Abstract In this paper, we study area-filling curves, i.e. continuous and injective mappings defined on [0, 1] whose graph has positive measure. Current literature calls them “Osgood curves”, but their invention is due to H. Lebesgue. Stromberg Tseng constructed homogeneous curves offered an elegant example. We show that appropriate variant of Knopp’s construction attains the same homogeneity r...

biological diversity and species richness have been declined throughout the world as a result of human activities. measuring species richness is important in rangeland conservation to evaluate the status and trends of native plant species, detecting non-native species invasion and monitoring rare species. however, heterogeneity in plant distribution makes inventories difficult. in this study tw...

Phylogenetic diversity–area curves are analogous to species–area curves and quantify the relationship between the phylogenetic diversity of species assemblages and the area over which assemblages are sampled. Here, we developed theoretical expectations of these curves under different ecological and macroevolutionary processes. We first used simulations to generate curves expected under three ec...