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Research article
Using supernetworks to distinguish hybridization from lineage-sorting
Barbara R Holland
Steffi Benthin
Peter J Lockhart
Vincent Moulton
Katharina T Huber
1 
Allan Wilson Centre, I titute of Fundamental Sciences, Ma ey University, Palmerston North, New Zealand
2 
Allan Wilson Centre, I titute of Molecular BioSciences, Ma ey University, Palmerston North, New Zealand
3 
School of Computing Sciences, University of East Anglia, Norwich, UK
author email
corre onding author email
BMC Evolutionary Biology
doi:10.1186/1471-2148-8-202
The electronic version of this article is the complete one and can be found online at:
Received:
16 December 2007
Accepted:
14 July 2008
Published:
14 July 2008
2008 Holland et al; lice ee BioMed Central Ltd.
This is an Open Acce article distributed under the terms of the Creative Commo Attribution Lice e (
), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A tract
Background
A simple and widely used a roach for detecting hybridization in phylogenies is to reco truct gene trees from independent gene loci, and to look for gene tree incongruence. However, this a roach may be confounded by factors such as poor taxon-sampling and/or incomplete lineage-sorting.
Results
Using coalescent simulatio , we investigated the potential of supernetwork methods to differentiate between gene tree incongruence arising from taxon sampling and incomplete lineage-sorting as o osed to hybridization. For few hybridization events, a large number of independent loci, and well-sampled taxa acro these loci, we found that it was po ible to distinguish incomplete lineage-sorting from hybridization using the filtered Z-closure and Q-imputation supernetwork methods. Moreover, we found that the choice of supernetwork method was le important than the choice of filtering, and that count-based filtering was the most effective filtering technique.
Conclusion
Filtered supernetworks provide a tool for detecting and identifying hybridization events in phylogenies, a tool that should become increasingly useful in light of current genome sequencing initiatives and the ease with which large numbers of independent gene loci can be determined using new generation sequencing technologies.
Background
In recent years there has been growing interest in the problem of building explicit models of reticulate evolution
]. This work has to a large part been motivated by biological research highlighting the potential importance of hybridization in the origin of biotic diversity, biological invasion and rapid adaptation
One simple and widely used a roach for detecting hybridization has been to compare gene trees built from independent gene loci, and to co ider gene tree incongruence as evidence for hybridization
]. However, hybridization is not the only po ible cause of gene tree incongruence. Other explanatio include phylogenetic error
], unrecognised gene duplication and lo [
], incomplete lineage-sorting
] and lateral gene tra fer
In light of current genome sequencing efforts and the ease of sequencing large numbers of independent gene loci using new generation sequencing technologies, it is important to find ways to differentiate between various explanatio of gene tree incongruence. Here we focus on distinguishing hybridization from incomplete lineage-sorting. In this regard, a helpful concept might be "principal trees", which are the trees di layed by a hybridization network (see the su ection
Simulatio for a more formal definition of principal trees). If a phylogeny contai no hybridization or lateral gene tra fer, then the expectation is for one principal or " ecies" tree. However, if hybridization has occurred, then there will be multiple principal trees. In the a ence of incomplete lineage-sorting, each principle tree will represent the evolutionary history for a large collection of loci, but where incomplete lineage-sorting occurs gene trees may differ from their underlying principal tree.
Here we investigate the potential of filtered Z-closure
] and Q-imputation
] supernetworks to distinguish phylogenetic signals arising from principal trees from phylogenetic signals caused by a combination of incomplete taxon-sampling and incomplete lineage-sorting in evolutionary histories involving hybridization. We co ider these methods since they are not only designed to cope with conflicting phylogenetic signals, but also with data that current genome sequencing efforts can fail to gather (for example, for multi-gene data sets, such as those generated from expre ed sequence tag (EST) databases, gene sequences are often mi ing for ecies of interest). In particular, using gene trees generated under a coalescent proce , we test whether these methods can be used to filter out phylogenetic signals that do not corre ond to edges in principal trees, signals that have the potential of confounding efforts to reco truct complex phylogenies.
