Linking individual behaviour to community scale patterns in fungi

The fungi comprise a separate kingdom of life and epitomise the indeterminate growth form. Very little is known about the factors that influence the nature of fungal diversity and the link between individual behaviour and the structure and function of fungal communities is particularly poorly understood. Here, we present a theoretical framework that is capable of elucidating this link. An individual-based model for fungal community dynamics is introduced that has been developed from a physiologically based model for the fungal phenotype. The model is used to explore the role of individual interactions, the production of an external inhibitor field and the quality of the external environment on the structure and diversity of the resulting community. We show that traits relating to growth rate, autophagic behaviour and the production of inhibitors are key in influencing the success of a particular genotype in a community. The species richness increases with the amount of available resource. This is the first model of fungal community dynamics that introduces the concept of a biomass-based abundance distribution function that can be described by the log-normal form which typically corresponds to communities in equilibrium. The species abundance curve was stable to changes in the relative location of inocula, although the ranked abundance of the individuals was not. We present the first attempt to identify the traits that affect the form of that curve. Future studies should examine the role of environmental heterogeneity and spore dispersal

Processing and Transmission of Information

Contains reports on two research projects.National Aeronautics and Space Administration (Grant NsG-334

Sixty Years of Fractal Projections

Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand's projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.Comment: Submitted to proceedings of Fractals and Stochastics

Golden gaskets: variations on the Sierpi\'nski sieve

We consider the iterated function systems (IFSs) that consist of three general similitudes in the plane with centres at three non-collinear points, and with a common contraction factor \la\in(0,1). As is well known, for \la=1/2 the invariant set, \S_\la, is a fractal called the Sierpi\'nski sieve, and for \la<1/2 it is also a fractal. Our goal is to study \S_\la for this IFS for 1/2<\la<2/3, i.e., when there are "overlaps" in \S_\la as well as "holes". In this introductory paper we show that despite the overlaps (i.e., the Open Set Condition breaking down completely), the attractor can still be a totally self-similar fractal, although this happens only for a very special family of algebraic \la's (so-called "multinacci numbers"). We evaluate \dim_H(\S_\la) for these special values by showing that \S_\la is essentially the attractor for an infinite IFS which does satisfy the Open Set Condition. We also show that the set of points in the attractor with a unique ``address'' is self-similar, and compute its dimension. For ``non-multinacci'' values of \la we show that if \la is close to 2/3, then \S_\la has a nonempty interior and that if \la<1/\sqrt{3} then \S_\la$ has zero Lebesgue measure. Finally we discuss higher-dimensional analogues of the model in question.Comment: 27 pages, 10 figure

Mojave Desert - Satellite Image Map

Produced for the Mojave Desert Ecosystem Program under the United States Department of Defense Legacy Program in cooperation with the Department of the Interior. Cartography and image processing by: Remote Sensing and Geographic Information Systems Laboratory Department of Geography and Earth Resources College of Natural Resources Utah State University Logan, Utah 84322–5240 Cartographic preparation and printing by U.S. Geological Survey, 1998. Image map produced from 15 Landsat Thematic Mapper images recorded from 1991–1993, provided by U.S. Geological Survey (USGS), as part of the Multi–Resolution Land Characteristics Consortium Activities. Bands 7, 4, 2. Simulated natural color composite. Land ownership compiled from 1:100,000-scale Bureau of Land Management Surface Management Status maps. Populated places produced from USGS Geographic Names Information System. Roads produced from USGS 1:100,000-scale Digital Line Graph data. Project boundary based on the Mojave Desert Section delineated by Robert G. Bailey, 1995, with a 50 kilometer buffer

Mojave Desert - Shaded Relief

Produced for the Mojave Desert Ecosystem Program under the United States Department of Defense Legacy Program in cooperation with the Department of the Interior. Cartography and image processing by: Remote Sensing and Geographic Information Systems Laboratory Department of Geography and Earth Resources College of Natural Resources Utah State University Logan, Utah 84322–5240 Cartographic preparation and printing by U.S. Geological Survey, 1998. Shaded Relief derived from U.S\u3e Geological Survey (USGS) National Elevation Database. Solar elevation 25°, azimuth 315°, exaggeration 5x, ambient light 0.5 Land ownership compiled from 1:100,000-scale Bureau of Land Management Surface Management Status maps. Populated places produced from USGS Geographic Names Information System. Roads and water bodies produced from USGS 1:100,000-scale Digital Line Graph data. Project boundary based on the Mojave Desert Section delineated by Robert G. Bailey, 1995, with a 50 kilometer buffer