There are a number of commonly-used Z operations that may be paired oo. Such pairings include (1) the domain and range operations, (2) domain and range restriction, and (3) domain and range anti-restriction. Not only are the operations within each pair very closely related in terms of what they do, they also give rise to a number of very similar laws. Ockham's razor (or the Law of Parsimony) su...

The desire to minimize the number of individual new entities postulated is often referred to as quantitative parsimony. Its influence on the default hypotheses formulated by scientists seems undeniable. I argue that there is a wide class of cases for which the preference for quantitatively parsimonious hypotheses is demonstrably rational. The justification, in a nutshell, is that such hypothese...

The fact that Parsimony may fail is not new. However, here we proved that no mater of what topology the true 9-taxon and greater species tree is the only thing you need to fail Parsimony is to have in this tree three consecutive edges with lengths T1, T2, T3 of some proportions. Obviously, the probability to meet these lengths is growing in general with the size of species tree. Therefore, Pars...

Systematic and biogeographical relationships within the Hawaiian clade of the pantropical understory shrub genus Psychotria (Rubiaceae) were investigated using phylogenetic analysis of 18S-26S ribosomal DNA internal (ITS) and external (ETS) transcribed spacers. Phylogenetic analyses strongly suggest that the Hawaiian Psychotria are monophyletic and the result of a single introduction to the Haw...