Methods
Overview
Analogous to the supertree framework
] our i ut is a set of trees on overla ing but not nece arily identical taxa. We refer to the
complete taxa set
as the union of the taxa sets of the i ut tree complete lits
are bipartitio of the complete taxa set and
trivial lits
are lits where one part co ists of precisely one element. Furthermore
partial trees
partial lits
are trees and lits on a su et of the complete taxa set. We denote a lit of the taxa set X as A|B where A and B are both su ets of X, A ∪ B = X, and A ∩ B is the empty set.
Our overall a roach is to first generate a collection of partial trees along a hybridization network in the presence of incomplete lineage-sorting (modelled by the coalescent proce ), to then a ly a supernetwork method to this collection of partial trees to obtain a collection of complete lits, and to then a ly a filter to reduce the complexity of this collection. The reduced collection of complete lits is then compared to the lits a ociated with the hybridization network to determine if they have been accurately recovered. We use this a roach to study two supernetwork methods – Z-closure
] and Q-imputation
], and two types of filter – one counting-based and one homoplasy-based
Supernetwork methods
We begin with a brief description of the two supernetwork methods that we co idered. Supernetwork methods take as i ut a set of partial trees and produce a set of complete lits. Unlike the supertree framework, these lits need not be compatible, allowing po ible conflict within the set of i ut trees to be represented. The first supernetwork method we co ider, Z-closure, is underpi ed by the Z-closure rule and is introduced in
] and implemented in SplitsTree4
]. The method begi with a collection of partial trees from which a list of partial lits is obtained – each partial lit coming from an edge in some partial tree in the list (see e.g.
]). The Z-closure rule takes a pair of partial lits A|B and C|D, and if A ∩ C, B ∩ C and B ∩ D are all non-empty and A ∩ D is empty, then it replaces the partial lits A|B and C|D with the extended lits A| B ∪ D and A ∪ C | D (c.f. Figure
). To e ure that as many partial lits in the list as po ible are extended to complete lits, the rule is iteratively a lied to the partial lits in the list by taking pairs of partial lits and either overwriting them with two lits on a more inclusive taxa set, or, if the rule does not a ly, returning the same two partial lits. When the Z-closure rule can no longer be a lied the method retur the list of complete lits that have been generated.
An example of two a licatio of the Z-rule, which underpi the Z-closure supernetwork method, where two partial lits di layed in the i ut trees (A) are extended to complete lits as shown in (B) and (C). The bold lines that form the 'Z' shape indicate that the intersection of the taxon sets is non-empty, eg in (B) {C,D}∩ {D,M} = {D}, {D,M}∩ {M,P,T} = {M}, {M,P,T}∩ {O,P,T} = {P,T}, but {C,D}∩ {O,P,T} = ∅ so the Z-rule can be a lied.
Note that the output of Z-closure is dependent on the order of elements in the list of partial lits, and so we repeat the procedure for 10 random orderings keeping a cumulative count of how many times each complete lit a ears. (Simulatio indicate that this order dependence is not strong
], so there would be little benefit in performing a larger number of random orderings.) Also note that the Z-closure implementation used for this paper differs slightly from that in SplitsTree4 in that it kee track of multiple copies of partial lits and complete lits, as this information is required by the counting filter that we a ly later.
The other supernetwork method we co ider, Q-imputation
], also uses partial trees as i ut but uses an alternative a roach to generating complete lits that is based on the four-taxon subtrees (quartets) of the partial trees. For each partial tree with mi ing taxa – that is, taxa that are in the complete taxa set but not in the taxa set for that tree – the mi ing taxa are i erted in the tree. This is done by proce ing the mi ing taxa in a fixed order and placing each taxon within the partial tree to maximise the number of quartets that contain the mi ing taxon and are also quartets of the other partial i ut trees. Once all the trees have been completed the list of complete lits di layed by the completed trees is returned. (In the ecial case where all the trees are on identical taxa sets, the Q-imputation method reduces to the co e us network method
Filtering methods
We a ly two different kinds of filter to the lists of complete lits obtained from the two supernetwork methods, a homoplasy-based filter and a counting-based filter. The homoplasy filter
] requires two user-defined parameters
. The level of homoplasy for each complete lit and partial tree is determined by recoding the lit as a binary character, reducing it to the same taxa set as the partial tree, and evaluating the number of character state changes required to explain the character on the partial tree (i.e. the parsimony score). Splits that have a parsimony score greater than a given number
in more than a given number
of the partial trees are filtered out. The counting filter has one user-defined parameter
and kee the
n lits that a ear most frequently in the list of complete lits (ties are broken arbitrarily). Note that for Q-imputation this is equivalent to the filter described in
] for some choice of threshold.
