**Supplementary Material for**

**A rigorous analysis of the pattern of intron conservation supports the
Coelomata clade of animals**

Jie Zheng, Igor B. Rogozin, Eugene V. Koonin\*, Teresa M. Przytycka\*

{zhengj, rogozin,koonin,przytyck}@ncbi.nlm.nih.gov

*National Center for Biotechnology Information, National Library of
Medicine, National Institutes of Health, Bethesda, MD 20894, USA*

*\*Corresponding authors*

**A. Dependence of intron retention on conservation in other branches**

Table S1. Test for dependence of intron retention on conservation in
other branches - Arabidopsis as outgroup (Out 1)

Table S2. Test for dependence of intron retention on conservation in
other branches - outgroup Out 2: Fungi (Af, Cn, Sp, Sc)

+---------------+-------------------+----------------+----------------+
| Ecdysozoa     |                   |                |                |
+---------------+-------------------+----------------+----------------+
|               | non-conserved in  | Conserved in D | p-value in     |
|               | D                 |                |                |
|               |                   |                | Fisher test    |
+---------------+-------------------+----------------+----------------+
|               | ANO/NO            | ANOD/NOD       |                |
+---------------+-------------------+----------------+----------------+
| r~A~ / (1-    | 5/24              | 35/52          | 0.026          |
| r~A~ )        |                   |                |                |
+---------------+-------------------+----------------+----------------+
|               | ANO/AO            | ANOD/AOD       |                |
+---------------+-------------------+----------------+----------------+
| r~N~ / (1-    | 5/22              | 35/40          | 0.012          |
| r~N~ )        |                   |                |                |
+---------------+-------------------+----------------+----------------+
| Coelomata     |                   |                |                |
+---------------+-------------------+----------------+----------------+
|               | Non conserved in  | conserved in N | p-value in     |
|               | N                 |                |                |
|               |                   |                | Fisher test    |
+---------------+-------------------+----------------+----------------+
|               | ADO/DO            | ADON/DON       |                |
+---------------+-------------------+----------------+----------------+
| r~A~ / (1-    | 40/242            | 35/52          | 5.98e-7        |
| r~A~ )        |                   |                |                |
+---------------+-------------------+----------------+----------------+
|               | ADO/AO            | ADON/AON       |                |
+---------------+-------------------+----------------+----------------+
| r~D~ / (1-    | 40/22             | 35/5           | 0.012          |
| r~D~ )        |                   |                |                |
+---------------+-------------------+----------------+----------------+

**B. Conserved introns support Coelomata and variable introns support
Ecdysozoa**

Table S3. Dollo parsimony trees constructed for variable and conserved
introns

+-----------+----------------------+-----------------+----------------+
| Outgroup  | All introns          | Introns         | Introns        |
|           | conserved in at      | conserved in    | conserved in   |
|           | least 2 groups       | exactly 2       | at least 3     |
|           |                      | groups only     | groups         |
+-----------+----------------------+-----------------+----------------+
| Out 1     | Ecdysozoa            | Ecdysozoa       | Coelomata      |
|           |                      |                 |                |
|           | 429/695              | 419/598         | 87/97          |
|           |                      |                 |                |
|           | p=3.36e-10           | p=1.88e-23      | p=8.94e-17     |
+-----------+----------------------+-----------------+----------------+
| Out 2     | Ecdysozoa            | Ecdysozoa       | Coelomata      |
|           |                      |                 |                |
|           | 456/698              | 449/610         | 81/88          |
|           |                      |                 |                |
|           | p=2.22e-16           | p=1.05e-32      | p=2.24e-17     |
+-----------+----------------------+-----------------+----------------+
| Out 3     | Ecdysozoa            | Ecdysozoa       | Coelomata      |
|           |                      |                 |                |
|           | 737/990              | 731/916         | 68/74          |
|           |                      |                 |                |
|           | p=9.80e-56           | p=1.11e-77      | p=1.07e-14     |
+-----------+----------------------+-----------------+----------------+

> The ratio of the number of informative introns that support a given
> topology to the total number of informative introns is indicated. The
> p-value was computed using the binomial test as described in Section
> Materials and Methods.

