"An abnormally rapid period of morphological evolution"

We have seen that the statistical support values do not support the dinosaur to bird hypothesis. See earlier posts.
Consequently we are justified in looking at the dinosaur to bird hypothesis much more critically and to re-assess the explanations that have been given. For example, the "explanation" that the evolution rate was abnormally rapid.

http://www.cell.com/current-biology/fulltext/S0960-9822(14)01047-1
Stephen Brusatte et al
[R]ecent studies converge in identifying the dinosaur-bird transition as an abnormally rapid period of morphological evolution.

"Relative to the femur, the humerus is significantly longer and thicker in basal paravians than in non-paravian theropods." (Xu et al)
"The significant lengthening and thickening of the forelimbs indicates a dramatic shift in forelimb function at the base of the Paraves." (Xu et al)
"We find an increase in rates of body size and body size dependent forelimb evolution leading to small body size relative to forelimb length in Paraves." (Puttick et al)

http://www.bris.ac.uk/news/2014/february/origin-of-birds.html

"We were really surprised to discover that the key size shifts [body size and forelimb length] happened at the same time, at the origin of Paraves," said Mr Puttick of Bristol's School of Earth Sciences.  "This was at least 20 million years before the first bird, the famous Archaeopteryx, and it shows that flight in birds arose through several evolutionary steps."                     

As the quotes above show, basal paravians are very different than non-paravian theropods. The researchers who believe they are related, explain this as an "abnormally rapid period of morphological evolution". Of course that is not an explanation. It is an acknowledgement that they have no explanation.

http://www.cell.com/current-biology/fulltext/S0960-9822(14)01047-1
Stephen Brusatte et al
Gradual Assembly of Avian Body Plan Culminated in Rapid Rates of Evolution across the Dinosaur-Bird Transition

Our results demonstrate that the rise of birds was a complex process: birds are a continuum of millions of years of theropod evolution, and there was no great jump between nonbirds and birds in morphospace, but once the avian body plan was gradually assembled, birds experienced an early burst of rapid anatomical evolution. 

Although birds are clearly distinct compared to all other living vertebrates, the avian bauplan isn’t especially distinct relative to other coelurosaurs, particularly their closest relatives.

There is growing evidence that changes in discrete character evolution, body size, and limb anatomy occurred quickly in the vicinity of the origin of birds, either at the node Avialae, in close avialan outgroups [basal paraves] or beginning with slightly more derived birds [3, 4, 5, 6, 19, 20, 21, 22]. It is likely that different types of data will pinpoint changes at slightly different positions on phylogeny, but in general, recent studies converge in identifying the dinosaur-bird transition as an abnormally rapid period of morphological evolution.

The initial results of the branch (Dryad Fig. S4-13) and clade (Fig. S3; Dryad Fig. S14-23) tests strongly support significantly high rates in Avialae, and to a lesser degree Tyrannosauroidea.

Other clades show significantly low or non-significant rates, with the exception of two smaller clades: Graciliraptor + Microraptor + Shanag + Sinornithosaurus + Tianyuraptor (within Dromaeosauridae), and Anchiornis + Aurornis + Eosinopteryx + Xiaotingia (within Troodontidae) [basal Paraves] which frequently show high rates. 

Important note:

Anchiornis + Aurornis + Eosinopteryx + Xiaotingia (within Troodontidae) [basal Paraves] frequently show high rates. 
In other words, the authors recognize the gap at Paraves.

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

The discovery of Xiaotingia further demonstrates that many features

previously regarded as distinctively avialan actually characterize the

more inclusive Paraves. For example, proportionally long and robust

forelimbs are optimized in our analysis as a primitive character state

for the Paraves (see Supplementary Information). The significant
lengthening and thickening of the forelimbs indicates a dramatic shift
in forelimb function at the base of the Paraves, which might be related

to the appearance of a degree of aerodynamic capability.

We use the ratios of humeral length to femoral length, and humeral diameter to femoral diameter, as indicators of forelimb length and robustness. Relative to the femur, the humerus is significantly longer and thicker in basal paravians than in non-paravian theropods, derived dromaeosaurids and troodontids (the relatively short and slender forelimbs in the last two groups are secondarily evolved according to the current phylogenetic analysis).

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.915.8222&rep=rep1&type=pdf (2014)
http://science.sciencemag.org/content/sci/suppl/2014/07/30/345.6196.562.DC1/1252243.Lee.SM.revision1.pdf
Sustained miniaturization and anatomical innovation in the dinosaurian ancestors of birds
Michael S. Y. Lee,1,2* Andrea Cau,3,4 Darren Naish,5 Gareth J. Dyke5,6

Although there is no overall theropod-wide trend (fig. S7 and SM, part D), there is an exceptional trend within the single lineage that comprises much of the avian stem.

