Technical Comments

Response to Comments on “Productivity Is a Poor Predictor of Plant Species Richness”

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Science  23 Mar 2012:
Vol. 335, Issue 6075, pp. 1441
DOI: 10.1126/science.1214939

Abstract

Pan et al. claim that our results actually support a strong linear positive relationship between productivity and richness, whereas Fridley et al. contend that the data support a strong humped relationship. These responses illustrate how preoccupation with bivariate patterns distracts from a deeper understanding of the multivariate mechanisms that control these important ecosystem properties.

Debate over the productivity-richness relationship (PRR) has been strongly influenced by the way that scientific motives influence how theories are evaluated. Analyses of how scientists participate in the process of theory maturation (1) point out that attachment to particular explanations can result in a tendency to overlook inadequacies and contradictions. Such attachment can lead to a reliance on “theory demonstrations,” which selectively sift through data to find supporting evidence. “Theory investigations,” in contrast, have a different motivation: to evaluate the explanatory adequacy and limitations of theories so as to improve them. Theory investigations are challenged to be either exhaustive in their examination of evidence (e.g., through complete meta-analyses) or to rely on unfiltered samples that represent the variation nature has to offer. Generally, demonstrations seek qualitative (yes/no) support, whereas theory investigations seek to quantify the relative importance of different processes.

In our study (2), we investigated the PRR at the local, regional, and global scale and reported the patterns found with all sites included or with sites of anthropogenic origin (e.g., old fields and restored prairies) excluded. Along with the mean responses, we evaluated boundaries using nonlinear quantile regression. We emphasized that for all these different analyses, there was a great deal of unexplained variance.

Pan et al. (3) argue that our study provides clear and strong support for a positive linear relationship between productivity and richness. They selected one subset where we found a weak, positive linear PRR among site means (the straight dotted line in Adler et al., figure 3), culled additional sites, and then averaged across similar sites, boosting the apparent strength of the relationship. Pan et al. (3) claim that we were biased in our investigation of the PRR because of unbalanced replication of samples across the bins in the community classification scheme they used to post-process the data. Counter to their claim, there is no requirement for equal representation in bins unless one seeks homogeneity of variance across the relationship. Averaging across similar sites so as to create a single value for each bin, however, reduces unexplained variance by eliminating within-bin variance and exaggerates predictive capacity. The use of bins defined by an informal community classification scheme also confounds productivity with the classification scheme.

In sharp contrast to Pan et al., Fridley et al. (4) contend that our data show strong support for the humped-back model (HBM). Original support for the HBM comes from theory demonstrations, such as the Al-Mufti (5) study where data were hand-selected to represent a humped-back line. Theory investigations based on unfiltered samples and rigorous quantitative analyses since that time have consistently found PRR patterns to be weak and variable (68), consistent with our findings [although analyses that have filtered studies have produced more consistent results, with the form of relationship depending on the filtering applied (9, 10)].

Fridley et al.’s specific claims are that we (i) filtered data by eliminating anthropogenic sites; (ii) failed to properly test the HBM by not including litter; (iii) failed to include enough high-productivity sites to detect a hump; and, inconsistent with that point, (iv) claim the data show a humped relationship. We dispute their implication that we presented biased results and disagree with their conclusions as described here:

(i) We performed many analyses and summarized the full range of patterns found. One of the analyses prominently presented was across all sites (Adler et al., figure 3, solid line) and showed a weak but significant humped relationship. Another analysis excluded anthropogenic sites (Adler et al., figure 3, dotted line), anticipating that some might object to inclusion of highly altered sites (which Pan et al. did). This analysis showed a (weak) linear positive relationship. Within-site analyses of small-scale richness patterns showed very weak and highly variable patterns (Adler et al., figure 2).

(ii) The majority of studies of the PRR have described productivity as the variable of theoretical interest rather than accumulated biomass, including Fridley et al. themselves at times [(9), p. 127]. To be comparable with previous theory investigations, we analyzed productivity without including litter accumulated from previous years.

(iii) Sites were selected without filtering and represent the variance encountered when ecologists are asked to sample natural grasslands. Selectively including sites with high productivity, as suggested by Fridley et al., would bias the sample, leaving us with no estimate of the predictive adequacy of the PRR. That said, 20 of the 48 sites included in our study contained individual plots with productivity levels greater than 500 g/m2 and 8 had levels greater than 800 g/m2 (and ranged over 1500 g/m2), counter to the impression given by Fridley et al.

(iv) Fridley et al. suggest, based on visual examination and no formal analysis, that there is a clear modal PRR relationship, contradicting their own claim that more high-productivity sites are needed to detect a humped relationship. However, production and richness data are log-normally distributed in this case (Adler et al., figure 2), and a random bivariate sample from a log-normal distribution will necessarily have a humped appearance in linear space (Fig. 1A). Plotting data from a bivariate log-normal distribution in log-log space (Fig. 1B) reveals the randomness. The observed data (Fig. 1, C and D) show only modest deviations from random expectations, illustrating why quantitative analyses failed to detect strong patterns.

Fig. 1

(A) Random expectations for plot-level data, based on data characteristics in figure 2 in Adler et al. (2). Note the apparent hump produced by log-normal distributions of both biomass and species richness. (B) Random expectations for Adler et al. data in log-log space. (C) Observed data in linear space. (D) Observed data in log space.

We note that even if productivity and richness were strongly correlated, we still would be unable to resolve underlying mechanisms. There have been well over 100 theories proposed to explain diversity patterns (11). A linear positive relationship is predicted by many different possible mechanisms (12), and the HBM likewise represents a large collection of conflicting theories (7).

We reiterate that it is past time to develop the multivariate expectations for our multiprocess theories and to evaluate those expectations quantitatively (13). Insights into the mechanisms controlling diversity cannot be achieved by continued fixation on bivariate patterns such as the PRR.

References and Notes

  1. Acknowledgments: This work was generated using data from the Nutrient Network collaborative experiment, funded at the site scale by individual researchers and coordinated through Research Coordination Network funding from NSF to E.T.B. and E.W.S. (grant DEB-0741952). We thank the Minnesota Supercomputing Institute for hosting project data and the Institute on the Environment for hosting network meetings. The authors declare no competing interests. The data used in the primary analyses are available in the supporting online material of our original paper. We thank G. Guntenspergen, K. McKee, and J. Powell for review of an earlier draft of the manuscript.
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