LECTURE SUPPLEMENTS

Note: These materials are intended as supplements for students in Ant. 301. These pages are in development and will contain errors.

Population Growth
Carrying Capacity
The Tragedy of the Commons

Ecology's central dogma remains: "There is no free lunch" and ecologists as a group are notable for their pessimism. Because they often support actions to conserve the natural resources that make it possible for our posterity to enjoy a high quality of life, they are frequently at odds with traditional religious beliefs, political practices, and social privileges, hence the application of the adjective "subversive." In 1839, P.F. Verhulst recognized that the growth rates of animal populations are logistical or s-shaped when the logarithm of the total number of individuals are plotted against time. In 1869 Ernst Haeckel used the term "ecology" to refer to the study of interrelationships between organisms and their natural environments. He recognized that the individual was a product of both environment and heredity.

Population Growth

No system can long survive the effects of unopposed growth. This is the basis of Malthusian insight. A.A. Bartlett (1978) constructed the following example of unopposed positive feedback. Suppose that the 30 pieces of silver Judas received for betraying Christ had been worth $30, and that Judas had put this into a bank account bearing 5 percent compounded interest, payable in gold. Using the 1978 price of gold, based on an initial capital of about 2.5 grams of gold, this Judas Account would be worth a weight of gold equal to the weight of the entire earth (5.983 x 1027 grams) in 1,292 years. Thus, about the time of Dante's death, heirs of Judas could have presented themselves at the bank and demanded the earth's weight in gold.

Such is the power of exponential growth, or "geometric growth," as Malthus mistakenly called it. The Intrinsic Rate of Natural Increase (also called the Malthusian parameter and designated by the symbol r) is the net rate of growth (births + immigration - deaths - emigration) per individual in the population per unit of time. The change in population in a unit of time can be computed by multiplying the Intrinsic Rate of Natural Increase by the number of individuals present in the population at that time:

Change in population = r x N

during time t

where: r = Intrinsic Rate of Natural Increase

N = Population size

T = Time

If rates of birth, death, immigration, and emigration are consistent, the pattern of population growth fits an exponential curve that can be predicted by the formula:

Nt = N₀(e^rt)

where: Nt= Population at time t

N₀= Starting population size

r= Intrinsic Rate of Natural Increase

t= Time

The proliferation of rabbits after their introduction to Australia is a famous example of population growth. In 1859, a southern Australian farmer homesick for England, imported two dozen wild English rabbits and set them free on his land. Within six years, Thomas Austin's 24 rabbits had multiplied to 22 million. This type of growth is illustrated in Figure 6-7, which shows the growth of a hypothetical colony with r = 0.0063 and a starting population of 24. Rabbits spread across Australia at a rate of 70 miles (42k) a year, reaching every corner of the continent by 1907. By the 1930s, the rabbit population in Australia was estimated at 750 million. Notice that the changes in population increment are not as evident in the early time periods when compared to the later ones. Populations, left to their own courses, accelerate toward catastrophe.

Rabbits became a plague, eating the best grass, fouling water holes, devouring crops, gnawing young trees... Seven rabbits eat as much as one sheep. It was estimated that half of each dollar spent by Australian farmers on machinery, fertilizer, or seeds actually went to feed rabbits. In the early 1950s, the Australians introduced Myxomatosis , a disease fatal to European rabbits, reducing the rabbit population by 90 percent. Wool production immediately increased by 70 million pounds (clip weight of wool).

The basic reproductive rate of a species (R₀), sometimes called the net reproductive rate (NRR), is defined as the average number of surviving female offspring produced by an adult female in the absence of density-dependent constraints. As most populations are fettered by density dependent constraints of some kind, R₀ is notoriously difficult to determine.

What is R₀ for humans? An estimate was made from studies of isolated human populations such as Hutterite communities of South Dakota and Canada that were founded in the 1870s and sustained with little immigration. These communities, with high standards of nutrition and health care, have low rates of birth control. Healthy Hutterite females have completed family sizes of about 11 (R₀ = 5.5) but they delay first reproduction until their early 20s, which suggests R0 values as high as 7 might be attained were reproduction started earlier.

