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Applied and Environmental Microbiology, August 2007, p. 5276-5283, Vol. 73, No. 16
0099-2240/07/$08.00+0 doi:10.1128/AEM.00514-07
Copyright © 2007, American Society for Microbiology. All Rights Reserved.

Department of Biological Sciences, Kent State University, Kent, Ohio 44242,1 Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, Michigan 48109-1048,2 School of Natural Resources and Environment, University of Michigan, Ann Arbor, Michigan 48109-1041,3 Sustainable Agricultural Systems Laboratory, USDA-ARS, Beltsville Agricultural Research Center, Beltsville, Maryland 207054
Received 6 March 2007/ Accepted 19 June 2007
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TABLE 1. Indices used to quantify the diversity of simulated bacterial communities and their associated community profilesa
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Given the aforementioned properties of microbial community profiles, what can comparison of diversity indices applied to them tell us about the underlying diversity of the communities? Here, we make use of database information to answer this question for simulated communities with various levels of diversity. We examine T-RFLP of bacterial ribosomal genes because it is a popular, high-throughput method which we hope will not be abused, and databases and bioinformatics tools are available to support our simulations. The utilities of several diversity indices, including species richness, evenness, and integrated diversity indices, are evaluated.
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FIG. 1. Illustration of how the species abundance distribution and TRF distribution interact to form a simulated T-RFLP profile. Illustrated steps include calculating relative abundances in a lognormal species abundance distribution based on systematically iterated distribution parameters (1), defining a TRF size probability distribution (one of the four empirical restriction enzyme databases was used for OTU sampling and sequence sampling simulations, whereas a new TRF size distribution was generated for each iteration in parametric sampling simulations) (2), randomly assigning each species in the simulated community to a TRF size according to the TRF size probability distribution (3), summing signals from TRFs and applying a relative abundance (fluorescence) threshold and upper and lower fragment size cutoffs (4), and comparing diversity statistics calculated on the underlying community (species abundance distribution) and the simulated T-RFLP profile by calculating correlation coefficients and plotting data density graphs (5).
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2)0.5]. The abundance of each species in octave R(NR) equals N02R. The focus of our simulations was relative abundance, so the abundance of each species was found relative to N0, and then the total arbitrarily scaled population size of the community (from
to
) was determined so that relative abundances could be calculated.
The simulations consisted of systematically varying initial parameters which determined the diversity and shape of the distribution, including a, ST, and S(Rmax). The parameter S(Rmax) is the number of species in the octave with the most abundant species. The parameter a was varied from 0.15 to 0.3 by intervals of 0.05, and S(Rmax) was varied from 1 to 7 by intervals of 2. While it is often assumed that S(Rmax) equals 1, we did not see an a priori reason to assume this when considering species with highly diverse ecological niches, as is the case for soil bacteria. ST was varied from 10 species to different maxima, depending on the analysis (Table 2), by intervals of 10 species. For a given set of these parameters, S(0) was calculated as ST x a/
0.5, and then Rmax was determined iteratively. The number of species in each octave, its relative abundance, and ST for the resulting distribution were then calculated. To accommodate the fixed value of a and the discrete lognormal distribution, values of ST and S(Rmax) were allowed to vary slightly below and above their initial values, respectively, after the number of octaves in the distribution was determined. Combinations of parameters which did not result in meaningful distributions were discarded (e.g., distributions with a values of 0.2, S(Rmax) values of 5, and 40 or fewer species were not used, because at least 42 species are required for this combination of parameters).
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TABLE 2. Database and simulation information for restriction enzymes used to create empirical TRF size distributions
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Simulations of community diversity and T-RFLP profiles.
