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The rarefaction curve is a very useful statistical tool for biodiversity analysis. It represents the number of species on Y axis, adjsted by individuals, samples (Gotelli & Graves,1996; Gotelli & Colwell, 2001) or even ponds (Gioria et al 2011) on X axis. Since X axis deals with distinct kinds of units, I was wondering if other types of units could be used on X axis. Below I try to explain my doubt with this hypothetical situation: Imagine a sampling procedure** that registers on sp1 trees***, all the birds species that use this tree species for make nests. Next, on sp2 trees, again register all the birds species that use sp2 trees to make nests. Continue to collect this data on other tree species of the study area and you will end with a data table like this:

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Now here comes the questions:

(1) - With this dataset, is wrong to make a rarefaction curve using the number of tree species on X axis, and the number of nesting birds on Y axis?****

(2) - Does anyone knows any paper describing something similar to the rarefaction procedure described in question 1?

** Supose also that this example is aplied during mating season only

*** Data from sp1 tree can include only one tree(or individual) or many trees (or individuals), and so on to other tree species. This is because some tree species will be naturally rare or abundant.

**** I belive that in pratical terms, the construction of this curve is analogue to a sample-based rarefation curve, so, in other words, it is possible to made. But, it is conceptually right to made it? if so, wich kind of conclusions could and could not be made. this is a valid procedure, so one can construct a rarefaction curve for nesting bird species adjusted by the number of tree species, that we could call: tree species-based rarefaction curve for nesting bird species (a more detailed nomenclature) or species-based rarefaction curve ( a more generalized nomenclature). This kind of analysis could give anwser to this type of question: "With 5 tree species, on average, how many nesting birds species could we find?"

REFERENCES

Gotelli, N. J., & Graves, G. R. (1996). Null models in ecology.

Gotelli, N. J., & Colwell, R. K. (2001). Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness. Ecology letters, 4(4), 379-391.

Gioria, M., Bacaro, G., & Feehan, J. (2011). Evaluating and interpreting cross-taxon congruence: potential pitfalls and solutions. Acta Oecologica, 37(3), 187-194.

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Interesting question! Yes, tree species can be validly treated as sampling units (your rows, indexed by i), with the nesting bird species (columns, indexed by j) as the entities being scored for each sampling unit. But I am assuming that the actual (i,j) counts in your table represent "the number of individual trees of Tree Species i that have at least one nest of Bird Species j."

If that is what you intend, then sample-based rarefaction, with tree species as sampling units, will ignore the actual (i,j) counts and treat them as 0 if (i,j) = 0 (undetected) and 1 (detected) otherwise. (But I must say, there is notable absence of 0s in your matrix, compared to any real dataset I can imagine.)

With this approach, you can answer not only "With N tree species, on average, how many nesting bird species could we find?", but also, "If we double the number of tree species examined, in the same forest using the same methods, how many nesting bird species could we expect to find (with confidence intervals)? Or "What is the asymptotic estimate of the number of nesting bird species in this forest (with confidence intervals)?" See Colwell et al. (2012a) and Chao et al. (2016).

But, since you have counts (not just detected/undetected) for (i,j), you could also use abundance-based rarefaction, within tree species (rows), to estimate the asymptotic number (or the expected number for some number of bird species examined) of nesting bird species in each tree species. And/or you could use abundance-based rarefaction, within bird species (columns), to estimate the asymptotic number (or the expected number for some number of tree species examined) of tree species used by each bird species.

One example of a species-as-sampling unit rarefaction comes to mind. In Colwell et al. (2012b) we turned sample-based rarefaction around to estimate the number of extinct parasites that met their doom with the extinction of their hosts.

Chao, A., N. J. Gotelli, T. C. Hsieh, E. L. Sander, K. H. Ma, R. K. Colwell, and A. M. Ellison. 2014. Rarefaction and extrapolation with Hill numbers: a framework for sampling and estimation in species diversity studies. Ecological Monographs 84:45–67.

Colwell, R. K., A. Chao, N. J. Gotelli, S.-Y. Lin, C. X. Mao, R. L. Chazdon, and J. T. Longino. 2012a. Models and estimators linking individual-based and sample-based rarefaction, extrapolation, and comparison of assemblages. Journal of Plant Ecology 5:3-21.

Colwell, R. K., R. R. Dunn, and N. C. Harris. 2012b. Coextinction and persistence of dependent species in a changing world. Annual Review of Ecology, Evolution, and Systematics 43:183-203.

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