Does conspecific negative density dependence in forests really correlate with species rarity and latitude?

By Lisa Hülsmann and Florian Hartig (U Regensburg), with short comments by Ryan Chisholm (NUS) and Matteo Detto (Princeton).

By Betteridge’s law, the answer to this question is of course no. Or better: we don’t know. But let’s back up a bit:

Global gradients in CNDD

Almost a year ago, LaManna and coauthors published a paper in Science (1), claiming that conspecific negative density dependence (CNDD) in forests, defined as the effect of local conspecific adult density on the recruit-to-adult ratio in 10x10m and 20x20m quadrats, increases toward the tropics and for rare species.

The strength and clarity of the identified effects was astonishing (at least to us), as were the implicated consequences: both in the original Science paper and in their press releases (i, ii), the authors interpret their results as suggesting that CNDD controls species abundance and diversity distributions, thus explaining causally why some species are rare and some are common, and why there is a latitudinal diversity gradient. They repeat these statements on youtube:

Our analysis of this paper

In a Technical Comment, published today in Science (2), we suggest an alternative, albeit somewhat less glamorous explanation for the results: the statistical CNDD estimators used in LaManna et al. were severely biased. And the strength of the bias depended on species abundance, and several other process and community characteristics that potentially correlate with latitude (Fig. 1, more details in our comment, see also our code on GitHub here). Because of this dependence, all the patterns reported in the original publication can emerge even when no CNDD is present whatsoever. We conclude that the methods used in LaManna et al. cannot even reliably detect the mere presence of CNDD, let alone any of the reported differences in CNDD with latitude or species abundance.


Fig. 1, from Hülsmann & Hartig: 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. The statistical methods by LaManna et al. estimate strong CNDD and CNDD-abundance correlations, although CNDD is zero in all simulations except for the CNDD subplots. Line colors correspond to parameter values in the upper subpanels; black lines depict CNDD-abundance correlations for the tropical Barro Colorado Island (BCI) forest plot. See here for details of the simulation settings.

Other responses to the arcticle

Science published a second technical comment by Ryan Chisholm and Tak Fung along with our comment, which reports similar results (Ryan also wrote a blog post about their study here). Moreover, we heard informally that Matteo Detto and colleagues had submitted another comment that was, however, not accepted for publication. We invited both to give a short summary of their conclusions regarding the study:

By Ryan Chisholm: In Chisholm and Fung (3), we show in more detail why the bias arises. LaManna et al. used an unusual “statistical trick”, whereby they transformed some data points but not others prior to model fitting, in order to account for the presence of quadrats with saplings but no adults. This “selective transformation” affected more data points in tropical than in temperate plots, which ultimately led to a greater bias in CNDD estimates in tropical plots and an artefactual latitudinal gradient in CNDD. A second statistical problem with the model was the lack of an intercept term, even though an intercept term was clearly suggested by the data and biologically is needed to account for immigration. After identifying the source of the bias, we performed a more appropriate statistical analysis, which does not use a “selective transformation” and includes an intercept in the model, and, on the same data, found no statistically detectable latitudinal trend in CNDD.

By Matteo Detto: I simulated a spatial neutral model where individuals reproduce and displace their offspring according to Gaussian dispersal and saplings become adults without interacting with neighbors.  Both the within site pattern (the rare species bias) and the between sites pattern (the latitudinal gradient) produced by the neutral model were similar to the original patterns presented in LaManna et al., suggesting again that the patterns reported in LaManna et al. may be solely a result of a biased statistical estimator (Fig. 2).


Fig. 2 (by Matteo Detto). A neutral model reproduces the variation in CNDD with species richness comparable to that found by LaManna et al. This should be impossible if the method was unbiased, because species in the neutral model are identical and no CNDD exists. LaManna et al.’s Ricker model, fitted to simulated data from a spatially explicit neutral model, produced artificially inflated median CNDD values in species-rich plots (see panel A), presumably because of a rare-species bias in estimates of CNDD (see panel B). The spatial neutral model simulates individuals on an arena of 50 ha with about 200,000 individuals. Adults disperse their offspring according to a Gaussian kernel with a standard deviation of 16 m, immigration from a metacommunity is allowed with probability = 0.1. All species are identical and no CNDD or local interactions exist. The size of the metacommunity determines local richness and each color represents a simulation with a different metacommunity.

Response by LaManna et al.

