tion between a population and the environment. What qualifies as an injury, what does it mean to
say ‘without injury’? Normative judgments may well be inescapable in such evaluations.
A similar definition was introduced a decade later by Leopold Hawden and Palmer, 1994, p.
141. He defined carrying capacity as the maxi- mum density which a particular range is capable
of supporting Dhondt, 1988, p. 339. Since the definitions of HawdenPalmer and Leopold many
others have been formulated which restate, vary, or develop these basic ones see Dhondt, 1988;
Pulliam and Haddad, 1994. All these definitions, however, are, as Pulliam and Haddad 1994
point out, a poor descriptor of the dynamics of many natural populations. An important reason
for this is the complexity of actual ecosystems. Their biotic interactions and multiple steady
states are characterized by nonlinear dynamics and population thresholds which are all influ-
enced and modified by environmental variations in space and time e.g. exogenous disturbance.
Hardin states: ‘‘There is no hope of ever making carrying capacity figures as precise as, say the
figures for chemical valence or the value of the gravitational constant. On St. Matthew Island the
growth of reindeer moss is no doubt greater in some summers than others…’’ Hardin, 1986, p.
600.
In principle, there are at least three major rea- sons why the simple logistic model of population
growth may be a poor predictor in practice: 1. Exogenous environmental forces may cause
variation in the carrying capacity, K, or in the Malthusian parameter, r, or in the lag involved
in the response of a population. While these variations are frequently temporary, they can
also be permanent.
2. Variations in population sizes may cause K, r, or the lag-factor to alter permanently. For
example, a sudden and large increase in the population of a species may permanently de-
stroy environmental resources which the spe- cies utilizes to some extent, or populations in
particular ranges may slowly and irreversibly degrade their environment. These environmen-
tal alterations are internal to the system, often exhibit hysteresis and can occur either in the
absence of exogenous environmental change or due to human intrusion.
3. Exogenous environmental variation combined with certain sizes of population may bring
about permanent alterations in the coefficients of the logistic model. In other words, interac-
ti6e permanent effects can easily occur between the state of the environment and particular
population sizes.
McLeod 1997 analyzed different models and methods for determining and calculating carrying
capacity, and showed that complex characteris- tics, uncertainties and stochastic environments
cannot be overcome or captured by these models. Rather, the concept of carrying capacity can only
be calculated for deterministic and slightly vari- able systems, and only for cases where behaviour
and ecological relationships of the species change slowly on the human time scale Cohen, 1995a, p.
247. In variable environments, carrying capacity might be useful as a measurement of short-term
potential densities as a function of resource availability but not of long-term equilibrium den-
sities McLeod, 1997, p. 540.
4. Application of carrying capacity to environmental impacts of human activity
Since the late 1960s and early 1970s, the con- cept of carrying capacity has been applied to
capture, calculate, and express environmental lim- its brought about by human activity. Two main
areas of application can be distinguished. First, in applied ecology application of basic ecology to
human aims and aspirations, the concept of car- rying capacity is employed in relation to manage-
ment of particular habitats or ecosystems like rangeland or wildlife, and to management of
tourism for example, in national parks, tourist resorts. Second, carrying capacity has been em-
ployed in human ecology analysis of interactions between individuals, environment and society,
and of demands of humans towards the environ- ment to discuss and illustrate the ecological im-
pacts and limits of the growing human population and rising consumption. As will be shown, both
of these new applications brought about major
modifications to the concept, alienated it ever more from Malthus’ initial ideas and thereby sup-
ported some of the principal criticisms. Most im- portantly, it has become evident that the concept
has an important normative and institutional component. A judgment of an environmental situ-
ation or the decision of limits — e.g. the carrying capacity — is influenced by value-judgments and
institutional settings.
Cohen 1995a, p. 248ff. mentions at least five distinct concepts of carrying capacity that exist in
applied ecology, each of which entails different aims of management or different institutional
backgrounds. According to Cohen these concepts vary depending on whether the aim is to maximize
i the standing stock of a population plantsani- mals, ii the steady yield of the population, iii
the number of protected plants, whether iv the harvested population is subject to discounting,
and v the population is an open-access resource, subject to revenue and cost curves. Consequently,
the comprehension of carrying capacity depends on the pursued aims. This becomes particularly
clear from the example of rangeland management in Zimbabwe investigated by Scoones 1993.
