Evolution of functionally conserved enhancers can be accelerated in large populations: a population–genetic model

Abstract

The evolution of cis-regulatory elements (or enhancers) appears to proceed at dramatically different rates in different taxa. Vertebrate enhancers are often very highly conserved in their sequences, and relative positions, across distantly related taxa. In contrast, functionally equivalent enhancers in closely related Drosophila species can differ greatly in their sequences and spatial organization. We present a populationgenetic model to explain this difference. The model examines the dynamics of ® xation of pairs of individually deleterious, but compensating, mutations. As expected, small populations are predicted to have a high rate of evolution, and the rate decreases with increasing population size. In contrast to previous models, however, this model predicts that the rate of evolution by pairs of compensatory mutations increases dramatically for population sizes above several thousand individuals, to the point of greatly exceeding the neutral rate. Application of this model predicts that species with moderate population sizes will have relatively conserved enhancers, whereas species with larger populations will be expected to evolve their enhancers at much higher rates. We propose that the different degree of conservation seen in vertebrate and Drosophila enhancers may be explained solely by differences in their population sizes and generation times.

Waiting for Two Mutations: With Applications to Regulatory Sequence Evolution and the Limits of Darwinian Evolution

“…Since B mutants have probability u 2 , there is a reasonable chance of having a B mutation before the number of A mutants returns to 0. n et al (2004) call this stochastic tunneling, since the second mutant (type B) arises before the first one (type A) fixes. Carter and Wagner (2002) had earlier noted this possibility but they did not end up with a very nice formula for the average fixation time; see their (2.2) and the formulas for the constants given in their Appendix. The assumption 1= ffiffiffiffiffi u 2 p >2N implies that throughout the scenario we have just described, the number of type A mutants is a small fraction of the population, so we can ignore the probability that the A mutants become fixed in the population.…”

“…Note that in this case, wild-type individuals cannot produce individuals with a second active binding site. For a different example of this general process, see p. 955 of Carter and Wagner (2002). ized to have maximum value 1, the dynamics may be described as follows: Each individual is subject to possible replacement at rate 1. A copy is made of an individual chosen at random from the population.…”

“…This problem was studied earlier by Carter and Wagner (2002). In the next section, we present the model and then a simpler theoretical analysis based on work of Komarova et al (2003) and Iwasa et al (2004Iwasa et al ( , 2005, who studied the onset of cancer due to the inactivation of tumor suppressor genes.…”

Surveying phylogenetic footprints in large gene clusters: applications to Hox cluster duplications

“…This was first documented in the Drosophila even skipped stripe 2 enhancer [21] and has since been documented for many other invertebrate taxa. In vertebrates, however, no widespread binding site turnover has been documented, which might have to do with a variety of reasons [8]. Adaptive modification would be a change in the sequence of cis-regulatory sites due to directional natural selection and would thus be associated with functional differences.…”

Experiments on the role of deleterious mutations as stepping stones in adaptive evolution

“…In asexually reproducing organisms, however, there exists a simpler mechanism for crossing a fitness valley. Provided that a deleterious mutation is not lethal, the genome carrying it has some expected "half life" and a corresponding chance of reproducing one or more times before going extinct (2,(5)(6)(7)(8)(9)(10). Occasionally, the mutant subpopulation might acquire a second, hypercompensatory mutation that provides a net advantage (11,12).…”