Is this question really relevant? We have been discussing for at least two generations of scientists on that. Once you got a measure of "taxonomic diversity" as you do it, what are you going to do? Can you effectively use it no matter the index you adopt and for what? Species richness, the number of different species in an ecosystem, as well as alpha, beta and gamma diversity was for a long time the predominant measure of global biodiversity. This is now changing rapidly (see a recently published paper in Nature http://www.nature.com/nature/journal/v501/n7468/full/nature12529.html) as researchers are realizing that rather than considering the sheer number of species, it is which specific species that are present that is crucial for ecological functions underpinning the provision of ecosystem services.

can you explain bit more your questions? What do mean by additive partitioning?

By additive partitioning I am mainly referring to the methods for decomposing total diversity across a landscape into alpha and beta diversity at different spatial scales. Specifically, I have in mind the revival and modification of Lande's model showing that total diversity in a set of communities can be viewed as the sum of alpha and beta diversities, rather than the product. And of course I am referring to methods promoted and developed by Thomas Crist and Joseph Veech among others. See the following papers:

http://onlinelibrary.wiley.com/doi/10.1034/j.1600-0706.2002.990101.x/abstract?deniedAccessCustomisedMessage=&userIsAuthenticated=false

http://onlinelibrary.wiley.com/doi/10.1111/j.1461-0248.2006.00941.x/abstract?deniedAccessCustomisedMessage=&userIsAuthenticated=false

However, Baselga in several recent papers says his method needs to be used, which uses additive partitioning, but in a way that supposedly permits differentiating spatial turnover and nestedness components of beta diversity. In addition, Baselga and Jost in papers in 2010 mainly seem to highlight that multiplicative partitioning of diversity is to be preferred over additive partitioning, because multiplicative (assuming alpha and beta sum to gamma) partitioning yeilds "independent" alpha and beta components while the additive method does not. I am saying there has been some debate about this because Crist and Veech came back again in 2010 stating this is not the case and that additive partitioning is still valid etc. etc. ... and they said that in fact neither additive nor multiplicative partitioning results in independent alpha and beta components.

So, is additive partitioning valid or not as a method to analyze diversity patterns? As someone very interested in this topic and reading the literature, but seeing that both views are supported in the literature, it is difficult to tell which method should be preferred.

Of course this hints at the more general question of what is the best way to analyze spatial patterns of community diversity and community structure.

And yet there is a paucity of freshwater studies of additive partitioning. Since posting this question, I have only found a few papers that I didn't have before, mainly from Brazil. So my other question is why the lack of freshwater studies using these methods? I would appreciate any insights anyone could give on these difficult questions.

I would suggest taking a look at Lou Jost's work.

http://www.loujost.com/Statistics%20and%20Physics/Diversity%20and%20Similarity/DiversitySimilarityHome.htm

I hope you find this useful, if you don't have it already,

Cheers,

Juan

Though it does not deal with freshwater biota, sorry.

Hey Justin,

I don't have a strong biology background so I might be missing the mark here. My beef with the Chiarucci article, and I assume other applications, is that it only adresses explanatory variables (ie that hawaii is more isolated than the canaries) as explanatory afterthoughts instead of incorporating them into the analysis from the get go. On the other hand there are some more recent techniques that try to do this, such as variation partitioning with moran's eigenvector maps. I haven't come across anythinig about looking into temporal scales that I can think of.

Here is a review of various methods which will refer to the orginal articles

http://www.researchgate.net/publication/231608665_Community_ecology_in_the_age_of_multivariate_multiscale_spatial_analysis/file/3deec51977be910b7c.pdf

and how some people applied variation partitioning to freshwater ecosystems. I only bring up this one because I read it for a paper last semester, and im sure theres some for your fishies!

http://www.sciencedirect.com/science/article/pii/S1470160X13001441

and these guys ran simulations to assess it

http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2664.2010.01861.x/full

I hope I understood your question and was able to help out

Article Community ecology in the age of multivariate multiscale spat...

Hi Justin,

One thing is the partition of gamma diversity into alpha and beta components (for which only the multiplicative partition yields independent alpha and beta components). Regarding this issue, besides the papers you mention, I would also recommend Chao et al 2012 Ecology 93: 2037–2051.

A different issue is the partition of beta diversity into turnover and nestedness-resultant components (Baselga 2010 and 2012 GEB papers). Note that this is a framework to additively partition the Sorensen index of dissimilarity (which is as monotonic transformation of multiplicative beta diversity), separating two patterns that could potentially be behind beta diversity, i.e. species substitutions from site to site and species losses from site to site.

Hope this helps.

Cheers

Andres

Is this question really relevant? We have been discussing for at least two generations of scientists on that. Once you got a measure of "taxonomic diversity" as you do it, what are you going to do? Can you effectively use it no matter the index you adopt and for what? Species richness, the number of different species in an ecosystem, as well as alpha, beta and gamma diversity was for a long time the predominant measure of global biodiversity. This is now changing rapidly (see a recently published paper in Nature http://www.nature.com/nature/journal/v501/n7468/full/nature12529.html) as researchers are realizing that rather than considering the sheer number of species, it is which specific species that are present that is crucial for ecological functions underpinning the provision of ecosystem services.

Hi Giovanni,

I would say the question on whether to use additive or multiplicative partition of diversity is still relevant. The issue is relevant for any measure of diversity (i.e. functional, phylogenetic or any other), not only for species richness, and has a deep impact on partitioning diversity into independent alpha (within samples) and beta (between samples) components. This is only possible using the multiplicative partition (see references above).

Best wishes

Andrés

Hi Andrés my point is slightly different: researchers are nowadays realizing that rather than considering any measure of diversity (i.e., functional, phylogenetic or any other kind) it is which specific species that are present that is crucial for understanding ecological functions underpinning the provision of ecosystem services. Any measure of diversity and its additive or multiplicative partition thus results rather irrelevant to this end.

Hi again,

Well, then we are talking about different things. If the assumption is that the only thing that matters is "understanding ecological functions underpinning the provision of ecosystem services", then of course measures of biological diversity are not strictly necessary (although a correlation is expected between diversity and number of functions/services). But I do not agree with this assumption. Biological diversity has its own intrinsic value, so its measurement is interesting and relevant. [By the way, interesting and relevant are subjective terms]. If two communities provide the same ecological services but one has more species than the other, I do think that the distinction matters. If we could identify the key species allowing the functioning of ecosytems, should we do not care if the redundant ones become extinct? I would care.

Cheers

Andres

Dear Andrés I am happy that you agree on my point, then if we could identify the key species supporting the functioning of ecosystems of course we should care about redundant species (insurance) once we know their ecological function. The problem is that we know almost nothing about their individual functional role. Instead of putting great emphasis on biological diversity and its partition, I believe that we should focus on this as it is really crucial for conserving biological diversity itself that, I agree, has its own intrinsic value. I would add that unfortunately biodiversity "per se" does not correlate with the flow of ecosystem services our life is strictly dependent on.

Best wishes

Neither additive nor multiplicative DP give statistically independent alpha and beta (see Veech and Crist 2010 papers in Ecology and others in the series). Nonetheless, both methods can still be useful - just be aware of the limitations.