Talk:Unified neutral theory of biodiversity and biogeography

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    Reviewer A comments

    This is a well-done article, which however leans heavily towards the theoretical side, and to a particular subset of the literature to which the authors have made important contributions.

    I would first of all encourage much more and broader discussion of data.

    It also seems a major omission not to discuss the seminal contributions of Graham Bell to the theory, and the differences between his approach and that of Steve Hubbell.

    There also should be more discussion of the criticisms of the neutral theory, for example those of Brian McGill. That having been said, I think that the authors have finessed this by properly characterizing the neutral theory as a null model, like the frictionless pendulum, the Hardy-Weinberg equilibrium, or the random walk model of movement. In such cases one should not ask whether the model represents the details of the mechanisms, but rather whether consideration of those details alters substantively the expected observations at coarser scales.

    The contributions of Maritan and colleagues should be mentioned, for example Azaele, S.; Pigolotti, S., Banavar, J. R., Maritan, A. (2006). "Dynamical evolution of ecosystems". Nature 444: 926–928.

    So too should Jerome Chave's earlier work, Chave, J., Muller-Landau, H. C. & Levin, S. A. Am. Nat. 159, 1-23 (2002), which shows that both neutral and niche models can make indistinguishable predictions under some circumstances.

    Comment by 3rd-party reader (not reviewer A)

    I think a brief discussion of how Neutral Theory moves away from the notion of 'survival of the fittest', and still has been able to accurately predict some populations, would be beneficium scientia

    Author response to reviewer A

    This review clarified our perspective and helped us toward a more balanced view of how neutral theory developed. Responding to it led us to rectify some serious, not to say embarrassing, omissions.

    Bell is now cited in our account of the historical development of neutral theory.

    We deliberately emphasize the theoretical side of neutral theory. As Hubbell realized, the usefulness, and indeed, the genuinely seductive appeal, of neutral theory is that by making very simple assumptions (never has the phrase ‘keep it simple, stupid!’ been more apt), it offers the prospect of general theory which links species-abundance distributions, species-area curves, species turnover, how fast invading species spread, and the like --- theory capable in many cases of precise prediction. Our first duty is therefore to lay out our assumptions clearly (reviewer C shows that our article needs serious improvement in this respect) and convey as clearly as a short article can how these assumptions enable so wide a range of predictions.

    Neutral theory can be used, among other things, to develop more realistic theory. For example, Volkov et al. (2005) modified the mathematics of Volkov et al. (2003) to introduce species-specific dependence, identically for every species, into their neutral theory formalism. A very logical step. Unfortunately, their model of density dependence, dn/dt = a + bn, has no ecological basis. This model underlies their later work, rendering the conclusions of papers such as Azaele et al. (2006) unsound: a pity because Volkov et al. (2003) were both clear and as accurate as circumstances required.

    Theory, however, is only as good as its connection with reality. Neutral theory has relied dangerously on fitting observed species-abundance distributions without doing anything to independently estimate values of fitted parameters. Woodcock et al. have done better than most: they looked at a series of 18 “plots” of very different sizes which drew from the same source pool at the same immigration rate. Fitting the parameters for the smallest plot, their prediction of how plot distribution of species abundance varied with plot size was unexpectedly accurate, suggesting that even species-abundance theory has some <emph>predictive</emph> value. McGill et al. (2003, 2006) have shown how to test neutral theory more rigorously, which is essential even if, as we believe, neutral theory is primarily useful as a null hypothesis. McGill’s enterprise is especially necessary considering that, as Chave et al. (2002) have shown, many mechanisms can generate the same species abundance distribution. We are most grateful to Reviewer A for focusing our attention on these papers.