We did not see the response by LaManna et al. [to us, to C&F] before yesterday. If we had seen it before, we would have been happy to point out a few errors and misrepresentations of our arguments, in particular

  • The fact that the statistical method for estimating CNDD used in LaManna et al. is biased is a mathematically irrefutable fact (see above / our analysis). LaManna still seem to have problems to grasp that reality when stating wrt our null simulations “Some of these simulations produce spuriously strong CNDD for rare species, leading them to suggest that our methods might be biased.” (emphasis our own). We do not know how they define bias, but in our book, a method is biased if it produces wrong estimates in reasonable situations. Everyone that doubts that this is the case is welcome to run our code – unfortunately, the reverse is not true, because the code by LaManna et al. is again not made available by the authors [Edit: 27.5.18 – it seem the code has now been made available here].
  • The only question is how severe the bias is in the specific situation of this paper, and if anything else than bias is responsible for the results. We agree that this question is more difficult to answer, but the arguments brought forward by LaManna to defend the existence of a real signal are not convincing. For example, they state “If this [the bias] were correct, then our estimates of CNDD would be biased toward stronger effects for rare species at any latitude”, completely disregarding a whole paragraph in our comment and even a sentence in our abstract where we explain that a number of processes and factors (including the number of rare species) affects the bias, and that any of these processes might (and in the case of rare species certainly does) change with latitude, which explains why the bias may change with latitude.
  • In everything that follows, LaManna et al. conveniently disregard any of the other processes that we have shown to create bias, concentrating entirely on dispersal. Doing so, they first misrepresent how we simulated dispersal, stating “That is why analyses that assume global dispersal, as in Hülsmann and Hartig, underestimate or fail to detect CNDD when it is actually present”, before graciously admitting that we also considered non-global dispersal. This argument is double wrong, first because we did not assume global dispersal, except for a single simulation where we varied the dispersal parameter from zero to global, and secondly, because what they state is exactly the opposite of what we found (under global dispersal, we ALWAYS find CNDD, regardless of whether it is present or not, so there is no way we could “fail to detect CNDD”).
  • Going on about dispersal, LaManna et al. suggest that a different dispersal kernel would be more appropriate. We agree that their new kernel corresponds better to measured ecological dispersal kernels, but a) the dispersal kernel we used is (in terms of shape) the dispersal kernel they used in the simulations of their original Science paper, so it is surprising that they are so critical of this choice, and b) given our simulations (see also results by Matteo Detto above), we doubt that the change of the kernel significantly changes our conclusions. However, we will have to look at this in more detail. Unfortunately, data and code for reproducing their results is again not made available by the authors, and the description of the model in the text is certainly not sufficient to reproduce their results [Edit: 27.5.18 – it seem the code has now been made available here].


In conclusion, reading all comments and the responses by LaManna et al., we see no reason to revise our statements that

  • The statistical methods used in this paper are severely biased, and it is certainly suspicious that the bias creates pattern in null models that look very similar to the reported results
  • We wouldn’t know how to properly correct this bias, but we found none of the arguments or simulations of the authors convincing to rule out the hypothesis that all of the presented patterns are caused by processes and factors other than CNDD, in combination with the context-dependent bias.

As a last point: even if the claimed correlation could be more convincingly demonstrated, we think one should be careful about claims of causality between CNDD and large-scale diversity patterns. For example, temperature could be both a cause for higher diversity (via productivity) and stronger importance of pathogen control (CNDD) in the tropics. In such a scenario, both CNDD and diversity might appear to be causally linked, but the correlation is indeed only caused by another process that both affects CNDD and diversity. Therefore, while we think that local CNDD (if it exists) likely has strong effects on local community structure and abundance, in particular spatial patterns, we would be hesitant to postulate that this scales up, i.e. that local CNDD is a major factor for relative abundance at scales > 50m.

Site note on data / code availability

Science states that the journal aims at increasing the “transparency regarding the evidence on which conclusions are based”, including open data and code, but neither the code, nor the data for the study were deposited at Science or another independent data repository. After several emails with the authors, we were able to obtain parts of the code, but not the data. The authors referred us to exiting data sharing agreements with (mostly) their coauthors, which did not allow them to pass on the data and would have required us to request each single dataset with the responsible PI. In the end, we only used the BCI dataset, which was already available to us. We think journals should make stronger efforts to enforce that code and data is deposited in appropriate, permanent repositories. Even if data is not fully open, there should be a mechanism to make data available for reproducibility checks upon request, for example through appropriate data use agreements that must be confirmed prior to access.


  1. A. LaManna et al., Science 356, 1389–1392 (2017)
  2. L. Hülsmann & Hartig, F. Science eaar2435 (2018)
  3. A. Chisholm & Fung, T. Science eaar4685 (2018)



3 thoughts on “Does conspecific negative density dependence in forests really correlate with species rarity and latitude?

  1. Pingback: Our critique of a global forest analysis has been published in Science | Chisholm Lab

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