A Calculation for an
Optimum Human Population

Alan Wittbecker

A number of recent studies have suggested that the human population of the earth could be much larger. Several other studies have recommended lower population numbers based on resource availability.All of these studies are concerned with finding a maximum human population. Yet, as we know, maximums are rarely stable.Human populations are limited by the biological constraints of ecosystems, by biogeochemical cycles, by our knowledge of these systems, and, possibly, by human psychological and cultural limits.Therefore, an optimum human population is calculated, using a deductive, synthetic, conceptual model based on data generated from research on net primary (NPP) and net community (NCP) productivity.A deductive approach is used because accurate measurements of trophic level productivities in most ecosystems are lacking. Its synthetic character is more appropriate to integrate quantitative and qualitative data. The model is conceptual because of the inherent fuzziness of the systems.

Assumptions and Considerations
Ecosystems result from the interaction of all living and nonliving factors of the environment (Tansley 1935). These systems are profoundly affected by both random and purposive physical and biological factors. As a result, habitats change and organisms adapt. By modifying their habitats in the process of living, organisms change the characteristics of the system and force further adaptation.More important, organisms are limited by the productivity of the system in varying degrees. Human populations (homo sapiens sapiens) inhabit specific ecosystems and are parts of them.They are adapted to and limited by the productivity of ecosystems.

The total amount of biomass or energy produced by populations through growth and reproduction is the productivity of the system.Gross Primary Production (GPP) is the rate of energy storage by photosynthesis (equal to photosynthetic efficiency) in autotrophs(plants). The maintenance and reproduction of plants is paid for by the energy expenditure of Respiration (R). The amount of energy stored as organic matter after respiration is identified as Net Primary Production (NPP), which equals plant growth efficiency.The calculation of NPP is shown by:


NPP accumulates through the history of a system as plant biomass expressed as kilocalories per square meter (Kcal/m2).The kilocalorie is used as a unit of energy flow and production;it is a useful common denominator for these calculations. The biomass minus the decomposition in a system is the standing crop biomass of that system. The problem of confusing production (amounts)with productivity (rates) is avoided by considering all values per unit area (m2) over the entire year (m2/yr).The energy stored in heterotrophs ( consumers) is referred to as secondary production (SP) or assimilation. The storage of energy or organic matter not used by heterotrophs is Net Community Production (NCP). The relationship between productivities (where Ra = autotroph respiration and Rh = heterotroph respiration) is of the order shown by:

GPP = NPP + Ra = Ra + Rh + NCP

In a balanced ecosystem, NPP equals respiration; in an accumulating system, NPP usually exceeds respiration by 1 to 10 percent. Although stable ecosystems tend to produce a maximum GPP, species, biomass,and the production to respiration ratio (P/R) continue to change long after the maximum has been achieved. In fact, as the GPP approaches an asymptote, respiration increases. In a balanced system,tropical rainforests for instance, NCP approaches zero, as adapted heterotrophs become more efficient at using production. In accumulating systems, such as grasslands or young forests, NCP can range from 20 to 70 percent. A balanced system is integrated and self-perpetuating,where production (the photosynthetic fixture of carbon) is balanced by respiration (the oxidation of carbon). As a system becomes balanced, the pressure of selection of organisms shifts; the capacity to live in crowded circumstances with limited resources is favored.Populations that depend on rapid individual turnover (r-selection)are not as successful as populations of large, long-lived individuals(K-selection). As an ecosystem ages, pressure is put on populations by other populations. Competition and predation become more complex.

Mammals are the best regulated of highly evolved species. Their behavior is controlled and population regulated through the use of space. Most populations, furthermore, regulate their density well below the limits of the food supply, often by as much as 50 to 70 percent. Territoriality can be correlated inversely with trophic levels and productivity. But populations can also be limited by:

Human beings are mammals: omnivorous, social, bipedal, featherless,symbol-using, tool-making, game-playing, neotonous, bilateral-hemispheric,generalists. Furthermore, as Woodwell (1976) put it, "humans live as one species in a biosphere whose essential qualities are determined by other species." Mammals are bound by biological requirements that must be met if a population is to survive. These functional requirements are rather minimal for humans, however,being only food, clothing, shelter, and reproduction. Other requirements,such as respect, comfort, and self-fulfillment, depend on socio-cultural systems.