    Reviewer C Comments

    Overall comments:

    I definitely think this is an interesting article about neutral theory in ecology. However, I think it misses the opportunity to cover key basic, biological concepts needed to fully understand the idea of neutral theory in ecology in a way that is understandable to the non-expert in this field. Instead, it focuses on more advanced topics related to extending the basic model. These are interesting, but their importance would be missed by the introductory reader because the background to understand their importance is not covered. In particular, the reader must be motivated more to understand why the theory is useful as a null hypothesis (i.e. understand better the biological intuition behind this hypothesis), to care about these extensions and whether they change the predictions of the theory. The key part of the biological intuition I see missing is the contrast between stable coexistence and fitness-equalized coexistence, and what might bring about neutrality or fitness-equalization, as well as the idea that plants may be rather limited in the resource axes available for them to partition. I'd like to see the more introductory parts of the article expanded, and not written assuming a thorough knowledge of neutral theory in the population genetics context, and in particular for the summary at the top to better reflect the biological hypotheses encapsulated in neutral theory. I'm also concerned about the fact that the article says in a number of places that neutral theory "ignores adaptation". I disagree with this statement in that adaptation to the biotic environment is a key hypothesis of how species become similar to one another. I do agree that the theory does not incorporate habitat heteroteneity on the landscape and that some species may be better adapted to some environments than others. This would be a departure from "neutrality". So perhaps it is just that some distinction needs to be made. Perhaps overall the article could be improved by some involvement by Hubbell himself? He is a busy guy though, and might not get around to it.

    Comments on specific parts of the particle:

    A key element I see missing from the summary at the top is some explanation of why neutral theory assumes death and reproduction are independent of species. Also, perhaps the first section could be called "Motivations and Uses of Neutral Theory", and the idea of equivalence as an alternative to species differences for getting coexistence could be emphasized more. The difference between stable coexistence and the sort of fitness-equalized coexistence that exists in a neutral model could be described. Then, I like emphasizing its use as a null hypothesis, but mention might also be made of mechanisms that could actually lead to equivalence and when it might be expected to arise (e.g. particularly in highly diverse systems). The authors could also mention the alternative way neutral theory has been interpreted, as a model meant to predict the species abundance distribution and other macroecological patterns that some argue may not be sensitive to the coexistence mechanism or other details about the system--i.e. it is just a simplified model.

    Also, I was concerned about a particular sentence in the "Uses of Neutral Theory" section. The authors say that neutral theory "ignores adapatiation". I don't agree with this because it is adaptation to the biotic environment (interactions with other species) that is a key hypothesis about why similar species might arise.

    As I mentioned briefly above, in the "Basic Formalism and the Species Abundance Distribution" section I think it would be better to explain the formalism of neutral theory in ecology without drawing on population genetics knowledge at first, then describe analogy with neutral theory of population genetics later.  That way even someone that doesn't know the neutral theory of population genetics well would be able to understand it.

    The section on "Modelling speciation" could also be clearer. I haven't had the chance to read Rosindell's work yet (although I am really looking forward to it), and I had a little trouble understanding the advance here. There is a lot of detail on one mathematical point, without a clear explnation of what is meant that "Rosindell et al. (2010) solved the problem". Does this mean they came up with an analytically tractable neutral theory that incorporates a wide range of speciation modes? What predictions were they able to get? How much do the predicted patterns differ from the original case. More overview like this would be more useful than formulas.

    Similarly, the main point of "The spatially implicit neutral model section" section is unclear.

    There also seems to be a problem with equation in the "Neutral theory and biogeography" section. Is this an expression for z? Also, for many this is just a part of biogeography--biogeography is more about which species are where. Evan Economo has done some interesting work on patterns of nestedness predicted by neutral theory that could be mentioned here, although I am not sure if his papers are out yet. You could request from him, though.

    In the "Neutral theory as a null hypothesis" section, "Parthenogen" seems rather jargony, and it seems some mention should be made of potential resolutions to the issue raise, perhaps that the community was limited to a refuge (not sure if this is relevant here). Also, I'm confused by what is said--the species both spread faster and some species resisted more than neutral theory predicts. Doesn't it have to be one or the other?

