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Chapter 3 : The Uncountables

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Abstract:

In the 1980s and 1990s, it was widely recognized that the extent of microbial diversity in any environmental sample had never been experimentally determined, and some commentators believed bacterial diversity to be beyond practical calculation. The assumptions regarding the shape of the underlying community taxon-abundance distribution is undoubtedly open to criticism; however, what this article serves to do is to focus attention on determining what the underlying taxon-abundance distribution is by demonstrating that it is fundamental in determining the extent of prokaryotic diversity. The lognormal taxon-abundance distribution was used to assemble 30,000 communities, because it fitted the data better than the inverse Gaussian. The rationale for studying bacterial diversity given in this chapter is the prospect of the uncharted taxa being a reservoir of new drugs and metabolic processes. This chapter also describes the mathematical diversity estimators and taxon-abundance distributions and provides maps of the microbial world that will help guide future exploration and direct resources.

Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3

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FIGURE 1

Distribution of taxon abundances in communities of 10 individuals and in small samples of 200 individuals for (a) a lognormally distributed community; / is the ratio of the total number of individuals to the number of individuals belonging to the most abundant taxon, which can be used to index richness ( ); (b) a logseries distributed community; θ is one of the parameters of the lognormal that can be used as an index to species richness ( ); (c) a community where 200 taxa are equally abundant, and (d) a bimodal distribution (redrawn from ).

Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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FIGURE 2

The sample sizes required to correctly characterize a sample with a diversity of 5,000, undertaking a complete census, a 95% census, or using nonparametric methods. Note that if the diversity is uniform, nonparametric estimators are very efficient. However, if the diversity is lognormally distributed, a very large sample is required to obtain the correct answer. The simulations are described in more detail in , and this figure appeared in .

Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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FIGURE 3

A “quick and dirty” way to estimate diversity by assuming a distribution. (a) The total number of taxa in a community with a lognormal species abundance curve is simply the area under that curve (called the species curve). The individuals curve is the number of species at each abundance (the species curve) multiplied by their abundance (the -axis). There is therefore a mathematical relationship between the area under a species area curve, the number of individuals (the area under the individuals curve), and the maximum and the minimum abundance ( and ). (b) The relationship, over 30 orders of magnitude in population size, for various ratios of by assuming that is equal to 1 ( ). This figure appeared in .

Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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FIGURE 4

Expected sample abundances obtained using the lognormal (solid line) and inverse Gaussian distributions (dashed line). The predictions are posterior means as explained in the text. Actual data points are solid circles.

Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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FIGURE 5

Estimates of observed diversity as a function of number of 16S rDNA reads for the data set of . The dotted line gives a curve generated by fitting a Michaelis-Menten equation to the rarefaction curve. The solid line is the median observed diversity from generating artificial communities with parameters obtained by sampling from the likelihood, Equation (3), assuming a log-normal taxon-abundance distribution. The gray lines give 95% confidence intervals. The inset graph gives the same data magnified near the origin together with the actual rarefaction curve (dashed line).

Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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FIGURE 6

Estimates of number of genomes that can be assembled as a function of fragments read for the data set of . The solid line is the median expected number of genomes for the artificial communities used in Fig. 3 . The gray lines give 95% confidence intervals. The inset graph gives the same data magnified near the origin. conducted approximately 6.4 × 10 reads and assembled only a single genome.

Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3
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Tables

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TABLE 1

Diversity estimates from the data of

Citation: Sloan W, Quince C, Curtis T. 2008. The Uncountables, p 35-54. In Zengler K (ed), Accessing Uncultivated Microorganisms. ASM Press, Washington, DC. doi: 10.1128/9781555815509.ch3

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