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