Probability distributions and statistical inference for axial data

Observations on axes which lack information on the direction of propagation are referred to as axial data. Such data are often encountered in enviromental sciences, e.g. observations on propagations of cracks or on faults in mining walls. Even though such observations are recorded as angles, circular probability models are inappropriate for such data since the constraint that observations lie only in [0, π) needs to be enforced. Probability models for such axial data are argued here to have a general structure stemming from that of wrapping a circular distribution on a semi-circle. In particular, we consider the most popular circular model, the von Mises or circular normal distribution, and derive the corresponding axial normal distribution. Certain properties of this distribution are established. Maximum likelihood estimation of its parameters are shown to be surprisingly, in contrast to trigonometric moment estimation, numerically quite appealing. Finally we illustrate our results by several real life axial data sets. Received: September 2004/ Revised: December 2004     

Covariates affecting spatial variability in bison travel behavior in Yellowstone National Park.

Understanding mechanisms influencing the movement paths of animals is essential for comprehending behavior and accurately predicting use of travel corridors. In Yellowstone National Park (USA), the effects of roads and winter road grooming on bison (Bison bison) travel routes and spatial dynamics have been debated for more than a decade. However, no rigorous studies have been conducted on bison spatial movement patterns. We collected 121 380 locations from 14 female bison with GPS collars in central Yellowstone to examine how topography, habitat type, roads, and elevation affected the probability of bison travel year-round. We also conducted daily winter bison road use surveys (2003-2005) to quantify how topography and habitat type influenced spatial variability in the amount of bison road travel. Using model comparison techniques, we found the probability of bison travel and spatial distribution of travel locations were affected by multiple topographic and habitat type attributes including slope, landscape roughness, habitat type, elevation, and distances to streams, foraging areas, forested habitats, and roads. Streams were the most influential natural landscape feature affecting bison travel, and results suggest the bison travel network throughout central Yellowstone is spatially defined largely by the presence of streams that connect foraging areas. Also, the probability of bison travel was higher in regions of variable topography that constrain movements, such as in canyons. Pronounced travel corridors existed both in close association with roads and distant from any roads, and results indicate that roads may facilitate bison travel in certain areas. However, our findings suggest that many road segments used as travel corridors are overlaid upon natural travel pathways because road segments receiving high amounts of bison travel had similar landscape features as natural travel corridors. We suggest that most spatial patterns in bison road travel are a manifestation of general spatial travel trends. Our research offers novel insights into bison spatial dynamics and provides conceptual and analytical frameworks for examining movement patterns of other species.     

A role forAmanita muscaria L. in the circulation of cadmium and vanadium in a non-polluted woodland

The sporophore of the fungusAmanita muscaria L. contains greatiy elevated levels of cadmium (29.9 g g^–1 dwt) and vanadium (344.9 g g^–1 dwt) in comparison with the soil in a birch woodland (total (HNO₃-extractabie Cd 0.4 g g^–1 dwt, V 11.7 g g^–1 dwt). The significance of this remarkable concentration of normally rare and dispersed elements in terms of their circulation in the woodland has been investigated. Both elements are released from sporophore tissue in a form which can be taken up by a test plant (lettuce), cultivated in the woodland soil amended with different quantities of sporophore tissue, Cadmium levels in all plant tissues were elevated in comparison to the non-amended controls; only root vanadium levels responded to the amendment of the soil. The results are discussed in terms of their significance for the natural cycling of both elements. It is calculated that an abundant population of sporophores could circulate 1.4% of the total cadmium and 0.65% of the total vanadium pool found in the litter layer and 0–5 cm soil horizon in the sampled woodland over a period of 14 days (mean life span of a sporophore).     

Female-enhanced male competition determines the first mate and principal sire in the spider Linyphia litigiosa (Linyphiidae)

Summary Two to five days before sexual maturation, female sierra dome spiders (Linyphia litigiosa: Linyphiidae) undergo a transformation in their behavior toward males that visit their webs. During this latter part of their penultimate instar, females change from consistently positioning themselves far away from males to actively maintaining close proximity, reactions I call avoidant and associative behavior, respectively. Consistent associative behavior ceases after the female's first mating and thus is limited to soon-to-mature penultimate females. When a mate-seeking male fords an associative female, he attempts to guard her until she matures; this is often a multi-day affair. In contrast, males guard immature avoidant and mature mated females for only a single day. This dichotomy in male guarding times can be understood by the fact that associative behavior signals that the female will soon develop peak reproductive value. Upon completion of their final molt, 98% of females immediately mate with the current guarding male. Secondary suitors are not as likely to achieve mating. Moreover, first mates father 1.8 times more offspring, on average, than secondary mates. Whenever they meet on any female's web, males fight until one of the contestants withdraws. Fights typically are intensive, occasionally deadly, and often result in usurpation of the web by the newly arriving male. Larger males win more fights, but other qualities (e.g., vigor and persistence) appear to be important when contestants differ by less than 10–20% in body weight. Prolonged (i.e., multi-day) guarding of associative females enhances the intrasexual selection process by ensuring that every male that arrives at the web finds it already guarded. Therefore every male that finds the web becomes a participant in a series of male-male conflicts and web usurpations which span the period between the resident female's commencement of associative behavior and her sexual maturation. Since unforced male departures from the webs of associative females are rare, victors are retained on the web until they themselves lose a fight. This facilitates a steady increase in the fighting ability of sequential guards throughout the associative period, up until female maturation and mating. On my study site, first mates represented the final winners in a combative sorting process based on a minimum average of 2 fights; they were heavier and larger than secondary mates and randomly sampled males. The combination of (1) associative behavior by nearly mature females, (2) high mating propensity of newly mature females, and (3) first male sperm priority, constitutes a system whereby females enhance male-male competition and boost the expected fighting prowess of the principal sire of their progeny. Since males appear to make no material contribution toward progeny, the female's behavior probably functions to improve the genetic constitution of the offspring. In addition, the timing of associative behavior may limit prolonged guarding by food-stealing males to a period (1) encompassing the female's pre-molt fast and (2) before the heavy yolking of eggs, thereby ameliorating the nutritional costs of intrasexual selection.     

