Technical Comments

Comment on “Plant diversity increases with the strength of negative density dependence at the global scale”

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Science  25 May 2018:
Vol. 360, Issue 6391, eaar2435
DOI: 10.1126/science.aar2435


LaManna et al. (Reports, 30 June 2017, p. 1389) claim that subadult trees are proportionally less common at high conspecific adult density (CNDD) and that this effect increases toward the tropics and for rare species. We show that the CNDD-abundance correlation may have arisen from a methodological artifact and that a range of processes can explain the reported latitudinal pattern.

Conspecific negative density dependence (CNDD) has long been discussed as a key mechanism for maintaining local species richness and global biodiversity patterns. LaManna et al. (1) analyzed CNDD in 24 plots of the global CTFS-ForestGEO network, defining density dependence as an effect of local adult density on the recruit/adult ratio in 10 m × 10 m and 20 m × 20 m quadrats. Fitting this ratio against conspecific adult density with Ricker and offset-power models, they found that CNDD increases toward the tropics and with species rarity.

After carefully examining their statistical analysis, we believe that these patterns, intriguing as they are, may have arisen from a methodological artifact. We simulated synthetic data under a range of processes with and without CNDD (2) and found that both Ricker and offset-power models produce biased CNDD estimates as soon as a process breaks the spatial coupling between adults and recruits. For example, dispersal, adult mortality, or niche processes (35) can produce CNDD and CNDD-abundance correlations compatible with values reported in LaManna et al., despite no CNDD being present whatsoever (Fig. 1). Moreover, the strength of the bias depends on community characteristics such as species richness or adult proportion, which suggests an alternative explanation for the reported latitudinal pattern.

Fig. 1 Processes and community characteristics that create artifacts in estimated CNDD patterns.

(A and B) Weighted mean CNDD (A) and CNDD-abundance correlations (B) estimated by the Ricker model with simulated data, varying ecological parameters (CNDD, dispersal, adult survival, habitat specificity), and community characteristics (species richness, proportion of adults) at the 10 m × 10 m scale. CNDD is zero except for the CNDD subplots where the same value was used for all species. See (2) for details of the simulation settings. Line colors correspond to parameter values in the upper subpanels; black lines depict CNDD-abundance correlations for the tropical Barro Colorado Island (BCI) (16) forest plot. Parameters estimation follows LaManna et al.

One can understand the reason for this bias. If recruitment is not entirely local, the assumption that local counts of adults (A) and recruits (S) should be directly proportional does not hold, even without any CNDD (6). A special example of this is the frequent quadrats with recruits but no adults in the data. To explain these observations, the authors introduced a background adult density of A = 0.1 in the Ricker model. This decision, however, creates S/A ratios of ≥10 for the corrected observations with A = 0.1 and S > 0, much higher than the mean ratio of approximately 4 in the data where A > 0. To explain these seemingly high reproduction ratios in quadrats with only background adult density, the Ricker model must wrongly assume high intrinsic growth paired with strong density dependence (Fig. 2C). And because S > 0 and A = 0 occur more frequently for rare species and in the tropics, CNDD values and CNDD-abundance correlations emerge that are compatible with the patterns reported in LaManna et al., even when no CNDD is present (Fig. 2A).

Fig. 2 CNDD bias in Ricker and offset-power models.

(A and B) Estimated CNDD versus abundance [log10(N/ha)] per species from the Ricker model (A) and the offset-power model (B) at the 10 m × 10 m scale. Grayscale circles result from data simulated randomly without CNDD and changing spatial association between adults and recruits, ranging from perfect spatial coupling (lightest gray) to no spatial association (black). Blue triangles depict CNDD estimates for the tropical BCI (16) forest plot; orange squares denote the simulation model without CNDD used in the appendix of LaManna et al. (C) For the Ricker model, CNDD bias is highly correlated with the proportion of corrected adult counts. (D) Fitting a species-specific recruit/adult ratio in the offset-power model removes the CNDD-abundance correlation. See (2) for details of the simulation settings.

In the offset-power model, zeros were dealt with differently by adding a value of 1 to all observations. Again, this distorts recruit/adult ratios, as S/A ≠ (S + 1)/(A + 1), and more so for rare species with smaller values of S and A. When LaManna et al. then fitted a mixed-effects model with a random species effect on the CNDD slope but no random intercept (7), the rarity-dependent S/A distortion is compensated by species-specific CNDD (Fig. 2B). When we fitted the more natural standard random slope and intercept model that accounts for species-specific S/A ratios, the CNDD-abundance correlation vanished in simulated and real data (Fig. 2D).

