For any branching node at which the trip approaches a node and reflects off this node back along the same branch k, A trip is multiplied by a factor 2 p k − 1.
We can represent this using a symbol to separate the mutable and immutable parts of the trip: The second mechanism by which duplicate trips are produced is the addition of excursions along the same branch, starting from either end.
For the GJ node at which the trip approaches the gap junction, passes it and then continues along the same branch m, A trip is multiplied by a factor 1 − p GJ, n.
For the GJ node at which the trip approaches the gap junction, passes it and then continues along the same branch n, A trip is multiplied by a factor 1 − p GJ, m.
For the somatic node at which the trip approaches the soma and reflects off the soma back along the same branch k, A trip is multiplied by a factor 2 p s, k − 1.
For the GJ node at which the trip approaches the gap junction and reflects off the gap junction back along the same branch m, A trip is multiplied by a factor − p GJ, n.
For the GJ node at which the trip approaches the gap junction and reflects off the gap junction back along the same branch n, A trip is multiplied by a factor − p GJ, m.
In most cases sequencing and annotation errors are likely to inflate estimates of change; however, the simple method we have used to count differences in gene number is fundamentally conservative because we are unable to account for instances where both gains and losses occur within a family along the same branch of the tree.
Similarly, for two losses to be supported across different reconciliations, they must be found along the same branch of both the gene tree and species tree.
A similar tendency for selection to act on nearby sites along the same branch in a phylogeny has been noted previously for mammals (Bazykin et al. 2004).
