I. Input screen

Names of species/branches: species A, B, C, and D can be replaced by authentic names.
Note: names should not contain spaces or commas inside (e.g., “gray wolf” must be written as “gray_wolf”).

Settings:

Algorithms: Reverse is the preferred algorithm.
In the case of rapidly radiating species, the Stepwise algorithm might provide a better resolution.

Significance level: Default level “0.05” (95% probability) gives a balanced resolution for most cases, and level “0.01” (99% probability) rejects complex trees in favor of more simple trees in complex cases.
It could be used in case of contradiction between chi-square results and Empirical distribution or in case of not stable results of Empirical distribution.

Criterion (Selection of approximations): The Chi-square criterion allows getting estimations in a few seconds.
However, Chi-square could lead to an incorrectly preferred polytomy at the resolution boundary.
The Empirical distribution processes via a bootstrapping-like procedure to calculate critical values for each comparison and give a better resolution.
With an Empirical sample, size scale users could stabilize unstable results of Empirical distribution runs by more exact calculations of critical values.
However, the sample size is directly proportional to the running time of the Empirical distribution criterion (e.g., with a sample size equal to 500, a run takes tens of minutes, and with a sample size of 2000, it takes hours).

Marker Input: For the four lineages A,B,C,D, ten different patterns of relationships (y11-y44) can be derived.
The supportive number of verified diagnostic TEs of each pattern has to be inserted in the Marker Input field.
For calculation, the minimum input is one marker.

File Upload: Alternatively, all data can be uploaded from a text or excel file corresponding to the following example

With Start hammlet calculations! the process is commenced.
With Reset the user can return all values and settings to initial/default values.

II. Results screen

Example:

Names of species/branches: human, chimpanzee, gorilla and orangutan.

Algorithm: Reverse (stringent)

Significance level: 0.05 (default)

Criterion: Empirical distribution (exact and slow)

Empirical sample size: 1000

Marker Input: 0 0 0 0 0 0 1 0 37 48

The resulting Most Probable Tree Topology is indicated as T2 for the exemplified data, and the tree’s significance is placed as text below the tree topology.
KKSC values for individual tree splits are given in the grey part.
The log-likelihood table (LL-table) can be downloaded and provides optimal parameters for all five models.
With Download LL table (tsv format), one can retrieve the result table of the best trees from all five groups for further investigations.

Model indicating the tested model.
Alias describes models in “TTgg” annotation;
Order provides information about the permutation (where 1234 is equivalent to A,B,C,D);
LL presents the log-likelihood value for the resulting trees;
Ratio presents the value of the double log-likelihood ratio between resulting tree and polytomy (reflecting χ^2 value);
T(1) and T(3) provides the relative length of tree branches (T(1) and T(3)) that is proportional to the number of generations on corresponding branches);
γ1 and γ3 provide values of the hybridization coefficients.

III. Extended system for tree notation in text format

  1. Round brackets “( )” indicate clustering groups: e.g., (A(B,C)) shows clustering of B and C against the sister-group A.
  2. Square brackets “[ ]” indicate hybridization of two external branches: e.g., (A[B]C) show hybridization/introgression between A and C, resulting in branch B.
  3. Plus “+” indicates a common branch: e.g., (A(B,C+D)) shows a close relation of B to a common branch of C and D (later split into two branches).
  4. Vertical slash “|” indicating an ancestral hybridization situation, e.g., hybridization (A[C+D]B) following case when C plus D have two sister-groups (A|B(C,D).
  5. Comma “,” indicates a shared origin, e.g., in the tree (A(B,C)) comma shows that B and C share the same origin, and in the tree (A,B,(C,D)) first two commas announce polytomy with the shared origin of A, B and the common ancestor of C plus D.