Philipp Hummer


From the pattern backwards to the process: What correlations of traits can tell us about their underlying genetic architecture and co-development

MSc Student
Advisor: Mihaela Pavlicev

Unit for Theoretical Biology, Department of Evolutionary Biology
University of Vienna


Evolution depends on heritable phenotypic variation which is influenced by how the genotype maps onto the phenotype. This G-P map in turn is heavily dependent on the phenomenon of pleiotropy which describes mutations having effects on multiple different traits and the pleiotropic structure affects evolvability through developmental constraints. To describe pleiotropic structure, Wagner (1984) has formalized the B matrix which is also defined by its mathematical relation to phenotypic covariance matrices, such as the mutational effect covariance matrix M. Using this relation along with eigen-decomposition and hierarchical clustering, I have made efforts to relate patterns in the correlation matrix rM to a pleiotropic structure by utilizing the posterior probabilities of different structures achieving certain patterns. Yet, this mostly failed because the introduced stochastic variation was too strong and removed the information that could have led to distinct patterns. This thesis ‘second part then concerns the connection between pleiotropy and correlation. If there is no pleiotropic association between traits, they cannot correlate (in rM) and if they do, this must be due to pleiotropy. However, there is the hypothetical case of “hidden pleiotropy” which refers to pleiotropic effects canceling each other out in order lead to a lack of trait correlations and this case has been used to argue for universal pleiotropy in the G-P map. Yet, the analysis of constructed B matrices and numerical simulations show that hidden pleiotropy – particularly for many traits – is very improbable and that a lack of pleiotropy in the G-P map is a more likely explanation for a lack of trait correlations. Additionally, attempting to calculate the exact probabilities for achieving hidden pleiotropy from randomness has revealed that the way two traits are pleiotropically associated determines the probability of their correlation with a third trait beyond just their own correlation.