Simulatio The starting point for each simulation is a hybridization network such as the one shown in Figure
. Formally such networks are rooted, leaf-labelled, directed-acyclic-graphs in which the nodes are of one of four types: nodes with in-degree 2 and out-degree 1 corre ond to hybridizatio nodes with in-degree 1 and out-degree 2 corre ond to eciation event nodes with in-degree 1 and out-degree 0 corre ond to the extant ecie and one ecial node of in-degree 0 and out-degree 2 is the root. Such a network can be thought of as a collection of rooted principal trees: These trees are obtained by starting from the ti of the hybridization network (these are the nodes with in-degree 1 and out-degree 0) and choosing one of the two po ible paths at each hybridization node that is encountered on the way towards the root. The set of principal trees co ists of the trees po ible to obtain in this ma er (Figure
). This leads to a natural definition of the collection of lits a ociated with a hybridization network as being the union of the lits a ociated with each of the principal trees of the network (Figure
). We will refer to such lits as the true lits of the hybridization network. The purpose of the simulatio is to a e if filtered supernetworks can identify the lits present in the principal trees of the hybridization network. To be succe ful these lits need to be distinguishable from those arising from incomplete lineage-sorting under the coalescent proce .
(A) A hybridization network (number 7 from Table 1) with two hybridization nodes. (B) The principal trees of the hybridization network – these are found by choosing a single parent at each hybridization node and then su re ing the resulting internal nodes of degree 2. (C) The lits a ociated with the hybridization network are those di layed by the principal trees in (B). (D) A lit network di laying the lits in (C).
The main flow of our simulation is shown in Figure
. Given a hybridization network, a collection of trees was created by sampling with replacement from the collection of principal trees (the same tree may a ear multiple times). We used the software package COAL
] to simulate trees according to the coalescent proce given a principal tree with branch lengths ecified in coalescent units (the number of generatio divided by population size). We employed two different branch length settings. In each of the principal trees all branch lengths were either a igned coalescent units of 1 or all branch lengths were a igned coalescent units of 0.5. These choices for the branch length settings were also used in
], a more sophisticated a roach might be to a ign branch lengths to the hybridization network itself and then have the principal trees inherit these branch lengths. We also simulated a situation where there were no lineage-sorting effects. In this case the only random a ect to the data generation is the choice of the principal trees. Each tree was then pruned of
taxa at random with the restriction that each taxon in the network must a ear in at least one partial tree. These collectio of partial trees were then used as i ut to each of the supernetwork methods. Note that, although COAL produces rooted trees, neither of the 2 supernetwork methods co idered use any information about the root, so in effect they co ider only the corre onding unrooted trees.
Flowchart indicating the ste used in the simulation study.
Accuracy of the supernetwork methods was determined by counting the number of false positive and false negative lits. A
false positive
is a lit that is di layed by the supernetwork, but is not a true lit of the hybridization network; a
false negative
is a lit that is di layed by at least one of the principal trees of the hybridization network, but not di layed by the supernetwork. Note that these definitio differ from those used in
] in that they measure accuracy with re ect to an underlying hybridization network that has been used to generate the data.
We based our simulatio on ten different hybridization networks each labelled by 8 taxa, and representing 0 to 3 hybridization events (Table
). For each network the parameters in the simulation that varied were the number of trees (
= 5, 10, 15 or 20), the branch lengths used by COAL
= 8, 1, 0.5; where 8 represents the case where COAL was not used, i.e. there are no incomplete lineage-sorting effects) and the number of taxa mi ing from each tree (
= 0, 1, 2, or 3). For each parameter setting we made 100 replicate data sets, giving 6400 sets of partial trees for each of the ten hybridization networks.
