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Appendix 6.4

The following material is Appendix 6.4 mammals were reanalyzed using geometric mean for Chapter 6 of: Fowler, C.W. 2009. regression resulting in the linear relationship Systemic Management: Sustainable shown in Figures 2.31 and 6.21.1 Using a mean adult Human Interactions with human body weight of about 68 kg (150 pounds),2 and the Biosphere. Oxford University and the equation representing the relationship Press between density and body size, the mean dens- ity of herbivorous species that exhibit the body 1 The human evaluated by size of humans was estimated to be about 2.3 per interspecific comparisons square kilometer (6 per square mile). Spread over Information on the limits to natural variation the entire surface of the earth, the current human among nonhuman species that can be used to density of 11.7 per square kilometer (Appendix assess the human population measured either in 6.3) is 5.1 times the mean expected for terms of density or total population (Fowler 2005). the size of humans (Table 6.2). Of all the species in Density is considered first. Damuth’s (1987) sample, 85% were found at popu- lation densities that, for their size, were less than that of humans spread over the entire surface of 1.1 Density the earth.3 Peters (1983) argued that the observed relationship Restricted to terrestrial areas except Antarctica, between density and body size (as was shown in the mean density of humans (57.7 per square kilo- Fig. 2.31, and Fig. 6.21) can provide estimates of meter) is over 24 times the mean for similar-sized population density when body size is known (for species of herbivorous mammals. Of the 368 species racoons in his example). Alternatively, one can of herbivores in Damuth’s work, only 1.6% (6) were evaluate a population with known density. In par- more densely populated for their body size than ticular this can be done for humans (Cohen 1997, humans dispersed over all areas. Finally, at Fowler 2005). Species with either very sparse or over 288 people per square km of agricultural land, very dense may be compared to nor- the current human population is overpopulated by mative values within the density/body size rela- a factor of over 120 when compared to the mean of tionship to determine the degree to which they herbivorous mammals of the same body size. depart from such levels—the comparison is con- A normal human population consistent with her- sonant. As mentioned in Chapter 2, relationships bivores of similar body size would be about 48 mil- between body size and density has been examined lion people if we allow ourselves 20% of the earth and debated in a number of studies (Blackburn to live on. Yet there are over 130 times that many. et al. 1993, Brown 1995, Damuth 1981, 1987, Lawton Although there may be exceptions when local dens- 1990, Peters 1983, Schmid et al. 2001). ities are considered, no species in Damuth’s sam- This approach can be applied to humans, by ple is found at such high average densities for their comparing human population density with the body size. This is true even if 40% of the earth’s mean population density of species the same size land surface is considered habitable by humans. as humans (Cohen 1997, Fowler 2005, Fowler and Humans are the most densely populated species Perez 1999). Damuth’s (1987) data for herbivorous of mammal for their body size and exhibit clear

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abnormality in comparison to mammalian herbi- more densely populated than the most common vore species (Fig. 6.22). kinds of herbivorous species. This mode occurs at Because humans are not strictly herbivores, esti- about 20% of the expected levels for their body size mates of based on comparison with as shown in Figure 6.22A (as a result of the skewed herbivores are biased. Due to our higher trophic nature of this species frequency distribution).

