-g, Extension max gap, (positive integer)
-j, Extension cutoff, (decimal between 0 and 1)
-J, Reliable extension, (decimal between 0 and 1)

The three parameters control the extension of LTRs. An example of 2 neighbouring LTR pairs is shown in Figure 3. If $s[i_b\ldots m_e]$ and $s[j_b\ldots n_e]$ are similar enough, we extend LTRs from $s[i_b\ldots i_e]$ and $s[m_b\ldots m_e]$ to $s[i_b\ldots m_e]$ and $s[j_b\ldots n_e]$.

Figure 3: $P_1\{s[i_b\ldots i_e], s[j_b\ldots j_e]\} and P_2\{s[m_b\ldots m_e], s[n_b\ldots n_e]\}$

$P_1$ and $P_2$ are pre-sorted so that $j_b \geq i_b$, $n_b \geq m_b$ and $j_b \geq m_b$. Since $P_1$ and $P_2$ are two exact match pairs, we know

$$\begin{array}{rrr} len_{pair1}= & i_e-i_b+1= & j_e-j_b+1\\ len_{pair2}= & m_e-m_b+1= & n_e-n_b+1 \end{array}$$

Obviously, the gap lengthes between them are

$$\begin{array}{rr} gap_1=&m_b-i_e-1\\ gap_2=&n_b-j_e-1 \end{array}$$

Introduce $Diff$, number of base differences resulting from extension, as

$$Diff= \left\{ \begin{array}{ll} Length_{inner\_mis} & gap_1>0... ...1,gap_2\}-min\{gap_1,gap_2\} & otherwise\\ \end{array}\right.$$

where $Length_{inner\_mis}$ is the number of different(mismatches and indels) bases from global alignment of $s[i_{e}+1\ldots m_{b}-1]$ and $s[j_{e}+1\ldots n_{b}-1]$. The similarity of merged loci is then:

$$Sim = \frac{len_{pair1}+max\{gap_1,gap_2\}+len_{pair2}-Diff}{len_{pair1}+max\{gap_1,gap_2\}+len_{pair2}}$$

When LTR_FINDER decides whether two neighboring pairs should be merged, it first calculates $Diff$, make sure that it does not exceed the value of extension max gap, then calculates $Sim$. If $Sim < extension cutoff$, pair extension will stop here, $P_1\{s[i_b\ldots i_e], s[j_b\ldots j_e]\}$ will be reported as a candidate for LTR element; If $Sim > reliable extension$, new pair $P_2$ and inter-pair regions will be linked to the previous one $P_1$ to construct a longer new pair $P\{s[i_b\ldots m_e], s[j_b\ldots n_e]\}$, and LTR_FINDER continues to find next neighboring pairs; if $extension cutoff < Sim < reliable extension$, it means we are not sure whether continue to extend or stop. So LTR_FINDER first report a LTR element candidate $P_1\{s[i_b\ldots i_e], s[j_b\ldots j_e]\}$ while at the same time, the extension process will continue.