Testing of chromosomal clumping of gene properties

Clumping of gene properties like expression or mutant phenotypes along chromosomes is commonly detected using completely random null-models where their location is equally likely across the chromosomes. Interpretation of statistical tests based on these assumptions may be misleading if dependencies exist that are unequal between chromosomes or in different chromosomal parts. One such regional dependency is the telomeric effect, observed in several studies of Saccharomyces cerevisiae, under which e.g. essential genes are less likely to reside near the chromosomal ends. In this study we demonstrate that standard randomisation test procedures are of limited applicability in the presence of telomeric effects. Several extensions of such standard tests are here suggested for handling clumping simultaneously with regional differences in essentiality frequencies in sub-telomeric and central gene positions. Furthermore, a general non-homogeneous discrete Markov approach for combining parametrically modelled position dependent probabilities of a dichotomous property with a simple single parameter clumping is suggested. This Markov model is adapted to the observed telomeric effects and then simulations are used to demonstrate properties of the suggested modified randomisation tests. The model is also applied as a direct alternative tool for statistical analysis of the S. cerevisiae genome for clumping of phenotypes.