Preprocessing

This chapter explains how gene trees from the input gene forest are processed by aphid prior to calculating likelihood.

When referring to a tree, the construct "LCA(species_group)" refers to the single last common ancestor of these species in the tree, i.e. the closest node upstream from all species in the group.

Pruning

Every gene tree is first pruned so that only species of interest are kept. Species of interest are species occuring in either the triplet, the outgroup or the other section of the input [taxa] table.

This process reduces the number of node in every tree, but the branch lengths are conserved. For instance, pruning species A, C, E and H in the following raw gene tree with branch lengths a, b, c, etc.:

     │q
 ┌───┴────────┐
 │            │p
 │      ┌─────┴──────┐
 │      │            │o
 │      │        ┌───┴────────┐
 │a     │f       │            │n
 │      │        │      ┌─────┴──┐
 │   ┌──┴──┐     │      │l       │
 │   │     │e    │g  ┌──┴──┐     │
 │   │b    │     │   │     │k    │m
 │   │   ┌─┴─┐   │   │h  ┌─┴─┐   │
 │   │   │c  │d  │   │   │i  │j  │
 A   B   C   D   E   F   G   H   I

results in the following pruned tree:

       │q
       │+
       │p
  ┌────┴─────┐
  │          │o
  │          │+
  │f         │n
  │       ┌──┴──┐
┌─┴─┐     │l    │
│   │   ┌─┴─┐   │
│b  │e  │   │k  │m
│   │+  │h  │+  │
│   │d  │   │i  │
B   D   F   G   I

The process may a leave an artefactual nonzero scar on the root branch length when external nodes like A are pruned.

In subsequent analysis, every "tree" refers to a pruned tree whose root branch length is ignored.

Topology pass

The topology of every tree is analyzed with respect to the species of interest. A tree is rejected if either:

• One or several triplet species are missing from the tree.
• The triplet species form a paraphyletic group.
• No outgroup species appear in the tree.
• The outgroup species form a paraphyletic group.
• The LCA(triplet, outgroup) is not the root of the tree.
• If the triplet_other_monophyly parameter is set:
  • One or several other species branch from the outgroup side of the root.

For example, given the following species of interest:

triplet_other_monophyly = false

[taxa]
triplet = "((T, U), V)"
outgroup = "O P Q"
other = "X Y Z"

The following tree topology is included:

                │
      ┌─────────┴───────────┐
      │                ┌────┴───┐
┌─────┴──────┐         │        │
│            │         │        │
│        ┌───┴──┐   ┌──┴──┐     │
│        │      │   │     │     │
│     ┌──┴──┐   │   │   ┌─┴─┐   │
│     │     │   │   │   │   │   │
│   ┌─┴─┐   │   │   │   │   │   │
Y   T   U   V   Z   O   P   Q   X

But it is excluded with

triplet_other_monophyly = true

because the other species X branches between LCA(outgroup) and the root, instead of between LCA(triplet) and the root.

In subsequent analysis, every "tree" refers to a tree with an accepted topology.

Geometry pass

The geometry pass is an iterative combination of one or two filters applied at once. It happens in several steps:

• Step 1: calculate individual metrics for every gene tree
• Step 2: calculate global statistics over the whole forest based on the results (obtained in step 1).
• Step 3: calculate local statistics for every tree based on the global stastitics (obtained in step 2).
• Step 4: filter out trees whose local statistics (obtained in step 3) fall outside the desired range.
• Repeat from step 2 until no tree gets filtered out on step 4.

Individual metrics (step 1)

Three "mean branch lengths" are calculated for every gene tree \(g\) :

• The overal mean length from root to leaves, called mean_length: \(l_g\)
• The mean length from LCA(triplet) to the triplet species, called mean_triplet: \(t_g\)
• The mean length from root to either outgroup or other species (excluding triplet species), called mean_rest: \(r_g\)

In addition, if the max_clock_ratio parameter is set, then the "shape" of every tree is calculated as \[ q_g = \frac{t_g}{r_g} \]

Global statistics (step 2)

The global_mean_length is calculated over all \(G\) trees as: \[ L = \frac{\sum_g{l_g}}{G} \]

In addition, if the max_clock_ratio parameter is set, the "global shape" of the whole tree forest is calculated as \[ Q = \frac{\sum_g{t_g}}{\sum_g{r_g}} \]

Local statistics (step 3)

The relative mutation_rate of every tree is calculated as: \[ 𝛼_g = \frac{l_g}{L} \] This mutation rate is the value used during likelihood calculation, along with the corresponding gene sequence length.

In addition, if the max_clock_ratio parameter is set, the 'imbalance' of every tree is calculated as: \[ i_g = \max(\frac{Q}{q_g}, \frac{q_g}{Q}) \]

Filter (step 4)

Trees with any branch count larger than max_branch_count are rejected as outliers.

Trees with a relative mutation rate larger than max_relative_mutation_rate are rejected as outliers.

If a tree has a high imbalance value, it means that it is dissimilar to its enclosing forest, and the hypothesis that mutation rate is constant accross the tree is weakened. Therefore, trees with imbalance greater than max_clock_ratio, if set, are also rejected.

Filtering is over if no tree has been rejected at this step, otherwise a new filtering pass is repeated from step 2.

In subsequent analysis, every "tree" refers to a tree with an accepted geometry, and the local statistics used are the latest.