Omar De la Cruz

Complex life cycles and density dependence: assessing the contribution of egg mortality to amphibian declines

Abstract. In the last decade there has been increasing evidence of amphibian declines from relatively pristine areas. Some declines are hypothesized to be the result of egg mortality caused by factors such as elevated solar UV-B irradiation, chemical pollutants, pathogenic fungi, and climate change. However, the population-level consequences of egg mortality have not been examined explicitly, and may be complicated by density dependence in intervening life-history stages. Here we develop a demographic model for two amphibians with contrasting life-history strategies, Bufo boreas and Ambystoma macrodactylum. We then use the complementary approaches of elasticity and limitation to examine the relationships among stage-specific survival rates, larval-stage density dependence and amphibian population dynamics. Elasticity analyses showed that for a range of density dependence scenarios both species were more sensitive to changes in post-embryonic survival parameters, particularly juvenile survival, than to egg survival, suggesting that mortality of later stages may play an important role in driving declines. Limitation analyses revealed that larval density dependence can dramatically alter the consequences of early mortality, reducing or even reversing the expected population-level effects of egg mortality. Thus, greater focus on later life stages and density dependence is called for to accurately assess how stressors are likely to affect amphibian populations of conservation concern.

Gene, region and pathway level analyses in whole-genome studies

In the setting of genome‐wide association studies, we propose a method for assigning a measure of significance to pre‐defined sets of markers in the genome. The sets can be genes, conserved regions, or groups of genes such as pathways. Using the proposed methods and algorithms, evidence for association between a particular functional unit and a disease status can be obtained not just by the presence of a strong signal from a SNP within it, but also by the combination of several simultaneous weaker signals that are not strongly correlated. This approach has several advantages. First, moderately strong signals from different SNPs are combined to obtain a much stronger signal for the set, therefore increasing power. Second, in combination with methods that provide information on untyped markers, it leads to results that can be readily combined across studies and platforms that might use different SNPs. Third, the results are easy to interpret, since they refer to functional sets of markers that are likely to behave as a unit in their phenotypic effect. Finally, the availability of gene‐level P‐values for association is the first step in developing methods that integrate information from pathways and networks with genome‐wide association data, and these can lead to a better understanding of the complex traits genetic architecture. The power of the approach is investigated in simulated and real datasets. Novel Crohns disease associations are found using the WTCCC data. Genet. Epidemiol. 34: 222–231, 2010.

A Signature of Evolutionary Constraint on a Subset of Ectopically Expressed Olfactory Receptor Genes

Olfactory receptor (OR) genes constitute the basis for the sense of smell. It has long been observed that a subset of mammalian OR genes are expressed in nonolfactory tissues, in addition to their expression in the olfactory epithelium. However, it is unknown whether OR genes have alternative functions in the nonolfactory tissues. Using a dedicated microarray, we surveyed OR gene expression in olfactory epithelium as well as a number of nonolfactory tissues, in human and chimpanzee. Our observations suggest that ectopically expressed OR orthologous genes are expressed in the same nonolfactory tissues in human and chimpanzee more often than expected by chance alone. Moreover, we found that the subset of orthologous OR genes with conserved ectopic expression evolve under stronger evolutionary constraint than OR genes expressed exclusively in the olfactory epithelium. Thus, although we cannot provide direct functional data, our observations are consistent with the notion that a subset of ectopically expressed OR genes have additional functions in nonolfactory tissues.

Metric spaces and the axiom of choice

We study conditions for a topological space to be metrizable, properties of metriz- able spaces, and the role the axiom of choice plays in these matters.

Weak choice principles

We consider several weak forms of the Axiom of Choice obtained debilitating some well known choice principles. Implication relations among them and independence results are established using, in some cases, permutation models or symmetric models. The relationship between Ramsey’s Theorem and these choice principles is also explored, showing that, in this context, the known results are the best possible.

Unions and the axiom of choice

We study statements about countable and well-ordered unions and their relation to each other and to countable and well-ordered forms of the axiom of choice. Using WO as an abbreviation for “well-orderable”, here are two typical results: The assertion that every WO family of countable sets has a WO union does not imply that every countable family of WO sets has a WO union; the axiom of choice for WO families of WO sets does not imply that the countable union of countable sets is WO. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Properties of the real line and weak forms of the Axiom of Choice

We investigate, within the framework of Zermelo-Fraenkel set theory ZF, the interrelations between weak forms of the Axiom of Choice AC restricted to sets of reals. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Weak Forms of the Axiom of Choice and Partitions of Infinite Sets

There are many equivalent versions of the Axiom of Choice, and also many interesting consequences which are strictly weaker in terms of consistency strength. We examine various of these weaker forms of the Axiom of Choice and study how they are related to each other.