Landscape genetics of Phaedranassa herb. (Amaryllidaceae) in Ecuador

Speciation can be understood as a continuum occurring at different levels, from population to species. The recent molecular revolution in population genetics has opened a pathway towards understanding species evolution. At the same time, speciation patterns can be better explained by incorporating a geographic context, through the use of geographic information systems (GIS). Phaedranassa (Amaryllidaceae) is a genus restricted to one of the world’s most biodiverse hotspots, the Northern Andes. I studied seven Phaedranassa species from Ecuador. Six of these species are endemic to the country. The topographic complexity of the Andes, which creates local microhabitats ranging from moist slopes to dry valleys, might explain the patterns of Phaedranassa species differentiation. With a Bayesian individual assignment approach, I assessed the genetic structure of the genus throughout Ecuador using twelve microsatellite loci. I also used bioclimatic variables and species geographic coordinates under a Maximum Entropy algorithm to generate distribution models of the species. My results show that Phaedranassa species are genetically well-differentiated. Furthermore, with the exception of two species, all Phaedranassa showed non-overlapping distributions. Phaedranassa viridiflora and P. glauciflora were the only species in which the model predicted a broad species distribution, but genetic evidence indicates that these findings are likely an artifact of species delimitation issues. Both genetic differentiation and nonoverlapping geographic distribution suggest that allopatric divergence could be the general model of genetic differentiation. Evidence of sympatric speciation was found in two geographically and genetically distinct groups of P. viridiflora. Additionally, I report the first register of natural hybridization for the genus. The findings of this research show that the genetic differentiation of species in an intricate landscape as the Andes does not necessarily show a unique trend. Although allopatric speciation is the most common form of speciation, I found evidence of sympatric speciation and hybridization. These results show that the processes of speciation in the Andes have followed several pathways. The mixture of these processes contributes to the high biodiversity of the region.

Using extreme value theory to value stock market returns

Extreme stock price movements are of great concern to both investors and the entire economy. For investors, a single negative return, or a combination of several smaller returns, can possible wipe out so much capital that the firm or portfolio becomes illiquid or insolvent. If enough investors experience this loss, it could shock the entire economy. An example of such a case is the stock market crash of 1987. Furthermore, there has been a lot of recent interest regarding the increasing volatility of stock prices. ^ This study presents an analysis of extreme stock price movements. The data utilized was the daily returns for the Standard and Poor's 500 index from January 3, 1978 to May 31, 2001. Research questions were analyzed using the statistical models provided by extreme value theory. One of the difficulties in examining stock price data is that there is no consensus regarding the correct shape of the distribution function generating the data. An advantage with extreme value theory is that no detailed knowledge of this distribution function is required to apply the asymptotic theory. We focus on the tail of the distribution. ^ Extreme value theory allows us to estimate a tail index, which we use to derive bounds on the returns for very low probabilities on an excess. Such information is useful in evaluating the volatility of stock prices. There are three possible limit laws for the maximum: Gumbel (thick-tailed), Fréchet (thin-tailed) or Weibull (no tail). Results indicated that extreme returns during the time period studied follow a Fréchet distribution. Thus, this study finds that extreme value analysis is a valuable tool for examining stock price movements and can be more efficient than the usual variance in measuring risk. ^

Quantifying protein folding pathways

A deep understanding of the proteins folding dynamics can be get quantifying folding landscape by calculating how the number of microscopic configurations (entropy) varies with the energy of the chain, Ω=Ω(E). Because of the incredibly large number of microstates available to a protein, direct enumeration of Ω(E) is not possible on realistic computer simulations. An estimate of Ω(E) can be obtained by use of a combination of statistical mechanics and thermodynamics. By combining different definitions of entropy that are valid for a system whose probability for occupying a state is given by the canonical Boltzmann probability, computers allow the determination of Ω(E). ^ The energy landscapes of two similar, but not identical model proteins were studied. One protein contains no kinetic tracks. Results show a smooth funnel for the folding landscape. That allows the contour determination of the folding funnel. Also it was presented results for the folding landscape for a modified protein with kinetic traps. Final results show that the computational approach is able to distinguish and explore regions of the folding landscape that are due to kinetic traps from the native state folding funnel.^

On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.