A closer look into the dinosaur subspecies: Sauropodomorphs[5] first evolved in the early Jurassic epoch and persisted on the Earth till the late Cretaceous period, amassing almost 130 million years as a species on this planet. They are typically identified by their leaf-shaped tooth crowns, a small head, and a neck that is at least as long as the trunk of the body and longer than the limbs. Some common examples of this species are the brachiosaurus and the diplodocus. The Sauropodomorpha are descendants of their early ancestor Prosauropods. Later evolutions were referred to as Sauropods. The Prosauropods are generally stocky in appearance, with hind legs which were longer than their forelimbs. They were five-toed with a long tail which helped the dinosaur balance while walking and running. [8]

Theropods[5] are part of dinosaur subclade Theropoda and a sister species to the Sauropods (under the Saurischian order). They belong to the Saurischian dinosaur order alongside Sauropodomorphs. A distinct feature of Theropods is that they are primarily bipeds, that is, they rely on their hind limbs for motion. They are slender,long-legged and are theorized to move faster than herbivore dinosaurs. Their lineage is almost entirely known for carnivorous dinosaurs[5].

Ornithischians[5] were mainly herbivorous dinosaurs that inhabited the land roughly 200 million years ago until the ultimate extinction of all dinosaur species at the end of the Cretaceous period. Ornithischia, otherwise translated to bird-hipped, consists of dinosaurs such as the triceratops and stegosaurus. Referred to as bird-hipped due to their hip bones being arranged similar to those of birds, that is, it was down-sloping and pointed towards the tail instead of pointing forward as seen in other reptilians/dinosaurs. This was also known as a caudally oriented pubis.[9] Common genetic trends seen in all under the Ornithischian order include an extra bone at the tip of the jaw and foliated teeth(broad and flat teeth). Other variations seen in different lineages within this order include a network of bony tendons that intersected the protrusions of their vertebral column (as seen in Stegosauruses) and evolved jaws that were stronger and consisted of several rows of teeth (for example, the Hadrosaur).

The bones considered are the femur which form a portion of the hind leg. In dinosaurs the femur is crowned by a femoral head which forms a right angle with the (femoral) shaft[10]. Followed by comparison in terms of the humerus, the largest bone in the forelimb [10], and the tibia, present in the lower leg adjacent to the fibula.

2.1.1 Femur circumference with respect to length

Table 1 Slope and coefficient values for femur circumference vs. length

Name of species/group	Slope of line (regression coefficient)	Regression intercept
Sauropodomorpha	0.42	-2.8
Theropoda	0.38	-22.53
Ornithischia	0.40	4.39

Reviewing figure 1 and table 1 for the dinosaur groups under the Saurischian order. We observe a significant variation in the regression coefficients which implies no comparable ratio was followed between the 2 groups. On considering all 3 groups of dinosaurs we notice that they are all around the same with only a 0.2 difference between each. We are also able to conclude that over their period of existence the Sauropodomorphs saw a 0.42 increase in femur circumference with respect to femur length. Followed by Ornithischians who saw a 0.4 increase and lastly Theropods with a 0.38 increment.

For Sauropods, we can also associate this change in bone length with an increase in body size. This is consistent with previous findings about the body size evolution of the Sauropods starting in the early Jurassic which eventually led to them being some of the largest animals to be recorded to date. [11] The earliest dinosaur present in the data is the Saturnalia Tupiniquim, dating back to the early Carnian age (nearly 230 mya), it was a small dinosaur estimated to weigh only about 10kg and 1.5 meters in length [12]. The latest species found were the Jainosaurus septentrionalis, Magyarosaurus dacus and Rapetosaurus krausei of which the R. krausei has an estimated length of 15 meters and weighed about 40 kg.[13] It was also noted that the S. tupiniquim was bipedal as opposed to subsquent generation Sauropods such as the R. krausei being quadrupedal. We believe this can be attributed to an increase in body mass, which led to a slow evolutionary shift from only hind leg locomotion to use of all 4 limbs.

As for Theropods they seem to show the least change in femur circumference with the passage of time. This can be connected to a speculated evolution in Theropods which is said to have taken in place in the Mesozoic age. Although the evolution does not account for an increase in femur length rather change in the tibia, fibula and metatarsal length is more prominently recorded.[5]

In Ornithischians there is a 0.4 increase in femur circumference in correlation to length. However, no strong links can be established for increase in femur length with pedal transition or body size evolution.[14][15]

2.1.2 Humerus circumference with respect to length

Table 2 Slope and coefficient values for humerus circumference vs. length

Name of species/group	Slope of line (regression coefficient)	Regression intercept
Sauropodomorpha	0.35	82.3
Theropoda	0.35	10.58
Ornithischia	0.46	-4.85

Looking to confirm any relations between humerus circumference and length amongst the 3 groups. We observe that the same regression coefficient is recorded for Sauropodomorphs and Theropods. The regression coefficient for Ornithischians seem to be substantially greater than both the other species.

From here we can seemingly confirm that both Sauropodomorphs and Theropods are indeed descendants from the same order, by acknowledging that the rate of change of humerus circumference with respect to length was 0.35 for both.

