Anthropoid humeri from the late Eocene of Egypt

A number of recent studies have, by necessity, placed a great deal of emphasis on the dental evidence for Paleogene anthropoid interrelationships, but cladistic analyses of these data have led to the erection of phylogenetic hypotheses that appear to be at odds with biogeographic and stratigraphic considerations. Additional morphological data from the cranium and postcranium of certain poorly understood Paleogene primates are clearly needed to help test whether such hypotheses are tenable. Here we describe humeri attributable to Proteopithecus sylviae and Catopithecus browni, two anthropoids from late Eocene sediments of the Fayum Depression in Egypt. Qualitative and morphometric analyses of these elements indicate that humeri of the oligopithecine Catopithecus are more similar to early Oligocene propliopithecines than they are to any other Paleogene anthropoid taxon, and that Proteopithecus exhibits humeral similarities to parapithecids that may be symplesiomorphies of extant (or “crown”) Anthropoidea. The humeral morphology of Catopithecus is consistent with certain narrowly distributed dental apomorphies—such as the loss of the upper and lower second premolar and the development of a honing blade for the upper canine on the lower third premolar—which suggest that oligopithecines constitute the sister group of a clade containing propliopithecines and Miocene-Recent catarrhines and are not most closely related to Proteopithecus as has recently been proposed.

Symmetries in geology and geophysics

Symmetries have played an important role in a variety of problems in geology and geophysics. A large fraction of studies in mineralogy are devoted to the symmetry properties of crystals. In this paper, however, the emphasis will be on scale-invariant (fractal) symmetries. The earth’s topography is an example of both statistically self-similar and self-affine fractals. Landforms are also associated with drainage networks, which are statistical fractal trees. A universal feature of drainage networks and other growth networks is side branching. Deterministic space-filling networks with side-branching symmetries are illustrated. It is shown that naturally occurring drainage networks have symmetries similar to diffusion-limited aggregation clusters.

Scaling in geology: landforms and earthquakes.

Landforms and earthquakes appear to be extremely complex; yet, there is order in the complexity. Both satisfy fractal statistics in a variety of ways. A basic question is whether the fractal behavior is due to scale invariance or is the signature of a broadly applicable class of physical processes. Both landscape evolution and regional seismicity appear to be examples of self-organized critical phenomena. A variety of statistical models have been proposed to model landforms, including diffusion-limited aggregation, self-avoiding percolation, and cellular automata. Many authors have studied the behavior of multiple slider-block models, both in terms of the rupture of a fault to generate an earthquake and in terms of the interactions between faults associated with regional seismicity. The slider-block models exhibit a remarkably rich spectrum of behavior; two slider blocks can exhibit low-order chaotic behavior. Large numbers of slider blocks clearly exhibit self-organized critical behavior.