position, the optimal human population would Figure 6.22C shows our species’ location in log 10 probably occur at even lower density. To demon- scale where we find ourselves at over 120 times the strate, we consider a relationship between body size population density of other species after account- and population density for (Marquet ing for body size. 2002, Peters 1983). Table 6.2 shows overpopulation Figure 6.23 shows a comparison of the estimates indices for a number of density and body-size rela- of human sustainable for the earth tionships, including that for carnivores.4 Thus, for as a whole, based on three approaches. One (top similarly-sized carnivorous mammals, the human panel) is based on conventional scientific consid- population is 2470 times more dense than expected erations (derived—the combination of data from as more optimal. Compared to a mixture of species Fig. 6.20 and Table 6.1). The second (middle panel) from a variety of trophic levels, the overpopula- is an interspecific comparison (empirical) assuming tion factor is 578. Tudge (1989) stated: “There is an we can sustainably occupy about 20 million square ecological law—a simple extrapolation of bedrock kilometers of the earth’s surface as vegetarians (i.e., physics which says that large, predatory animals the density information from Fig. 6.22 converted to are rare. We break that law: we are large and we numbers). The third (bottom panel, Fig. 6.23), shows have a penchant for , and our popula- the population size that approximates the mode of tion now stands at 5 billion . . . ”. The comparison geographic range size for species of our body size made here examines the extent to which we “break (a geographic range of approximately 2 million this law” to exhibit abnormality in violation of sq. km., Figs 2.14 and 2.28). It adds another order one of the tenets of management (Tenet 5, Chapter of magnitude to the difference between measures 1) and underlying principles laid out in Mangel based on conventional approaches and those based et al. (1996). on interspecific comparison. It also corresponds to The pattern in distribution of species across the estimated population level of about 5 million density is very asymmetrical. Without log trans- for prehistoric humans and is within the range formation, most species occur at densities well of variation observed for populations of other below the mean. More than 73% of Damuth’s sam- large mammals (Freedman 1989, see below) of our ple for herbivorous mammals exhibit densities body size. We must remain mindful, however, that below the mean of about 119 per square kilometer. has not been adequately accounted for Another way to evaluate in that the data used to present the distributions is to contrast human population density with the for the bottom panels is based on data from herbiv- modal (most frequent) densities for other species. 5 ores. As a world society, we may wish to retain the Such a comparison should again account for the capacity to consume some meat. recognized effects of body size. To do so, popula- Even though there are obvious further refine- tion density can be expressed as a multiple of the ments needed in this process, the bottom panel of value expected from the regression in Figure 6.21. Figure 6.23 would have to serve as a better basis for Figure 6.22A is the frequency distribution of the management (e.g., establishing goals, and points of subsample of species that fall in the range of 0 to reference for measuring progress in solving the 2 for such multiples as compressed into one bar in problem of overpopulation) than either of the top the graph of Figure 6.22B. panels. To avoid having any component of ecosys- An evaluation of human overpopulation in this tems exhibiting abnormality (Tenet 5, Chapter 1, way results in even more extremes. Figure 6.22B Mangel et al. 1996) and avoid the combination of covers values beyond the multiple of two to include risks involved, our species would be much better off humans. The human population is about 600-fold with a population within the range of the bottom

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panel. It might be argued that it would be prefer- assumptions, models, and calculations that inject able to be near the mode as the example of sustain- errors, bias, and uncertainty. In the case of density, ability represented by most species as it would be geographic range size is a complicating factor when consistent with attempts to maximize sustainabil- it is not known on a species-by-species basis. In the ity. But, as always, things are not as simple as this above, it is not clear what the normal geographic and a precise location within the normal range range might be for humans. This emphasizes of natural variation is debatable (a point visited the importance of making comparisons between in Chapter 5 in consideration of maximizing bio- humans and other species with measurements as diversity). A point estimate cannot be entertained consonant as possible (identical units, and categor- as an option if we are to integrate into management ies, with isomorphic information) to the question the consideration of data such as that of Figures being addressed. To assess human population size 2.20–2.22. A population with no variation is exhib- directly, it should be compared to information on iting abnormal population variation—no species the limits to natural variation among the mean has a constant population. Now, however, debate population size of other species, rather than dens- over which metric and statistical distributions are ity. Density can be used directly on an area-by-area most important for accurately providing guidance basis. Most countries of the world have densities is overshadowed by the degree to which humans higher than the mean or modes of frequency dis- have departed from all of them at this point in tributions above (Appendix 6.5). time. To account for trophic level, the human As a total population, however, the human popu- species would arguably be most risk free at even lation is also the largest for its body size (Freedman lower population levels than accounted for by com- 1989, Nowak 1991). The human population is at least parisons with herbivores. two orders of magnitude larger than the largest Figure 6.23 illustrates the difference (about three populations for other large mammals (Fig. 6.24). The orders of magnitude) between results obtained in crabeater seal (Lobodon carcinophagus) has a popula- comparing conventional approaches to evaluating tion of less than 15 million (MacDonald 19846). The our population with those based on information on white tailed (Odocoileus virgianus) has a total the limits to natural variation—to integrate a much population perhaps as large as 28 million. Mule more complete consideration of complexity. It also deer (Odocoileus hemionus) may number as many as indicates that the overpopulation factors in Table 6 million. Other similar sized species with large 6.1 are underestimates by an order of magnitude populations include wildebeest (Chonnochaetes or more. This graph brings us through a more com- taurinus, about 3.1 million), pronghorn antelope plete appraisal of overpopulation by humans when (Antilocapra americana, approximately 1 million), based on density. It accounts for bias in the initial several species of dolphins (Stenella, each less than calculation of density based on assumed habi- 20 million), and northern fur seals (Calhorinus ursi- tat following conventional approaches. But geo- nus, about 2 million). Humans are over two orders graphic range size must be dealt with directly (as a of magnitude more numerous and two to three distinct management question) and the advantages orders of magnitude more densely populated than of direct comparisons with population numbers these extremes. per se are clear. However, these extremes are limited basis for comparison if the question involves sustainabil- 1.2 Total population ity. Current circumstances include the effects of many human abnormalities (a few of which are Complications arise in comparisons such as those exemplified in this chapter). Some of these species above, when we address a question with noncon- (e.g., white tailed deer, crabeater seal) may exhibit sonant information; the question of sustainable large populations because of the disrupting influ- density is better addressed with information on ence of humans—many in ways we are outside the density and addressing questions of sustainable normal range of natural variation. Some species of total population with density information involves nonhuman mammals are in marine environments

