Partitioning changes in ecosystem productivity by effects of species interactions in biodiversity experiments

Reviewer #1 (Public Review):

[Editors' note: this is an overall synthesis from the Reviewing Editor in consultation with the reviewers.]

The three reviews expand our critique of this manuscript in some depth and complementary directions. These can be synthesized in the following main points (we point out that there is quite a bit more that could be written about the flaws with this study; however, time constraints prevented us from further elaborating on the issues we see):

(1) It is unclear what the authors want to do. It seems their main point is that the large BEF literature and especially biodiversity experiments overstate the occurrence of positive biodiversity effects because some of these can result from competition. Because reduced interspecific relative to intraspecific competition in mixture is sufficient to produce positive effects in mixtures (if interspecific competition = 0 then RYT = S, where S is species richness in mixture -- this according to the reciprocal yield law = law of constant final yield), they have a problem accepting NE > 0 as true biodiversity effect (see additive partitioning method of Loreau & Hector 2001 cited in manuscript).

(2) The authors' next claim, without justification, that additive partitioning of NE is flawed and theoretically and biologically meaningless. They misinterpret the CE component as biological niche partitioning and the SE component as biological dominance. They do not seem to accept that the additive partitioning is a logically and mathematically sound derivation from basic principles that cannot be contested.

(3) The authors go on to introduce a method to calculate species-level overyielding (RY > 1/S in replacement series experiments) as a competitive growth response and multiply this with the species monoculture biomass relative to the maximum to obtain competitive expectation. This method is based on resource competition and the idea that resource uptake is fully converted into biomass (instead of e.g. investing it in allelopathic chemical production).

(4) It is unclear which experiments should be done, i.e. are partial-density monocultures planted or simply calculated from full-density monocultures? At what time are monocultures evaluated? The framework suggests that monocultures must have the full potential to develop, but in experiments, they are often performing very poorly, at least after some time. I assume in such cases the monocultures could not be used.

(5) There are many reasons why the ideal case of only resource competition playing a role is unrealistic. This excludes enemies but also differential conversion factors of resources into biomass and antagonistic or facilitative effects. Because there are so many potential reasons for deviations from the null model of only resource competition, a deviation from the null model does not allow conclusions about underlying mechanisms.

Furthermore, this is not a systematically developed partitioning, but some rather empirical ad hoc formulation of a first term that is thought to approximate competitive effects as understood by the authors (but again, there already are problems here). The second residual term is not investigated. For a proper partitioning approach, one would have to decompose overyielding into two (or more) terms and demonstrate (algebraically) that under some reasonable definitions of competitive and non-competitive interactions, these end up driving the respective terms.

(6) Using a simplistic simulation to test the method is insufficient. For example, I do not see how the simulation includes a mechanism that could create CE in additive partitioning if all species would have the same monoculture yield. Similarly, they do not include mechanisms of enemies or antagonistic interactions (e.g. allelopathy).

(7) The authors do not cite relevant literature regarding density x biodiversity experiments, competition experiments, replacement-series experiments, density-yield experiments, additive partitioning, facilitation, and so on.

Overall, this manuscript does not lead further from what we have already elaborated in the broad field of BEF and competition studies and rather blurs our understanding of the topic.

Reviewer #2 (Public Review):

This manuscript is motivated by the question of what mechanisms cause overyielding in mixed-species communities relative to the corresponding monocultures. This is an important and timely question, given that the ultimate biological reasons for such biodiversity effects are not fully understood.

As a starting point, the authors discuss the so-called "additive partitioning" (AP) method proposed by Loreau & Hector in 2001. The AP is the result of a mathematical rearrangement of the definition of overyielding, written in terms of relative yields (RY) of species in mixtures relative to monocultures. One term, the so-called complementarity effect (CE), is proportional to the average RY deviations from the null expectations that plants of both species "do the same" in monocultures and mixtures. The other term, the selection effect (SE), captures how these RY deviations are related to monoculture productivity. Overall, CE measures whether relative biomass gains differ from zero when averaged across all community members, and SE, whether the "relative advantage" species have in the mixture, is related to their productivity. In extreme cases, when all species benefit, CE becomes positive. When large species have large relative productivity increases, SE becomes positive. This is intuitively compatible with the idea that niche complementarity mitigates competition (CE>0), or that competitively superior species dominate mixtures and thereby driver overyielding (SE>0).

