Which morphological characters are influential in a Bayesian phylogenetic analysis? Examples from the earliest osteichthyans

Abstract

There has been much recent debate about which method is best for reconstructing the tree of life from morphological datasets. However, little attention has been paid to which characters, if any, are responsible for topological differences between trees recovered from competing methods on empirical datasets. Indeed, a simple procedure for finding characters supporting conflicting tree topologies is available in a parsimony framework, but an equivalent procedure in a model-based framework is lacking. Here, I introduce such a procedure and apply it to the problem of the ‘psarolepid’ osteichthyans. The ‘psarolepids’, which include the earliest known osteichthyans, are weakly supported as stem osteichthyans under parsimony but strongly supported as sarcopterygians in Bayesian analysis. The Bayesian result is driven by just two characters, both of which relate to the intracranial joint of sarcopterygians. Important characters that support a stem osteichthyan affinity for ‘psarolepids’, such as the absence of tooth enamel, have virtually no effect in a Bayesian framework. This is because of a bias towards characters with relatively complete sampling, a bias that has previously been reported for molecular data. This has important implications for Bayesian analysis of morphological datasets in general, as characters from different body parts commonly have different levels of coding completeness. Methods to critically appraise character support for conflicting phylogenetic hypotheses, such as that used here, should form an important part of phylogenetic analyses.

1. Introduction

There has been much debate on whether parsimony or Bayesian approaches are most suitable for the analysis of morphological data [1–8]. These debates focused on results from simulations, discussions of model assumptions and stratigraphic fit. Much has been made of differences in resolution between methods, with Bayesian analysis producing less resolved trees [3]. However, beyond the degree of resolution, effectively a product of how trees are summarized [5,9], it is generally thought the two approaches reconstruct similar trees [8].

However, Bayesian and parsimony analyses can occasionally produce conflicting topologies that cannot be explained by differences in resolution. One example is the ‘psarolepids’, a putative clade that includes the earliest known osteichthyans (bony fishes) [10–12]. They have been considered as stem sarcopterygians (lobe-finned fishes) or stem osteichthyans [12–14]. The most recent analyses found ‘psarolepids’ to be stem osteichthyans with weak support under parsimony, whereas Bayesian analysis recovers ‘psarolepids’ as sarcopterygians with a high posterior probability [15,16]. The phylogenetic position of ‘psarolepids’ has implications for our understanding of early osteichthyan evolution: if they are sarcopterygians, this pushes the minimum divergence time of sarcopterygians and actinopterygians (ray-finned fishes) deep into the Silurian period [12].

A significant advantage of parsimony analysis is the simplicity with which characters that support different tree topologies can be identified. This direct connection between the phylogenetic results and the morphological characters that support them allows critical appraisal of the results and important coding errors can be easily identified. For Bayesian analysis, character support is sometimes investigated using parsimony [17] but is often not investigated at all. Using parsimony for this purpose is unsatisfactory, since character support is analysed using a different criterion to that used to find the trees and is likely to be misleading. Here I introduce a simple procedure to identify characters supporting different tree topologies in a model-based framework. This procedure is applied to the question of ‘psarolepid’ relationships.

2. Material and methods

The matrix was from a recent description of ‘Ligulalepis’ [15] and was unchanged apart from the deletion of an invariant character (#256, number of dermopalatines). Characters 63, 125, 145, 164, 259, 261 and 265 were ordered. Parsimony analysis was performed in TNT [18], using new technology search (using ratchet, tree fusing, sectorial search and drift search algorithms with default settings) for 1000 replications followed by branch swapping to fully explore the tree islands. A constrained search was performed with ‘psarolepids’ in a clade with sarcopterygians. Characters supporting the alternative topologies were extracted in PAUP* [19]. To examine the influence of homoplasy on the parsimony result, two implied weights analyses [20] were performed in TNT with concavity values of 3 and 10, respectively. Bayesian analysis was performed in MrBayes 3.2.6 [21], with four independent runs of 10 million generations. Convergence was confirmed using Tracer [22] and mean standard deviation of split frequencies (0.0087).

The differences in the phylogenetic position of the ‘psarolepids’ between parsimony and Bayesian analysis previously reported [15,16] and also found here (see results), could be driven by the branch lengths prior in the Bayesian analysis. To test this, an analysis was run in which all codings for the ‘psarolepids’ were changed to unknown, but the group was constrained to a small number of phylogenetic positions: stem osteichthyans, stem sarcopterygians or stem actinopterygians. The phylogenetic position of ‘psarolepids’ is therefore driven by the prior in this analysis.

