Genome-wide evidence for speciation with gene flow in Heliconius butterflies

Most speciation events probably occur gradually, without complete and immediate reproductive isolation, but the full extent of gene flow between diverging species has rarely been characterized on a genome-wide scale. Documenting the extent and timing of admixture between diverging species can clarify the role of geographic isolation in speciation. Here we use new methodology to quantify admixture at different stages of divergence in Heliconius butterflies, based on whole-genome sequences of 31 individuals. Comparisons between sympatric and allopatric populations of H. melpomene, H. cydno, and H. timareta revealed a genome-wide trend of increased shared variation in sympatry, indicative of pervasive interspecific gene flow. Up to 40% of 100-kb genomic windows clustered by geography rather than by species, demonstrating that a very substantial fraction of the genome has been shared between sympatric species. Analyses of genetic variation shared over different time intervals suggested that admixture between these species has continued since early in speciation. Alleles shared between species during recent time intervals displayed higher levels of linkage disequilibrium than those shared over longer time intervals, suggesting that this admixture took place at multiple points during divergence and is probably ongoing. The signal of admixture was significantly reduced around loci controlling divergent wing patterns, as well as throughout the Z chromosome, consistent with strong selection for Müllerian mimicry and with known Z-linked hybrid incompatibility. Overall these results show that species divergence can occur in the face of persistent and genome-wide admixture over long periods of time.

Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

Loan sales under asymmetric information

Loans are illiquid assets that can be sold in a secondary market even that buyers have no certainty about their quality. I study a model in which a lender has access to new investment opportunities when all her assets are illiquid. To raise funds, the lender may either borrow using her assets as collateral, or she can sell them in a secondary market. Given asymmetric information about assets quality, the lender cannot recover the total value of her assets. There is then a role for the government to correct the information problem using fiscal tools.