However, it is very important to understand that CE and SE capture the "statistical structure" of RY that underlies overyielding. Specifically, CE and SE are not the ultimate biological mechanisms that drive overyielding, and never were meant to be. CE also does not describe niche complementarity. Interpreting CE and SE as directly quantifying niche complementarity or resource competition, is simply wrong, although it sometimes is done. The criticism of the AP method thus in large part seems unwarranted. The alternative methods the authors discuss (lines 108-123) are based on very similar principles.

The authors now set out to develop a method that aims at linking response patterns to "more true" biological mechanisms.

Assuming that "competitive dominance" is key to understanding mixture productivity, because "competitive interactions are the predominant type of interspecific relationships in plants", the authors introduce "partial density" monocultures, i.e. monocultures that have the same planting density for a species as in a mixture. The idea is that using these partial density monocultures as a reference would allow for isolating the effect of competition by the surrounding "species matrix".

The authors argue that "To separate effects of competitive interactions from those of other species interactions, we would need the hypothesis that constituent species share an identical niche but differ in growth and competitive ability (i.e., absence of positive/negative interactions)." - I think the term interaction is not correctly used here, because clearly competition is an interaction, but the point made here is that this would be a zero-sum game.

The authors use the ratio of productivity of partial density and full-density monocultures, divided by planting density, as a measure of "competitive growth response" (abbreviated as MG). This is the extra growth a plant individual produces when intraspecific competition is reduced.

Here, I see two issues: first, this rests on the assumption that there is only "one mode" of competition if two species use the same resources, which may not be true, because intraspecific and interspecific competition may differ. Of course, one can argue that then somehow "niches" are different, but such a niche definition would be very broad and go beyond the "resource set" perspective the authors adopt. Second, this value will heavily depend on timing and the relationship between maximum initial growth rates and competitive abilities at high stand densities.

The authors then progress to define relative competitive ability (RC), and this time simply uses monoculture biomass as a measure of competitive ability. To express this biomass in a standardized way, they express it as different from the mean of the other species and then divide by the maximum monoculture biomass of all species.

I have two concerns here: first, if competitive ability is the capability of a species to preempt resources from a pool also accessed by another species, as the authors argued before, then this seems wrong because one would expect that a species can simply be more productive because it has a broader niche space that it exploits. This contradicts the very narrow perspective on competitive ability the authors have adopted. This also is difficult to reconcile with the idea that specialist species with a narrow niche would outcompete generalist species with a broad niche. Second, I am concerned by the mathematical form. Standardizing by the maximum makes the scaling dependent on a single value.

As a final step, the authors calculate a "competitive expectation" for a species' biomass in the mixture, by scaling deviations from the expected yield by the product MG ⨯ RC. This would mean a species does better in a mixture when (1) it benefits most from a conspecific density reduction, and (2) has a relatively high biomass.

Put simply, the assumption would be that if a species is productive in monoculture (high RC), it effectively does not "see" the competitors and then grows like it would be the sole species in the community, i.e. like in the partial density monoculture.

Overall, I am not very convinced by the proposed method.

(1) The proposed method seems not very systematic but rather "ad hoc". It also is much less a partitioning method than the AP method because the other term is simply the difference. It would be good if the authors investigated the mathematical form of this remainder and explored its properties.. when does complementarity occur? Would it capture complementarity and facilitation?

(2) The justification for the calculation of MG and RC does not seem to follow the very strict assumptions of what competition (in the absence of complementarity) is. See my specific comments above.

(3) Overall, the manuscript is hard to read. This is in part a problem of terminology and presentation, and it would be good to use more systematic terms for "response patterns" and "biological mechanisms".

Examples:
- on line 30, the authors write that CE is used to measure "positive" interactions and SE to measure "competitive interactions", and later name "positive" and "negative" interactions "mechanisms of species interactions". Here the authors first use "positive interaction" as any type of effect that results in a community-level biomass gain, but then they use "interaction" with reference to specific biological mechanisms (e.g. one species might attract a parasite that infests another species, which in turn may cause further changes that modify the growth of the first and other species).

