These two talks are for a less mathematical audience.
The first explains the problem of measuring ecological diversity, and the problem with old, traditional measures like Shannon entropy or Gini-Simpson index. The second introduces the species similarity matrix Z and the viewpoint parameter q.
Now you know how to measure the diversity of a given community.
But if you are given the number of species and their similarity matrix Z, and the viewpoint parameter q, if you get to design a community (decide the relative abundance of each species), how would you maximize the diversity? Which distribution of relative abundances will maximize the measured diversity? The posted talk gives the answer, and the surprising result that the answer does not depend on q.
The first explains the problem of measuring ecological diversity, and the problem with old, traditional measures like Shannon entropy or Gini-Simpson index. The second introduces the species similarity matrix Z and the viewpoint parameter q.
https://www.maths.ed.ac.uk/~tl/riken/
Now you know how to measure the diversity of a given community.
But if you are given the number of species and their similarity matrix Z, and the viewpoint parameter q, if you get to design a community (decide the relative abundance of each species), how would you maximize the diversity? Which distribution of relative abundances will maximize the measured diversity? The posted talk gives the answer, and the surprising result that the answer does not depend on q.