Cranium Shape – Look at each skull from the top. Specifically, look at the shape of the cranium (the part of the skull where the brain is located). If the shape is boxy, we consider it to be Cuboid (C). In other words, it more closely resembles that of a box than that of a ball. If the shape is rounded, then we consider it to be Spheroid (S). In other words, it more closely resembles that of a ball than that of a box.
Table 2
Skull
Letter
Code

L (mm)

Class
AVG L

W (mm)

Class
AVG W

H (mm)

Class
AVG H

ASV
(LxWxH/1000)
(cm^{3})

ESV
(cm^{3})

Cranium
Shape
(C/S)

S










N










E










G










H










A










B










K










L










All of the measurements in this table should be taken with the top of the skull facing upwards (natural resting position) with the lower jaw removed.
Procedure Part II: Organizing Your Data
Once you have collected all the data for Tables 1 and 2 in Part I of the lab, you can begin organizing your data (if you have not already calculated FMI, you should do so now). You also will begin calculations for comparative analysis so that you can draw conclusions about relatedness of these 9 hominins. To do so, fill in the Table 3 below following your teacher’s guidance. Once you and your team have gathered all of the data for Table 1, you will need to compile the data from all other teams for FB and SL into Table 3. When you have compiled the class data, you can then calculate the class average for FB (Class AVG FB) and SL (Class AVG SL); and from these data you can calculate the Class FMI (AVG FB/AVG SL). These calculated averages can then be transferred into the corresponding gray shaded columns in Table 1.
Table 3
Skull Letter Code

FB (mm)

FB (mm)

FB (mm)

FB (mm)

Class AVG FB

SL (mm)

SL (mm)

SL (mm)

SL (mm)