Simulations were performed using a macro written in SAS Proc IML. For a given simulation, true community diversity was varied by altering the parameters of the species abundance distribution as described above, and 10 replicate T-RFLP profiles were generated for each species abundance distribution. Replicate T-RFLP profiles were generated by repeating the random assignment of sequences to species in the distribution. The TRF signal in the simulated T-RFLP profile (representing height or area) was assumed to be proportional to the relative abundance of the species. TRF signals were pooled when two species had the same TRF size in base pairs. TRFs smaller than 50 bp and greater than 600 bp were deleted, and TRFs were expressed as relative abundances of the total signal detected in the T-RFLP profile. TRFs below a threshold (0.1, 1, or 4% of the total profile signal) were also deleted, and relative abundances of remaining TRFs were recalculated. Diversity statistics (Table 1) were calculated on both the T-RFLP profile (TRF indices) and the species abundance distribution that it was derived from (true indices).
The utilities of TRF indices were assessed by calculating their correlation coefficients with true indices. However, testing the statistical significance of the correlation coefficients is not appropriate, because the very large number of data points makes all correlations significant, even those very close to zero and obviously not useful as an analytical tool. Therefore, we used graphical displays of the data cloud (data density plots) to further interpret correlation coefficients. These were constructed by plotting the mean values and percentile ranges of a true index over each 5-percentile interval of a TRF index.
Theoretical TRF size distributions and simulations.
"Parametric sampling" consisted of using mathematical approximations of TRF size distributions, allowing the total number of species in abundance distributions to be increased beyond the number of empirical sequences available in the database. Candidate models for the general form of the parametric TRF size distribution were evaluated for their abilities to fit the HhaI, RsaI, MspI, and HaeIII TRF size distributions. Models were initially screened by one of two methods. The first involved visually comparing empirical TRF frequency plots arranged by size (bp) to plots generated using combinations of normal and uniform probability distributions. The second screening method consisted of fitting nonlinear equations supplied with the software GOSA (Bio-Log, Ramonville, France) (e.g., exponential decay, two-phase exponential decay, lognormal, normal, power, Pareto, and polynomial, etc.) to empirical TRF frequencies arranged as rank abundance data. We were modeling TRF size distributions for the purpose of evaluating TRF diversity indices by simulation, so our main criterion was the ability of the models to generate correlations similar to those obtained in empirical simulations when performed over the same range of ST. After the initial screen, simulations were performed to 1,200 and 4,000 species by using selected models, and correlations were compared to results from OTU sampling and sequence sampling, respectively. Simulations were performed as described above, except that assignment of TRF size to each species was according to a probability distribution defined by the model in question (the parametric TRF size distribution) rather than an empirical TRF size distribution. Also, variability between empirical TRF size distributions was incorporated into the simulations by creating a new parametric TRF size distribution for each iteration within a simulation. This was done by allowing random variability in model parameters based on the range of parameter values obtained during fitting of the model to the four empirical TRF size distributions. Correlation matrices obtained using different parametric TRF size distribution models were compared to OTU sampling and sequence sampling correlation matrices by conducting Mantel tests and by calculating the mean absolute deviation between correlation matrices.
Our goal was to simulate communities with up to 10,000 species. Through the above-described process, we chose to use the following model in further simulations: an assemblage of six normal curves and one uniform random distribution. Each normal curve had a randomly generated probability (PO) that a species would have a TRF size derived from that curve. PO values for all the normal curves summed to 90%, while the underlying random-uniform-distribution PO was 10%. Each normal curve was defined by a randomly generated mean (25 to 650 bp) and standard deviation (SD; 2 to 20 bp). The uniform random distribution ranged from 1 to 1,400 bp. Parametric TRF size distributions were sampled by randomly assigning each species in an abundance distribution to one of the six normal curves or the uniform distribution (according to their PO values) and then randomly assigning a specific TRF size within the assigned curve.
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TABLE 3. Representative correlation coefficients from OTU sampling simulations of communities with up to 1,200 species, using a TRF relative abundance threshold of 1%a
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FIG. 2. Data density plots for OTU sampling simulations of communities with up to 1,200 species, using a relative abundance threshold of 1% and the HhaI TRF distribution. These plots summarize a data cloud. Lines can be interpreted as contour lines of data point density around a "peak" showing the central relationship between the two variables. Overlapping percentile ranges for two values of the TRF index indicate the potential for the true indices to be the same for the two communities. Therefore, the slope of the central relationship, as well as the width of the percentile ranges, is important. The TRF diversity index data were broken up into five percentile groups. The mean value for the TRF index in each group was plotted against the following true community index values: mean (diamond), 25th and 75th percentiles (bold line), 10th and 90th percentiles (thin line), and 2.5th and 97.5th percentiles (dashed line). In panels A and B, n was 940 for each group. In panel C, n was 638 to 1,998 due to TRF-S ties.
