Hill numbers have become an elegant and powerful unifying tool in the measurement of many levels of biological diversity. Although mathematically possible, the use of negative values for the exponent q seems to lack biological interpretation. Is that always correct? If the aim of a study is to over-emphasize rare taxa, should we go beyond (or "below") species richness (q = 0) in such case?
Rodrigo Alves, Exactly, the use of negative ( q ) exponents in the formula of Hill numbers is justifiable in specific ecological and conservation contexts, particularly when the emphasis on rare species is crucial. In conservation prioritization, negative ( q ) values highlight endangered or rare species, directing efforts towards their protection. Additionally, these exponents can underscore the importance of rare species in ecosystem stability and resilience, where their unique ecological functions are critical. Negative ( q ) values are also valuable in assessing species turnover, providing insights into how rare species' distributions change across different habitats. Furthermore, they can correct for sampling biases in biodiversity studies, ensuring that underrepresented rare species are given appropriate weight. Thus, negative ( q ) exponents are essential in scenarios where the presence and roles of rare species are of significant interest.
Wish you Goodluck!
Hi, Rodrigo. Hope you're doing well.
I'm afraid to say that you should not use the abundance weighting factor "q" below zero. It has some mathematical and ecological issues. First, the main researchers on Hill numbers (Chao, Jost, Hsieh, Gotelli) have never recommended you to do so. I'm not telling you to strictly follow other researchers perspective, but if it was something that matters, they would've highlighted it. Second, in the core equation for Hill numbers you have the exponential 1/(1-q), if you use negative q, then 1/(1-(-2)) ≡ 1/(1+2) for example, you have a positive exponential 1/3 for your weighting parameter (mathematical issue). That would output surrealistic and irrelevant patterns of your assemblage with effective diversity values high above the empirical richness that you have, where almost all of it would be considered as rare species and no assessment will be reliable (ecological issue). If you a looking to measure variations of rare species, use Hill numbers (q=0,1,2) at alpha and beta levels and you'll have a full description of what is going on with your assemblages. Stay aware that the beta diversity with Hill numbers are not subdivided into turn-over and nestedness and you wil not be able to access the species identity.
Cheers
Matheus