SCIE1000: Python and Communication - Maximal Running Speed of Mammals - Science Assignment Help

Assignment Task:

1 A scenario 
A newly created public science museum is to open in St Lucia. A feature of the museum is that each exhibit item is accompanied by three explanations, each written for a different audience. One explanation is pitched to the “rookie scientist,” another to the “seasoned scientist”, and a third to the “grizzled scientist.” Patrons read the explanation tailored to the level at which they feel most comfortable. Some characteristics of a typical audience member in each category are described in Figure 1. 

Figure 1: Characteristics of a typical patron in each category 
The museum is planning an exhibition called “Mother Nature: Fierce beauty, always in balance.” The aim is summarized in the following passage from the exhibition prospectus: 
“Science is a lens through which we understand and explain what we see in the natural world. This un derstanding does nothing to diminish our amazement at the spectacle; rather, it is path to deeper appreciation because it provides new reasons to be awestruck. With this exhibition we use science to engender in our patrons a sense of wonder at the delicate balances that exist within ecosystems, even as a brutal competition for survival rages throughout.” 
The museum director has asked the SCIE1000 teaching team for help in finding skilled volunteers to develop exhibit items. Once developed, the items will be maintained and potentially modified by museum staff, each of whom has a strong background in high-school mathematics, together with at least a beginners level of Python experience. We assured the director that SCIE1000 students are skilled at: making mathematical models using a mathematical toolkit familiar to any student of Maths B (or equivalent); writing Python programs, including those which use arrays, loops, plots and new functions; and communicating scientific information to various audiences. This is important as you will need all of these skills to effectively complete this project for the museum. 
Based on this boasting by the SCIE1000 teaching team, you have been asked to develop an exhibit item called “Chase on the Serengeti.” The item is inspired by the following quote from a recent scientific paper [5]: 
“The study shows that overall, the athletic capabilities of the two pursuit predators closely match their respective common prey, leading to a sustainable success rate, survival of both and reflecting an evolutionary arms race.” 
The item will be a Python program for museum patrons to interact with. 

2 An overview of the task 
You will create a Python program that will run on a machine in the exhibition hall of the new science museum. At the heart of your program will be a simulation of a chase between a predator and their prey. To do this, you will use the masses of these animals to model their top speed and their speed profiles over the course of the chase. The models to be used are described in Section 4 of this document. Your program will perform calculations concerning the model of the chase, and display relevant information. It will extend the template provided in Section 5, and follow the logical flow laid out in the flow chart provided in Section 5. You will document your code with comments so that it can be easily maintained and extended by anyone with a strong background in high-school mathematics and a beginner’s level of Python experience 
In summary, this assignment requires you to produce and deliver a file containing a well-documented Python program. A detailed list of program requirements is provided in Section 5 of this document. 
A rubric (marking criteria) for this assignment will be posted on blackboard. 
Your deliverable is to be uploaded through Blackboard by 1 pm on 30 October 2020. The time-stamp from Blackboard will be used to determine the time of submission. Late submissions will be penalised. Consult Section 5.3 of the Electronic Course Profile for more information concerning late submissions. 

3 About getting help 
This assignment is a piece of summative assessment. It is designed to let you demonstrate your level of mastery of several learning objectives in this course. As such, it is very important that the work you submit is all your own. This does not mean that you cannot receive help in regards to this assignment, but that help must be limited. There will be no workshop time allocated to working on your assignment. You can use MyPyTutor, available through Blackboard, to practice and learn Python concepts. Your teaching team, the SLC tutors, your classmates, your friends, and anyone else for that matter, can answer as many general questions about Python and modelling in general as you care to ask. They can even help you understand what particular error messages may mean. They must not, however, tell you what to write or correct your code. Until the assignment submission time, you should not look at anyone else’s code and you should not show your code to anyone. Both of these actions are examples of behaviour that may be considered academic misconduct. No code from your assignment attempt should be posted on the course Piazza site, or any other site, at any time. You should type or create every character in the files you submit. 
Your teaching team and tutors will not answer questions about the nature of the task, or elaborate on the requirements, in person. Any questions you have about the assignment task should be posted on the course Piazza site. This is the only place where you can receive authoritative answers to questions. In this way, all students will have access to the same information. Sometimes the answer to a question on Piazza will be “See the assignment task sheet.” Such an answer is not intended to be grumpy, but to avoid restating information. Trying to say the same thing in different places can lead to misunderstandings or unintended inconsistency. This task sheet has been carefully constructed, and part of your job is to interpret the information it contains. Some choices have been left to your judgement, and this is intentional. 
The file you submit will be checked using software that detects plagiarism. Consult Section 6.1 of the Electronic Course Profile for more information and procedures concerning plagiarism. 