2.1.3 Tibia circumference with respect to length

Table 3 Slope and coefficient values for tibia circumference vs. length

Name of species/group	Slope of line (regression coefficient)	Regression intercept
Sauropodomorpha	0.39	31.99
Theropoda	0.43	-56.46
Ornithischia	0.36	14.53

Finally, taking a look at tibia circumference with respect to length values, we are able to summarise that Theropoda shows the greatest value for increase, that is, 0.43. They are followed by Sauropodomorpha with a 0.39 increase in circumference with length and the smallest increment being shown in Ornithischians. The tibia bone is present in the lower portion of the hind legs of dinosaurs. It is present below the femur. If compared with femur circumference-length ratios. We notice that Theropods show a greater tibia growth rate than femur. This is contradictory to the idea that Theropods are believed to be smaller in size compared to other dinosaur groups due to them being a predator species. Species adapted to hunting are regarded as smaller and lighter in size (depending on their prey) as opposed to Sauropodomorphs (herbivores) who were known for their considerable size and bulkiness. [16]

2.1.4 Relation between humerus and femur length

Table 4 Slope and coefficient values for humerus vs. femur length

Name of species/group	Slope of line (regression coefficient)	Regression intercept
Sauropodomorpha	0.82	-65.64
Theropoda	0.38	42.96

From Figure 13 we observe that femur and humerus length ratios derived for Sauropodmorpha and Theropoda show a linear relationship. This can be intuitively explained by simply stating that as humerus length increases, the femur length also proportionally increases to maintain a consistent or steady body size growth[17] and ensure body symmetry. Furthermore, the large value of the slope of humerus-femur length for Sauropodomorphs can be explained by a growth-curve study on Tyrannosauria, particularly the massive Tyrannosaurus (Theropod) [18]. The study revealed that a significant increase in growth rates, up to four times, played a pivotal role in the evolution of the impressive size seen in this species. The same study was then conducted for Sauropodomprha which uncovered a similar pattern.[19]

With this paper, we seek to uncover an unknown relation between 2 biologically unrelated species: Humans and Dinosaurs. Further, we also look to strengthen claims about birds being today’s living dinosaur descendants. We attempt to establish these relations by analyzing length-diameter curves.

2.2.1 Femur length vs. diameter

Table 5 Slope and coefficient values for femur length vs. diameter

Name of species/group	Slope of line (regression coefficient)	Regression intercept
Sauropodomorpha	0.13	-5.62
Theropoda	0.12	-7.48
Ornithischia	0.11	3.8
Humans	0.09	4.82
Terrestrial Birds	0.09	-0.42

We can deduce from Figure 16 and Table 5, a minimal value distinction for all above species. All the dinosaur taxa ratios differ from each other only by 0.1, with Sauropodomorpha being the highest at 0.13. The most unexpected result however is humans and birds having equal coefficient values.

For long, the origin of the bird puzzled scientists. However, today, the Theropod hypothesis is almost universally accepted which links them to be descendants to carnivorous dinosaurs such as Deinonychus, Velociraptor, Troodon and Oviraptors which share a great deal of similarities with birds[7]. However, this is inconsistent with our values, which do not indicate a relationship between Theropods and birds.

We also notice a close ratio between Ornithischians and birds, this may be due to their shared ancestry and several osteological similarities such as homologous pelvic bones (a retroverted pubis and elongated iliac). A study also concluded convergence between birds and basal ornithischians, which further affirms this ratio.[20]

2.2.2 Humerus length vs. diameter

Table 6 Slope and coefficient values for humerus length vs. diameter

Name of species/group	Slope of line (regression coefficient)	Regression intercept
Sauropodomorpha	0.11	25.62
Ornithischia	0.15	-5.9
Humans	0.13	2.91
Terrestrial Birds	0.05	1.08

Comparing the increase in humerus length with respect to diameter in Table 6, our results vary.

We see ornithischians having the highest slope of 0.15, which is consistent with the high value of humerus circumference-length ratio, suggesting that overall Ornithischians saw the largest rate of increase in forelimb bones (humerus, being the largest of them).

Birds seem to have the lowest ratio of 0.05, which we believe can be attributed to their small size as well as their diets (nutrients and amount consumed).

As for Sauropods, the humerus length in relation to diameter (0.11) is still less than the femur diameter in relation to length (0.13). This follows a similar trend in circumference- length graphs as well, further alluding to the connection between 3 linear quantities of length, circumference and diameter.

To answer for the similarities in values obtained for human and bird bone comparisons, we turn to the theory of convergent evolution[21]: the phenomenon of different species developing similar features or traits while evolving simultaneously. Here, the traits acquired by the species are not a result of shared ancestry but are rather due to external factors, such as environment or survival pressure.

A study conducted on intelligence in corvids (large-brained birds) and apes details how enlarged brain sizes in both corvids and apes could have been a result of convergent evolution and verifies the resembling environmental conditions faced by both species. From this study, the dietary overlap between the 2 species is of relevance to us. Both corvids and primates displayed an evolution of intelligence when they engaged in extractive foraging, specifically as omnivores. Similar diets suggest the availability of the same nutrients and proteins which we can articulate as proportional bone growth in both species. However, no detailed experiments or studies have been carried out on relationship between convergent evolution and body size growth.[21] [22]

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