# 3.6: Limits on populations

[ "article:topic", "Biofundamentals", "authorname:klymkowskym" ]

It is a given (that is, an empirically demonstrable fact) that all organisms are capable of producing many more than one copy of themselves. Consider, as an example, a breeding pair of elephants or a single asexually reproducing bacterium. Let us further assume that there are no limits to their reproduction, that is, that once born, the offspring will reproduce periodically over the course of their lifespan. By the end of 500 years, a single pair of elephants could (theoretically) produce ~15,000,000 living descendants.72 Clearly if these 15,000,000 elephants paired up to form 7,500,000 breeding pairs, within another 500 years (1000 years altogether) there could be as many as 7.5 x 106 x 1.5 x 107 or 1.125 x 1014 elephants. Assuming that each adult elephant weighs ~6000 kilograms, which is the average between larger males and smaller females, the end result would be ~6.75 x 1018 kilograms of elephant. Allowed to continue unchecked, within a few thousand years a single pair of elephants could produce a mass of elephants larger than the mass of the Earth, an absurd conclusion. Clearly we must have left something out of our calculations! As another example, let us turn to a solitary, asexual bacterium, which needs no mate to reproduce. Let us assume that this is a photosynthetic bacterium that relies on sunlight and simple compounds, such as water, carbon dioxide, and some minerals, to grow. A bacterium is much smaller than an elephant but it can produce new bacteria at a much faster rate. Under optimal conditions, it could divide once every 20 minutes or so and would, within approximately a day, produce a mass of bacteria greater than that of Earth as a whole. Again, we are clearly making at least one mistake in our logic.

Elephants and bacteria are not the only types of organism on the Earth. In fact every known type of organism can produce many more offspring than are needed to replace themselves before they die. This trait is known as superfecundity. But unlimited growth does not and cannot happen for very long - other factors must act to constrain it. In fact, if you were to monitor the populations of most organisms, you would find that the numbers of a particular organism in a particular environment tend to fluctuate around a so-called steady state level. By steady state we mean that even though animals are continually being born and are dying, the total number of organisms remains roughly constant.

So what balances the effects of superfecundity, what limits population growth? The obvious answer to this question is the fact that the resources needed for growth are limited and there are limited places for organisms to live. Thomas Malthus (1766-1834) was the first to clearly articulate the role of limited resources as a constraint on population. His was a purely logical argument. Competition between increasing numbers of organisms for a limited supply of resources would necessarily limit the number of organisms. Malthus painted a rather gloomy picture of organisms struggling with one another for access to these resources, with many living in an organismal version of poverty, starving to death because they could not out-compete others for the food or spaces they needed to thrive. One point that Malthus ignored, or more likely was ignorant of, is that organisms rarely behave in this way. It is common to find various types of behaviors that limit the direct struggle for resources. For example, in some organisms, an adult has to establish (and defend) a territory before it can successfully reproduce.73 The end result of this type of behavior is to stabilize the population around a steady state level, which is a function of both environmental and behavioral constraints.

An organism’s environment includes all factors that influence the organism and by which the organism influences other organisms and their environments. These include factors such as changes in climate, as well as changes in the presence or absence of other organisms. For example, if one organism depends in important ways upon another, the extinction of the first will necessarily influence the survival of the second.74 Similarly, the introduction of a new type of organism or a new trait (think oxygenic photosynthesis) in an established environment can disrupt existing interactions and conditions. When the environment changes, the existing steady state population level may be unsustainable or many of the different types of organisms present may not be viable. If the climate gets drier or wetter, colder or hotter, if yearly temperatures reach greater extremes, or if new organisms (including new disease-causing pathogens) enter an area, the average population density may change or in some cases, if the environmental change is drastic enough, may even drop to zero, in other words certain populations could go extinct. Environmental conditions and changes will influence the sustainable steady state population level of an organism (something to think about in the context of global warming, whatever its cause).

An immediate example of this type of behavior involves the human population. Once constrained by disease, war, and periodic famine, the introduction of better public health and sanitation measures, a more secure food supply, and reductions in infant mortality has led the human population to increase dramatically. Now, in many countries, populations appear to be heading to a new steady state, although exactly what that final population total level will be is unclear.75 Various models have been developed based on different levels of average fertility. In a number of countries, the birth rate has already fallen into the low fertility domain, although that is no guarantee that it will stay there!76  In this domain (ignoring immigration), a country’s population actually decreases over time, since the number of children born is not equal to the number of people dying. This itself can generate social stresses. Decreases in birth rate per woman correlate with reductions in infant mortality (generally due to vaccination, improved nutrition, and hygiene) and increases in the educational level and the reproductive self-determination (that is, the emancipation) of women. Where women have the right to control their reproductive behavior, the birth rate tends to be lower. Clearly changes in the environment, and here we include the sociopolitical environment, can dramatically influence behavior and serve to limit reproduction and population levels.

A single cell of the bacterium E. coli would, under ideal circumstances, divide every twenty minutes. That is not particularly disturbing until you think about it, but the fact is that bacteria multiply geometrically: one becomes two, two become four, four become eight, and so on. In this way it can be shown that in a single day, one cell of E. coli could produce a super-colony equal in size and weight to the entire planet Earth.

- Michael Crichton (1969) The Andromeda Strain

### References

72 Darwin’s elephants: http://www.idlex.freeserve.co.uk/idl.../elephant.html

73 Territorial Defense, Territory Size, and Population Regulation: https://iriss.stanford.edu/sites/all...pulcre2005.pdf

74 Why the Avocado Should Have Gone the Way of the Dodo http://www.smithsonianmag.com/arts-c...976527/?no-ist and Neotropical Anachronisms: The Fruits the Gomphotheres Ate: http://www.sciencemag.org/content/215/4528/19.short

75 Global population growth: https://www.ted.com/talks/hans_rosli...ulation_growth and The Joy of Stats: http://youtu.be/jbkSRLYSojo

76 Hans Rosling: Religions and babies: http://www.youtube.com/watch?v=ezVk1ahRF78

### Contributors

• Michael W. Klymkowsky (University of Colorado Boulder) and Melanie M. Cooper (Michigan State University) with significant contributions by Emina Begovic & some editorial assistance of Rebecca Klymkowsky.