LaManna et al. realized that CNDD estimates could be biased and therefore ran a number of simulations and null models to explore and potentially correct this bias. However, our results (Figs. 1 and 2) clearly contradict their assertion that their “results are generally robust to these potential biases.” Examining their null models, we find several shortcomings: (i) Their analyses and corrections often only pertained to mean values and not to CNDD-abundance correlations, and where they did, simulations were not run with those critically low abundances that distort CNDD estimates; (ii) their null simulations included only dispersal, but none of the other factors that we show to create bias (Fig. 1); and (iii) their assumption that only 10% of the recruits derive from outside the quadrats produces unrealistically low dispersal relative to empirical values for primary dispersal (8). Even a uniform kernel with a 10-m radius would predict 52% of all seeds to disperse outside a 10 m × 10 m quadrat. With our null simulations, we tend to find clear CNDD signals and CNDD-abundance correlations similar to what LaManna et al. reported under perfectly neutral (CNDD = 0) conditions. Accordingly, we find their low CNDD estimates for rare temperate species far more surprising than strong CNDD and CNDD-abundance slopes in the tropics.

A reliable correction of CNDD estimates, even with more realistic null models, seems very difficult. One would require species-specific values for dispersal and all other spatial processes that we have shown to influence CNDD estimates (9). Species-specific values are important because a correlation of traits such as dispersal or habitat specificity with species abundance or latitude could create additional artifacts (10), let alone the effect of intraspecific trait variation. Based on this, we believe it is virtually impossible to devise appropriate corrections or null models for the analysis presented by LaManna et al. Directly analyzing CNDD in demographic rates such as growth and mortality of saplings (11), which are much less affected by dispersal, seems far more promising to us.

The biased estimator questions the evidence for the reported CNDD patterns, but does not constitute proof of their absence. Yet, when combining our analysis with general ecological knowledge, we find it rather unlikely that the patterns reported in LaManna et al. are primarily caused by CNDD. A previous study found no support for a latitudinal CNDD pattern in tree mortality (12), and although some studies have reported CNDD-abundance correlations in the tropics (11, 13), effect sizes tended to be much smaller than what LaManna et al. reported, particularly as they inappropriately contrasted CNDD and heterospecific density effects. Strong CNDD-abundance correlations also seem unlikely from theoretical considerations. It is frequently assumed that CNDD is mediated by specialized pathogens (14). It would be surprising if such strict mutualisms could persist and exert effective control for exceedingly rare species. Moreover, if CNDD applied only to rare species, these would be stabilized against each other, but the question remains how infrequent species could escape competition from common ones that do not suffer from strong CNDD.

If not real CNDD, what then causes the latitudinal patterns in the (biased) CNDD estimates? Diversity differences alone could create a latitudinal pattern in mean CNDD but would not lead to a latitudinal shift of the CNDD-abundance correlation (Fig. 1). However, either latitudinal differences in spatial processes [e.g., stronger habitat effects or reduced dispersal in temperate regions (9)] or latitudinal differences in the size structure could create the pattern. Size structure is a highly sensitive parameter for the bias because LaManna et al. distinguished adults and recruits according to their diameter (Fig. 1, adult proportion). Because the original data were not fully available to us, we could not examine these possibilities in more detail.

We believe that LaManna et al.’s results should be interpreted far more carefully. Given the instability of the statistical methods, we do not see strong evidence for any of the reported CNDD patterns. To us, the findings mainly suggest that the spatial association between adults and recruits in the tropics is surprisingly weak, as already reported by (15), and that either this spatial association becomes stronger toward the temperate zone, or another parameter (possibly size structure) creates the latitudinal pattern in the biased estimator. A latitudinal gradient of abundance-dependent CNDD would also be compatible with our findings, but overall, we find it far more likely that a range of ecological processes—possibly in combination with CNDD, but not primarily driven by it—are responsible for the reported patterns.

References and Notes

  1. Code and technical details of the data simulations and analyses are archived at
  2. Note that LaManna et al. stated that they applied a random intercept and slope for CNDD (supplementary material, p. 5), but the code we obtained from the authors suppresses the random intercept, which is in line with the results they reported.
Acknowledgments: We thank R. Condit and S. P. Hubbell for providing the BCI data and for discussion that improved this comment. The BCI forest dynamics research project was founded by S. P. Hubbell and R. B. Foster and is now managed by R. Condit, S. Lao, and R. Perez under the Center for Tropical Forest Science and the Smithsonian Tropical Research Institute in Panama. Numerous organizations have provided funding, principally the U.S. National Science Foundation, and hundreds of field workers have contributed.
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