- on line 70, the authors state that "positive interaction" increases productivity relative to the null expectation, but it is clear that an interaction can have "negative" consequences for one interaction partner and "positive" ones for the other. Therefore, "positive" and "negative" interactions, when defined in this way, cannot be directly linked to "resource partitioning" and "facilitation", and "species interference" as the authors do. Also, these categories of mechanisms are still simple. For example, how do biotic interactions with enemies classify, see above?

- line 145: "Under the null hypothesis, species in the mixture are assumed to be competitively equivalent (i.e., absence of interspecific interactions)". This is wrong. The assumption is that there are interspecific interactions, but that these are the same as the intraspecific ones. Weirdly, what follows is a description of the AP method, which does not belong here. This paragraph would better be moved to the introduction where the AP method is mentioned. Or omitted, since it is basically a repetition of the original Loreau & Hector paper.

Other points:

- line 66: community productivity, not ecosystem productivity.
- line 68: community average responses are with respect to relative yields - this is important!
- line 64: what are "species effects of species interactions" ?
- line 90: here "competitive" and "productive" are mixed up, and it is important to state that "suffers more" refers to relative changes, not yield changes.
- line 92: "positive effect of competitive dominance": I don't understand what is meant here.

Reviewer #3 (Public Review):

Summary:

This manuscript by Tao et al. reports on an effort to better specify the underlying interactions driving the effects of biodiversity on productivity in biodiversity experiments. The authors are especially concerned with the potential for competitive interactions to drive positive biodiversity-ecosystem functioning relationships by driving down the biomass of subdominant species. The authors suggest a new partitioning schema that utilizes a suite of partial density treatments to capture so-called competitive ability. While I agree with the authors that understanding the underlying drivers of biodiversity-ecosystem functioning relationships is valuable - I am unsure of the added value of this specific approach for several reasons.

Strengths:

I can find a lot of value in endeavouring to improve our understanding of how biodiversity-ecosystem functioning relationships arise. I agree with the authors that competition is not well integrated into the complementarity and selection effect and interrogating this is important.

Weaknesses:

(1) The authors start the introduction very narrowly and do not make clear why it is so important to understand the underlying mechanisms driving biodiversity-ecosystem functioning relationships until the end of the discussion.

(2) The authors criticize the existing framework for only incorporating positive interactions but this is an oversimplification of the existing framework in several ways:
a. The existing partitioning scheme incorporates resource partitioning which is an effect of competition.
b. The authors neglect the potential that negative feedback from species-specific pests and pathogens can also drive positive BEF and complementarity effects but is not a positive interaction, necessarily. This is discussed in Schnitzer et al. 2011, Maron et al. 2011, Hendriks et al. 2013, Barry et al. 2019, etc.
c. Hector and Loreau (and many of the other citations listed) do not limit competition to SE because resource partitioning is a byproduct of competition.

(3) It is unclear how this new measure relates to the selection effect, in particular. I would suggest that the authors add a conceptual figure that shows some scenarios in which this metric would give a different answer than the traditional additive partition. The example that the authors use where a dominant species increases in biomass and the amount that it increases in biomass is greater than the amount of loss from it outcompeting a subdominant species is a general example often used for a selection effect when exactly would you see a difference between the two? :
a. Just a note - I do think you should see a difference between the two if the species suffers from strong intraspecific competition and has therefore low monoculture biomass but this would tend to also be a very low-density monoculture in practice so there would potentially be little difference between a low density and high-density monoculture because the individuals in a high-density monoculture would die anyway. So I am not sure that in practice you would really see this difference even if partial density plots were incorporated.

(4) One of the tricky things about these endeavors is that they often pull on theory from two different subfields and use similar terminology to refer to different things. For example - in competition theory, facilitation often refers to a positive relative interaction index (this seems to be how the authors are interpreting this) while in the BEF world facilitation often refers to a set of concrete physical mechanisms like microclimate amelioration. The truth is that both of these subfields use net effects. The relative interaction index is also a net outcome as is the complementarity effect even if it is only a piece of the net biodiversity effect. Trying to combine these two subfields to come up with a new partitioning mechanism requires interrogating the underlying assumptions of both subfields which I do not see in this paper.

