Diversity and Relationships within Crown Mammalia Robert J. Asher Department of Zoology, University of Cambridge, Cambridge, UK Introduction As with any crown group, Mammalia is defined by extinction, and comprises all descendants of the common ancestor shared by the three synapsid lineages that happen to exist today: monotremes, marsupials, and placentals. A more inclusive, apomorphy-defined synapsid clade is Mammaliaformes, composed of all descendants of the first synapsid to evolve a functional, squamosal-dentary jaw joint. In addition to Mammalia, Mammaliaformes includes Adelobasileus, Sinoconodon, morganucodonts, docodonts, and haramiyids (see chapters by Angielczyk & Kammerer and Martin, this volume). My goal in this chapter is to outline the crown clade Mammalia, to describe its major constituents, to trace how the core ideas on mammalian evolution and interrelations have developed since the early 20th century, and to summarize how certain fossil groups are related to extant, high-level clades, with an emphasis on Placentalia. Mammalian interrelationships are depicted in Fig. 1 based primarily on overlap across four phylogenetic studies using large samples of data and taxa: Meredith et al. (2011, 36 kilobases of nuclear DNA from 164 mammals), Mitchell et al. (2014, 44 kilobases of mitochondrial and nuclear DNA for 203 mammals), Tarver et al. (2016, 32 megabases of nuclear DNA for 36 mammals, 15.6 kilobases of microRNA for 42 mammals, and reanalyses of datasets from Hallström & Janke 2010, O'Leary et al. 2013, and Romiguier et al. 2013), and Esselstyn et al. (2017, ultraconserved elements from 3787 genes across 100 mammals). These studies are not completely congruent; cases of disagreement (with exceptions detailed below) have been represented with polytomies. Nonetheless, given all of the ways in which these topologies could differ (e.g., 3.37x1049 RJ Asher, "Diversity and Relationships of Crown Mammalia", Handbook of Zoology: Mammalia 1 distinct, rooted, bifurcating trees for the 36 genomically sampled taxa in Tarver et al. 2016), they are very close in overall shape and, I predict, future discoveries will agree far more than disagree with the phylogenetic relationships shown in Fig. 1. It is occasionally convenient to refer to Linnean ranks, for example that the identity of most families and orders has been established since the 19th century, but that interrelationships among orders have been well understood only since the late 1990s. I recognize the biological arbitrariness of Linnean ranks and therefore minimize their use. However, they do have some utility, as evident in the practical, legal framework articulated by the International Code of Zoological Nomenclature (ICZN, 1999). The fact that this code does not apply above the rank of family has led to inconsistency regarding the use of some high level names. Here, I follow Simpson (1945) in arbitrating among such names based on priority and stability, as summarized by Asher & Helgen (2010). On another, practical note, I capitalize taxon names when used as proper nouns and when referring to genera. For example, I capitalize formal cladistic names (e.g., mammals in the genus Homo belong to the clade Primates) but do not capitalize adjectives or common nouns (e.g., the capybara is a hystricognath rodent). Quotes surrounding a high-level taxon indicate that it is not monophyletic (e.g., "Edentata"). Another semantic but important point worth making concerns the use of adjectives like "molecular" and "morphological" to describe phylogenetic trees. One of the key postulates of evolutionary theory is that living things share common ancestry. Tree-diagrams represent this common ancestry, and investigators have used comparative anatomy, embryology, biogeography, intuition, and molecular data to build such diagrams. Broadly speaking, molecular methods have been known since the early 20th century, and encompass immunochemical (Nuttall et al. 1904) and hybridization (Kirsch et al. 1991) techniques, as well as direct comparisons of protein (Zuckerkandl & Pauling 1965) and nucleotide (Irwin et al. 1991) sequences. The ease of applying quantitative methods to compare species, along with the massive quantities of genomic characters with readily defined states, has meant that where RJ Asher, "Diversity and Relationships of Crown Mammalia", Handbook of Zoology: Mammalia 2 available, molecular data have become crucial in establishing the topology and confidence int