There, management decisions are based on two types of carrying capacities — an economic and
an ecological one. Moreover, each category of carrying capacity itself exhibits a range of possible
levels dependent on aims, farming methods and ecological features. For instance, the economic
carrying capacity varies depending on productiv- ity objectives and land availability: whether farm-
ers aim at maximizing weight of beef produced or protein output, or whether they pursue multiple
objective farming in which cattle are used as draught animals and are kept for production of
meat, milk, and calf, and finally whether farmers can move them somewhere else in case of
droughts. These aims and conditions determine the economic carrying capacity and the ecological
one as well, and, in consequence, the most ade- quate management strategies. Further, farming
methods affect the ecological carrying capacity. For instance, in periods of drought, farmers in
Zimbabwe move their animals to other areas, and consequently relieve the pressure on pasture land.
Their rotational grazing strategy and use of a few preferred grazing areas e.g. riverbanks, drainage
lines also determine carrying capacity levels. Ad- ditionally, these ecological carrying capacities
themselves vary as a function of a wide range of ecological dynamics which must be understood to
assess ecological carrying capacities. This complex network of different objectives, particular farming
methods and ecosystem dynamics have to be taken into account for determining carrying ca-
pacities. Therefore, as Scoones concludes, ‘‘it is essential… that planning is locally based with
farmers, with local knowledge of resources and their use, being the primary participants in design
and development.’’ Scoones, 1993, p. 114.
In a similar vein, in tourism, different defini- tions of carrying capacities and a multitude of
aims lead to equivocal applications. Carrying ca- pacity in tourism is conceived as a maximum
number of visitors that can be tolerated without irreversible or unacceptable deterioration of the
physical environment and without considerably diminishing user satisfaction see also Mathieson
and Wall, 1982, p. 21; Tisdell, 1988, p. 244; Davis and Tisdell, 1996, p. 232. Needless to say that it
is difficult to determine such a number. As Mathieson and Wall 1982, p. 21 point out,
separate capacities exist for each of the economic, physical or environmental and social subsystems
of relevance see also Davis and Tisdell, 1996, p. 232. Lindberg et al. 1997 express considerable
discontentment with the concept of carrying ca- pacity in tourism see also Tisdell, 1988, p. 88;
Davis and Tisdell, 1996. They claim that the concept is ‘not adequate to address the complexity
found in tourism situations’. In particular, they criticize the concept as being imprecise, a fact
which hinders its operational specification. Fur- thermore, the subjectivity of the concept is often
not realized by policy proponents who often per- ceive it as a scientific, objective concept. Finally,
in its application to tourism planning, Lindberg et al. 1997 consider that its focus on tourist use-
levels or numbers of visitors involves misguided simplicity, and instead they advocate a focus on
site conditions. Mathieson and Wall 1982, p. 21 do not go as far but state nevertheless that there
is a ‘need for clear and precise statements of goals, and assessments of the extent to which
these goals are realized’. Again, the concept of carrying capacity only becomes operational if i
the question about the desired conditions is asked and answered, if ii sociopolitical, economic and
subjective components are taken into account, and iii concerned parties are involved — but, so
far, this has rarely been incorporated into ideas of tourist carrying capacity. From the above discus-
sion of the application of carrying capacity in applied ecology, it is clear that it involves norma-
tive characteristics and multiple levels often vary- ing with objectives. Thus, carrying capacity by
default is ambiguous.
Another application of carrying capacity to hu- man society stresses that nature’s bounds can be
transgressed by rapidly growing population, accel- erated use of natural resource and society’s inter-
ference with
ecological systems
and cycles
Ehrlich and Holdren, 1971; Holdren and Ehrlich, 1974; Hardin, 1986. The ‘little change’ of the
concept of carrying capacity which Hardin 1986, p. 602 considered necessary to apply it to human
population and to illustrate the natural limits, in fact has to be profound if the concept is to be of
any practical use in the new context. Actually, the newly titled concept of human or social carrying
capacity implies a deep transformation and devia- tion from the initial biological and demographical
positivist concept as is illustrated below.
