Concerted evolution

Although the patterns of gene relationships produced through duplication and divergence can be quite complex, the processes are relatively easy to understand. In some multigene families, however, something quite different seems to be going on. In many plants and animals genes encoding ribosomal RNAs are present in hundreds of copies and arranged end to end in long tandem arrays in one or a few places in the genome (Figure 3). Brown et al. [1] compared the ribosomal RNA of Xenopus laevis and X. mulleri and found a surprising pattern. There was little or no detectable variation among copies of the repeat units within either species, in spite of substantial divergence between them. This pattern can't be explained by purifying selection. Members of the gene family presumably diverged before X. laevis and X. mulleri diverged. Thus, we would expect more divergence among copies within species than between species, i.e., the pattern we see in the globin family. Explaining this pattern requires some mechanism that causes different copies of the repeat to be homogenized within each species while allowing the repeats to diverge between species. The phenomenon is referred to as concerted evolution.

Figure 3: Diagrammatic representation of ribosomal DNA in vascular plant genomes (from Muir & Schlötterer, 1999 http://webdoc.sub.gwdg.de/ebook/y/1999/whichmarker/m11/Chap11.htm).

Two mechanisms that can result in concerted evolution have been widely studied: unequal crossing over and gene conversion. Both depend on misalignments during prophase. These misalignments allow a mutation that occurs in one copy of a tandemly repeated gene array to ``spread'' to other copies of the gene array. Tomoko Ohta and Thomas Nagylaki have provided exhaustive mathematical treatments of the process [3,4]. We'll follow Ohta's treatment, but keep it fairly simple and straightforward. First some notation:

$$\begin{eqnarray*} f &=& \mbox{P}(\mbox{two alleles at same locus are ibd}) \\ c... ....\ of loci in family} \lambda &=& \mbox{rate of gene conversion} \end{eqnarray*}$$

Now remember that for the infinite alleles model

$$f = \frac{1}{4N_e\mu + 1} \quad , \\$$

and $f$ is the probability that neither allele has undergone mutation. By analogy

$$g = \frac{1}{4N_e\lambda + 1} \quad , \\$$

where $g$ is the probability that two alleles at a homologous position are ibd in the sense that neither has ever moved from that position in the array. Thus, for our model

$$\begin{eqnarray*} f &=& P(\mbox{neither has moved})\mbox{P}(\mbox{ibd}) \\ && ... ...1} \\ c_1 = c_2 &=& \frac{\lambda}{\lambda + (n-1)\mu} \quad . \end{eqnarray*}$$

Notice that $(n-1)\mu$ is approximately the number of mutations that occur in a single array every generation. Consider two possibilities:

• Gene conversion occurs much more often than mutation: $\lambda \gg (n-1)\mu$.

  Under these conditions $c_2 \approx 1$ and $f \approx 1$. In short, all copies of alleles at every locus in the array are virtually identical - concerted evolution.

• Gene conversion occurs much less often than mutation: $\lambda \ll (n-1)\mu$.

  Under these conditions $c_2 \approx 0$ and $f \approx \frac{1}{4N_e\mu + 1}$. In short, copies of alleles at different loci are almost certain to be different from one another, and the diversity at any single locus matches neutral expectations - non-concerted evolution.