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that collectively make up about 70% of the earth’s approximately four orders of magnitude difference surface, compared to the 20% represented by ter- between human and the mean (based on log trans- restrial surfaces outside the Antarctic. Population formations) of other population levels is reduced sizes, taken individually, are poor standards of ref- to three. Our population is about 700-fold larger erence, especially our own in its current state in than that which would maximize diversity based that the integrative power of a pattern of multiple on population size (Fowler 2008). observations is lost. It is difficult to escape the conclusion that our The point of mentioning these extremes is that population is close to three orders of magnitude all other species of mammals of our body size have too large—there are about a 1000-fold too many of

much smaller populations than that of humans us. This is a problem that, like our CO2 production (Fig. 6.24). For most species, of course, populations and energy consumption (among others as shown are much smaller than these extremes. The mean in this chapter) are problems much larger than population size for species of body mass similar previously recognized. to that of humans, shown in Figure 6.24, is about 2.34 million. The current human population is Notes about 2500 times that large or over three orders of magnitude more numerous than this mean. The 1. This form of regression analysis takes into account geometric mean of these populations is 157 thou- the fact that there is variability in the estimates of adult sand (i.e., when based on log transformations). body mass as well as in the estimates of population 10 density and better represents the underlying relation- Based on comparison with this mean the human ship between the two variables. Debate and discus- population is 36.7 thousand-fold larger than the sion of the issue of regression techniques is found in mean (over four orders of magnitude larger). Such a number of related papers (see Blackburn et al. 1993, comparisons are also subject to bias if the question LaBarbera 1989, McArdle 1988, Ricker 1973, 1984). Also, is: What is a sustainable human population in the the data used in this regression do not include domes- absence of abnormal human impact? Again, this is tic species. because of the reduced nature of many of the pop- 2. The body mass used here may be slightly large com- ulations as contributed to by the host of historical pared to the world average of mean adult body size of anthropogenic effects. Many species included in humans (65 kg from Nowak 1991). It is not clear what Figure 6.24, plus even more that are not, are endan- mean body weight would reflect that of the human as gered largely as a result of human influence. a species independent of petro/technical influence. The average weight of women and men in the 30–39 age group Whether with or without abnormal human influ- for Americans (1994 World Almanac) is 152 lbs (68.9 kg) ence, the extent of human overpopulation evalu- based on the midpoints of the size ranges (170 lbs— ated with the preliminary comparisons of total 77.1 kg—for men, 134 lbs—60.8 kg—for women). It can be populations are comparable to results based on assumed that at least part of a desirable index of stand- density as well as those based on estimated prehis- ard of living is reflected in body weight. Thus, in look- torical population levels. The human population is ing for sustainable population size one option that serves approximately 1000-fold overpopulated if assessed as a standard of reference is the body weight (mass) of as falling between the two categories in the lower Americans although it is potentially biased. right of Table 6.2. These two categories are: spe- 3. Species that occur under any line parallel to the cies in general and carnivores more specifically. regression line in Figure 6.21 exhibit densities less than Humans are assumed to have a involving some fixed multiple of the expected density represented by the line. Eighty-five percent (313 of 368) of the spe- 20% of the earth’s terrestrial surface. This approxi- cies in Damuth’s (1987) work showed densities that place mate 1000-fold overpopulation assessment is not them under such a line located to pass through the point unlike those obtained from Figure 6.24, even is we where humans are represented as spread over the entire account for human influence through assumption. surface of the earth. For example, if we assume that our influence on 4. These comparisons ignore the effects of ordinary the populations of other species has been to reduce linear regression as conducted in the original analysis them, on the average, to 10% of normal levels, the and presented here without reanalysis. The effects of