The most fertile woman, according to the Guinness Book of World Records (1986), was Feodor Vassilyev of Russia (1707-1782) who had 67 surviving children. It is important to recognize the difference between fertility (the number of children a women bears) and fecundity (the ability to conceive). Birth rate is the proportion of neonates (infants born in the current year) in a population. For convenience, the birth rate is multiplied by 1000, allowing the rate to be expressed as "births per 1000 population"; mortality rates are calculated in the same fashion. The rate of natural increase is computed by subtracting mortality rates from birth rates. Table 6-5 gives examples of these statistics from several modern countries. A rate of natural increase of 10 per thousand is an increase in 1% of the total population.

Natural Increase/ Doubling Time (per thousand) (years)

5 /140

8 /88

10/ 70

18 /39

20 /35

30/24

40 /17

Also important is the demographic composition of the population. Compare the population pyramids of India and Sweden. In modern communities, births usually occur among young parents, and death rates are not high until older age. Therefore, if the bulk of a population is young, the population is expanding. A youthful population implies a population momentum as youngsters mature into parents and live to see their great-grandchildren. Even if birth control were to restrict family sizes to replacement levels (about 2 children per family), India's 1990 population will continue to grow as its youths reach reproductive age and will not stabilize until it approaches 2 billion inhabitants! Given that the 1990 completed family size in India is about 4.3 children per couple, it seems doubtful that India's already overloaded ecosystem can cope with its growth in the near future.

Population momentum also accounts for part of China's failure to arrest its growth at 1.2 billion. China has one of the most intense government sponsored programs to control population growth. It promoted an ideal of a one-child family in an attempt to bring the average family size to 1.5 children, the figure needed to stop its population growth near 1.2 billion.

The world reached a human population of one billion in 1800, two billion by 1930 ( 130 years doubling time), three billion by 1960, four billion in 1975 (40 years doubling time), five billion in 1985 and about 5.3 billion by mid 1990. The 1990 rate of natural increase is about 18 per thousand, producing a projected doubling time of 39 years for the world's population. The maximum human population that earth ecosystems can sustain is estimated to be about 12 billion people. Density dependent negative pressures should slow our rate of growth, but given the current trend of events, it seems likely that world population will reach 12 billion no later than the year 2050. The probable conditions at that time and events that will accompany the subsequent population regression are not difficult to imagine. Events could occur with a speed that one might not anticipate due to the "doubling" feature of exponential growth.

Imagine an algae-covered pond with a growth rate that doubles its population every month. The month before the pond surface was covered by growth of algae, half its surface area was covered. The month earlier, only a quarter , before that an eighth....Only a few months earlier, the spread of algae would not be apparent. The algal growth rate produced dramatic changes in the pond from what seemed inconsequential in its early stages. If we apply our "pond concept" to the earth and human populations, it seems likely that humanity is entering the last "doubling" that our planet's resources will support (return to outline).

Carrying Capacity

What happens when a population exceeds its resource base? The population continues to grow until the available resources are consumed. After that point in time a die-off occurs. The magnitude of the die-off and the amount of habitat damage (effecting the resource base for survivors of the future) reflects in part the degree of excess population above capacity prior to the die-off.

For example, small group of 25 reindeer were released on the 41 square-mile Saint Paul Island off the coast of Alaska in 1911 (Scheffer, 1951). The reindeer grazed primarily on lichens which were abundant at the time of release and the population expanded exponentially until 1938, when the lichens became overgrazed. With the destruction of their food supply, the population plummeted to only eight animals in 1950.

If a cardinal aim of policy is to minimize the loss of life, a rational game manager kills in order to maintain populations at sustainable levels. From an ecological perspective it is the carrying capacity, not the individual life, that has to be respected.

The same logic applies to human populations. Imagine a hypothetical country, "Utopia," where the population is beyond the prudent carrying capacity of the land. Now that the crash has begun, tens of thousands of people are starving, the economy is destroyed, and millions of people face disaster. Well-meaning people, upholding the sanctity of life rather than the sanctity of the carrying capacity eagerly send in food from the outside thus ensuring that the Utopian population will remain above the carrying capacity. For the moment, the crisis is relieved and the population growth continues, supplemented by outside food. As the Utopian population grows, there is progressively less food production in Utopia and the need for outside assistance steadily increases. Eventually, the price of subsidy exceeds the level that outsiders are willing (or able) to sustain and Utopians again face starvation. The difference is that now the situation is much worse. A larger and more dependent population now has even less resources for recovery than before. The resulting crisis will be more severe, with many more people starving and the standard of living in the post-starvation period will be much lower. When uninformed of ecological principles (or disregarding them), decision-makers with good intentions can transform a temporary crisis into a permanent disaster with a greatly elevated level of suffering. In the logic of a child, we may avoid the vaccination and catch the plague.