**C. Full arguments of Test 1 and Test 2**

**Test 1** *[Argument:]{.underline}* First, we rule out parallel loses
(or independent gains) as a possible explanation of the tree topology
obtained with conserved introns. Next, we argue that, under the
assumption that the tree obtained with conserved introns is correct, the
inconsistency between this tree and the tree computed with variable
introns is due to homoplasy. It is easy to show that none of the
informative conserved introns could have undergone parallel losses,
regardless of the tree topology (Coelomata or Ecdysozoa). For a parallel
loss to occur, the intron must be present in the outgroup; otherwise,
the parsimonious scenario for any intron will necessarily include gain
in a subtree and, at most, a single loss. Furthermore, for an intron
position to be informative, it must contain the intron in one and only
one of the two species *H. sapiens* or *C. elegans* (if the intron is
present in both or none, the number of losses would be the same in the
Coelomata and Ecdysozoa trees). Consequently, the third species in which
the intron is conserved must be one of the insects. Thus, the set of
conserved, potentially, informative introns that might be involved in
parallel losses is limited to those that are conserved in the outgroup,
in exactly one of the species pair *H. sapiens/C.elegans*, and exactly
one of the two insect species. However, introns with this pattern of
presence-absence have two losses in each of the topologies and thus are
not informative. Therefore, none of the informative, conserved introns
have parallel losses in any of the two trees, i.e., we proved that, in
the case of conserved introns, parallel losses could not bias the result
towards the Coelomata or Ecdysozoa tree.

The second part of the argument deals with the properties of informative
variable introns. As in the case of strongly conserved introns, all
informative variable introns must be present in exactly one of the
species pair *H. sapiens*/*C. elegans* (otherwise, they are not
informative). Since a variable intron is only conserved in two lineages,
the other lineage has to be either the outgroup or one of the insects.
Thus, there are four sets of informative variable introns. Using data
for the largest, all non-animal outgroup Out 3 (Supplementary Table S4
and Table S5), we have:

1)  Introns conserved in Human and outgroup (let *m~HO~* be the number
    of such introns, *m~HO~* = 711 ) -- one loss in the Ecdysozoa tree,
    two parallel losses (C.elegans and an insect) in the Coelomata tree;
    supports Ecdysozoa

2)  Introns conserved in C. elegans and outgroup (let *m~CO~* be the
    number of such introns, *m~CO~* = 85) -- one loss in the Coelomata
    tree, two parallel losses (*H. sapiens* and the common ancestor of
    the insects) in the Ecdysozoa tree; supports Coelomata

3)  Introns conserved in human and one insect (let *m~HI~* be the number
    of such introns, *m~HI~* = 168) - one loss in the Coelomata tree,
    two parallel losses in the Ecdysozoa tree (the second insect and *C.
    elegans*); supports Coelomata

4)  Introns conserved in C.elegans and one insect (let *m~CI~* be the
    number of such introns, *m~CI~* = 26) - one loss in the Ecdysozoa
    tree and two parallel losses (human and an insect) in the Coelomata
    tree; supports Ecdysozoa.

Thus, assuming that the Coelomata topology is correct, the support for
the Ecdysozoa topology obtained in the analysis of the variable introns
results from the pattern of intron distribution in set 1 that is, under
this assumption, explained by parallel intron losses (an analog of LBA)
in *C. elegans* and insects.

This argument holds for any set of five taxa and any set of characters
as long as the goal is to differentiate between two pre-defined tree
topologies, such as Coelomata and Ecdysozoa. Thus, this approach
resolves the discrepancy between the results obtained for a conserved
set of characters and a variable set of characters in favor of the
result obtained with the conserved characters -- as long, of course, as
the number of such characters is sufficient to obtain statistically
significant results.

**Test 2** *[Argument:]{.underline}* We show that the value of
*d~H~/d~C~* affects the result of the Dollo parsimony reconstruction.
For each of the two sets of introns (the conserved and the variable
ones), there exists an equilibrium value *d~H~/d~C~* where the Coelomata
tree and the Ecdysozoa tree have the same cost (Error: Reference source
not found). These equilibrium values can be computed directly from the
frequencies of intron patterns (Table S4 and Table S5) in both sets as
described below. We show that there exists an interval of *d~H~/d~C~*
values where the tree constructed from the two sets of introns is the
same, and this common tree has the Coelomata topology.

First, we compute the equilibrium value for the variable introns. Let
*m~HI~* , *m~CI~* , *m~OH~* , and *m~OI~* be the number of variable
introns in each of the four groups as defined for Test 1. By counting
deletions of each of the four groups of introns (see the argument of
Test 1), the equilibrium value of the *d~H~/d~C~* ratio is obtained from
the equation that equalizes the extra costs:

$m_{\text{HI}}d_{C} + m_{\text{CO}}d_{H} = m_{\text{CI}}d_{H} + m_{\text{HO}}d_{C}$*.*

Substituting specific numbers (Table S4 and Table S5), we obtain:

$\frac{d_{H}}{d_{C}} = \frac{m_{\text{HO}} - m_{\text{HI}}}{m_{\text{CO}} - m_{\text{CI}}} = 9\text{.}3$.

If d~H~/d~c~ \> 9. 3, the resulting tree has the Coelomata topology, and
otherwise, the tree has the Ecdysozoa topology.