Hybridization networks used in simulatio .
We a lied 4 different homoplasy filters to the lists of complete lits returned by Z-closure and Q-imputation:
• (HF1) keep only lits with no homoplasy (i.e. a parsimony score of 1) on all partial trees,
• (HF2) keep only lits with no homoplasy on 75% or more of the partial trees,
• (HF3) keep only lits with no homoplasy on 50% or more of the partial trees,
• (HF4) keep lits with a parsimony score of 2 or le on all partial trees.
We also a lied the counting filter (CF) to both Z-closure and Q-imputation. For each hybridization network we selected
n lits, where
was fixed to be the number of unique non-trivial lits a ociated with the principal trees of the network (Table
Results and Discu ion
Results were generated for each of the hybridization networks given in Table
, but for brevity, in Figures
and Table
we only show results for hybridization network 7 (the network shown in Figure
). Results for the other hybridization networks follow the same general trends [see Additional file 1].
False positives for hybridization network 7 using the counting filter to select the 8 highest weight lits.
False positives (A) and false negatives (B) with increasing numbers of i ut trees for Z-closure (ZC) and Q-imputation (Q) keeping lits with no homoplasy on any tree (HF1), keeping lits with no homoplasy on 75% or more of the trees (HF2), keeping lits with no homoplasy on 50% or more of the trees (HF3), keeping lits with a homoplasy score of 1 or le on all of the trees (HF4), or keeping the 8 highest weight lits (CF) for hybridization network 7. Values are averages over the 12 combinatio of coalescent branch length
and number of mi ing taxa
. The maximum po ible number of false negatives for this hybridization network is 8.
False positives (A) and false negatives (B) with increasing number of i ut trees for the highest setting of mi ing taxa (
= 3) and the smallest setting for coalescent branch lengths (
= 0.5) for hybridization network 7. A reviatio are as descibed in Figure 4. The maximum po ible number of false negatives for this hybridization network is 8.
False positives (A) and false negatives (B) as the number of mi ing taxa
increases from 0 to 3 for hybridization network 7. Results are averaged over the 12 po ible settings for number of gene trees
and coalescent branch lengths
. A reviatio are as descibed in Figure 4. The maximum po ible number of false negatives for this hybridization network is 8.
False positives (A) and false negatives (B) for the two different branch length settings using in the coalescent simulation (
= 0.5 and
= 1), and for the control without incomplete lineage-sorting (
= 8) for hybridization network 7. Results are averaged over the 16 po ible settings for number of gene trees
and number of mi ing taxa
. A reviatio are as descibed in Figure 4. The maximum po ible number of false negatives for this hybridization network is 8.
Filtering
shows the change in the average number of lit false positives and false negatives with re ect to the number of gene trees. The results are averaged over 100 repetitio and the 12 combinatio of number of mi ing taxa
and coalescent branch lengths
As can be seen in Figure
, the (HF1) filter is far too stringent in combination with either Z-closure or Q-imputatio it gives almost no false positives but false negatives increase with increasing
towards the maximum value of 8. The (HF4) filter is not stringent enough in combination with either Z-closure or Q-imputatio it gives almost no false negatives but false positives increase with increasing
. Moreover, (HF3) is ineffective in combination with Z-closure as the number of false positives increases with increasing number of partial trees, in combination with Q-imputation the average number of false positives stays close to 2 for all values of
. (HF2) is the most effective of the homoplasy filters, as for both Z-closure and Q-imputation both types of errors either decrease or stay reasonably co tant with increasing
, a property that we would expect any filtered supernetwork method to satisfy. The counting filter also di lays this property for both Z-closure and Q-imputatio both false positives and false negatives decrease with increasing number of i ut trees.
is similar to Figure
except that rather than averaging over all values of
we focus on the difficult case with the highest number of mi ing taxa and the most incongruence generated by incomplete lineage-sorting (
= 0.5). While all the filtered supernetwork methods shown in Figure
control false negatives, false positives increase with increasing
for both Z-closure and Q-imputation using (HF3).