(5) The partial density treatment does not isolate competition in the way that the authors indicate. All of the interactions that the authors discuss are density-dependent including the mechanism that is not discussed (negative feedback from species-specific pests and pathogens). These partial density treatment effects therefore cannot simply be equated to competition as the authors indicate.:
a. Additionally - the authors use mixture biomass as a stand-in for competitive ability in some cases but mixture biomass could also be determined by the degree to which a plant is facilitated in the mixture (for example).

(6) I found the literature citation to be a bit loose. For example, the authors state that the additive partition is used to separate positive interactions from competition (lines 70-76) and cite many papers but several of these (e.g. Barry et al. 2019) explicitly do not say this.

(7) The natural take-home message from this study is that it would be valuable for biodiversity experiments to include partial density treatments but I have a hard time seeing this as a valuable addition to the field for two reasons:
a. In practice - adding in partial density treatments would not be feasible for the vast majority of experiments which are already often unfeasibly large to maintain.
b. The density effect would likely only be valuable during the establishment phase of the experiment because species that are strongly limited by intraspecific competition will die in the full-density plots resulting in low-density monocultures. You can see this in many biodiversity experiments after the first years. Even though they are seeded (or rarely planted) at a certain density, the density after several years in many monocultures is quite low.

Reviewer #4 (Public Review):

Summary:

This manuscript claims to provide a new null hypothesis for testing the effects of biodiversity on ecosystem functioning. It reports that the strength of biodiversity effects changes when this different null hypothesis is used. This main result is rather inevitable. That is, one expects a different answer when using a different approach. The question then becomes whether the manuscript's null hypothesis is both new and an improvement on the null hypothesis that has been in use in recent decades.

Strengths:

In general, I appreciate studies like this that question whether we have been doing it all wrong and I encourage consideration of new approaches.

Weaknesses:

Despite many sweeping critiques of previous studies and bold claims of novelty made throughout the manuscript, I was unable to find new insights. The manuscript fails to place the study in the context of the long history of literature on competition and biodiversity and ecosystem functioning. The Introduction claims the new approach will address deficiencies of previous approaches, but after reading further I see no evidence that it addresses the limitations of previous approaches noted in the Introduction. Furthermore, the manuscript does not reproducibly describe the methods used to produce the results (e.g., in Table 1) and relies on simulations, claiming experimental data are not available when many experiments have already tested these ideas and not found support for them. Finally, it is unclear to me whether rejecting the 'new' null hypothesis presented in the manuscript would be of interest to ecologists, agronomists, conservationists, or others. I will elaborate on each of these points below.

The critiques of biodiversity experiments and existing additive partitioning methods are overstated, as is the extent to which this new approach addresses its limitations. For example, the critique that current biodiversity experiments cannot reveal the effects of species interactions (e.g., lines 37-39) isn't generally true, but it could be true if stated more specifically. That is, this statement is incorrect as written because comparisons of mixtures, where there are interspecific and intraspecific interactions, with monocultures, where there are only intraspecific interactions, certainly provide information about the effects of species interactions (interspecific interactions). These biodiversity experiments and existing additive partitioning approaches have limits, of course, for identifying the specific types of interactions (e.g., whether mediated by exploitative resource competition, apparent competition, or other types of interactions). However, the approach proposed in this manuscript gets no closer to identifying these specific mechanisms of species interactions. It has no ability to distinguish between resource and apparent competition, for example. Thus, the motivation and framing of the manuscript do not match what it provides. I believe the entire Introduction would need to be rewritten to clarify what gap in knowledge this proposed approach is addressing and what would be gained by filling this knowledge gap.

I recommend that the Introduction instead clarify how this study builds on and goes beyond many decades of literature considering how competition and biodiversity effects depend on density. This large literature is insufficiently addressed in this manuscript. This fails to give credit to previous studies considering these ideas and makes it unclear how this manuscript goes beyond the many previous related studies. For example, see papers and books written by de Wit, Harper, Vandermeer, Connolly, Schmid, and many others. Also, note that many biodiversity experiments have crossed diversity treatments with a density treatment and found no significant effects of density or interactions between density and diversity (e.g., Finn et al. 2013 Journal of Applied Ecology). Thus, claiming that these considerations of density are novel, without giving credit to the enormous number of previous studies considering this, is insufficient.

