In this paper we derive some similarity solutions of a nonlinear equation associated with a free boundary problem arising in the shallow-water approximation in glaciology. In addition we present a classical potential symmetry analysis of this second-order nonlinear degenerate parabolic equation related to non- Newtonian ice sheet dynamics in the isothermal case. After obtaining a general result connecting the thickness function of the ice sheet and the solution of the nonlinear equation (without any unilateral formulation), a particular example of a similarity solution to a problem formulated with Cauchy boundary conditions is described. This allows us to obtain several qualitative properties on the free moving boundary in the presence of an accumulation-ablation function with realistic physical properties.
Climatic changes during the Pleistocene were responsible for dramatic redistributions of plant species worldwide. On the rugged southern hemisphere island of Tasmania, temperature increases following the last glaciation saw upslope migration of climatically suitable species from lowland refugia and the expansion of eucalypt-dominated forests and woodlands in the Central Highlands. We integrate multiple lines of evidence (chloroplast and nuclear DNA markers, seedling morphology, and survival in common garden experiments) from a group of closely related endemic eucalypts (the alpine white gums) to argue that (i) the Central Highlands of the island were colonised by multiple glacial refugia with hybridisation among species and previously separated populations, and (ii) natural selection has filtered the admixed populations, resulting in local adaptation to the harsh sub-alpine environment. Chloroplast haplotype diversity decreased and nuclear microsatellite diversity increased with altitude, chloroplast sharing among taxa was common, and nuclear DNA differentiation of morphologically distinct taxa was lower in the Central Highlands compared with lowland regions. Local adaptation in the highlands was signalled by evidence from (i) a glasshouse trial in which directional selection (QST > FST) had shaped seedling morphological trait variation and (ii) population survival differences in 35-year-old reciprocal plantings along the major environmental gradients. We conclude that the evolutionary response of these island endemic trees to past climate change has involved the interplay of both hybridisation and natural selection, highlighting the importance of maintaining species interactions under future climate change.
Abstract The one dimensional heat conduction equation is applied to a non‐uniform soil in which harmonic boundary conditions are specified. The analytic solutions are derived for practical use and satisfy a law that the thermal diffusivity is proportional to the square of the speed of the temperature wave. Depending on the nature of this speed the solutions may be categorized as circular, parabolic, hyperbolic, or exponential. A practical example is given in which the damping depth and thermal capacity of the soil both vary with depth. It shows that there may be considerable differences between uniform and nonuniform soils as far as temperature is concerned. A case of a slowly varying soil layer is also examined and is compared with the constant soil solution.
PooFlip is a photographic life-size guide to the scats of Tasmanian native mammals. It can be used to identify the terrestrial native mammals from their scats. PooFlip also includes a guide to the native mammals of Tasmania with illustrations by Jane Burrell.
Previous studies of phenotypic variation among natural populations in the Eucalyptus risdonii/E. tenuiramis cindicated that the two taxa are linked by a cline in the retention of the juvenile leaf form (paedomorphocline) and that division into the two taxa, E. risdonii and E. tenuiramis, on the basis of these ontogenetic differences obscures the phenetic relationships within and between the taxa. This study attempts to remove the environmental and ontogenetic variation to reveal the genetically based variation by examining seedling morphology. The results suggest that genetic variation between geographically contiguous populations of E. risdonii and E. tenuiramis is relatively small and continuous, and classification into either taxon on the basis of seedling phenotype is not possible for populations in this transitional area. The major dichotomy between phenetic clusters is not between forms that can be assigned to E. risdonii and E. tenuiramis on the basis of ontogenetic differences, but between geographically isolated forms of E. tenuiramis. The ambiguous variation in the adult phenotype is clarified by the marked difference in seedling morphology between the two East Coast populations and the other E. tenuiramis populations which, on present data, appear to be separated by a geographical disjunction. When viewed in terms of the phenetic distance between populations of the two closest species (E. coccifera and E. nitida), the magnitude of the difference between the East Coast E. tenuiramis and the other phenetic groups in the E. risdonii/E. tenuiramis complex is emphasised. The relationship and origin of populations intermediate between E. tenuiramis and E. coccifera are also discussed.