The application of carrying capacity to the human species requires the recognition that the
carrying capacity is foremost socially determined, rather than biologically fixed due to the important
influence of human consumption patterns, tech- nologies, infrastructure, and impacts on the envi-
ronment or food availability. This is captured by the differentiation between biophysical carrying
capacity K
B
and social carrying capacity cul- tural or human carrying capacity, K
S
, and the acknowledgement that the former can only be
higher or equal than the latter K
B
] K
S
Ehrlich and Holdren 1971; Hardin, 1986; Daily and
Ehrlich, 1992. Biophysical carrying capacity K
B
expresses ‘the maximal population size that could be sustained biophysically under given technologi-
cal capabilities’, whereas social carrying capacity K
S
specifies ‘the maxima that could be sustained under various social systems’ Daily and Ehrlich,
Fig. 2. Biophysical K
B
and social K
S
carrying capacity.
1992, p. 762. K
S
represents higher or equal consumption and pressure on the environment
and thus is lower equal than K
B
. As Hardin 1986, p. 603 puts it: ‘‘Carrying capacity is in-
versely related to the quality of life.’’ Both kinds of carrying capacity are illustrated in Fig. 2.
These two different carrying capacity levels and their consequences on optimal population size can
also be illustrated by a simple model Fig. 3 which represents a society with a given technology
and which describes the relationship between in- come or consumption per head y, and population
number N, by the function y = fN.
The function y = fN represents a commonly- assumed theoretical relationship between popula-
tion level and income or consumption per head. It is based on the assumption that the productivity
and hence income and consumption of a human population increase with the growth in population
size at low population level, but eventually de- clines with increasing population number because
of economic constraints e.g. resources, infrastruc- ture. y
B
depicts income or consumption which is
Fig. 3. Economic model allowing for biophysical and socially determined subsistence levels.
possible at biophysical carrying capacity K
B
minimum subsistence level. It represents a lower equal income or consumption compared with y
S
which is the income or consumption related to social carrying capacity K
S
y
B
5 y
S
. As y
S
in- creases the maximal population number or carry-
ing capacity declines or remains equal. The minimum population size N
Min
needed to achieve the socially determined subsistence level in
this model is N
S Min
, and it is higher than the biophysical minimum population N
B Min
. N
Min
as an economic concept can be compared with ‘min-
imum viable population’ in biology. This model initially exhibits economies of scale. The maxi-
mum population size which satisfies the biophysi- cal subsistence level is N
B Max
, and is greater than that providing the socially determined subsistence
level N
S Max
. Another major variation in the concept of car-
rying capacity has been the introduction of dam- age or impact to the Earth’s ecological system.
These terms have been used by some authors e.g. Daily and Ehrlich, 1992 to replace the predomi-
nance on population-number of the initial con- cept. These authors suggest that limits to human
population are set by total damage of the global population rather than by population number per
se. The new focus, impact, instead of maximum population K, stresses the significance of institu-
tional settings, human values, traditions, eco- nomic and consumption patterns, distribution,
and infrastructure even more. The normative na- ture and need for value judgements for the opera-
tionalization of this notion of carrying capacity is manifest.
Daily and Ehrlich 1992, p. 762 consider this impact I to be a product of three interdependent
factors: the population’s size P, its affluence or per-capita consumption A, and the environmental
damage T, inflicted by technologies: I = PAT. Daily and Ehrlich’s notion of impact implies that
there are different levels of carrying capacity de- pending on value judgments and predominant
system dynamics. Society can opt for different levels of carrying capacity, it can even opt for
levels which allow it to stay within the limits avoiding significant irreversible degradation, but
which can mean degradation of the environment
Fig. 4. Carrying capacity depends on the nature of the social welfare function.
nonetheless. Pulliam and Haddad 1994, p. 154 explain this with the example of biodiversity.