For the rest of this section, we restrict our attention to the best homoplasy filter (HF2) and the counting filter (CF).
Mi ing taxa
shows the trends in the number of false positives and false negatives as the number of mi ing taxa per tree,
, increases from 0 to 3. Results are averaged over the 12 po ible settings for number of partial trees
and coalescent branch lengths
. The (HF2) and (CF) filters exhibit very different behaviour. For (HF2) as
increases the number of false positives increases, in particular going from 2 to 3 mi ing taxa produces a dramatic increase. Conversely the number of false negatives decreases, presumably due to the fact that as the number of mi ing taxa gets large more lits meet the requirement of the filter. This effect was not o erved for (CF) where the total number of lits is ca ed; here both false positives and negatives increase with growing
Incomplete lineage-sorting
Recall that the parameter
affects the probability that the trees generated by COAL
] will match the principal tree sampled from the hybridization network,
= 8 corre onds to trees that match exactly. Figure
shows the trends in the number of false positives and false negatives for different values of
. Results are averaged over the 16 po ible settings for the number of partial trees
and the number of mi ing taxa
. As expected, both methods and filters perform better when
is large.
Overall performance
shows the number of false positives for hybridization network 7 (Figure
), which has 2 hybridization events and 8 true lits, for
= 0, 1, 2 or 3,
= 0.5, 1 or 8, and
= 5, 10, 15 or 20 for both Z-closure and Q-imputation with (CF). If two out of three of the conditio (
) are favourable (i.e. many i ut trees, few mi ing taxa, and the probability that the i ut trees are congruent with the principal trees is high) then both methods work well. However if two or three of the conditio are unfavourable then both methods start to break down.
Figures
show the average number of false positives and false negatives re ectively (averaged over
) versus the number of true lits for hybridization networks 1–9. Hybridization network 10 is not shown in the figures, as it is an outlier with 24 true lits, but results for this network follow the same trends as the other hybridization networks. For (CF) both types of errors increase slowly with increasing number of true lits. For (HF2) false positives a ear fairly co tant, but false negatives increase linearly with a slope close to one with increasing number of true lits.
False positives (A) and false negatives (B) averaged over 48 combinatio of number of mi ing taxa
, number of gene trees
, and coalescent branch lengths
versus the number of true lits for hybridization networks 1–9. Note that the number of true lits is the maximum po ible number of false negatives.
Conclusion
We have evaluated the potential of Z-closure and Q-imputation filtered supernetworks to identify lits belonging to the sets of principal trees a ociated with hybridization networks. We have found that this a roach can recover these lits when there are few hybridization events. However, our results imply that (1) if gene trees have many mi ing taxa then many gene trees are required; (2) if the gene trees are frequently incongruent with the principal trees of the hybridization network due to incomplete lineage-sorting then a large number of near complete gene trees is required; (3) and if there are few gene trees available they need to be both near complete and highly congruent with the principal trees.
In our simulatio the counting filter picked the n best-su orted lits, where n was chosen to be the known number of true non-trivial lits. Of course with real data n will not be known, although in practice n could be chosen by, for example, greedily introducing lits with highest su ort as long as the corre onding network does not become too complex to easily interpret. A roaches to do this are described in
] for co e us networks. Note that by increasing n the risk of introducing false positive lits is increased, although the risk of failing to identify true positive lits is reduced.
De ite these limitatio , with the potential now of obtaining large numbers of lits from independent gene loci using new generation sequencing technologies, our findings may neverthele be a licable for tree-like phylogenies where some degree of hybridization is inferred
]. In such cases, filtered supernetworks can be used to identify the true lits of the underlying hybridization network. Once these are obtained, the method of
] can be used to convert the lit system into a hybridization scenario.
