Recombinations, chains and caps: resolving problems with the DCJ-indel model

Table 1 All safe types of DCJ operations

Safe operation	\(-\Delta c_\circ\)	\(\Delta p_{a\|b}\)	\(\Delta \max (p_{A\circ a},p_{B\|a})\)	\(\Delta \max (p_{A\|b},p_{B\circ b})\)	\(-\Delta p_{A\|B}\)
\(K\rightarrow K'+C_\circ\)	− 1	0	0	0	0
\(P_{A\circ A}\rightarrow P_{A\|B},P_{A\|B}\)	0	0	0	0	− 2
\(P_{B\circ B}\rightarrow P_{A\|B},P_{A\|B}\)	0	0	0	0	− 2
\(P_{A\circ A},P_{B\circ B}\rightarrow P_{A\|B},P_{A\|B}\)	0	0	0	0	− 2
\(P_{a\|b},P_{a\|b}\rightarrow (P_{a\circ a})^,(P_{b\circ b})^\)	0	− 2	0	0	0
\(P_{A\circ a},P_{B\|a} \rightarrow P_{A\|B},(P_{a\circ a})^*\)	0	0	− 1	0	− 1
\(P_{A\|b},P_{B\circ b}\rightarrow P_{A\|B},(P_{b\circ b})^*\)	0	0	0	− 1	− 1

Each reduces the \(F\) by 1, no matter the number of other components in the graph. Above are all safe operations in a pure DCJ scenario. The operations below can also function as safe deletions if one of the resultants in brackets is removed. For reference: \(F= n -c_{\circ } + \left\lceil {(p_{a |b} + \max (p_{A \circ a},p_{B |a}) + \max (p_{A |b},p_{B \circ b}) - p_{A |B})/2}\right\rceil\)

ISSN: 1748-7188