‘‘Loss of biological diversity degrades the environment by lowering living standards and
closing options for future improvement. How- ever, this loss can be sustainable; life, albeit
impoverished, may go on in perpetuity in the presence of fewer species.’’
The impact-concept illustrates the need for many far-reaching decisions. Cohen 1995a, p.
262 discusses a dozen examples of choices neces- sary to answer the question of how many people
the Earth can support. Such questions are for instance: What average level of material well-be-
ing should we choose and how should well-being be distributed? What technology should we use?
What domestic and international political institu- tions, economic and demographic arrangements
should we adopt? Which physical, chemical, and biological environments do we want to live in?
What time-scale should we consider?
If we assume that the value-laden, normative answers to these questions are expressed in a
welfare function of a Bergson-type Bergson, 1938, the resulting optimal level of human popu-
lation can be graphically illustrated by a simple model as shown in Fig. 4. In this model, which is
of a similar type of that in Fig. 3, utility per head rises at a decreasing rate as the population grows.
Utility or well-being per head U is a function of population size N. In the case U = gN where
g¦B0, U is shown by the curve marked HJKLM. J represents the maximum individual utility and
occurs at a population size of N
2
. Beyond this point social utility keeps on rising up to a point
N
3
if the set of social welfare functions repre- sented by W
B
apply. However, if the set of social welfare functions W
A
indicated in Fig. 4 apply, social utility will rise until population reaches N
4
. The socially optimal population size ‘social car-
rying capacity’ is therefore determined by the chosen social welfare contours W
A
, W
B
, and so on. As Fig. 4 indicates, carrying capacities de-
pend on normatively based social welfare func- tions see also Tisdell, 1990, p. 160. If higher
welfare contours as those indicated in Fig. 4 were chosen this would mean that the carrying capacity
will be transgressed.
Discussions of welfare economics indicate that the welfare curve of Bergson-type cannot be es-
tablished objectively by adding up individual utili- ties Rothschild, 1993, p. 71. Other approaches
seem necessary to bring population number and human welfare into a relationship which is so-
cially
acceptable for
present and
future generations.
One attempt to approach social welfare func- tions is to make use of ideas and expressions of
society about how to live and what to aim for. This can provide an image of social carrying
capacity, making this concept more concrete. Au- thors like Daily and Ehrlich 1992, p. 763 fall
back on normative concepts which focus on con- ditions of the environment by calling upon sus-
tainability and environmental standards. They stress the following connection:
‘‘A sustainable process is one that can be maintained without interruption, weakening, or
loss of valued qualities. Sustainability is a nec- essary and sufficient condition for a population
to be at or below any carrying capacity.’’
This definition of sustainability represents an equilibrium state like the concept of carrying ca-
pacity in applied ecology does. Furthermore, in order to determine the level of maximal sustain-
able use of resources Daily and Ehrlich 1992, p. 765 introduce the idea of a limit or threshold
‘below which the constituent stocks are so small that the resource cannot be used sustainably’. Yet,
sustainability requirements and acceptable stan- dards are influenced by human choices. Thus, it
has become clear that applications of the concept of carrying capacity to problems induced by hu-
mans leads to a shift from a positivist-type con- cept to a normative one. This shift means that
there is no longer an objective, single level of carrying capacity equilibrium population as in
the blowfly experiment. Rather it is replaced by different more or less stable states of environment
dependent on value-judgements, institutional ar- rangements, technologies, consumption patterns,
and human aims. These factors must be concili- ated, be agreed upon and considered for estimat-
ing the acceptable pressure on the environment, and for developing accompanying management
schemes. Therefore, political and social ideas and norms about technologies, institutions, consump-
tion, distribution etc. have to be discussed, har- monized and agreed upon to approach a stable
quality of the environment equilibrium situa- tion. If discrepancies become visible, in other
words, if human activities will not stay within the carrying capacity, society will have to discuss its
values, develop its technologies and institutions, and review its aims.
5. More on resilience and sustainability as an indicator of carrying capacity