Let G1 and G2 be simple graphs and let n1 = |V (G1)|, m1 = |E(G1)|, n2 = |V (G2)| and m2 = |E(G2)|. In this paper we derive sharp upper and lower bounds for the number of spanning trees τ in the Cartesian product G1 G2 of G1 and G2. We show that: τ(G1 G2) ≥ 2(n1−1)(n2−1) n1n2 (τ(G1)n1) n2+1 2 (τ(G2)n2) n1+1 2 and τ(G1 G2) ≤ τ(G1)τ(G2) [ 2m1 n1 − 1 + 2m2 n2 − 1 ](n1−1)(n2−1) . We also characteri...

Abstract: Surveys were carried out for chimpanzees, Pan troglodytes schweinfurthii, in the areas of Ntakata (300 km2 between the Mkamba River and the Lubalisi River, 05°45′ –06°15′ S, 30°00′ –30°15′ E), and Kakungu (200 km2 between the Lubalisi River and the sources of the Rubufu River, 05°55′ –06°15′ S, 30°00′ –30°15′ E), Tanzania, during the dry seasons of 2001 and 2003. The predominant veget...

The interplay of gene flow, genetic drift, and local selective pressure is a dynamic process that has been well studied from a theoretical perspective over the last century. Wright and Haldane laid the foundation for expectations under an island-continent model, demonstrating that an island-specific beneficial allele may be maintained locally if the selection coefficient is larger than the rate...

Coevolution is one of the major processes organizing the earth's biodiversity, but it remains unclear when and how it may generate species diversity. The study by Parchman et al. () in this issue of Molecular Ecology provides the clearest evidence to date that divergent local adaptation in a coevolving interaction may lead to speciation on one side of an interaction but not necessarily on the o...

The Polar Regions have long been recognized as important sinks for the aerosol, including mercury derived from natural and anthropogenic sources at lower latitudes. The volatile metals like Hg and Pb introduce to atmosphere mostly through burning of fossil fuel. Generally, the distribution of mercury in environmental media is related to pH, oxygen content, organic matter, reducing agents and mi...

Topography describes the complex form of a surface--the undulations which make up its character. Topography comes in all shapes and forms; what is true for the surface of our planet is also true for the surfaces of engineered structures. If you have ever driven across the Flint Hills in south-eastern Kansas, you probably recognize that the only indicator you have that you are climbing a hill is...

People judged the inclination of hills viewed either out-of-doors or in a computer-simulated virtual environment. Angle judgments were obtained by having people (1) provide verbal estimates, (2) adjust a representation of the hill's cross-section, and (3) adjust a tilt board with their unseen hand. Geographical slant was greatly overestimated according to the first two measures, but not the thi...

A 27-year-old Chinese male presented with a 2-year history of headache and a right temporal field defect. A magnetic resonance imaging (MRI) scan revealed a 5cm tumour in the sphenoid with bilateral cavernous sinus extension and posterior extension to the clivus (Figure 1A). This was reported as an erosive skull base tumour and he was referred to neurosurgery. His serum prolactin was measured a...