The positive feedback of biological growth will be opposed by the negative feedback of predation, disease, war, natural and socially induced sterility, and many other factors that interfere with reproduction and favor death - in Malthus' terms, by "misery and vice." In spite of the Pollyanna attitude nurtured by our remarkable technological progress of the past 200 years, death is still a necessity and a boon.

Population growth is sometimes observed to slow down as carrying capacity (K) is approached. Growth of this kind is easily modeled by the Pearl-Verhulst logistic equation:

Most animal populations are observed to fluctuate around K. The precipitous population collapse observed with Saint Paul Island reindeer occurred when the food supply was catastrophically damaged by overgrazing. If population growth can be slowed while it is at a sustainable level, a stable density can be maintained, subject to less catastrophic fluctuations.

Reductions in growth rates are usually the result of competition, disease, or predation. It should be noted that if population is being managed for harvest, the logistic equation predicts that the maximum sustainable yield occurs when the population is at half of its carrying capacity - the point where the population is growing most rapidly.

Suppose humans on Saint Paul Island noticed the starving reindeer and imported some predators to reduce the number of reindeer. As reindeer populations plummeted, hunting pressure from starving predators could push their reindeer prey to extinction, literally killing the last reindeer on the island before the predators themselves starved. However, without predators, a few surviving reindeer might establish a population level that reflects the carrying capacity of the lichens as the area recovers from overgrazing.

A type of population oscillation is seen in more stable predator-prey relationships.

One of many possible theoretical models for predator-prey interactions is illustrated below:

Note that the oscillations of the predator population are offset in time when compared to those of the prey species. Each population varies within bounds that are determined by the other. When prey density is graphed against predator density, the values fall within a limited set of bounds, resulting in population stability (within the bounds of the oscillations). If these bounds keep the prey species within the carrying capacity of its environment, the predator prevents the prey from experiencing the catastrophic collapse observed in Saint Paul Island reindeer.

Opportunistic species are adapted to niches that are periodically disturbed and consequently exhibit great oscillation of population size. Species found in niches with relatively stable resources and that exhibit much less amplitude in short-term population fluctuations are called equilibrium species. Opportunistic species are referred to as r-selected and equilibrium species as K-selected. K-selected species invest heavily in a few quality offspring.

Not all elements of the human carrying capacity are expandable. Since capital investment is an important element of production costs, population growth brings some benefits. Food production and energy extraction have increased greatly, but the fundamental absorptive capacity of the earth for harmful waste products has not increased. Time moves no faster now than it did a thousand years ago, so high quality goods that require much time in their production, e.g., cabinet-quality hardwoods, have become increasingly scarce. Amenities that cannot possible be increased in quantity - lonely beaches and wilderness areas are examples- continually decrease on a per capita basis.

In biology, a "climax community" is a recognized fiction fostered by the short time span of human attention, and the impact of our actions can produce consequences that outlive the time frame of our immediate interest. Indeed, climax communities are evolving entities that continue to change. The real social value of actions is determined more by their consequences than their intentions. "The road to Hell is paved with good intentions," is an apt ecological attitude since good intentions, even though they may explain poor results, do not excuse them. Ecologists must take a long view of time. Not as long as geologists, but certainly much longer than that used in business-as-usual and politics-as-usual, where the horizon is no more than five years off. Shortsightedness grows logically out of an economic practice of "discounting the future" in terms of the going rate of interest. The higher the rate of interest, the more heavily the future is discounted, which means that shortsightedness "pays." Times of trouble - inflation, social disorder, revolution - raise the interest rate and thus make provision for the future more difficult. In consequence, it becomes ever harder to escape the trouble. Positive feedback generates a vicious circle.

The modern trend toward agribusiness, large business-operated farms, promotes a focus on yearly income, often at the sacrifice of long-term productivity. The most profitable course, from an investment point of view, is to convert the capital of the farm to income as quickly as possible and move on to the next investment. The family farmer is more likely to value the farm itself, more likely to preserve its soil, and to try to pass it on to the next generation. The family farmer is also more likely to preserve stands of woodlands or other natural features for their beauty or esthetic value, even though this is not the most financially profitable course of action in the short term.

Consider the regeneration time of a field that has been cleared. Anyone who operates on an annual income basis is going to manage the field either for crops or for grazing. It would not be profitable to let it lie fallow for a century.