One of our most interesting findings is that the choice of whether to use Z-closure or Q-imputation seems to have much le impact on accuracy with regards to recovering the lits in the underlying hybridization network than the choice of filter. For both Q-imputation and Z-closure the counting filter (CF) has the desirable property that as the amount of data increases (more genes or more complete gene trees) the rate of both false positives and false negatives goes down. Several settings were tried for the homoplasy-based filter (HF1 – HF4). HF1 was too stringent, and HF3/HF4 tended to either suffer from increasing false positives or increasing false negatives as the number of gene trees increased. HF2 gave the best compromise between these extremes.
Using the HF2 filter, we found that Z-closure had a higher false positive rate than Q-imputation over a range of parameter combinatio (Figure
). One explanation might be that Z-closure can potentially generate more lits than Q-imputation. For example, given
fully resolved gene trees on 8-
= 1, 2, 3), Q-imputation can generate at most 5*
non-trivial complete lits, whereas Z-closure can produce at most 10*(5-
non-trivial complete lits (where 10 is the number of random orderings). Hence the maximum number of lits that Z-closure could generate decreases as
grows, whereas the number of lits that Q-imputation could generate stays co tant. What we o erve for both methods and filters is that false positives increase with increasing
(Figure
). Therefore, the maximum number of lits that Z-closure and Q-imputation could generate does not a ear to explain the difference in false positive rates. We think a more likely explanation is that Q-imputation places mi ing taxa in such a way as to maximize agreement with the i ut trees, hence tending to produce multiple copies of the same lits. Conversely, Z-closure aims to find all po ible complete lits that can be derived by extending partial lits using the Z-closure rule, a proce that can yield many different lits. Hence we expect that Q-imputation would be likely to generate fewer false positives than Z-closure in general. This difference is not greatly reduced by HF2 as, in contrast to CF, it does not place a cap on the total number of lits.
We found that HF2 resulted in more false negatives than CF (Figure
). This may be due to the fact that this filter only selects lits that have no homoplasy when restricted to 75% of the i ut trees. Since the principal trees are obtained from a network, they can be different and in some cases may only agree on a small number of edges. Even a true lit may have a high homoplasy score when restricted to a particular principal tree. In contrast, CF only selects lits that occur with high frequency, irre ective of whether they are in agreement with any of the i ut trees.
Although all the trees used in our simulatio were fully resolved, both supernetwork methods co idered here can be a lied to partially resolved trees. Thus, when inferring gene trees to be used as i ut to a supernetwork method, it would probably be a reasonable a roach to only retain those edges in the estimated gene trees that have high su ort (e.g. bootstrap su ort or posterior probability higher than some cut-off value).
In cases where there are many hybridization events, e ecially between individuals that are not closely related, there will be many principal trees and corre onding lits (as in hybridization network 10). Many of these lits will occur at low frequencies making them hard to distinguish from phylogenetic error. This mea that phylogenetic inference will be limited, as gene-tree incongruence will be exte ive. In such cases, rather than attempt to reco truct a hybridization network, it may be more a ropriate to formulate objective tests to better understand the complexity of the data and the extent to which hybridization contributes to this complexity. Joly, McLenachan and Lockhart (submitted manuscript) have recently proposed such a test.
An unexplored idea worthy of study is the investigation of model-based, rather than combinatorial, methods of filtering. One a roach might be to co ider posterior probability distributio on ecies trees
]. It will be interesting to investigate whether such posterior distributio can also be analysed for evidence of distinct principal trees in cases where evolutionary relatio hi are complex.
Authors' contributio BRH developed and a lied the simulation scheme, implemented the modified Z-closure method, homoplasy filter and counting filter, and contributed to writing the ms, e ecially the methods and results section. SB conducted initial simulatio with Z-closure. PL e ured biological relevance, and contributed to writing the ms, e ecially the introduction and conclusio . VM e ured mathematical correctne and developed the overall concept. KH e ured mathematical correctne and developed the overall concept, contributed to writing the ms, e ecially the methods and results section.
Acknowledgements
All authors thank the Isaac Newton I titute for Mathematical Sciences, Cambridge, UK for hosting them in the context of their Phylogenetics Programme where part of the work presented in this paper was carried out. BRH and PJL thank Marsden Fund MAU0509 and MAU0510, VM thanks the Engineering and Physical Sciences Research Council (EPSRC), grant EP/D068800/1.
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