Support indices do not support the dino to bird theory

This is a summary and continuation of the material of the Jan 17 post.
It is widely believed that the dinosaur to bird theory is well supported. That is believed because cladistic analyses have been run and presented that appear to support that theory. However when we drill down into the analyses that have been done we see that the calculated statistical support values for all the core nodes are “poorly supported”.

The nodes on a cladogram are evaluated by calculating support indices (Bremer, bootstrap/jackknife, GC). 
The support indices for the core nodes in the dino to bird cladograms show that all the core nodes are poorly supported. For example:
Maniraptoriformes is poorly supported
Maniraptora is poorly supported.
Oviraptorosauria + Paraves (Pennaraptora) is poorly supported.
Paraves is poorly supported.

1. Rationalizations of the poor support:

Homoplasies

http://www.ivpp.cas.cn/qt/papers/201403/P020140314389417822583.pdf (2011)
An Archaeopteryx-like theropod from China and the origin of Avialae
Xing Xu1,2, Hailu You3 , Kai Du4 & Fenglu Han2

It should be noted that our phylogenetic hypothesis is only weakly supported by the available data. Bremer support and bootstrap values for the recovered coelurosaurian subclades are, in general, low, and a bootstrap value less than 50% and a Bremer support value of 2 are obtained for a monophyletic Deinonychosauria including the Archaeopterygidae (see Supplementary Information). This low support is partly caused by various homoplasies, many of which are functionally significant, that are widely distributed across coelurosaurian phylogeny29.

But this does not explain why these particular nodes (which are the core nodes) are poorly supported when the other subgroups are supported.  


Lack of knowledge

http://evolution.berkeley.edu/evolibrary/article/phylogenetics_03

Lack of knowledge
Usually, a polytomy means that we don't have enough data to figure out how those lineages are related. By not resolving that node, the scientists who produced the phylogeny are telling you not to draw any conclusions — and also to stay tuned: often gathering more data can resolve a polytomy.

However note that there are enough characters in the study to make conclusions about all of the other major coelurosaurian subgroups so it is not a problem of not having enough data:

http://www.cell.com/current-biology/fulltext/S0960-9822(14)01047-1 (2014)
https://www.cell.com/cms/10.1016/j.cub.2014.08.034/attachment/3d79921a-ae54-4bd9-b128-fa7140c7691f/mmc1.pdf (Supplemental Information)

Gradual Assembly of Avian Body Plan Culminated in Rapid Rates of Evolution
across the Dinosaur-Bird Transition 
Stephen L. Brusatte, Graeme T. Lloyd, Steve C. Wang, and Mark A. Norell 

All of the major coelurosaurian subgroups that have long been considered monophyletic are also found to be monophyletic here. These include Tyrannosauroidea, Compsognathidae, Ornithomimosauria, Alvarezsauroidea, Therizinosauroidea, Oviraptorosauria, Dromaeosauridae, Troodontidae, and Avialae

Maniraptoriformes—is only poorly supported (Bremer support of 1 and jackknife percentage of less than 50%), and relationships at its base are unresolved. There is a basal polytomy consisting of four clades: Ornitholestes, Compsognathidae, Ornithomimosauria, and Maniraptora (i.e., the clade of all taxa more closely related to birds than to Ornithomimus: [S52]). 

Maniraptora—the clade defined as all taxa closer to birds than to Ornithomimus—is comprised in the present study of Alvarezsauroidea, Therizinosauroidea, Oviraptorosauria, and Paraves. This clade is supported by a Bremer value of 2 but a jackknife percentage of less than 50%.

Oviraptorosauria and Paraves is supported by a Bremer value of 1 and a jackknife percentage of less than 50%. 

Paraves—consisting of dromaeosaurids, troodontids, and avialans—is also poorly supported, as it also has a Bremer value of 1 and a jackknife of less than 50%.

2. Contradictions:

Not only are the support indices low but the analyses also underestimate the amount of contradiction.
The studies include a very large number of characteristics.
Let's look at the very first one:

1. Vaned feathers on forelimb symmetric (0) or asymmetric (1). The barbs on opposite sides of the rachis differ in length; in extant birds, the barbs on the leading edge of flight feathers are shorter than those on the trailing edge.

Note that there is no value for when the taxon does not have any form of feather. This means that the dinosaurs (without feathers) are scored as "?" (unknown).

This means that they are not scored as contrary to the feathered taxa.
This underestimates the contradiction between dinosaurs and primitive birds.




3. Basal Polytomies

http://www.cell.com/current-biology/fulltext/S0960-9822(14)01047-1 (2014)

http://www.cell.com/cms/attachment/2019474733/2039573094/mmc1.pdf (Supplemental Information)

Gradual Assembly of Avian Body Plan Culminated in Rapid Rates of Evolution
across the Dinosaur-Bird Transition 
Stephen L. Brusatte, Graeme T. Lloyd, Steve C. Wang, and Mark A. Norell 

There is a large polytomy at the base of the clade that includes all coelurosaurs more derived (closer to avialans) than tyrannosauroids.

http://datadryad.org/resource/doi:10.5061/dryad.84t75

BrusatteetalRevisionDryadFile2.pdf (13.57 Mb)

This lack of resolution is due to the uncertain phylogenetic position of a small handful of taxa, including the fragmentary basal coelurosaur Kinnareemimus (a purported ornithomimosaur: [S49]), the aberrant coelurosaur Epidendrosaurus (which is known only from two juvenile individuals: [S50]), the paravians Pyroraptor and Hesperonychus, and the avialan Limenavis.