The economic procedure of discounting the future makes a certain amount of sense, but the permanent features of an enduring civilization must be built on actions that ignore this sort of economic theory. There are times in the life of every community when even the investment that must be made in bearing and rearing children cannot be justified by "hard-nosed" economics. The future belongs to the descendants of those who reject the simple implications of economic theory (return to outline).

The Tragedy of the Commons

With the conquest of disease, we must replace the negative feedback of density-dependent crowd diseases with community regulation of the numbers of children. Otherwise, nature will eliminate the excess population in a cruel manner. There is no better illustration of the conflict between freedom and population growth than another of Hardin's ideas, "the tragedy of the commons." "Commons" refers to those resources that everyone shares in common - air, water, space, parks.

An unmanaged commons selects in the short term for selfish behavior that will tragically exhaust the resources. A managed commons, usually called "socialism," selects for managerial behavior that primarily protects the interest of the manager. On the other hand, a private politico-economic system can favor a positive feedback of social power that threatens to create unbearable economic and social inequalities. The commons would seem to be best protected if every citizen could be persuaded to value long-term resources over short-term returns.

Contamination of the commons with pesticides illustrates the problem. The risks of overuse were first recognized with DDT (dichloro-diphenyl-trichloro-ethane), the first of a long series of chlorinated hydrocarbons to become popular biocides. Unfortunately, marketing attitudes and use of petrochemicals have promoted overdosing. If a little biocide is good, it is tempting to think that a lot more would be even better. Prior to World War II, the primary pesticides used in gardening and agriculture were either stomach poisons (sodium arsenite, lead arsenate, nicotine) or contact poisons (pyrethrum, rotenone, and nicotine). The commonly used contact poisons were naturally occurring insecticides that were extracted from plants. Their effects were quick but temporary. At the end of the war, the United States had large stockpiles of chemicals and a wartime technology that could be diverted from war uses to the production of agrochemicals (fertilizers and pesticides).

DDT (and other similar chemicals) quickly found use in the control of insects. It was important in controlling typhus (spread by lice) and malaria (spread by mosquitoes). Millions of people worldwide owe their health and their lives to the effectiveness of DDT. It was relatively cheap and overdosing was common. Unlike the organic contact poisons, DDT did not decompose in the ecosystem. Indeed DDT became a contaminant of ecosystems throughout the world, even Antarctica. As concentrations in ecosystems increased, DDT and other chlorinated hydrocarbons were carried into the atmosphere and dispersed by wind and rain. In England, every inch of rainfall delivered about one ton of DDT to the countryside. As DDT passes from the environment into the living components of the ecosystem, it becomes progressively concentrated as it moves up the food web. Figures for Lake Michigan illustrate the problem (Boughey, 1971:373):

Source/ DDT concentration (in parts per million)

lake sediments/ 0.0085

invertebrates/ 0.41

fish /8.0

herring gulls/ 3177.0

Humans, also at the top of a food web, experienced similar consequences. In the late 1960s, body fat of the average human contained from 5 to 27 ppm DDT. In Sweden, human milk had an average of 0.117 ppm DDT. Similar observations were made in England, the United States, and Australia.

DDT was incriminated in dramatic population declines among predatory birds, and although it seemed to have little toxicity for humans, there were many other highly toxic pesticides being manufactured and distributed in large quantities. Rachel Carson's 1962 book, Silent Spring was one of the first well-documented warnings of the ecological effects of pesticides, and restraints now exist upon the manufacture and use of these materials. The problem with these chemicals is that pesticides are not applied only to pests. They are applied to ecosystems that happen to include the pests.

Interactions

Susceptibility to disease is determined by genotype, degree of crowding, nutritional status, quality of water, sanitation, social stress and perhaps numerous other factors. Agricultural yield, the most fundamental requirement for adequate nutrition, is affected primarily by soil condition and climate, and to a lesser extent by pollution, agricultural practices, and transportation of resources. The myth that nature is constructed of "balanced" systems encourages us to imagine a permanence to communities that is unjustified. The "balance" of nature is a misunderstanding of Hardin's fourth foundation stone: " Thou shalt not transgress the carrying capacity." Organisms that exceed the limits of their support systems risk damaging both themselves and their supporting communities. The universe tends to be populated by relatively permanent structures, and species that exceed their limitations are likely not to be "permanent." (return to outline)

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