Like other mammals, humans change their habitats to suit themselves.Other mammals alter their habitats through chewing, digging, and burrowing. Rodents, such as Ellobius spp. or Marmotaspp., can dislodge earth at a tremendous rate (18 to 120 m3/ha/yr).In many cases these activities improve the conditions for the growth of vegetation. Mammalian grazing promotes regrowth and the movement of seeds. Bison (Bison bison) and prairies dogs (Cynomys ludovicianus) were responsible for much of the character of the American plains. Rodent caches may account for 15 percent of Ponderosa seedlings (Pinus ponderosa).Beavers (Castor canadensis) and other rodents create their own microsystems. Wide-ranging caribou (Rangifer tarandus)transfer energy between systems. Shrews (Sorex spp.) consume major portions of larch sawfly larval populations.

Humans have modified animal and plant associations in a different way, simplifying patterns of energy and chemical exchange, solidifying themselves at the end of many food chains as a dominant species.A dominant is a species with greater influence than any other in its biotic community, changing the lives of other species and the character of the habitat. By its influence of all ecosystems,humanity has become a pandominant species. As such, humanity reclaims, overgrazes, clears, depletes, and wastes at a level that threatens the stability and existence of many systems. One of the ecological consequences of human activity is the degradation of wild habitats for human developments (food, housing, and recreation)and the introduction of novel elements into the biosphere, that is, elements that have not been added slowly over time as the result of natural processes. The biomass of the human species probably far exceeds the biomass of any nondomestic species, and that biomass is supplemented by the tremendous biomass of domestic animals, which is four times greater than the human biomass (Borgstrom,1975). This biomass forms an equivalent population that consumes much of the same food as humans, such as milk, fish, and grain.The domination of humanity is related to other characteristics as well:

This dominance has major effects on ecosystems: transient perturbations in energy relations (from oil spills, burning); chronic changes/shifts of systems (from dams, irrigation, chemical wastes); species manipulation(from the import and export of exotics); and, interference competition with wild species (as opposed to exploitative competition, which can be stabilizing). None of these effects are exclusive to humans as a species, but they are excessive, rapid, compounded, and very large-scale.

There are minimum viable populations for mammalian species(usually considered about 500 individuals). For the human species,it is unlikely that the lower limits will be approached in the foreseeable future. There are several other lower limits to keep in mind, however, as shown in Table 1. These limits are conservative estimates.

Table 1. Minimum Limits

 genetic minimum  5,000
 fertility  50,000
 ideomass  500,000
 social contact minimum  1,000,000
 for evolutionary advantage  10,000,000

There is a maximum carrying capacity for humanity. The carrying capacity is the population sustainable on a long-term basis of renewable and nonrenewable resources or energies. For humans,this capacity must include domesticates, as human equivalents,since many domesticates compete for protein consumption. Domestic animals can extend the carrying capacity somewhat, since many of them consume agricultural wastes or use lands marginal for agriculture, but they are not as efficient as wild populations.Technology could expand the carrying capacity to some extent,with higher yield crops and resource substitution, but also it could reduce the capacity with unforeseen side-effects (the use of pesticides, for example). War and social disorder reduce the ultimate capacity. Furthermore, the capacity decreases as theper capita use of energy and resources increases. Carrying capacity calculations often just consider food energy, but all needs--clothing, shelter, transportation, information generation,aesthetic satisfaction--must be included. Given the current political and technological situation for humanity, it is difficult to imagine how equilibrium could be reached without a significant reduction of human populations.

Previous Studies
Many theorists have estimated maximum or optimum sustainable populations for humanity. DeWit (1967) estimated the maximum human population at 1 trillion, 22 billion (1.022 x 10 to 12th). With 750 square meters added per capita, for forest and recreation,this number would be trimmed down to 146 billion. With consideration for animal protein in diets, 73 billion. These calculations are based on very simple variables--the light scattering coefficient(.3), leaf area index (5), and a mean synthetic rate. Apparently,there are a number of simple assumptions, also: ideal photosynthetic conditions, a strict monoculture without any natural habitats,and human occupation of the first consumer level of all food chains,thus entirely eliminating all competing wild animals. An exclusively human earth would confront its sociological, technological,and aesthetic limits immediately.

Colin Clark (1967) put the population of the earth at 47 billion,at an American standard; 157 billion on a Japanese standard. Who knows how many could have been crowded in with the lowest standard?Earlier, Clark (1958) had foreseen a population of merely 28 billion,using a Dutch standard of productivity and density (365 people per square kilometer). Apparently, he neglected to account for the ghost acreage used by the Dutch. Furthermore, he assumed a very large total arable land area--in fact, 63 percent of the total surface area of the planet (by counting the tropics twice).

