Technical Comments

Comment on “Conspecific Negative Density Dependence and Forest Diversity”

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Science  26 Oct 2012:
Vol. 338, Issue 6106, pp. 469
DOI: 10.1126/science.1225520


Johnson and colleagues (Reports, 18 May 2012, p. 904) claim that conspecific negative density dependence is a pervasive mechanism driving forest diversity, especially for rare tree species. We show that their results are due to a statistical bias in their analysis caused by the exclusion of joint absences.

Johnson and colleagues (1) used the correlation of seedling density with conspecific tree density to show that there is a negative density dependence, which they argue is driven by host-specific enemies. However, their analysis is biased because they only included seedling abundances of zero in plots with conspecific trees, whereas they excluded zero seedling abundances in plots that lacked conspecific trees. Excluding these joint absences (of both seedlings and adults) may result in negative biases and cause apparent conspecific density dependence.

To test the implications of this bias, we randomly generated uncorrelated tree and seedling abundances as a null model and analyzed the simulated null model community twice, once without joint absences and once with. Excluding joint absences resulted in a negative conspecific density dependence (median –0.16, Wilcoxon test P < 2.2 × 10−16) and a highly significant correlation of abundance and conspecific density dependence (P < 2.2 × 10−16). These results are essentially indistinguishable from the findings of Johnson and colleagues (Fig. 1A). Analyzing the null-model data without excluding joint absences resulted in a median density dependence of near the true value of zero and no correlation of abundance and density dependence (P = 0.25) (Fig. 1B).

Fig. 1

Analysis of the null data set with the exclusion of joint absences results in a strong negative bias (A) and negative correlation of density dependence and abundance. The same null data set analyzed with joint absences included shows no density dependence (B). Null data set generated using random, uncorrelated negative binomial distributions for both trees and seedlings. Dashed line indicates the mean density dependence in each analysis.

We applied the same procedures to 1144 20-m by 20-m forest plots on a systematic 8-km by 8-km grid spanning from 34°53'S to 47°13'S across all natural forests in New Zealand (2). We found overall positive conspecific density dependence regardless of statistical approach, but including joint absences resulted in density dependence 3.7 times more positive than when excluding joint absences (0.12 versus 0.032).

Therefore, Johnson and colleagues have not shown conspecific negative density dependence as a mechanism driving diversity. Their use of heterospecific density dependence as a null model is inappropriate, as few plots have no heterospecific trees and therefore few joint absences are excluded. The positive density dependence in the New Zealand data is most likely to result from local seed dispersal.

References and Notes

  1. Acknowledgments: I.A.D. was supported by funding from the Royal Society of New Zealand Marsden Fund and J.M.H. by the Ministry of Business, Innovation, and Employment (CO9X0802). We acknowledge the use of data from the Natural Forest plot data collected between January 2002 and March 2007 by the Land Use and Carbon Analysis System program for the Ministry for the Environment and Department of Conservation (available from
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