Biplots in Reduced-Rank Regression

Regression problems with a number of related response variables are typically analyzed by separate multiple regressions. This paper shows how these regressions can be visualized jointly in a biplot based on reduced-rank regression. Reduced-rank regression combines multiple regression and principal components analysis and can therefore be carried out with standard statistical packages. The proposed biplot highlights the major aspects of the regressions by displaying the least-squares approximation of fitted values, regression coefficients and associated t-ratios. The utility and interpretation of the reduced-rank regression biplot is demonstrated with an example using public health data that were previously analyzed by separate multiple regressions.     

Aquatic ecosystem responses to fire and flood size in the Okavango Delta: observations from the seasonal floodplains

The frequency of fires in the Okavango Delta seasonal floodplains peaked at an intermediate frequency of flooding. Floodplains are commonly burnt every 3–5 years. This study showed fundamental changes in ecosystem properties due to burning. A burnt seasonal floodplain in the aquatic phase had oxygen levels well above saturation, 100–200%, while the levels in the un-burnt control site were below saturation and, at night, could decline to 10–40% saturation. The total phosphorous and total nitrogen concentrations were similar on both floodplains but considerably enriched relative to inflowing water, due to nutrient release from the flooded soil-sediment and animal droppings. Zooplankton biomass was very high in both systems although the abundance of fish fry was ten times higher on the un-burnt floodplain. In a low flood year the un-burnt floodplain water had high nutrient levels, primary production, methane emission, and subsequent uptake of methane in biota, as well as a high zooplankton biomass. The very high flood the following year showed the opposite with much lower production at all levels owing primarily to greater dilution of nutrients. The abundance of fish, however, was much higher during the high flood year. Macrophytes and litter provide direct shelter for fish fry but also promote low oxygen levels when decaying. Large flooded areas result in high fish production by removing obstacles related to congestion. This interplay between hydroperiod and fire may be crucial for the maintenance of high biological productivity both in the aquatic and terrestrial phases in a very nutrient poor wetland landscape. Understanding these interactions is crucial for optimal management.     

Filamentous bacteriophage Pf1 structure determined at 7 Å resolution by refinement of models for the α-helical subunit

The molecular structure of filamentous bacteriophage Pf1 has been determined to 7 Å resolution by analysis of X-ray diffraction data from partially oriented fibers of virus particles. The continuous intensity distribution along layer-lines was measured by numerically separating contributions from overlapping layer-lines. The data were phased by an iterative refinement technique that used the known spatial extent and high α-helical content of the virus particle to refine a structural model. This refinement converges to a unique structural solution that is consistent with the X-ray data and with information derived from physical and chemical studies. The coat protein consists of two α-helical segments: one, almost parallel to the particle axis, is centered at a radius of about 15 Å; the other, at about 25 Å radius, is tilted by about 25 ° to the particle axis. This structure is consistent with every generalization about α-helical packing. The inner and outer segments interlock along most of their length with a crossing angle of 20.5 °. The inner α-helical segments also interact with symmetry-related copies of themselves, as do the outer segments. The double layer of tightly packed, intricately interlocked α-helices forms a stable, 20 Å thick protein coat around the viral DNA.