### Undergraduate Mathematics Colloquium

The next Undergraduate Colloquium is**Thursday, 12/01/16**.

For details please see the following link: http://www.math.uh.edu/colloquium/undergraduate/

**Speaker: **Professor Richard Azevedo, University of Houston

**Abstract:**"Spiraling complexity: A Test of the Snowball Effect In a Computational Model of RNA Folding"

**Time: **4:00 p.m.—5:00 p.m.

**Location**: PGH 646

**Description**:

Genetic incompatibilities can emerge as a by-product of genetic divergence. According to Dobzhansky and Muller, an allele that fixes in one population may be incompatible with an allele at a different locus in another population when the two alleles are brought together in hybrids. Orr showed that the number of Dobzhansky-Muller incompatibilities (DMIs) should accumulate faster than linearly (i.e., snowball) as two lineages diverge. Several studies have attempted to test the snowball effect using data from natural populations. One limitation of these studies is that they have focused on predictions of the Orr model but not on its underlying assumptions. Here we use a computational model of RNA folding to test both predictions and assumptions of the Orr model. Two populations are allowed to evolve in allopatry on a holey fitness landscape. We find that the number of DMIs involving pairs of loci (i.e., simple DMIs) does not snowball - rather, it increases approximately linearly with divergence. We show that the probability of emergence of a simple DMI is approximately constant, as assumed by the Orr model. However, simple DMIs can disappear after they have arisen, contrary to the assumptions of the Orr model. This occurs because simple DMIs become complex (i.e., involve alleles at three or more loci) as a result of later substitutions. We introduce a modified Orr model where simple DMIs can become complex after they appear. Our modified Orr model can account for the results of the RNA folding model. We also find that complex DMIs are common and, unlike simple ones, do snowball. Reproductive isolation, however, does not snowball because DMIs do not act independently of each other. We conclude that the RNA folding model supports the central prediction of the Orr model that the total number of DMIs snowballs, but challenges some of its underlying assumptions.

*Pizza will be served after the lecture.*