Replacement series designs emerged as a consensus for biodiversity experiments because they directly test a relevant null hypothesis. This is not to say that there are no other interesting null hypotheses or study designs, but one must acknowledge that many designs and analyses of biodiversity experiments have already been considered. For example, Schmid et al. reviewed these designs and analyses two decades ago (2002, chapter 6 in Loreau et al. 2002 OUP book) and the overwhelming consensus in recent decades has been to use a replacement series and test the corresponding null hypothesis.

It is unclear to me whether rejecting the 'new' null hypothesis presented in the manuscript would be of interest to ecologists, agronomists, conservationists, or others. Most biodiversity experiments and additive partitions have tested and quantified diversity effects against the null hypothesis that there is no difference between intraspecific and interspecific interactions. If there was no less competition and no more facilitation in mixtures than in monocultures, then there would be no positive diversity effects. Rejecting this null hypothesis is relevant when considering coexistence in ecology, overyielding in agronomy, and the consequences of biodiversity loss in conservation (e.g., Vandermeer 1981 Bioscience, Loreau 2010 Princeton Monograph). This manuscript proposes a different null hypothesis and it is not yet clear to me how it would be relevant to any of these ongoing discussions of changes in biodiversity.

The claim that all previous methods 'are not capable of quantifying changes in ecosystem productivity by species interactions and species or community level' is incorrect. As noted above, all approaches that compare mixtures, where there are interspecific interactions, to monocultures, where there are no species interactions, do this to some extent. By overstating the limitations of previous approaches, the manuscript fails to clearly identify what unique contribution it is offering, and how this builds on and goes beyond previous work.

The manuscript relies on simulations because it claims that current experiments are unable to test this, given that they have replacement series designs (lines 128-131). There are, however, dozens of experiments where the replacement series was repeated at multiple densities, which would allow a direct test of these ideas. In fact, these ideas have already been tested in these experiments and density effects were found to be nonsignificant (e.g., Finn et al. 2013).

It seems that the authors are primarily interested in trees planted at a fixed density, with no opportunity for changes in density, and thus only changes in the size of individuals (e.g., Fig. 1). In natural and experimental systems, realized density differs from the initial planted density, and survivorship of seedlings can depend on both intraspecific and interspecific interactions. Thus, the constrained conditions under which these ideas are explored in this manuscript seem narrow and far from the more complex reality where density is not fixed.

Additional detailed comments:

It is unclear to me which 'effects' are referred to on line 36. For example, are these diversity effects or just effects of competition? What is the response variable?

The usefulness of the approach is overstated on line 52. All partitioning approaches, including the new one proposed here, give the net result of many types of species interactions and thus cannot 'disentangle underlying mechanisms of species interactions.'

The weaknesses of previous approaches are overstated throughout the manuscript, including in lines 60-61. All approaches provide some, but not all insights. Sweeping statements that previous approaches are not effective, without clarifying what they can and can't do, is unhelpful and incorrect. Also, these statements imply that the approach proposed here addresses the limitations of these previous approaches. I don't yet see how it does so.

The definitions given for the CE and SE on line 71 are incorrect. Competition affects both terms and CE can be negative or have nothing to do with positive interactions, as noted in many of the papers cited.

The proposed approach does not address the limitations noted on lines 73 and 74.

The definition of positive interactions in lines 77 and 78 seems inconsistent with much of the literature, which instead focuses on facilitation or mutualism, rather than competition when describing positive interactions.

Throughout the manuscript, competition is often used interchangeably with resource competition (e.g., line 82) and complementarity is often attributed to resource partitioning (e.g., line 77). This ignores apparent competition and partitioning enemy-free niche space, which has been found to contribute to biodiversity effects in many studies.

In what sense are competitive interactions positive for competitive species (lines 82-83)? By definition, competition is an interaction that has a negative effect. Do you mean that interspecific competition is less than intraspecific competition? I am having a very difficult time following the logic.

Results are asserted on lines 93-95, but I cannot find the methods that produced these results. I am unable to evaluate the work without a repeatable description of the methods.

The description of the null hypothesis in the common additive partitioning approach on lines 145-146 is incorrect. In the null case, it does not assume that there are no interspecific interactions, but rather that interspecific and intraspecific interactions are equivalent.