Impending Recovery of Kirtland's Warbler: Case Study in the Effectiveness of the Endangered Species Act

Dendroica kirtlandii ). This particular recovery program actually began before passage of the federal ESA, when biologists alerted the Michigan Department of Natural Resources of the perilously low population of this bird, which only breeds under jack pine (Pinus banksiana) trees in Michigan. By the time an ESA Recovery Team was formed for this bird in 1975 (the first such team created under the ESA), a legacy of consensus and interagency cooperation was well established. This has led to successful efforts at habitat management and control of its nest parasite, the brown-headed cowbird (Molothrus ater). While the Kirtland's warbler is not yet recovered, its population is near an all-time high, and its recovery is possible within the next decade. When (and if) this happens, it will be clearly attributable to this successful model of federalism for natural resources management.     

Emissions from charbroiling and grilling of chicken and beef

Emission rates for fine particle (<2.5 microm) mass (PM2.5), carbon (organic/elemental), inorganic ions (SO4(2-), NO3-, NH4+), elements (primarily metals), and speciated organic compounds are reported for charbroiling hamburger, steak, and chicken. The PM2.5 rates for charbroiling meats ranged from 4.4 to 11.6 g/kg of uncooked meat in this study. No mass-emission rates are available from grilling, but the speciated organic data are available for these samples. Emission rates varied by type of appliance, meat, meat-fat content, and cooking conditions. High-fat hamburger cooked on an underfired charbroiler emitted the highest amount of PM2.5. The emissions were almost exclusively composed of organic carbon, with small amounts of elements and inorganic ions. Water-soluble K+ and Cl-, which are used as indicators of wood smoke in source apportionment studies, were also present in meat-cooking emissions. The speciated organic compounds that were measured include polycyclic aromatic hydrocarbons (PAHs), cholesterol, and the long-chain gamma-lactones. Charbroiling emissions yielded an average of approximately 3-5 times more PAHs, approximately 20 times more cholesterol, and approximately 10 times more lactones than grilling. These data were utilized in the ambient source apportionment analysis for the 1997 Northern Front Range Air Quality Study source apportionment.     

Sources of PM10 and sulfate aerosol at McMurdo Station, Antarctica

Source contributions to PM10 and sulfate aerosol at McMurdo Station, Antarctica during the austral summers of 1995-1996 and 1996-1997 were estimated using Chemical Mass Balance (CMB) receptor modeling. The average PM10 (particles with aerodynamic diameters less than 10 microm) concentration at Hut Point, located less than 1 km downwind of downtown McMurdo, was 3.4 microg/m3. Emissions profiles were determined for potentially important aerosol source types in McMurdo: exposed soil, power generation, space heating, and surface vehicles. Soil dust, sea salt, combustion emissions, sulfates, marine biogenic emissions as methanesulfonate, and nitrates contributed 57%, 15%, 14%, 10%, 3%, and 1%, respectively, of average estimated PM10 at Hut Point (3.2 microg/m3). Soil dust, sea salt, and combustion sources contributed 12%, 8%, and 20%, respectively, of the average PM10 sulfate concentration of 0.46 microg/m3. Marine biogenic sources contributed 0.17 microg/m3 (37%). The remaining sulfate is thought to have come from emissions from Mt. Erebus or hemispheric pollution sources.     

Urban stormwater quality control analysis with detention ponds.

This paper presents methodologies for the development of stormwater quality control measures based on the derived probability distribution approach. These stormwater control measures, such as the fraction of pollutant removed from storage facilities, are closed-form analytical models and can be effectively used to evaluate pollutant loads to receiving waters. In this study, a simple form of rainfall-runoff transformation with lumped parameters is first extended to take into account the spatial variations in model parameters. Second, the infiltration process is further incorporated to the rainfall-runoff transformation. This study demonstrates that analytical models can be developed with various levels of complexity based on different hydrologic considerations. The performance of the analytical models is evaluated in a case study, and the results indicate that, with an appropriately formulated rainfall-runoff transformation, analytical stormwater runoff models are capable of providing comparable results to continuous simulation models in the evaluation of the long-term performance of storage facilities.