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TABLE 4. TRF indices with the highest correlation with select true indicesa
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Sequence sampling.
When species richness was extended to 4,000 species by using sequence sampling (Table 2) and a 1% peak threshold, almost all correlations between true and TRF indices declined compared to those described above for simulations using up to 1,200 species and OTU sampling (data not shown). The highest correlation remained between H' and TRF-Evar, which declined from 0.81 to 0.71 (SD = 0.03) (Table 4), whereas the correlation between H' and TRF-H' declined from 0.71 to 0.51 (SD = 0.08). Differences between results for sequence sampling and OTU sampling for 4% or 0.1% thresholds were similar to the differences described for the 1% threshold. Correlations remained basically the same or declined slightly (data not shown).
Parametric sampling for complex communities.
A variety of parametric TRF size distributions were compared to the four empirical size distributions obtained from TRF-CUT. The comparisons were based on shapes of the size distributions and on how well correlations between true and TRF indices obtained with communities of up to 1,200 or 4,000 species matched results obtained using empirical TRF size distributions over the same range of ST. According to both Mantel tests and the mean absolute deviations, assemblages of six normal curves plus an underlying random uniform distribution were the most similar to results obtained using the empirical distributions (Table 5). This distribution performed better by these criteria than a two-phase exponential-decay model, which had the best fit of built-in nonlinear equations according to analysis with the software GOSA. When the simulations were limited to 1,200 species (1% threshold), the correlation of H' and TRF-H' declined to 0.64 for the parametric distribution, whereas the correlation of H' and TRF-Evar was 0.82; these values were the closest to those obtained by OTU sampling for all models tested.
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TABLE 5. Evaluation of different models in creating correlation matrices similar to average empirical matricesa
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FIG. 3. Data density plots for parametric sampling simulations of communities with up to 10,000 species, using a relative abundance threshold of 1%. See the legend to Fig. 2 for explanation. n was 7,973 for each group.
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TABLE 6. Representative correlation coefficients from parametric sampling simulations of communities with up to 10,000 species, using a TRF relative abundance threshold of 1%
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When typical peak height or area thresholds (
1%) were used, richness and diversity indices applied to T-RFLP profiles had limited capabilities to discriminate between levels of diversity in the underlying community. The number of bands in T-RFLP profiles (TRF-S) did a very poor job at predicting the number of taxa in the community (S) in all simulations. Loisel et al. (26) found that the number of bands did not correspond with S for other community profiling methods (single-stranded conformation polymorphism and denaturing gradient electrophoresis profiles) and proposed that the Curtis estimator could be used to evaluate the diversity of the underlying community. The Curtis estimator is based on the reciprocal of the Berger-Parker index (1/d), which we did not find to be particularly useful here, as demonstrated by low correlations between TRF-1/d and true community indices.
H' is a well-known and widely used diversity index integrating both species richness and evenness, although interpretation of the index itself is not without some conceptual difficulties (19, 21). TRF-H' did correlate well with the true community value of H' in the simulations using the lowest number of species (10 to 1,200). However, this correlation declined substantially in simulations using greater numbers of species, to the point where TRF-H' cannot be considered a useful metric of diversity. We were surprised to find that one community evenness index applied to T-RFLP profiles, TRF-Evar, consistently had the highest correlations with the true community value of H' in all simulations using 1% or 4% thresholds (correlations above 0.71 to 0.81 and 0.56 to 0.66, respectively). The fact that different taxa can generate the same TRF (1, 8) may in part explain why evenness of T-RFLP profiles (reflected in TRF-Evar) is affected by true community richness as well as true evenness (reflected in true H'). An increase in species richness will likely increase the average number of taxa contributing to each TRF, which will reduce the impact of differences in abundance and increase the evenness of the profile. Additionally, our results may indicate that evenness within the most abundant taxa is often affected by the overall species richness of a community.
