Awesome work and question about alpha

[dmcglinn]

Dear @kpmainali,

I was very excited to read your recent paper https://www.science.org/doi/full/10.1126/sciadv.abj9204

and the R package works like a dream - nice work on the CI's.

I'm still working on digesting your approach completely. One question that arose on this thread:

https://twitter.com/Jon_Chase03/status/1490885105753067522

that I am trying to work through is how your work relates to Carmona and Pärtel (2020)

Particularly their equ. 5. It would seem that the approaches are similar but the measure of effect size is different where they are examining a difference of expected and observed co-occurrence under the hyper-geometric and your approach is to estimate the log odd ratios (i.e., co-occurrence affinity). Do I have that correctly? Did you consider the simpler equ. 5 of Carmona and Pärtel (2020). I'm just having trouble wrapping my head around the co-occurrence affinity metric and its necessity.

Also it's interesting to consider how the null expectations may change with soft (rather than hard) constraints on the row and column totals of the occurrence matrix (sensu Haegman and Etienne 2010) as it isn't clear from first principles why hard constraints should be preferred necessarily although I agree that is a common starting point in a lot of papers on this topic.

Thanks for your hard work on this important topic!

Dan

[kpmainali]

By mentioning Carmona and Partel, I am assuming you are referring to z-score as it was used in Keil 2019 Ecosphere. We have provided a detailed answer to this question in our paper (the last paragraph of the section "The affinity model"). I have also copied the response here:

By analyzing our simulated data with this approach, we show that the standardized Jaccard’s index correctly centers the value of zero at the center of null, as expected for a reliable statistic (section S2 and fig. S1, first column).... However, the standardized Jaccard’s index still presents two problems as a reliable metric. First, for a given scenario of prevalence, the distribution is not symmetric. This means that values equidistant from the center of the null in opposite directions (e.g., 2 versus −2) indicate different strengths of positive and negative association. Second, across the examples of prevalences, a given distance below the center of the null distribution can mean different degrees of negative association. As a result, standardized J results in overprediction or underprediction of the association depending on where the value falls in the null distribution and what the prevalence is (section S2 and fig. S1, third column). In contrast, the cumulative probability distribution of our metric alpha is completely free from these problems (section S2 and fig. S1, second column).

[dmcglinn]

Hey @kpmainali! Thanks for your quick reply here. Yes I was referring to the z-score approach (although I had not made that connection back to the terminology in your paper). Your logical sounds totally reasonable. We're working on improving estimates of beta-diversity using the hypergeometric is several other related projects at the moment as we build the mobr package. The dev branch has integrated the calculation of beta_C which attempts to correct for sampling effort, total number of individuals in the community, and incomplete sampling of the species pool (i.e., low coverage) (Engle et al 2021). I'd be curious to hear your thoughts about beta_C: https://github.com/MoBiodiv/mobr/blob/dev/R/beta_C.R

Our approach is somewhat unique in that we apply the hypergeometric at two scales. One at the local individual sample scale and one at the landscape scale. The comparison between the two can indicate both the scale-dependent nature of biodiversity and the degree of species turnover that is underlaid by different components of community structure.

[kpmainali]

@dmcglinn I have not forgotten this one... Currently swamped with a number of deadlines and some family situation. Will get back to it in a week or so.

[influence-of-canopy-on-temperature]

Hi, @kpmainali!
Based on your discussion with @dmcglinn, I would like to ask you if you evaluate that your index is robust to compare community matrices with different alpha and gamma diversity. I our study, we were using Simpson's dissimilarity because it is robust to changes in alpha diversity, but it is not for gamma diversity. Thus, we were randomly sampling the columns (species) of the community matrices in order to constrain the datasets to the same gamma diversity. If your index can compare datasets with different alpha and gamma diversity, we would happily switch to your approach.
Best regards,
Vitor Vieira Vasconcelos