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geometric mean regression would be to accentuate esti- Fowler, C.W., and M.A. Perez. 1999. Constructing spe- mated overpopulation. cies frequency distributions—a step toward systemic 5. This corresponds to what may be the peak of overall management. NOAA Techinical Memorandum NMFS- risk aversion represented by naturally occurring species AFSC-109. U.S. Department of Commerce, Seattle, WA. treated as nature’s Monte Carlo sampling procedure or Freedman, B. 1989. Environmental : the impacts of examples of natural Bayesian integration (Fig. 1.4). This pollution and other stresses on structure and is to be contrasted, however, with values that maximize function. Academic Press, New York, NY. (Fowler 2008) which are higher than statis- Kooyman, G.L. 1981. Crabeater seal, Lobodon carcinopha- tical measures of central tendency. gus (Hombron and Jacquinot, 1842). In S.H. Ridgeway 6. Recent populations have been at least 7 million and R.J. Harrison (eds). Handbook of marine mam- (Boveng 1993, Erickson and Hanson 1990). Kooyman mals, Vol. 2, Seals, pp. 221–235. Academic Press, New (1981) emphasizes the uncertainty in estimates of the York, NY. population for this species with estimates ranging from LaBarbera, M. 1989. Analyzing body size as a factor in 2 to 75 million. ecology and . Annual Review of Ecology and Systematics 20: 97–117. Lawton, J.H. 1990. and population References dynamics of animal assemblages. Patterns in body Blackburn, T.M., V.K. Brown, B.M. Doube, J.J.D. size: space. Philosophical Transactions of the Greedwood, J.H. Lawton, and N.E. Stork. 1993. The Royal Society of London, Series B 330: 283–291. relationship between abundance and body size in Mangel, M., L.M. Talbot, G.K. Meffe, et al. 1996. Principles natural animal assemblages. Journal of Animal Ecology for the conservation of wild living resources. Ecological 62: 519–528. Applications 6: 338–362. Boveng, P.L. 1993. Variability in a crabeater seal popu- Marquet, P.A. 2002. Of predators, prey, and power laws. lation and the near the Antarctic Science 295: 229–2230. Peninsula. Ph.D. Dissertation, Montana State McArdle, B.H. 1988. The structural relationship: University, Bozeman, MT. regression in biology. Canadian Journal of Zoology 66: Brown, J.H. 1995. . University of Chicago 2 3 2 9 – 2 3 3 9 . Press, Chicago, IL. McDonald, J.N. 1984. The reordered North American Cohen, J.E. 1997. Population, economics, environment selection regime and late Quaternary megafaunal and culture: an introduction to human carrying cap- In P.S. Martin and R.G. Klein (eds). acity. Journal of 34: 1325–1333. Quaternary extinctions: a prehistoric revolution, pp. Damuth, J.D. 1981. Population density and body size in 404–439. University of Arizona Press, Tucson, AZ. mammals. Nature 290: 699–700. Nowak, R.M. (ed.). 1991. Walker’s mammals of the World (5th Damuth, J.D. 1987. Interspecific of population edn). Johns Hopkins University Press, Baltimore, MD. density in mammals and other animals: the inde- Peters, R.H. 1983. The ecological implications of body size. pendence of body mass and population energy-use. Cambridge University Press, New York, NY. Biological Journal of the Linnnean Society 31: 193–246. Ricker, W.E. 1973. Linear regression in research. Erickson, A.W. and M.B. Hanson. 1990. Continental esti- Journal of the Research Board of Canada 30: mates and population trends of Antarctic ice seals. In 4 0 9 – 4 3 4 . K.R. Kerry and G. Hemple (eds). Antarctic ice ecosystems: Ricker, W.E. 1984. Computation and uses of central trend ecological change and conservation, pp. 253–264. Springer lines. Canadian Journal of Zoology 62: 1897–1905. Verlag, Berlin. Schmid, P.E., M. Tokeshi, and J.M. Schmid-Araya. 2001. Fowler, C.W. 2005. , health, and the human Relation between population density and body size in population. EcoHealth 2: 58–69. stream communities. Science 289: 1557–1560. Fowler, C.W. 2008. Maximizing biodiversity, informa- Tudge, C. 1989. The rise and fall of Homo sapiens sapiens. tion and sustainability. Biodiversity and Conservation Philosophical Transactions of the Royal Society of London, 17: 841–855. Series B 325: 479–488.

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