Our study quantifies rates of evolutionary innovation in dinosaurs using 1549 (data set 1) and 421 (data set 2) skeletal and other anatomical traits distributed across the entire body. A clear pattern emerges: Branches along the bird stem undergo substantially faster morphological evolution than those of the rest of the tree. 

Recent discoveries have highlighted the dramatic evolutionary transformation of massive, ground-dwelling theropod dinosaurs into light, volant birds. Here, we apply Bayesian approaches (originally developed for inferring geographic spread and rates of molecular evolution in viruses) in a different context: to infer size changes and rates of anatomical innovation (across up to 1549 skeletal characters) in fossils. These approaches identify two drivers underlying the dinosaur-bird transition. The theropod lineage directly ancestral to birds undergoes sustained miniaturization across 50 million years and at least 12 consecutive branches (internodes) and evolves skeletal adaptations four times faster than other dinosaurs. The distinct, prolonged phase of miniaturization along the bird stem would have facilitated the evolution of many novelties associated with small body size, such as reorientation of body mass, increased aerial ability, and paedomorphic skulls with reduced snouts but enlarged eyes and brains.

These results reconcile contradictory studies identifying presence (4–8) or absence (9–11) of a trend toward size reduction in theropods. Although there is no overall theropod-wide trend (fig. S7 and SM, part D), there is an exceptional trend within the single lineage that comprises much of the avian stem.

http://science.sciencemag.org/content/sci/suppl/2014/07/30/345.6196.562.DC1/1252243.Lee.SM.revision1.pdf
Also see Figure S6.



Let's look at body size and forelimb length.

Notice that the changes appear for the first time at the origin of Paraves (not earlier).

https://www.scientificamerican.com/article/how-dinosaurs-shrank-and-became-birds/

That shrinkage sped up once bird ancestors grew wings and began experimenting with gliding flight. Last year, Benton’s [Puttick] team showed that this dinosaur lineage, known as paraves, was shrinking 160 times faster than other dinosaur lineages were growing. “Other dinosaurs were getting bigger and uglier while this line was quietly getting smaller and smaller,” Benton said. “We believe that marked an event of intense selection going on at that point.”

http://www.bris.ac.uk/news/2014/february/origin-of-birds.html

Mark Puttick and colleagues investigated the rates of evolution of the two key characteristics that preceded flight: body size and forelimb length.  In order to fly, hulking meat-eating dinosaurs had to shrink in size and grow much longer arms to support their feathered wings. 

"We were really surprised to discover that the key size shifts happened at the same time, at the origin of Paraves," said Mr Puttick of Bristol's School of Earth Sciences.  "This was at least 20 million years before the first bird, the famous Archaeopteryx, and it shows that flight in birds arose through several evolutionary steps."                                     

High rates of evolution preceded the origin of birds (2014)
Puttick, M.N., Thomas, G.H., and Benton, M.J. in Evolution: DOI: 10.1111/evo.12363 

The origin of birds (Aves) is one of the great evolutionary transitions. Fossils show that many unique morphological features of modern birds, such as feathers, reduction in body size, and the semilunate carpal, long preceded the origin of clade Aves, but some may be unique to Aves, such as relative elongation of the forelimb. We study the evolution of body size and forelimb length across the phylogeny of coelurosaurian theropods and Mesozoic Aves. Using recently developed phylogenetic comparative methods, we find an increase in rates of body size and body size dependent forelimb evolution leading to small body size relative to forelimb length in Paraves, the wider clade comprising Aves and Deinonychosauria. The high evolutionary rates arose primarily from a reduction in body size, as there were no increased rates of forelimb evolution. In line with a recent study, we find evidence that Aves appear to have a unique relationship between body size and forelimb dimensions. Traits associated with Aves evolved before their origin, at high rates, and support the notion that numerous lineages of paravians were experimenting with different modes of flight through the Late Jurassic and Early Cretaceous.

http://science.sciencemag.org/content/317/5843/1378.full

The taxon's small body size and phylogenetic position imply that extreme miniaturization was ancestral for Paraves (the clade including Avialae, Troodontidae, and Dromaeosauridae), phylogenetically earlier than where flight evolution is strongly inferred. In contrast to the sustained small body sizes among avialans throughout the Cretaceous Period, the two dinosaurian lineages most closely related to birds, dromaeosaurids and troodontids, underwent four independent events of gigantism, and in some lineages size increased by nearly three orders of magnitude.

Also see:
http://pterosaurnet.blogspot.ca/2014/03/body-size-and-forelimb-length.html