    Author response to reviewer C

    Overall comments

    Although the viewpoints of Reviewers A and C are very different, correcting the faults pointed out by Reviewer A, and other faults we became aware of in our response, addressed some of the concerns of Reviewer C.

    Reviewer C is all too justified in asking us to be clearer about our assumptions and their biological relevance. Neutral theory is useful because, by making simple assumptions that capture the essence of multipopulation dynamics when not encumbered by adaptive divergence between species, one can frame a general theory encompassing species abundance distributions, species area curves, species turnover, rate of spread of successful invaders, which often makes precise predictions.

    Hubbell, like Caswell before him, modeled ecological neutral theory on the neutral theory of population genetics, which, in Kimura’s capable hands, generated a vast array of predictions from comparably simple, indeed formally identical, assumptions. As it destroys the usefulness of words to change their meaning arbitrarily, I retain the definition of neutral theory implied by Caswell (1976) and Hubbell (1979, 1997, 2001).

    Therefore we will begin by presenting our assumptions, and the reasons for them, before going ahead with the population genetics analogy. It will be made clear that Hubbell’s assumption that an individual’s prospects of death or reproduction are independent of species, is what makes Hubbell’s neutral theory capable of its remarkably vast range of prediction, as the analogous assumption did for neutral theory in population genetics. Leigh has not forgotten Kimura’s telling him how thrilling it was when, thanks to neutral theory, he could finally make precise, testable, meaningful predictions in population genetics. Using neutral theory as a null hypothesis helps one get on with Hubbell’s program of how satisfactorily explanations of species diversity in terms of adaptive divergence explain the data.

    We will have to make clear that neutral theory does not predict stable coexistence. The stuff about neutral theory ignoring adaptation will be dropped: the coauthors disagree over the sense, if any, in which neutral theory ignores adaptation, but, more to the point, we derive the same conclusions from the same mathematics, so our beliefs concerning this wording make no empirical difference whatever. Nonetheless, the argument that communities evolve toward neutrality seems too speculative to put in an encyclopedia article.

    We recently sent a copy of this article to Hubbell and invited him to comment on it if he wishes.

    Specific comments

    First paragraph. Re fitness equalization. It is clear that species diversity represents a balance between speciation and extinction. Even in diverse forests, populations of individual tree species show distinct signs of regulation by their own density. It does appear that the validity of the neutral theory of species-area curves far transcends the validity of the neutral assumption itself, and this must be pointed out in the appropriate place. This may be true for other aspects of neutral theory. Unfortunately, until we can derive species-abundance distributions without assuming panmictic source pools we had all better keep quiet about the significance of well-fit species abundance distributions. Please note that panmictic source pools have nothing to do with neutrality, and everything to do with the limitations of neutral theorists, including ourselves

    Second paragraph: the stuff about “ignoring adaptation” is being omitted.

    Third paragraph. Definitions are meant to be short. Most of this will be addressed in “Species Abundance Distributions: The Basic Framework

    Fourth paragraph: I hope the Rosindell speciation story, finally presented in detail, is now clear.

    Fifth paragraph: the material on the spatially implicit neutral model has been reorganized and reworked in a way that we hope clarifies things. We have cited Economo and Keitt (2009) in this connection.

    Sixth paragraph. Yes, I presented a formula for z. This formula remains the closest neutral theory has yet come to estimating speciation rate u. Because we were asked to present the unified neutral theory of biodiversity <emph>and biogeography</emph>, and species-area curves appeared in Hubbell’s book, they belong here.

    Seventh paragraph. I am sorry about the jargon. On the other hand, we do not think this is the place for this article to suggest that the world is really neutral when neutral theory does so poorly in tests concerning predictions of change with time. The world would be much poorer without neutral theory, because it is a wonderful null hypothesis: trying to paint it as the truth would be a fruitless exercise.

    We thank the reviewer, whose comments have helped us to improve the manuscript.

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