A novel procedure was used to analyse characters supporting alternative phylogenetic positions for the ‘psarolepids’ in a likelihood framework. Two tree samples from MrBayes were used, one from an analysis with ‘psarolepids’ constrained within sarcopterygians, and one with a constraint on crown osteichthyans excluding ‘psarolepids’. The matrix was loaded into R using corHMM [23], and the tree samples loaded using ape [24]. The likelihood of each character was calculated for each tree from a set of 10% of each post-burnin sample (181 trees), using phytools [25]. The equal rates model was applied or a custom rate matrix for the ordered characters. The two samples of likelihood values were compared using a t-test, producing a p-value for each character. The median estimated evolutionary rate for each character and the difference in mean likelihood between the two tree samples for each character were recorded. This analysis was repeated three times on tree samples from independent runs of the Bayesian analysis.

Because the results (see below) suggested that relatively completely coded characters were the most influential in Bayesian analyses, this was tested by inserting missing data into the data matrix for characters 45 and 122 (see below). All osteichthyans coded for these characters, but unknown for character 19 (scale peg), were changed to unknown. One exception was the coding for Onychodus for character 45, which was retained so that the parsimony analysis was unaffected. Both the parsimony and Bayesian analyses were rerun on this edited dataset, and the likelihood calculations were rerun for these two characters.

3. Results

The parsimony analysis produced 1936 trees of length 819, with ‘psarolepids’ as stem osteichthyans (figure 1). When ‘psarolepids’ were constrained to be stem sarcopterygians, 4744 trees of length 820 were recovered. Results from implied weights depended on the concavity value (K) used. With K = 3, ‘psarolepids’ were recovered as sarcopterygians, with tree length 83.95. ‘Ligulalepis’ was recovered as a stem gnathostome in this analysis. Constraining ‘psarolepids’ to be stem osteichthyans with K = 3 led to a tree length of 83.994, an increase of 0.054%. With K = 10, ‘psarolepids’ were recovered as stem osteichthyans, as in the unweighted analysis. The Bayesian analysis placed ‘psarolepids’ as stem sarcopterygians with a posterior probability of 0.93.

Figure 1.

Results from parsimony and Bayesian analysis produce conflicting results for ‘psarolepid’ osteichthyans. The parsimony tree (a) shows a stem osteichthyan position for ‘psarolepids’. The crown osteichthyan node has Bremer support of 1. The Bayesian analysis (b) has ‘psarolepids’ as sarcopterygians with posterior probability 0.93. (Online version in colour.)

The data rather than the prior drive the strong support for ‘psarolepids’ as sarcopterygians in the Bayesian analysis. The analysis with data removed from ‘psarolepids’ led to essentially equal support for a stem and crown osteichthyan position: ‘psarolepids’ were excluded from the crown in 46% of the posterior sample.

The characters showing the largest differences in mean log likelihood value between the two topologies are shown in table 1. Many of these characters also differ in length under a parsimony framework. However, the difference in mean likelihood is by far the greatest for character 45 (dermal cranial joint) and 122 (endoskeletal cranial joint), both of which support a sarcopterygian position for ‘psarolepids’. Two characters supporting a stem osteichthyan position, character 78 (tooth enamel) and 130 (eyestalk attachment) appear to have little influence. The total difference in mean log likelihood between the two tree samples for all characters supporting a stem osteichthyan position was 16.09. For characters supporting a sarcopterygian position, it was 21.4. This difference is largely explained by characters 45 and 122 (table 1). Results from three independent runs are congruent (full results available on figshare [26]).

Table 1.

The characters with the largest difference in likelihood calculated across two samples of trees with ‘psarolepids’ either as stem osteichthyans or sarcopterygians. Highlighted characters are those that also differ in parsimony length. The top 10 characters (as ranked by a difference in mean likelihood) are shown, and all those that differ in length under parsimony. Character state in bold is that present in ‘psarolepids’. Likelihood is in log units, and the proportion of missing data includes inapplicable codings.

When missing data were inserted into characters 45 and 122, it had no effect on the parsimony results but had a large effect on the Bayesian analysis. Parsimony analysis produced trees of length 819, with ‘psarolepids’ as stem osteichthyans, while constraining ‘psarolepids’ to be sarcopterygians produced trees of length 820, exactly as in the complete dataset. For the Bayesian analysis, the posterior probability for ‘psarolepids’ as sarcopterygians dropped from 0.93 to 0.38. The difference in mean (log) likelihood for the two tree topologies dropped from 2.289 to 1.264 for character 45 and from 2.607 to 1.080 for character 122.