Class AVG SL

Class FMI
AVG FB/ AVG SL

S












N












E












G












H












A












B












K












L












To complete Table 4, copy your L, W and H data from Table 2 into the first columns with the corresponding labels in Table 4. Collect the data from the other teams in your class and complete Table 4 by calculating the average for L, W and H (Class AVG L, Class AVG W, Class AVG H) and record these averages in the corresponding gray shaded columns of Table 4, and then Table 2 as well. Now you can complete your calculations for ASV and ESV in Table 2, which are defined as follows:
ASV  Approximate Skull Volume: calculate the product of AVG L, AVG H, and AVG W, and divide your answer by 1000.
Table 4
ESV  Estimated Skull Volume: the measurements that you took of the skull will overestimate the cranial capacity because skulls are not cubes. To correct this, you should divide the number that you calculated in the previous column (ASV) by 2 for species S, N, E, G and H, and by 3 for all other species (A, B, K and L). You use a different correction factor for each group of skulls because the skull shapes vary between the two groups.
Next, convert your fist estimates for Cranial Capacity (CC) into an approximate measurement (CCC) by using the formula CC x 300 cm^{3}  the estimated volume of an average human fist is 300 cm^{3}. These calculations can be added to Table 1.
At this point in time, your teacher will provide you with the Actual Cranial Capacity (ACC) for each skull based on scientists’ measurements. Use these data to complete the appropriate column in Table 1.
Compare your data for FMI to the class FMI, which is based on average class data.
1. Why is the class FMI usually a better indicator of the location of the foramen magnum than your individual calculation?
Compare the data that you calculated for cranial capacity (CCC) to the Actual Cranial Capacity (ACC), which has been determined by scientists in Table 1.
2. Which of your calculations have overestimated the cranial capacity?
3. Which of your calculations have underestimated the cranial capacity?
4. Which of your calculations are within the range of the Actual Cranial Capacity?
5. What could you do to get your Calculated Cranial Capacity value closer to the actual value?
6.a Imagine using ping pong balls instead of fists as your unit of measure for cranial capacity, do you think that your calculated value would be closer to or further from the actual value?
b. Why?
7.a What about using an even smaller unit of measure, such as grains of rice or sand? Do you think that your calculated value would be closer to or further from the actual value?
b. Why?
c. What new problems might you encounter when using such small units of measure?
d. How could you overcome those problems? What tools could you use?
8.a After measuring the skull volume using rulers, you applied a correction factor to arrive at your ESV. Why was a correction factor necessary?
b. Why was a different correction factor used for different groups of species?
c. What was the shape of the cranium of the skulls for which you applied a correction factor 2?
d. What was the shape of the cranium of the skulls for which you applied a correction factor 3?
Your teacher will now also provide you with the Skull Letter Codes that correspond to each time period in your Geological Time Scale graph. Once your teacher has identified the time period that corresponds to each skull, write the single letter code for each skull in the area that you shaded within the Geological Time Scale graph. Once you have added the single letter codes into this graph, you can then transfer these identified ages into the appropriate places in the last column (Age) of Table 1.
9. Which time interval has the greatest number of hominin species coexisting?
10. What is the time period during which species S has been the only surviving hominin?
As scientific investigators, your team will now begin to compare the data that you have collected from different skulls. Specifically, you will put some of your Class FMI data onto a graph in order to compare them to each other.
The location of the foramen magnum in the skulls will reveal some interesting information about the way that the hominins lived. The FMI is an indicator of the location of the foramen magnum on the underside of the skull. The closer to 0.3 the FMI of a species is, the better adapted this hominin is to upright/bipedal walking. In order to visualize any trends in the location of the foramen magnum among the hominin skulls, you will enter the Class FMI for the 4 skulls (L, H, G, N) on the Foramen Magnum Index graph (see below). Determine the FMI for dog (a quadruped) and human (a biped) using the scales provided. Focus on the bottom end of the foramen magnum, which is labeled for these two species and write this number on the line above the diagrams of these 2 skulls. Next in Table 1, locate the Class FMI values for the 4 other hominin species (L, H, G, N). Write these values on the lines above each corresponding scale. Now you can plot your numbers on the provided scales with round dots approximately the same size of the illustrated foramen magnum of the dog.
Foramen Magnum Index graph
11. Examine the Foramen Magnum Index graph. Do you notice any trend in the FMI as you look from left (dog) to right (human) among the hominin skulls? And if so, describe it.
12. Determine which of the skulls in this graph is the oldest by looking at the Geological Time Scale graph. Now, compare the FMI of this oldest species to that of the dog and human. Do you think that this species was bipedal or quadrupedal? Why?
13. Which of the 4 species (L, H, G, N) is best adapted to upright walking? Why?
14. Do any of the Class FMI in Table 1 closely match the one provided for the human in your graph? If so, which one(s)?
Procedure Part III: Analyzing Your Data
In order to determine whether a relationship exists between the Foramen Magnum Index and Cranial Capacity, you will plot these two parameters for each species in the provided FMICranial Capacity graph below. For this you need to first complete Table 5 using your Class FMI from Table 1. The provided Average Cranial Capacity is based on the Actual Cranial Capacity (ACC), also from Table 1. You will notice that there is a new Skull Letter Code “M” in Table 5. This “M” is also the only data point already filled in on the FMICranial Capacity graph and represents the macaque, an oldworld monkey species that is quadrupedal. From this data point “M” you can determine the macaque’s Average Cranial Capacity and FMI and add them to Table 5. With Table 5 now completed, plot the values in the graph and write the Skull Letter Code next to each data point. Do not connect the dots with lines. Instead, once you have plotted the points for all of the skulls, you should draw a “bestfit curve”. While there is a way to mathematically determine the location of such a curve, you can estimate it by visualizing the sum of the distances from each point above and below the curve. These 2 sums should be approximately the same. If you are having trouble finding the bestfit curve, your teacher will assist you.
Table 5
Skull Letter Code

Average Cranial Capacity (ccm)

Class FMI (from Table 1)

S

1350


N

1450


E

1025


G

900


H

550


A

450


B

450


K

400


L

463


M



FMICranial Capacity graph
15.a Excluding the macaque M, group the 9 species into 3 clusters of two or more points that are near each other. Draw a circle around each cluster and list the letters for each of these clusters.
b. Comparing cluster 1 (with 5 data points) to M (macaque), which variable accounts for the major difference between them, FMI or Cranial Capacity?
c. Comparing cluster 2 (with 2 data points to the right of cluster 1) to cluster 1, which variable accounts for the major difference between them, FMI or Cranial Capacity?
d. Comparing cluster 3 to cluster 2, which variable accounts for the major difference between them, FMI or Cranial Capacity?
e. Using the Geological Time Scale graph as a reference, list the three clusters in order of their relative age:
cluster #___ is older than cluster #___ is older than cluster #___
f. As you go from oldest to most recent cluster of hominin species, which factor (FMI or Cranial Capacity) changed more?
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