Burlingh et al. (1975) estimated the absolute maximum food production of the world at about 30 times the production of 1970(and presumably an equally high human population). They arrived at this figure on a basis of quality of soil, climate, and water.It does not seem that any biological factors were considered.Weinberg and Hamilton presented a steady state model of 10 billion at 400,000 Kcal per day for the year 2050, but made no mention of how the population would stabilize at that level or what kind of economics would support it or for how long.

Most of these optimistic studies see the limits of world food supply as being determined by the physical limitation of land,water, light, and chemicals (Pirie, 1976) or by the logistics of transportation and conscience (Moore and Lappe, 1975; Gabel,1975). They assume that areas of cultivation can be expanded into planetary biological support systems, that efficiency can be enhanced(at the risk of genetic instability), and that novel sources of food will be used (ignoring cultural limitations). These requirements may never be met, as others have realized.

H. R. Hulet (1970) assumed that plant and animal products were equally necessary. By making them equal requirements--animal and plant production at 4.2 x 10 to 15th Kcal each--he suggested that the earth could support an optimum population of 1.2 billion. Considering the Law of the Minimum, he offered a series of optimum populations as a function of resources (Table 2). He concluded that as technological and agricultural systems expanded,population could also. But, the rates of use for the minimum items he provided were not renewable or slow; they were based on American standards of consumption. In America, energy use is increasing at 6 percent per annum; three times faster than the population.Therefore, resources would be limited long before a maximum population was reached.

Table 2. Population Functions (after Hulet)
 wood production (4 x 10 to 6th cal/yr/cap)  1,000,000,000
 fertilizer rate  900,000,000
 energy rate  600,000,000
 aluminum rate  500,000,000

Westing (1980) estimated a global carrying capacity based on five areas of renewable resources (Table 3). His estimates range from 1.5 to 3.9 billion. These numbers are for a maximum population,however, not an optimum. It is important to remember that an optimum is almost always less, much less, than a maximum. Note also that his paper, written ten years after Hulet's, when wood production had increased significantly, gives a doubled figure for a population limited by the availability of wood. In fact, neither Hulet's nor Westing's rate is sustainable. Annual timber cutting in the United States in 1963, for example, exceeded annual growth by 50 percent. Most cutting since then has exceeded growth by various percentages. Furthermore, wooded areas are still being cleared for agriculture, housing developments, and industrial areas. Westing recognized that most usable renewable and nonrenewable resources fundamental for human life are used in direct competition with wildlife. He commented that most studies did not consider wildlife and habitats.

Table 3. Population Estimates (after Westing)
total land
 2--3.1 billion
 cultivated land  1.5--3.3 billion
 forest land   2--2.9 billion
 cereals   1.7--3.3 billion
 wood   1.9--3.9 billion

For a straight energy calculation of an optimum population,assuming the unavailability factor has been subtracted first,refer to Table 4. The French Per Capita energy use is approximately the same as the world average. Portuguese energy use is the same as agricultural trade. The main difference between this model and earlier ones is the pattern of utilization and the assumptions of minimal waste and no growth.

Table 4. Optimum Populations (1980 Per CapitaUse)
 United States 120 x 10 to 6th Kcal  189 million
 France 4 x 10 to 4th Kcal   567 million
 Japan/Argentina   1.13 billion
 Portugal  2.84 billion
 India/China   5.27 billion

Whittaker and Likens (1975) have suggested that an agricultural world, where humanity lived as peasants, could support at least 2 billion, perhaps 5 or 7 billion. The current high levels of population, at a large range of standards, can only be maintained through the constant takeover of natural habitats for arable land,or through the draw down of fossil fuels, and by economically cheating the poor and powerless. Since the quantity of wild lands and fossil fuels is quite limited, either human populations must adjust to renewable resources or technology must provide substitutes, to avoid a population crash.

Eugene Odum (1970) suggested using land area as a measure of human carrying capacity. The minimum per capita acreage requirements,with a temperate area like Georgia as a model for a quality environment,is 5 acres (2.02 ha). The percentage of areas is broken down in Table 5. The natural areas are based on minimum space needs for watersheds, as estimated by land use surveys. Food-producing land includes acreage for domestic livestock. Extrapolating this technique to the entire planet, assuming that wilderness area has been considered in the calculation of natural areas, and converting for the differences in productivity of ecosystems, the population calculation comes to 3.969 billion. This figure is very close to the 1970 world population.

