Using mixture models to detect differentially expressed genes

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local false discovery rate is provided for each gene, and it can be implemented so that the implied global false discovery rate is bounded as with the Benjamini-Hochberg methodology based on tail areas. The latter procedure is too conservative, unless it is modified according to the prior probability that a gene is not differentially expressed. An attractive feature of the mixture model approach is that it provides a framework for the estimation of this probability and its subsequent use in forming a decision rule. The rule can also be formed to take the false negative rate into account.

A simple implementation of a normal mixture approach to differential gene expression in multiclass microarrays

Motivation: An important problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. We provide a straightforward and easily implemented method for estimating the posterior probability that an individual gene is null. The problem can be expressed in a two-component mixture framework, using an empirical Bayes approach. Current methods of implementing this approach either have some limitations due to the minimal assumptions made or with more specific assumptions are computationally intensive. Results: By converting to a z-score the value of the test statistic used to test the significance of each gene, we propose a simple two-component normal mixture that models adequately the distribution of this score. The usefulness of our approach is demonstrated on three real datasets.

Genetic resource impacts of habitat loss and degradation; reconciling empirical evidence and predicted theory for neotropical trees

The theoretical impacts of anthropogenic habitat degradation on genetic resources have been well articulated. Here we use a simulation approach to assess the magnitude of expected genetic change, and review 31 studies of 23 neotropical tree species to assess whether empirical case studies conform to theory. Major differences in the sensitivity of measures to detect the genetic health of degraded populations were obvious. Most studies employing genetic diversity (nine out of 13) found no significant consequences, yet most that assessed progeny inbreeding (six out of eight), reproductive output (seven out of 10) and fitness (all six) highlighted significant impacts. These observations are in line with theory, where inbreeding is observed immediately following impact, but genetic diversity is lost slowly over subsequent generations, which for trees may take decades. Studies also highlight the ecological, not just genetic, consequences of habitat degradation that can cause reduced seed set and progeny fitness. Unexpectedly, two studies examining pollen flow using paternity analysis highlight an extensive network of gene flow at smaller spatial scales (less than 10 km). Gene flow can thus mitigate against loss of genetic diversity and assist in long-term population viability, even in degraded landscapes. Unfortunately, the surveyed studies were too few and heterogeneous to examine concepts of population size thresholds and genetic resilience in relation to life history. Future suggested research priorities include undertaking integrated studies on a range of species in the same landscapes; better documentation of the extent and duration of impact; and most importantly, combining neutral marker, pollination dynamics, ecological consequences, and progeny fitness assessment within single studies.