4. Discussion

Previously, it has been suggested that differences in tree topology between parsimony and Bayesian analysis were due to down-weighting of homoplasious characters [17]. However, it is unlikely that this can explain all differences, including those reported here for ‘psarolepid’ osteichthyans. First, the number of steps for the characters supporting the two tree topologies in parsimony is essentially the same (full results available on figshare [26]). Secondly, implied weights parsimony also down-weights homoplasious characters and should produce essentially congruent results with Bayesian analysis if homoplasy were the main explanation for topology differences [27]. On this dataset, results from implied weights analysis depend on the concavity parameter used, and either way, the difference in tree length between the two topologies is very small, certainly insufficient to explain the strong support for ‘psarolepids’ as sarcopterygians in a Bayesian analysis. The two most important characters in a likelihood framework are 45 and 122, but these actually have more parsimony character changes than others such as character 19.

Missing data are known to be an important factor for Bayesian analysis of molecular data [28–31] but have received less attention for morphological data [27]. There are two ways that missing data can have an effect. First, missing data increase the chances of unobserved character changes. Two characters with the same number of character changes under parsimony might have different estimated rates in a likelihood framework if they have different amounts of missing data. Thus, the Bayesian analysis will down-weight characters with unobserved homoplasy. The second way missing data can have an effect concerns branch lengths. If a clade is characterized by a particular character, but the least nested members of this clade and the immediate outgroups have missing data, this increases the number of branches on which the necessary character transition can occur. Missing data essentially have the effect of increasing the branch length over which a character transition can occur, increasing the likelihood of a transition [28]. This will reduce the penalty of additional character state transitions necessitated by particular tree topologies, such as independent origins of tooth enamel when ‘psarolepids’ are sarcopterygians. Relatively completely coded characters, on the other hand, will force character state transitions on particular branches.

Missing data are the likely explanation for the strong support for ‘psarolepids’ as sarcopterygians in the Bayesian analyses. The two most important characters are number 45 (dermal cranial joint) and 122 (endoskeletal cranial joint). Both characters have fewer missing data than the other characters supporting the alternative topologies (43% for character 45 and 44% for character 122). In particular, both are scored for the majority of osteichthyans, including key taxa branching from the base of the group. Stochastic character maps of character 122 show how forcing a stem osteichthyan position for ‘psarolepids’ forces character state transitions to occur on particular branches, for example, loss of the intracranial joint on the branch leading to actinopterygians (figure 2a). On the other hand, for character 78 (tooth enamel), support for a stem osteichthyan position is entirely reliant on the coding for Psarolepis. Examples of stochastic character maps show that there are many options for patterns of character transitions due to missing data in essentially all the osteichthyans in key positions (figure 2b). Notably, the support for a sarcopterygian position for ‘psarolepids’ can be completely removed simply by the addition of missing data to characters 45 and 122, which has no effect on parsimony.

Figure 2.

Examples of stochastic character maps for a character with relatively complete coding, versus a character with a large proportion of missing data. (a) Character 122 is relatively completely coded and supports a sarcopterygian position for ‘psarolepids’. Because of the relatively complete coding, additional character state transitions required due to a stem osteichthyan position for ‘psarolepids’ must occur on a single branch. (b) Character 78 has a lot of missing data. Therefore, additional character state changes required by a sarcopterygian position for ‘psarolepids’ can occur on any of several branches. (Online version in colour.)

The results presented here have important implications for whether Bayesian or parsimony methods should be favoured. For ‘psarolepids’, the two characters driving the Bayesian result are correlated: they are the dermal and endocranial part of the sarcopterygian cranial joint. Therefore, support for the placement of ‘psarolepids’ as sarcopterygians is over-inflated in this analysis. Although character correlation also affects parsimony, the effect is not further compounded by the influence of missing data as in the Bayesian analysis. In addition, although accounting for missing data might be seen as a desirable effect, the bias towards globally sampled characters will favour certain classes of character in a morphological dataset. Cranial characters (such as the intracranial joint) will be more influential than postcranial and histological characters (such as tooth enamel). This kind of bias is probably common to most morphological datasets. Regardless of whether or not Bayesian or parsimony is the preferred method, character support should be critically analysed. In the case of ‘psarolepids’, the dominance of two correlated characters in the Bayesian result suggests that the parsimony result should be considered as the favoured hypothesis based on current data, although support remains weak.

Data accessibility

Datasets, scripts and complete results for all analyses are available from figshare: doi:10.6084/m9.figshare.7999400 [26].

Competing interests

I declare that I have no competing interests.

Funding

This project was supported by NWO Vidi grant 864.14.009 (to Martin Rücklin).