Values of Beta diversity < 1

[ada59]

Hi @KaiHsiangHu,

Thank you for developing this great package! I wanted to double-check a result that I have obtained with both real data and a fictional data example to understand the behaviour of the Hill numbers. I’ve noticed that I sometimes obtain values of pairwise beta diversity below 1. From reading the paper by Chao & colleagues (https://doi.org/10.1002/ecm.1588) I understood beta < 1 was not possible, since 1 is the minimum beta diversity when the assemblages compared are completely identical (but apologies in advance if I have misunderstood the theory!). When these values emerge, I also get negative values for the Jaccard (1-U) index, which I am unsure how to interpret. I have the example below, to illustrate this result. Thanks very much in advance for any help you can offer!

Ada

require(iNEXT.beta3D) species_site_vector1 <- c(1, 1, 1, 4) # assemblage 1 (four species) species_site_vector2 <- c(1, 2, 3, 4) # assemblage 2 (four species) species_site_vector3 <- c(3, 3, 4, 4) # assemblage 3 (four species) l <- list(cbind(species_site_vector1, species_site_vector2), cbind(species_site_vector2, species_site_vector3), cbind(species_site_vector1, species_site_vector3)) outBeta <- iNEXTbeta3D(l,
diversity = "TD", q = c(0, 1, 2), datatype = "abundance", nboot=0)

[KaiHsiangHu]

Dear @ada59 ,

Thank you for your praise and support our package very much!

As you know, beta diversity is larger than or equal to 1 theoretically. But when the data size is not enough for estimation precisely or when the true beta diversity from population is almost equal to 1 (means high similarity), iNEXT.beta will may compute estimated beta diversity with bias which cause the estimated beta diversity has less than 1. (In fact, alpha diversity usually has larger bias than gamma diversity.)

Thanks again. Wish you have nice day!

Best regards KaiHsiang

[ada59]

Dear @KaiHsiangHu,

Thank you for clarifying. This is very good to know. All the best,

Ada

[Martincabruco]

Dear @KaiHsiangHu,

I hope this message finds you well. My name is Martin, and I am writing to you with a question about the results I obtained using your iNEXTbeta3D package.

We applied your package to calculate true beta diversity indices for reptile communities inhabiting cocoa agroforestry systems in three regions with different land use contexts. Because the package does not directly calculate pairwise site comparisons, we created a loop to obtain beta diversity values between pairs of sites within the same region. All analyses were conducted with a sample coverage value of 83%, as our sampling coverage varied widely among agroforests (between 0.61 and 0.98). We attempted to account for this variation when calculating multiple dimensions of reptile diversity.

However, for several pairs of sites, we obtained diversity values below 1, ranging from 0.49 to 0.99. I understand that this could be due to overestimation of alpha diversity when data are insufficient, as you mentioned in your previous answer.

Could you please advise me on how to deal with these cases, should I exclude site pairs with values significantly below 1, or would it be reasonable to include them in subsequent analyses as sites with very similar communities?

Thanks in advance for your time and guidance.

Best regards from Brazil, Martin