Australia has the highest incidence of melanoma in the world. Melanocytic nevi and mutations in the CDKN2A gene are the main risk factors for the development of cutaneous melanocytic melanoma, and particularly in those of European descent. My study uses genetic epidemiological methods to investigate causes of variation in the number of melanocytic nevi and pigmentary traits such as freckles, eye colour, hair colour and skin colour collected on a sample of adolescent twins and siblings from the Brisbane Twin Nevus Study (1992-2006). Information was available for 2524 individuals from 973 families (from the first visit when the twins were aged 12 years), and from a repeat visit (two years later) for 1598 individuals from 791 families. Using the twin study design extended to siblings and parents, variance components analyses showed that the proportion of phenotypic variance explained by genetic factors ranged from 43 to 99 percent for the traits studied. The atypical nevus count and freckles showed sex differences in the magnitude of genetic and environmental effects. Genetic correlations among counts of three types of nevus (flat, raised and clinically atypical) ranged from 0.46 to 0.63. Nevus count was genetically correlated with skin colour (r=0.23). I analysed genome-wide linkage data using a total of 1190 microsatellite (STR) markers from three scans for 644 families with 1646 twins and siblings, plus genotypes for 1033 parents. These were combined with an additional 169 families with genome-wide association 100K SNP (single nucleotide polymorphism) data, where I selected a linkage analysis panel of 13,000 SNPs making a total of 3365 individuals from 811 families (each individual had more than 200 markers typed). Suggestive linkages for flat nevus count (FNC) were identified on chromosomes 2p25 and 9p21 with lod scores of 3.19 and 2.62 respectively. For raised nevus count (RNC), a suggestive QTL with a lod score of 2.20 was found on chromosome 2q37.2, and for atypical nevus count (ANC) a lod score of 2.71 was found on chromosome 7p14.1. There was suggestive evidence of linkage for freckling on chromosomes 2 and 9. Eye colour was strongly linked (lod=17.86) to chromosome 15, at the OCA2 locus. I have also carried out genetic association analyses using the 100K SNP data in 169 families, and additional fine mapping using SNPs (as well as STR markers) in the complete data set. A sample size of 169 families (461 twins) for genome-wide association data means that statistical power is low. From the 100K SNP data, the best association for total nevus count (TNC) was with SNP rs2420070, p=6.0×10-6 on chromosome 10, and included another two nearby SNPs; rs7086663, p=2.0×10-4 and rs7090904, p=1.5×10-4. These 3 SNPs also showed possible association with FNC; rs2420070, p=3.9×10-6, rs2420070, p=1.3×10-4 and rs2420070, p=8.9×10-5. For raised nevus count the top three associated SNPs were rs1885238, p=1.8×10-5 on chromosome 9; rs10503048, p=3.7×10-5 on chromosome 18 and rs4769189, p=4.0×10-5 on chromosome 13. SNP rs1412341 which is located near CDKN2A on chromosome 9, was also associated with p=2.8×10-4. There were a total 18 SNPs which showed evidence of association with atypical nevus count, the strongest signal being with rs951099 (p=3.7×10-5) on chromosome 9. In a fine-mapping dataset, I studied the association of CDKN2A SNP rs2218220 with TNC, FNC, RNC and ANC. The best SNP, rs2218220, gave p values of 2.8×10-10, 7.7×10-8, 2.7×10-12 and 9.1×10-8, respectively. A SNP, rs1800407 (R419Q) located in the OCA2 gene (chromosome 15q11.2-15q12) showed evidence of association with eye colour and particularly with blue and green eye colours, (p=1.7×10-12 and p=6.0×10-7). SNP rs12913832 from the Hect Domain and RCC1-like Domain 2 gene (HERC2) on chromosome 15q13.1, was also strongly associated with eye colour p=3.6×10-155. This SNP was associated with blue (p= 7.9×10-150) and brown (p=5.3×10-158), but not green eye colour. In addition I confirmed the association of the MC1R SNP rs1805007 and freckling (p=4.8×10-12). This SNP was also associated with FNC (p=3.5×10-8), a finding not previously described in the literature. I also carried out multi-allelic association analysis using STR markers with these traits and uncovered suggestive findings for several regions. Finally, I conducted a multivariate association analysis searching for SNPs with pleiotropic effects. The most interesting results for all types of nevi were with rs801840, p=3.5×10-5, and rs10487075, p=4.9×10-5, both on chromosome 7q21.13. Another four SNPs on chromosome 8p23.1 also showed associations, rs7009724, p=1.4×10-4, rs10503389, p=1.9×10-4, rs7832398, p=6.2×10-4 and rs7005133, p=6.9×10-4 (close to a candidate gene, MFHAS1, implicated in sarcoma risk). In conclusion I have characterised a number of definite and possible genetic factors influencing important risk factors for melanoma.

This dissertation mainly focuses on the development of new numerical models to simulate transport phenomena and predict the occurrence of macrosegregation defects known as freckles in directional solidification processes. Macrosegregation models that include double diffusive convection are very complex and require the simultaneous solution of the conservation equations of mass, momentum, energy and solute concentration. The penalty method and Galerkin Least Squares (GLS) method are the most commonly employed methods for predicting the interdendritic flow of the liquid melt during the solidification processes. The solidification models employing these methods are computationally inefficient since they are based on the formulations that require the coupled solution to velocity components in the momentum equation Motivated by the inefficiency of the previous solidification models, this work presents three different numerical algorithms for the solution of the volume averaged conservation equations. First, a semi explicit formulation of the projection method that allows the decoupled solution of the velocity components while maintaining the coupling between body force and pressure gradient is presented. This method has been implemented with a standard Galerkin finite element formulation based on bi-linear elements in two dimensions and tri-linear elements in three dimensions. This formulation is shown to be robust and very efficient in terms of both the memory and the computational time required for the macrosegregation computations. The second area addressed in this work is the use of adaptive meshing with linear triangular elements together with the Galerkin finite element method and the projection formulation. An unstructured triangular mesh generator is integrated with the solidification model to produce the solution adapted meshes. Strategies to tackle the different length scales involved in macrosegregation modeling are presented. Meshless element free Galerkin method has been investigated to simulate the solidification processes to alleviate the difficulties associated with the dependence on the mesh. This method is combined with the fractional step method to predict macrosegregation. The performance of these three numerical algorithms has been analyzed and two and three dimensional simulations showing the directional solidification of binary Pb-Sn and multicomponent Ni base alloys are presented.