Effective amphibian conservation requires an understanding of how populations respond to specific natural and anthropogenic factors. Chemical contaminants are among the known sources of acute and chronic stress and have been linked with habitat degradation and amphibian declines. Manipulative experiments were conducted to investigate the performance (i.e., growth, survival) of amphibians that metamorphose from chemically-contaminated aquatic breeding sites. The heavy metal cadmium (Cd) was selected as the focal contaminant because it bioaccumulates, is highly toxic, and occurs in polluted water bodies around the world. Effects of larval exposure to Cd on amphibian metamorphosis and juvenile performance were tested using the southern leopard frog (Rana sphenocephala) and American toad (Bufo americanus), two common North American habitat generalists that utilize Cd-contaminated breeding sites. It was expected that Cd exposure would decrease the growth and survival of tadpoles and juveniles because Cd affects the physiological processes and body condition of amphibians and other taxa. In the first experiment, southern leopard frog and American toad tadpoles were reared separately in cattle tank mesocosms (1325-L volume) that had been dosed once at 0, 5, 18, 60, or 200 [mu]g Cd/L. The experimental endpoints were survival, mass and age at metamorphosis, and whole body Cd content. Both species had a decrease in survival and increase in larval period and Cd content with increasing aqueous Cd concentration. However, southern leopard frog mass increased and American toad mass decreased with Cd exposure. A subset of metamorphs from the first experiment was subsequently reared in terrestrial enclosures (2 m2) located in a field along a forest edge. Metamorphs were obtained from all five Cd concentrations (American toads) or just the 0, 5, and 18 [mu]g Cd/L treatments (southern leopard frogs). Juveniles were monitored for survival and growth in their first autumn and the following spring. There were no significant effects of Cd exposure history on the mass or growth rate of either species, but there a deleterious effect on American toad survival. Southern leopard frogs from the 18 [mu]g Cd/L concentration were larger than the controls throughout the study. A laboratory experiment was conducted on the terrestrial performance of southern leopard frog juveniles that metamorphosed from cattle tank mesocosms dosed once with 0, 5, or 18 [mu]g Cd/L. Individuals were kept in separate containers for two months and fed either a low or high level diet of mealworms (Tenebrio molitor). Overall survival was 99 percent, indicating neither Cd nor diet were lethal. Initial differences in mass among Cd treatments were maintained within each diet level and those on the high diet weighed more than twice those on the low diet. The effect of Cd exposure history on juvenile mass depended on food abundance.A fourth study was conducted to determine the combined effects of Cd concentration and interspecific competition on amphibian metamorphosis. Southern leopard frogs were the focal species and American toads were the competitor. Metamorphs were collected from cattle tank mesocosms that had been dosed once at 0, 5, or 18 [mu]g Cd/L. Cadmium exposure decreased survival, increased mass and age at metamorphosis, and resulted in significant body burdens for the southern leopard frogs. Interspecific competition from the American toads increased survival and shortened the larval period, decreased mass at metamorphosis, and had no effect on contaminant uptake. The effect of Cd on metamorph age depended on whether American toads were present. A subset of southern leopard frog metamorphs from the fourth study was reared in terrestrial enclosures (9 m2) in two habitat types for the final experiment. Enclosures were located in deciduous forests or open fields and juvenile growth and survival was determined in the first autumn following metamorphosis. Cadmium exposure history affected growth rate, mass, and survival. Initial differences in mass due to larval Cd exposure were maintained over time in each habitat type, but growth was highest in field enclosures and survival was highest in forest enclosures. The forest sites were cooler and wetter, which may have improved juvenile survival. This research suggests that aquatic breeding sites polluted with Cd produce fewer, older, and contaminated amphibian metamorphs relative to uncontaminated sites. Those that survive to metamorphosis do not appear to be hindered by reduced terrestrial survival or growth as juveniles. However, Cd exposure influenced juvenile performance through interactions with terrestrial habitat quality. Assessments of the effects of contaminants on amphibians that incorporate multiple routes of exposure and other potential stressors may produce different outcomes than assessments that only manipulate the aquatic concentration.
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Let ? be an open and connected set in the complex plane. A mapping f : ? ? C is said to be conformal at a point z0 if it preserves angles and orientation between curves intersecting at z0. We discuss tangent lines and their relationship to the conformal property. This property is useful for determining the points at which a function is conformal. We provide several examples and a summary of boundary behavior properties. We discuss two types of conformal mappings, linear fractional transformations and the Schwarz-Christoffel transformation. Linear fractional transformations map lines and circles to either lines or circles; meanwhile, the Schwarz-Christoffel transformation maps the upper half-plane onto a polygon P. We prove several properties of these mappings and demonstrate their importance with the use of examples. These results are useful for solving boundary value problems on irregular regions. If we map such a region onto another region whose solution is known, we are able to then obtain a solution on the first region. Important physical applications of this thesis include determination of isotherms, streamlines, and air gap reluctance for magnetic circuits
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Let ? be an open and connected subset of the complex plane. A real valued function u : ? ? R is said to be harmonic if it has continuous first and second partial derivatives and satisfies Laplaces equation ?u = ? 2u ?x2 + ? 2u ?y2 = 0. We begin by investigating basic properties of harmonic functions and defining the harmonic conjugate gradient and harmonic conjugate functions. From this we prove the mean value property and maximum and minimum modulus principle for harmonic functions. Suppose we have a two dimensional plate of homogeneous material whose boundaries are heated to a constant temperature. We investigate solving the Dirichlet problem, which involves Laplaces equation and specific boundary values. Along with examples, we show that we can solve the Dirichlet problem on a disk using the Poisson integral along with Fourier series. We generalize the Dirichlet problem to any region by investigating conformal mappings. We find a solution to the Dirichlet problem on a general region in the plane by transforming it to a problem in the upper half plane and using the Poisson integral.
