GRAPHICAL DATA
Interpretation of Graphical and Numerical Data - Part # 2
Did you ever wonder why most invertebrates, especially terrestrial forms are relatively small?
The main reason for this size restriction has to do with their respiratory system and the rate at
which gases can be exchanged. The invertebrate respiratory system is diffusion-based and has
significant size limitations due its tubular respiratory structure known as tracheae. Essentially,
these are tubes running through the insect’s body and are connected to the environment
through external openings, which are called spiracles. Physiologically, the rate of delivery of
oxygen (absorption rate) is directly proportional to the concentration gradient along the length
of the tracheal surface responsible for the exchange, inversely proportional to the length of that
surface (tracheae), and directly proportional to the cross-sectional area of the surface. In
addition, the demand for oxygen is going to be proportional to the mass of the animal, or more
precisely its volume. As an insect increases in size, demand for oxygen will increase in proportion
to length cubed, but the rate of supply will only increase as length squared.
The following graphs represent absorption rates as a function ??(??) where ?? is the concentration
gradient (mg/L). Graph A reflects an ideal rate where the size or the organism does not
represent a limit to diffusion graphs B through F reflect the absorption rates for five
invertebrate taxa.
Curve Expressed by:
??(??) = ????
Curve Expressed by:
??(??) = '(
)*(
Graph A Graph B
Curve Expressed by:
??(??) =
????+
?? + ??+
Curve Expressed by:
??(??) = ??????/ß(
Graph C Graph D
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How would you read these graphs? For example, graph A shows that as the concentration of a
given gas increases the absorption rate also increases, and does so at the same rate. This
characterizes a linear relationship and is true for invertebrates that fall below a certain size.
Graph B appears to display a somewhat different relationship. Initially, the graph appears to
look like a line, but the absorption does not continue to increase linearly; instead, it seems to
level off and approach a certain value. Examine the remaining graphs and see if you can develop
a defensible argument/interpretation as to what each graph represents. Use your
interpretations of the graphs to answer to the following questions.
Q1: Regarding size constraints in invertebrates (i.e., size restrictions in invertebrates are
primarily due to gas exchange limits), what can you suggest about the size of the
invertebrate represented by graph B? Explain. (2 points)
Q2: (a) How does graph F differ from graph A? (1 point)
(b) Are the two invertebrates represented by these two graphs the same size?
Based on the data provided by the two graphs, can you answer this question?
Explain. (3 points)
Q3: (a) Describe the behaviour exemplified by the function in graph E. (1 point)
(b) How does graph E differ from the behaviour of the function exhibited by graph
D? Explain. (1 point)
Q4: In what ways do the curves in graphs B and graph C differ? Explain. (4 points)
Question 5 requires a number of interpretations on your part. It also requires both an ability to
correctly interpret the information presented by the six graphs, as well as an ability to apply the
fundamental principles of phylogenetic analysis. In order to successfully respond to this
question, a number of assumptions are required:
• Assume that all 6 graphs are representative of a unique species of invertebrate. Assume
further that graph “A” represents the out-group condition or the ancestral (primitive) state for
the character associated with absorption rate.
• We will also assume that the greater the absorption rate the more derived the taxon is. In
other words, the fastest rate of absorption at a concentration of 1 represents the most derived
taxon.
Curve Expressed by:
??(??) =
????
?? + ??+
Curve Expressed by:
??(??) = ????(1 + ????)
Graph E Graph F
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• Let us further assume that taxa whose absorption rates are most similar display the strongest
sister-group relationship and let us also assume that there is a trend toward increasing
absorption rates in the entire group.
Q5: (a) Based on the absorption rates displayed in graphs A through F, create a
cladogram that presents a plausible phylogenetic relationship among these taxa.
(0.5 points)
(b) Support your phylogenetic analysis by defending how you reached the
conclusion that the phylogenetic topology you present is valid. (2 points)
(c) Would exchanging the out-group with the next most primitive member of the
in-group alter your topology? Briefly explain your reasoning. (0.5 points)
Assignment Submission & Grade Distribution
Part # 1 Total Value = 10%
1. The introductory portion (Part # 1) of the Numeracy Assignment will be presented
during the tutorial on January 12th, 2018. Assignment questions will be assigned and will
be completed as homework. Submission of work will be through blackboard and is due
by 11:59 on Thursday January 19th. During the February 2nd tutorial, you will have the
opportunity to review and evaluate your responses with the instructor. Note that correct
answers will not be provided during the Tutorial. It is simply an opportunity for the
students to gauge there understanding. Students will have a chance to resubmit their
answers to Part # 1 once again. These responses will be submitted through blackboard
and will be due by 11:59pm, Thursday Feb. 9th. This will complete Part # 1 of the
assignment. The total value for Part # 1 of the assignment is 10% of your term grade.
The first 5% is automatically received upon submission of the assignment by Thursday at
11:59pm on January 25th. The second part, which is due Feb. 1st will be evaluated and a
mark out of 5% will be awarded.
MARK Breakdown for Part 1
1) 5% awarded automatically for submitting work by 11:59pm on January 19th.
2) 5% to be evaluated after resubmission of work by 11:59pm on Feb. 9th. For the
resubmission, marks are assigned on the basis of the following.
a. No Errors = 5% - this implies no missing arguments necessary to respond to all
questions
b. Minor Errors = 3.5% - this implies no missing arguments necessary to respond to all
questions but some details may be lacking
c. Serious Errors = 2.5% - this implies at least some critical missing arguments that
would be necessary to respond to all questions
d. Completely incorrect = 0%
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