Consider now the set of conserved introns. We showed that the only
informative introns among the conserved ones are those that are shared
by both insects and either human or *C. elegans* (see the argument of
Test 1 above). Let *n~HI~* be the number of introns that are conserved
in human and both insects. These introns have no losses in the Coelomata
tree and one loss (in the *C. elegans* branch) in the Ecdysozoa tree.
Similarly, let *n~CI~* be the number of conserved introns with the
intron present in C.elegans and both insects. For this set of introns,
there are no losses in the Ecdysozoa tree and one loss (in the human
branch ) in the Coelomata tree. Thus, the equilibrium ratio is obtained
from:

$$n_{\text{HI}}d_{C} = n_{\text{CI}}d_{H}$$

And, substituting the actual counts *n~HI~* and *n~CI~* in the conserved
intron set, we get:

$$\frac{d_{H}}{d_{C}} = \frac{n_{\text{HI}}}{n_{\text{CI}}} = \text{11}\text{.}3$$

Thus, if *d~H~/d~C~* \< 11. 3, then the tree for the conserved introns
has the Coelomata topology, whereas, for *d~H~/d~c~* \> 11. 3, the tree
has the Ecdysozoa topology.

The only interval of the d~H~/d~C~ ratio, for which both sets of introns
(conserved and variable) produce the same tree, is 9.3 \< d~H~/d~C~ \<
11.3, and in this interval, the tree has the Coelomata topology (see
Error: Reference source not found).

**D. Frequencies of intron patterns**

Table S4. Frequencies of variable intron patterns

  ----------------- ------------------- -------------- ---------------------
  Intron pattern    Pattern frequency                  
                    for the set with                   
                    given outgroup                     

                    Out1(Arabidopsis)   Out2(Fungi)    **Out3(All
                                                       non-animals)**

  11000             238                 217            **172**

  10100             81                  79             **67**

  01100             14                  13             **12**

  10010             50                  44             **33**

  01010             8                   8              **8**

  00110             80                  74             **70**

  10001             397                 428            **711**

  01001             48                  38             **85**

  00101             12                  14             **26**

  00011             11                  10             **19**
  ----------------- ------------------- -------------- ---------------------

Table S5. Frequencies of conserved intron patterns

  ----------------- ------------------- -------------- ---------------------
  Intron pattern    Pattern frequency                  
                    for the set with                   
                    given outgroup                     

                    Out1(Arabidopsis)   Out2(Fungi)    **Out3(All
                                                       non-animals)**

  11100             28                  19             **17**

  11010             26                  18             **15**

  10110             87                  81             **68**

  01110             10                  7              **6**

  11001             80                  101            **146**

  10101             24                  26             **38**

  01101             1                   2              **3**

  10011             19                  25             **36**

  01011             1                   1              **1**

  00111             7                   13             **17**
  ----------------- ------------------- -------------- ---------------------

The intron patterns are represented by binary vectors corresponding in
left to right order to: Hs, Ce, Dm, Ag, Out.

**E. Retention rates under Dollo parsimony**

Figure S1. Node labeling used in Table S6

Table S6. Retention rates of edges of Coelomata and Ecdysozoa trees

  ----------- ---------- ---------- ----------- ----------- -------- -----------
  Coelomata                                                          
  Tree                                                               
  Topology                                                           

              Variable                          strongly             
              introns                           conserved            
                                                introns              

  branch      retained   lost       retention   Retained    lost     retention
                                    rate                             rate

  (0, 1)      841        0          1           241         0        1

  (0, 8)      841        0          1           241         0        1

  (1, 5)      277        756        0.268       188         91       0.674

  (1, 2)      948        85         0.918       279         0        1

  (2, 4)      983        65         0.938       320         27       0.922

  (2, 3)      165        883        0.157       201         146      0.579

  (3, 6)      175        60         0.745       149         52       0.741

  (3, 7)      130        105        0.553       143         58       0.711

  Ecdysozoa                                                          
  Tree                                                               
  Topology                                                           

              Variable                          strongly             
              introns                           conserved            
                                                intron               

  branch      retained   lost       retention   retained    lost     retention
                                    rate                             rate

  (0, 1)      841        0          1           241         0        1

  (0, 8)      841        0          1           241         0        1

  (1, 4)      983        130        0.883       320         21       0.938

  (1, 2)      402        711        0.361       341         0        1

  **(2, 5)**  277        145        **0.656**   188         159      **0.542**

  (2, 3)      165        257        0.390       146         146      0.579

  (3, 6)      175        60         0.745       52          52       0.741

  (3, 7)      130        106        0.553       58          58       0.711
  ----------- ---------- ---------- ----------- ----------- -------- -----------

The edge labels are consistent with the Figure S1. The rates are
computed with Out3 outgourp based on data in Table S4 and Table S5.