Comment on "Computational Improvements Reveal Great Bacterial Diversity and High Metal Toxicity in Soil"

^* To whom correspondence should be addressed. E-mail: volkov{at}psu.edu

Gans et al. (1) reanalyzed the reassociation kinetics for bacterial DNA from pristine and metal-polluted soils. They claimed that a power law best described the abundance distributions and that more than one million species existed in pristine soil—an increase of two orders of magnitude compared with earlier estimates. Our analysis shows that the data analyzed in (1) constrain neither the species-abundance relationship nor the effective parameters, including the total diversity.

Consider the rate equation

(1)

where [C_i] is the concentration of single-stranded DNA of the i-th species at time t, [C_0i] is the concentration at t = 0, the coefficient [(1 + )/()] determines the order of the reaction, and k is a measure of the reaction rate. The empirical retardation factor is equal to 1 for a second-order reaction. As a solution, one obtains the basic equation used by Gans et al. (1).

(2)

Following Gans et al., we reconsidered data fits to equation 2 in (1) obtained for the case of a species-abundance distribution P(n). We considered two of the models studied in (1) for the species-abundance relationship, delta and zipf, described by the following equations.

(3)

where S is the total number of species and N is the total population, and

(4)

where N₀ n N₀ + and N₀, , and z are all free parameters. One can readily find analytic forms for the Cot equation in the two cases to be

(5)

and

(6)

respectively, where ₂F₁(·) is the hypergeometric function, = 1 + [()/(N₀)], and ß = [(k z(1–^z–1))/(S(1–z)(^z–1))].

Figure 1 shows the results of a least-squares fit of Eq. 5 (the delta model) to the data (2) analyzed in (1). For the noncontaminated sample, one obtains k/S = 0.033, = 0.092, and R²_adj = 0.9965; for the low-contaminated sample, one obtains k/S = 0.034, = 0.12, and R²_adj = 0.9925; and for the highly contaminated sample, one obtains k/S = 0.035, = 0.16, and R²_adj = 0.9963. Note the high quality of the fits, the notably similar values of k/S, and the somewhat low values of , the retardation factor. Were one to assume that k = 5.19 (as for Escherichia coli), one would find that S 150, which is unrealistically low and might merely reflect the number of abundant species. Interestingly, as shown in (1), the fit is much worse if is chosen to be 0.45 and not allowed to be a free parameter.

Fig. 1. Cot curves for noncontaminated (red), low-contaminated (blue), and highly contaminated (green) samples, along with the fits to the delta model of species abundance. [View Larger Version of this Image (19K GIF file)]

The presence of a large number of species in the sample leads to the retardation factor becoming smaller than that observed for a single species (e.g., E. coli). Equation 2 is valid only under the assumption of a special sample in which the species are segregated from each other. However, the actual sample is a mixture of all the species, such that the rate at which two single-stranded DNA molecules of the same species reassociate when in proximity to each other should decrease. This slower reassociation rate may be captured by a decrease of , which determines the rate of change of [([C]')/([C])] [C]^1/. It would be important to carry out careful studies of the influence of sample heterogeneity on the form of the Cot curve and on the values of the empirical parameters. Furthermore, the value of could very well depend on the degree of purity of the soil.

Figure 2 shows the fits of the data using Eq. 6 (the zipf model), with k = 5.19 (the reaction rate for E. coli) and = 0.45 (the retardation factor for E. coli), as carried out in (1). Interestingly, the quality of the fits does not degrade significantly when S varies over a wide range.

Fig. 2. Cot curves for (A) noncontaminated (red), (B) low-contaminated (blue), and (C) highly contaminated (green) samples, along with the fits to the zipf model of species abundance. In each case, the data are fitted to several versions of the model with varying numbers of species S as shown in the inset. The blue solid lines represent the best fit in accord with analysis in (1). The other lines are fits in which the number of species is decreased by factors of 8.2 and 82 for the pristine soil and increased by factors of 3.56 and 50 for the two polluted cases, with little degradation in the quality of fit. The most sensitive region of the Cot curve occurs when [C]/[C0] becomes small compared with 1, and the experimental data does not extend to this regime. [View Larger Version of this Image (11K GIF file)]

Thus, our reanalysis of the data using the framework developed in (1) suggests that the data, in and of themselves, constrain neither the species-abundance relationship nor the effective parameters, including the total diversity. This problem is exacerbated because there are no error estimates in the experimental data, and one can observe great variation in the model behavior upon changing the empirical retardation factor .

Accurately determining microbial diversity and gauging the impact of pollutants on it are extremely vital issues (3) that affect health, agriculture, and geochemical cycles. Unfortunately, the experimental data analyzed in (1) do not allow one to infer either that the diversity of pristine soil is orders of magnitude higher than previously thought or that metal pollutants have a devastating effect on microbial diversity.

References

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