Table 5. Acreage Per Capita (after Odum)
 food-producing land  30 percent
 fiber-producing land  20 percent
 natural support areas  40 percent
 artificial areas  10 percent

Samuel Eyre, Rodin et al., and others have calculated the potential productivity of the wild vegetation of the earth at around 1.19x 10 to 11th metric tons per year. Eyre attempted to describe the wealth of nations in terms of NPP, with nutrition equivalents in NPP for mineral resources. He contended that one must know the productive capabilities of land in its original vegetation to compare with productivities under human management. He found,for instance, that most wild lands are more productive than most agricultural acreage. What is left out of his considerations is the amount of healthy ecosystem necessary for cycling and renewal.Furthermore, all productivity is treated as economic, to be dispensed with by the nations that occupy the land, at will. Although Eyre's NCP model is more reasonable than most models, it still puts humanity in competition with any remaining wildlife for productivity in every ecosystem.

NCP Model
It is possible, however, to calculate a sustainable human population in balance with healthy ecosystems, using NCP instead of NPP.The population for this model would be much lower since NCP is generally lower. For instance, in tropical and temperate grasslands,NCP may approach 60 percent of NPP, although 30 percent is much more likely. Temperate forests may approach 30 percent. When NCP is used to calculate a maximum, the measurements are consistent with the low figures of several studies.Refer to Table 6 for calculations.

Table 6. Simple NCP Calculation of Population
Vegetation  Area  NPP  NPP  NCP  Population
 Unit  10 to 6th km  10 to 9th mt  10 to 15th Kcal  10 to 15th Kcal  10 to 9th
Tropical Rainforest  17.  47.4  195.5  0.187  0.17
Tropical Raingreen  7.5  13.2  55.5  0.052  .47
Temperate Summergreen  7.0  7.0  32.2  2.24  2.04
Mediterranean  1.5  1.2  5.9  0.03  0.03
Temperate Mixed  5.0  5.0  23.5  6.35  2.45
Boreal  12.0  7.8  36.0  0.84  0.76
Woodland  7.0  4.2  19.6  7.0  7.0
Tundra  8.0  1.3  5.6  0.006  0.005
Desert Scrub  18.0  1.3  5.4  0.005  0.005
Tropical Grassland  15.0  12.0  48.0  51.45  28.68
Temperate Grassland  9.0  7.2  28.8  9.36  5.4
Dry Desert  8.5  -  -  -  0.309
Ice Desert  15.5  -  0.1  0.001  0.02
Marsh  2.0  4.0  16.8  2.5  4.55
Stream  2.0  1.0  4.6  2.0  3.64
Ocean  332.0  41.5  199.2  0.199  1.81
Upwelling  0.4  0.2  1.0  0.1  0.09
Shelf  26.6  9.2  43.1  2.13  3.87
Reefs  0.6  1.2  3.6  0.54  0.49
Estuaries  1.4  2.5  11.3  0.07  0.06
Cropland  14.0  -  -  12.81  14.63*
Raw Totals  90.87        82.61
Calculated Optimum         0.45

* as percentage of forest/grassland in original vegetation, approximately 35% less NPP. This paper is concerned only with the values of natural productivities. Domestic lands were assigned productivities based on those of the original wild vegetation (which in fact is usually higher).

Of the NCP produced, 75% is unavailable, 5% is eaten by pests,65% of that harvested is inedible, 80% of that edible is lost in processing, and 25% is wasted during consumption, resulting in a final figure of 903 million (from a preliminary figure of 82.6 billion). This figure is almost identical to a flat 1 percent rate of the NPP, subjected to the same loss percentages. The same 50 percent calculation would be applied to obtain the optimum.The figure, 903 million, is a maximum. An optimum population,arrived at by a 50 percent rule, of 450 million would insure against problems due to fluctuations in productivity. Kozlovsky (1974)intuitively estimated 500 million as an equilibrium population.Lower densities of humans will always be able to harmonize more successfully with biological processes. For the long-term survival of the human species, adaptability to environmental changes is necessary. This requires a wide diversity of gene pools, which is achieved by a relatively large population divided into local,partly isolated groups. And this requires healthy regional ecosystems.The optimum size of the global human population is actually the sum of optimums for local habitats.

Before an optimum human population for the world can be put forward as a goal, other questions must be addressed.

How these questions, and others not asked, are answered determine an optimum human population. Knowing how many humans are alive to feed is easier than describing the basics of a quality of life.In calculating an optimum population within ecosystem restraints,few have considered minimum wilderness preservation, air and water quality, genetic minima, nonrenewable resources, appropriate technological innovation, the importance of cultural frameworks, adventure,research, beauty, uniqueness, and other intangible experiences.If human civilizations were based on balanced ecosystems, they would be more complex. The complexity encountered in trying to imagine them may serve as a Zen koan-work, to bring us to rational breakdown and to an alternative: humanity as a self-conscious,self-limiting, poetic species.

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