there are
strict limits to population capacity of any area. The Linnaean naturalists, for example, had long been emphatic about the
need for restraints to keep each species within its prescribed
adopted the mechanistic view of nature common among the naturalists of the 18th century. This
allowed him to abstract the individual organism including the human being from its place in
nature and society, considering it as an atomistic part with a fixed and independent set of qualities
instilled by God, adapted to the environment by mere mechanical arrangements Worster, 1985, p.
152. To sum up, it has to be stressed that Malthus’ theory is based on normative assertions
and on a mechanistic conception of nature and society.
Malthus’ role in the formation of Darwin’s ideas and his influence on the overall evolutionary
thinking of the 19th century is unequivocally evi- dent Young, 1969. Darwin adopted Malthus’
views of populations growing geometrically, and of restraints posed by limited resources. In his
Essay of
1844
, Darwin wrote: ‘‘Even slow-breeding mankind has doubled in
twenty-five years, and if he could increase his food with greater ease, he would double in less
time. But for animals, without artificial means, on an a6erage the amount of food for each
species must be constant; whereas the increase of all organisms tends to be geometrical, and in
a vast majority of cases at an enormous ratio.’’ Darwin, 1958, p. 117.
The idea of population pressure was central to Darwin’s development of the concept of natural
selection and hence of a mechanism to explain biological diversity and evolution. In Darwin’s
The Variation of Animals and Plants under Domes- tication
[1868]
, we read: ‘‘I saw, on reading Malthus on Population, that Natural Selection
was the inevitable result of the rapid increase of all organic beings’’ Darwin, 1969, p. 10. Fur-
thermore, Darwin revealed in his Autobiography:
‘‘In October 1838, that is fifteen months after I had begun my systematic enquiry, I happened
to read for amusement Malthus on Population, and being well prepared to appreciate the strug-
gle for existence which everywhere goes on from long-continued observation of the habits
of animals and plants, it at once struck me that under these circumstances favorable variations
would tend to be preserved, and unfavorable ones to be destroyed. The result of this would
be the formation of new species.’’ Darwin, 1993, p. 120.
Darwin’s reference to Malthus and his ideas clearly indicate a substantial influence of Malthus
on the most influential biological theory. However, Malthus’ influence was not limited to
biology as studies of human demography were also based on his ideas for a long time. In review-
ing developments in demography, Back 1983, p. 123 writes:
‘‘…[T]he manner of reasoning he [Malthus] employed, looked at population as a practically
self-propelled unit. We have the image of an expanding mass straining against the constraint
of natural resources. What is missing from this picture is the characteristically human ability to
plan, to think and to organize. Demography has followed this path for a long time…’’
The Malthusian idea of an uncontrollable pop- ulation growth only restricted by the bounds of
natural resources was first put into a mathemati- cal equation describing human population growth
by Pierre F. Verhulst, Professor of Mathematics in Brussels, Belgium, in 1838 Verhulst, 1838.
5
He checked the results of the equation with cen- suses of population developments in France, Bel-
gium, Russia and in Essex, England, over 20 years in the early 19th century and found confirming
results.The equation of logistic growth is:
dN dt
= rN
K − N K
where N is the population, r is the growth rate and K is the carrying capacity.
5
Verhulst wrote: ‘‘We know that the famous Malthus estab- lished the principle that human population tends to grow in
geometrical progression… This proposition is incontestable…’’ Verhulst, 1838, p. 113, translation by the authors.
One term of the logistic growth introduced by Verhulst is the constant relative growth rate later
called the Malthusian parameter r r = [birth rate b − death rate d]. It represents Malthus’ assump-
tion of exponential growth see Fig. 1. The equa- tion is:
dN dt
= rN
However, the existence of permanent geometri- cal exponential growth which is what Malthus
and his predecessors thought in principle about the inherent growth of populations, must be re-
jected as it does not include an upper limit Hutchinson, 1979, p. 3. Such growth can only be
observed for short time periods. Therefore, Ver- hulst’s equation takes into account limits to popu-
lation growth carrying capacity K
, which in Malthus’ terms stands for the shortage of food.
At K the birth rate equals the death rate leading to a stable or equilibrium population size dN
dt = rN = O, r = O see Fig. 1. Through the introduction of the term K − NK the growth
rate dNdt raises to a maximum as N reaches K2, and than falls asymptotically to zero as the popu-
lation N approaches K.
Nearly a century later, in 1920, Raymond Pearl, Professor of Biometry and Vital Statistics in Balti-
more Maryland, and his colleague Lowell J. Reed, probably unaware of Verhulst’s work, also
formulated a logistic growth curve, and fitted it to US census data Pearl and Reed, 1920. However,
both Verhulst’s and Pearl and Reed’s applications of this curve to empirical data are doubtful be-
cause of their failure to take account of immigra- tion deduce it from r and, in the case of Pearl
and Reed, the expansion of the American land frontier Cohen, 1995a, p. 85. Other than for a
short time span, their empirical data did not allow a reliable verification a fact Verhulst admitted
[1838, p. 115]. Yet, Pearl was successful in pro- moting his work which resulted in his and Verhul-
st’s name being attached to the curve now widely known as the Verhulst – Pearl logistic equation.
Since the development of this logistic equation, there have been numerous applications in which,
however, the equation has only sometimes been confirmed by empirical data for short time peri-
ods. It seems ‘‘that the logistic curve works until it doesn’t.’’ Cohen, 1995a, p. 87. A major reason
for this missing empirical confirmation might be the rigid assumptions of the logistic growth equa-
tion; the parameters r and K are not supposed to change in time, the environment is supposed to
provide a steady supply of nutrients and re- sources, the spatial boundaries of populations are
assumed to be fixed and known, the system is closed allowing no immigration or emigration, no
import or export Cohen, 1995a, p. 84.
With the introduction of the logistic growth equation, Malthus’ assumptions about population
growth and limits had finally found a mathemati- cal expression. However, empirical evidence in
support of these assumptions remain slight and there is also much uncertainty about demographic
and social developments, and ecological capacities and reserves. Hence, estimates about the carrying
capacity of the Earth, conducted in the second half of this century, vary largely and the results
range between less than 1 billion and 1000 billion people which can be supported by the Earth
Cohen, 1995b, p. 342.
Given the demographic transitions which had occurred in countries showing considerable eco-
nomic growth, increasing doubts were expressed about the value of Malthus’ theory as a predictor
of the growth of human population. Many high- income countries have experienced low or even
negative rates of net population growth. Some writers e.g. Leibenstein, 1957 suggest that
Malthus’ theory may hold in the circumstances of low income but not of higher levels of income,
e.g. due to escape from low-equilibrium trap Leibenstein, 1957 or changes in the net benefit
of family size Becker, 1960.
Fig. 1. Exponential and logistic population growth curve.
The joining and mathematical representation of Malthus’ assumptions of exponential growth and
existing limits to growth was an important first step in the development of the paradigm today
known as carrying capacity. In conclusion, the considerable impact of Malthus’ assumptions can
be attributed to their broadly favorable reception in his lifetime, to his influence on Darwin, and
consequently on biology, and also to the fact that the new science of demography initially adopted
Malthusian ideas.
3. Carrying capacity in biology and ecology