# Measuring evolutionary constraints by the dimensionality of the (phenotypic) matrices

Friday Seminar by Mihaela Pavlicev.

**Abstract**

The potential and direction of phenotypic evolution is constrained by the distribution of genetic and phenotypic variance. One descriptive parameter of the variance distribution is the dimensionality of trait space underlying the measured genotypic and phenotypic variance-covariance matrices. Traits are arbitrary and often correlated measurements. Dimensionality in the measured covariance matrix that is less than the number of measured traits is a consequence of intertrait correlations. Existing statistical methods to estimate dimensionality of underlying character variation often use biologically less plausible assumptions.

In my talk, I will present and compare two different (not mutually exclusive) approaches to this question. The first measures the rank of phenotypic variation, defined as the number of linearly independent columns or rows of a matrix. This measure is a discrete number of dimensions with any variance. I will be presenting an adjusted bootstrapping method, and assess its effectiveness by analyzing simulated data sets with known dimensionality. The second approach to be presented is effective dimensionality. This is a continuous measure of dimensionality that adjusts the number of traits by the total extent of their interdependence. The extent of interdependence is measured by the distribution of eigenvalues of correlation matrix. Both methods are explored for our purposes primarily on phenotypic data, both due to its availability and precision. Furthermore, the phenotypic variance represents the upper limit of the variance exposed to selection. However, the application of these methods is not necessarily limited to these data, although high estimation errors of e.g., genetic matrices impose restrictions to any method. The implications for the measurement of constraint and integration will be discussed.

**Other information**

The CEES seminar room has a coffee-machine – it is therefore recommended that you come a bit earlier and get yourself a good cup of coffee (for the price of 3 NOK).

Published Feb. 3, 2012 3:51 PM
- Last modified Mar. 8, 2021 10:20 AM