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@@ -124,21 +124,21 @@ Launch _JolyTree_ without option to read the following documentation:
 
 * In short, _JolyTree_ uses [_mash_](http://mash.readthedocs.io/en/latest/) to decompose each genome into a sketch of _k_-mers (options `-k`, `-q`, `-s`) and quickly estimate the _p_-distance between each pair of genomes. If required, every _p_-distance is transformed into an evolutionary distance (options `-c`, `-a`, `-f`). A ratchet-based optimal phylogenetic tree search is performed from the pairwise evolutionary distances using [_FastME_](http://www.atgc-montpellier.fr/fastme/usersguide.php) (option `-r`). Branch supports are finally estimated using [_REQ_](https://research.pasteur.fr/en/tool/r%ce%b5q-assessing-branch-supports-o%c6%92-a-distance-based-phylogenetic-tree-with-the-rate-o%c6%92-elementary-quartets/).
 
-* It is not recommended to modify the option `-k`. The optimal value of _k_ is automatically estimated by equation (2) in [Ondov et al. (2016)](https://genomebiology.biomedcentral.com/articles/10.1186/s13059-016-0997-x) from the desired probability _q_ of observing a random _k_-mer (option `-q`). Since _JolyTree_ v2.0, the default probability is _q_ = 0.000000001, as it enables pairwise distances to be conveniently estimated in many cases. Increasing _q_ is not recommended, but can be useful to minimize the number of unknown distances when dealing with distantly-related genome sequences. Lowering _q_ leads to larger _k_-mer size that can be useful when dealing with very closely-related genome sequences.
+* It is not recommended to modify the option `-k`. The optimal value of _k_ is automatically estimated by equation (2) in [Ondov et al. (2016)](https://genomebiology.biomedcentral.com/articles/10.1186/s13059-016-0997-x) from the desired probability _q_ of observing a random _k_-mer (option `-q`). Since _JolyTree_ v2.0, the default probability is _q_ = 0.000000001, as it enables pairwise distances to be conveniently estimated in many cases. Increasing _q_ is not recommended, but can be useful to minimize the number of unknown distances (i.e. non-overlapping _k_-mer sets) when dealing with distantly-related genome sequences. Lowering _q_ leads to larger _k_-mer size that can be useful when dealing with very closely-related genome sequences.
 
 * Default sketch size is 25% of the average genome size, which enables pairwise distances to be efficiently estimated with fast running times. Increasing the sketch size (option `-s`) yields more accurate estimates (especially with distantly-related genomes), but requires important disk space to store the sketch files. 
 
-* Lowering the cutoff value for correcting the evolutionary distances (option `-c`) does generally not modify the inferred phylogenetic tree; on the other side, it is generally not recommended to increase this cutoff value.
+* Lowering the cutoff value for correcting the evolutionary distances (option `-c`) does generally not modify the inferred phylogenetic tree; on the other side, it is inadvisable to increase this cutoff value.
 
 * The option `-c` allows multiple substitutions per character to be accurately estimated when an observed _p_-distance is quite large (e.g. > 0.1; see [Figure 3.1](https://books.google.fr/books?id=3Xc8DwAAQBAJ&pg=PA41) in Nei and Kumar 2000). In such cases, all the _p_-distances _p_ estimated by _mash_ are transformed into proper evolutionary distances _d_. Since _JolyTree_ v2.0, four _p_-distance transformations can be obtained using options `-c` and/or `-a`:
 <div align="center">
 
-| transformation          | formula                            | options                            |
-|:------------------------|:-----------------------------------|:-----------------------------------|
-| none                    | _d_ = _p_                          | `-c 1 -a $a` with any `$a` > 0 |   |
-| Poisson correction      | _d_ = - log<sub>_e_</sub>(1 - _p_) | `-c 1 -a 0`                      |
-| F81/EI correction       | _d_ = -_b_<sub>1</sub> log<sub>_e_</sub>(1 - _p_/_b_<sub>2</sub>) | `-a 0` |
-| F81/EI gamma correction | _d_ = -_ab_<sub>1</sub>[(1 - _p_/_b_<sub>2</sub>)<sup>-1/_a_</sup> - 1] | `-a $a` with specified gamma shape parameter |
+| transformation          | formula                                                                 | options                                                     | notes                                                                                             |
+|:------------------------|:------------------------------------------------------------------------|:------------------------------------------------------------|:--------------------------------------------------------------------------------------------------|
+| none                    | _d_ = _p_                                                               | `-c 1 -a $a` with any `$a` > 0                              | unaccurate estimate when _p_ > 0.1                                                                |
+| Poisson correction      | _d_ = - log<sub>_e_</sub>(1 - _p_)                                      | `-a 0` (use `-c 1` to force Poisson correction)             | default _p_-distance transformation of _mash_                                                     |
+| F81/EI correction       | _d_ = -_b_<sub>1</sub> log<sub>_e_</sub>(1 - _p_/_b_<sub>2</sub>)       | `-a 0` (use `-c 0` to force F81/EI correction)              | formula (4) in [Tamura and Kumar (2002)](https://academic.oup.com/mbe/article/19/10/1727/1258975) |
+| F81/EI gamma correction | _d_ = -_ab_<sub>1</sub>[(1 - _p_/_b_<sub>2</sub>)<sup>-1/_a_</sup> - 1] | `-a $a` with specified gamma shape parameter (default: 1.5) | formula (3) in Criscuolo (2020; _submitted_)                                                      |
 
 </div>
 
@@ -257,7 +257,7 @@ Below is a list of some phylogenetic trees inferred using _JolyTree_:
 
 * [_Klebsiella pneumoniae_](https://www.tandfonline.com/na101/home/literatum/publisher/tandf/journals/content/kgmi20/2020/kgmi20.v011.i05/19490976.2020.1748257/20200625/images/medium/kgmi_a_1748257_f0002_c.jpg) ([Huynh et al. 2020](https://doi.org/10.1080/19490976.2020.1748257 ))
 
-* [_Stromatolite bacterial communities_](https://www.biorxiv.org/content/biorxiv/early/2020/03/14/818625/F5.large.jpg) ([Waterworth et al. 2020](https://doi.org/10.1101/818625))
+* [_Stromatolite_ bacterial communities](https://www.biorxiv.org/content/biorxiv/early/2020/03/14/818625/F5.large.jpg) ([Waterworth et al. 2020](https://doi.org/10.1101/818625))
 
 * [_Campylobacter_ genus](https://figshare.com/articles/Data_Sheet_1_Taking_Control_Campylobacter_jejuni_Binding_to_Fibronectin_Sets_the_Stage_for_Cellular_Adherence_and_Invasion_pdf/12103260) ([Konkel et al. 2020](https://doi.org/10.3389/fmicb.2020.00564.s001))