Pyroraptor and Limenavis were also found to be unstable in the analysis of Turner et al. (2012) [S9], whereas Epidendrosaurus was excluded from the primary version of that analysis. The “wildcard” nature of these five taxa is largely due to enormous amounts of missing data—each taxon can only be scored for a small fraction of the 853 characters in the analysis 

http://www.ivpp.cas.cn/qt/papers/201403/P020140314389417822583.pdf (2011)
An Archaeopteryx-like theropod from China and the origin of Avialae
Xing Xu1,2, Hailu You3 , Kai Du4 & Fenglu Han2

Only clades with bootstrap values greater than 50% are shown in Figure S9. It is notable that only a few clades meet this criterion in the present analysis.

Also see Figure 7 in:
http://www.bio.fsu.edu/James/Ornithological%20Monographs%202009.pdf



4. Few characters support each node

https://www.researchgate.net/publication/305748962_Binary_Particle_Swarm_Optimization_Versus_Hybrid_Genetic_Algorithm_for_Inferring_Well_Supported_Phylogenetic_Trees

Binary Particle Swarm Optimization versus Hybrid Genetic Algorithm for Inferring Well Supported Phylogenetic Trees

Bassam AlKindy, Bashar Al-Nuaimi, Christophe Guyeux, Jean-François Couchot, Michel Salomon, Reem Alsrraj, Laurent Philippe

If, for example, you recover the same node through 95 of 100 iterations of taking out one character and resampling your tree, then you have a good idea that the node is well supported (your bootstrap value in that case would be 0.95 or 95%).

If we get low support, that suggests that only a few characters support that node, as removing characters at random from your matrix leads to a different reconstruction of that node. 

https://www.researchgate.net/publication/38384848_Applying_the_Bootstrap_in_Phylogeny_Reconstruction

https://projecteuclid.org/euclid.ss/1063994980
http://projecteuclid.org/download/pdf_1/euclid.ss/1063994980
Pamela Soltis

bootstrap values are low because of the small number of characters supporting each node

https://en.wikipedia.org/wiki/Symplesiomorphy

A plesiomorphy refers to the ancestral trait state, usually in reference to a derived trait state. A symplesiomorphic trait is also shared with other taxa that have an earlier last common ancestor with the taxa under consideration.

https://en.wikipedia.org/wiki/Synapomorphy

The concept of synapomorphy is relative to a given clade in the tree of life. What counts as a synapomorphy for one clade may well be a primitive character or plesiomorphy at a less inclusive or nested clade. For example, the presence of mammary glands is a synapomorphy for mammals in relation to tetrapods but is a symplesiomorphy for mammals in relation to one another, rodents and primates, for example. 

http://digitallibrary.amnh.org/handle/2246/6352
Turner et al

Maniraptora is poorly supported in the analysis (GC = 5). Most other derived maniraptoran clades, however, show surprisingly high levels of jackknife support. Alvarezsauroidea is moderate to weakly supported (GC = 25), but the less inclusive Alvarezsauridae and its constituent clades have high jackknife support (ranging from 70 to 83).
The sister taxon relationship of Patagonykus puertai with Shuvuuia deserti and Mononykus olecranus is strongly supported (GC = 80).

https://en.wikipedia.org/wiki/Computational_phylogenetics#Bootstrapping_and_Jackknifing

The statistical rigor of the bootstrap test has been empirically evaluated using viral populations with known evolutionary histories,^[35] finding that 70% bootstrap support corresponds to a 95% probability that the clade exists. However, this was tested under ideal conditions (e.g. no change in evolutionary rates, symmetric phylogenies). In practice, values above 70% are generally supported and left to the researcher or reader to evaluate confidence. Nodes with support lower than 70% are typically considered unresolved.

https://academic.oup.com/sysbio/article-abstract/42/2/182/1730933/An-Empirical-Test-of-Bootstrapping-as-a-Method-for?redirectedFrom=fulltext

Specifically, under conditions of equal rates of change, symmetric phylogenies, and internodal change of ≤20% of the characters, bootstrap proportions of ≥70% usually correspond to a probability of ≥95% that the corresponding clade is real. However, under conditions of very high rates of internodal change (approaching randomization of the characters among taxa) or highly unequal rates of change among taxa, bootstrap proportions >50% are overestimates of accuracy.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1924872/

The results show that there are strong correlations between clade confidence and the probability that a clade is valid for Bayesian posterior probabilities and for Maximum Likelihood bootstrap percentages and weaker correlations for Maximum Likelihood aLRT values.

CONTRARY

http://www.sciencedirect.com/science/article/pii/S1532046405001322

Numerous metrics have been developed that attempt to assess the reliability of phylogenetic trees. Several of these commonly used measures of tree and tree branch support are described and discussed in the context of their relationship to Popperian corroboration. Claims that measures of support indicate the accuracy of phylogenetic trees or provide information for tree choice are rebutted. Measures of support are viewed as being of heuristic value within a given phylogenetic framework for describing the precision of the data based on perturbations to the data. However, no direct link is observed between the calculation of measures of support and corroboration. Direct measures of support, but not re-sampling or randomization methods, may play a more specific role in phylogenetic inference by providing the tools to search for falsifiers that could be the subject of future rounds of hypothesis testing.

https://www.academia.edu/4605777/Behaviour_of_resampling_methods_under_different_weighting_schemes_measures_and_variable_resampling_strengths

In this contribution we use the terms‘‘real’’for those groups present in the strict consensus of the unaltered data set, and‘‘spurious’’ for the opposite situation.

Brusatte et al bootstrap (from TNT):