Wolfe and Shields [10] discovered an ancient genome doubling in the ancestry of Saccharomyces cerevisiae in 1997 after this organism became the first to have its genome sequenced [7]. According to [8], the recently sequenced Candida glabrata [4] shares this doubled ancestor. We extracted data from YGOB (Yeast Genome Browser) [3], on the orders and orientation of the exactly 600 genes identified as duplicates in both genomes, i.e., 300 duplicated genes.

We were able to obtain information from YGOB about which of the two duplicates in one genome is orthologous to which duplicate in the other genome. This is essential to the algorithm in Section 5.2. In general, we would have to infer this information through sequence comparison methods. This question is not pertinent to the algorithm in Section 5.3.

Though the results of the algorithm in Section 2 suggests that the theory in [8] is the most parsimonious, there is still enough uncertainty in yeast phyloge-netics and enough independent occurrences of genome doubling, that it is worth comparing the results of our two methods to dispute or confirm the common doubled ancestor hypothesis. In Fig. 5 we compare the analysis in the left hand diagram with that in the right, on the yeast data and on data of approximately the same size generated first according to the doubling first model and then according to speciation first.

We first analyzed the yeast data using the doubling first and speciation first algorithms. The results appear in the centre row of Table 1. (Because of the asymmetry of the doubling first algorithm with respect to T and U, there are two sets of inferences for this case.) We then used the numbers of rearrangements inferred for yeast, using the same number of markers and chromosomes, to simulate the same number of rearrangements in a random model, both with doubling first and speciation first.

We then applied both algorithms, doubling first and speciation first, to both sets of data. Note first in Table 1 that the number of rearrangements inferred for the doubling first model using the doubling first algorithm is not exactly the same as that used to generate the data, and likewise for the speciation first case. This is normal, because the inference of rearrangements often is more economical than the rearrangements actually used.

The rows in Table 1 show that the doubling first analysis is better than the speciation first analysis (457 rearrangements versus 632) when the data are generated by doubling first, whereas the speciation first analysis is better (589 versus 604) when the data is generated with speciation first. The doubling first analysis clearly accounts better for the yeast data (505-521 versus 622), while the simulations assure that the biases in the two methods cannot be invoked, so our analysis confirms the hypothesis in [8].

Table 1. Doubling first (d.f) and speciation first (s.f.) analyses each produce a more parsimonious analysis of simulations produced by the corresponding model (d.f. or s.f., respectively). Averages of at least five simulations shown, but the effect holds for each simulation individually. The d.f. analysis gives a far better fit to the yeast data than s.f. Second yeast row reverses the roles of U and T in the algorithm.

Table 1. Doubling first (d.f) and speciation first (s.f.) analyses each produce a more parsimonious analysis of simulations produced by the corresponding model (d.f. or s.f., respectively). Averages of at least five simulations shown, but the effect holds for each simulation individually. The d.f. analysis gives a far better fit to the yeast data than s.f. Second yeast row reverses the roles of U and T in the algorithm.

analysis^ |
doubling first (d.f.) |
speciation first (s.f.) | ||||||

data sourcej |
d(T,V ) |
d(V, U) |
d(V,A 0 A) |
total |
d(T,A 0 A) |
d(A,B) |
d(U, B 0 B) |
total |

sim by d.f.: |
102 |
213 |
166 |
481 | ||||

inferred: |
119 |
181 |
157 |
457 |
214 |
163 |
255 |
632 |

yeast: |
92 |
245 |
168 |
505 |
193 |
179 |
250 |
622 |

122 |
215 |
184 |
521 | |||||

sim by s.f.: |
177 |
164 |
225 |
566 | ||||

inferred: |
146 |
354 |
104 |
604 |
164 |
228 |
197 |
589 |

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