An intensively debated issue in ecology is whether the variations biodiversity patterns of different biological groups are congruent space and time. In addition, ecologists have recognized necessity accounting for both taxonomic functional facets when analysing spatial temporal congruence patterns. This study aimed to determine how cross-taxon beta diversity varies across time, using data from ...

Let Σg,n be a compact oriented genus g surface with n boundary components. The mapping class group of Σg,n, denoted Modg,n, is the group of orientation-preserving diffeomorphisms of Σg,n that restrict to the identity on ∂Σg,n, modulo isotopies that fix ∂Σg,n. The group Modg,n plays a fundamental role in many areas of mathematics, ranging from low-dimensional topology to algebraic geometry. At l...