The factors captured in our simulations which cause T-RFLP diversity indices to underestimate, and differ independently from, true community diversity include (i) TRFs of the same size generated from multiple taxa, (ii) exclusion of TRFs if they are outside the size range reliably resolved during electrophoresis, and (iii) TRFs not being detected if they fall below a fluorescence threshold. This fluorescence threshold is translated to a relative abundance threshold by the standardization processes that have been recommended to reduce effects of analytical variability in overall profile strength (2, 5, 32). While there are some similarities between the threshold and the lognormal distribution "veil line" of Preston (34), they differ in that the veil line is a consequence of random sampling, whereas the threshold specifically excludes rare TRFs. Hence, there is no reason to expect the well-known relationship between diversity and sampling effort (14) to hold for T-RFLP profiles, if sampling effort is increased by repeating the assay on the same DNA extract. The relationship may or may not hold if sampling effort is increased by repeating the analysis on replicate environmental samples, depending on the spatial scale of the sampling relative to the spatial variability of the community (35).
Sampling effort can also be increased by enhancing the sensitivity of detection of rare TRFs. We found that an order-of-magnitude increase in the simulated sensitivity of T-RFLP, from a 1% threshold to 0.1%, completely alters the relationships between true diversity indices and TRF indices. Evenness indices are replaced by richness or integrated indices as the best predictors of true S, H', and 1/D for a 0.1% threshold. To our knowledge, current technology cannot be used to consistently differentiate peaks from background noise at this low level, so we present the analysis for comparative purposes. This sensitivity to fluorescence threshold highlights the importance of choosing a common threshold to be applied uniformly across profiles.
All diversity indices tested here, other than TRF-S, are based on comparisons of peaks within a single profile and the assumption that these comparisons reflect differences in relative abundances of taxa. It is worth noting that this assumption is also tenuous due to complex interactions between taxa in ribosomal copy number, PCR bias, and DNA extraction bias (11). It is important to note that analysis of profiles by ordination is based on comparisons between rather than within samples and on the more realistic assumption that biases affecting taxa are the same across samples. The simulations are also conservative (in favor of diversity indices) because TRFs were assumed to be sized with single-base-pair resolution, which often cannot be achieved (22, 30).
While we have demonstrated that diversity indices applied to T-RFLP profiles do not tell us much about the underlying community diversity, empirical studies using the indices often find significant differences between communities from different environments. In other words, the indices do not vary randomly in the field. Significant differences could, however, arise from changes in the identities or relative abundances of the taxa present rather than species richness and evenness. Calculation of diversity indices results in an inevitable loss of information, as the community data are reduced to a single value. Indeed, we are unaware of any studies in which diversity indices indicated a difference between communities and multivariate methods (an ordination or cluster analysis) did not, whereas there are numerous studies where both methods of analysis indicated a difference between communities (9, 17, 20, 25) or where multivariate methods indicated a difference but diversity indices did not (4, 10, 15, 16, 40). It has been suggested that the greater sensitivity of multivariate methods for detecting community differences is true even across methods which seem optimal for each type of analysis (18).
From our analyses, we are led to conclude that T-RFLP-based estimates of diversity provide inaccurate insights into the actual diversity of bacterial communities, even as a comparative method. We suggest that previously published work using diversity indices applied to T-RFLP data should be reinterpreted. For example, Fierer and Jackson (9) found that diversity indices (TRF-S and TRF-H') and community ordinations of bacterial T-RFLP profiles were correlated with soil pH. Based on conclusions reached here, both of these analyses indicate that community composition responds to pH, but no reliable statements can be made regarding the diversity (richness or evenness) of those communities. In addition, there is little reason to apply diversity indices to T-RFLP data to detect differences in community composition, because multivariate methods are more sensitive and better suited for this task. If it is necessary to measure bacterial diversity using T-RFLP, we recommend using TRF-Evar as a measure of diversity because it was the index that best represented the true underlying community diversity.
Published ahead of print on 29 June 2007. ![]()
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