4 A model of The Hunt 
4.1 Animals on the Serengeti 
According to the United Nations Educational, Scientific and Cultural Organisation (UNESCO) [1]: 
“The vast plains of the Serengeti comprise 1.5 million ha of savannah. The annual migration to permanent water holes of vast herds of herbivores (wildebeest, gazelles and zebras), followed by their predators, is one of the most impressive natural events in the world.” 

4.2 Maximal running speeds of mammals 
The maximal running speed of a mammal on the Serengeti could mean the difference between life and death. The maxi mal running speed of mammals is often considered as a function of their mass. 
The mass of adult big cats on the Serengeti vary from ∼ 40 kg for a leopard and ∼ 140 kg for a hunting lioness. Both of these predators can maintain a maximum speed of 60 km · h−1. With a maximum speed of 110 km · h−1and an average mass of 75 kg, the cheetah is the fastest land mammal on the Serengeti. There are also other predators on the Serengeti, the Hyena can also reach speeds of 50 km · h−1 with an adult mass of ∼ 45 kg [4]. 
Herbivores on the Serengeti can be both much smaller and much larger than their carnivorous counterparts with masses ranging from ∼ 20 kg for the Thomson’s gazelle, to ∼ 400 kg for a plains zebra and ∼ 500 kg for the massive African buffalo. As you would imagine, the top speed of the gazelle is higher than that of the Buffalo, with speeds of 65 km · h−1 and 50 km · h−1respectively. Zebras can reach a top speed of 65 km · h−1. The most likely animal to be able to escape the clutches of the predators is the wildebeest with a weight of 250 kg and a top speed of 80 km · h−1[4, 2]. 
Using this information, biologists have developed power law models for maximal running speed as a function of mass in mammals. However, in a study of the maximal running speeds of 106 different mammals, the authors of [4] concluded: 
“For all mammals (n=106) ... an equation of the form 
log10(MRS) = 1.47832 + 0.25892(log10(M)) − 0.06237(log10(M))2, 
yields a significantly better fit to the data. 
In the above, M is the mass of the mammal (in kg), and MRS is its maximal running speed (in km·h−1). 

4.3 Acceleration and endurance of mammals 
Neither predators nor prey can reach their top speed instantaneously, nor can they keep up their top speed indefinitely. In [3], it was found that the time taken for an animal to reach its top speed is dependent on its mass, and that the model that best fits this relation is a power law of the form: 
tT S = aMb, 
where tT S is the time (in s) it takes the animal to reach top speed (or maximal running speed). To find the values of a and b the following data has been provided: 
log10(M) log10(tT S) 
1.48 0.16 
1.78 0.41 
2.08 0.67 
2.38 0.93 
2.68 1.18 
Table 1: Acceleration data for mammals 
The physical endurance of the predators and prey are related to how long it takes them to reach their top speed. We shall model an animal’s speed at any moment in the chase as a proportion of their top speed, with the constant of proportionality at any moment described in the tables below. 

Predators 
Time interval Proportion of top speed [0, tT S) time/tT S [tT S, 4tT S) 1.00 [4tT S, 6tT S) 0.40 [6tT S, ∞) 0.00 
Prey 
Time interval Proportion of top speed [0, tT S) time/tT S [tT S, 5tT S) 1.00 [5tT S, 8tT S) 0.55 [8tT S, ∞) 0.20 

Table 2: Models of the acceleration and endurance profiles for predators and prey 

4.4 How the chase begins 
When a predator hunts, it first sneaks as close to as possible to its prey. The chase begins when the prey notices the predator and starts to run. The distance between predator and prey at the moment that the prey notices the predator varies. Some predators are more stealthy than others; some prey are better at noticing an approaching predator than others. The terrain on which the chase takes place affects this as well. In the Serengeti there is a wide variety of terrain including: grassland, volcanoes, woodland forests, rivers, and plains. In these different terrains, it would be possible for predators to approach their prey at different distances. For example, in tall grass, a leopard may be able to get within 10 m of a nearby gazelle, but on wide open plains with less cover, the same leopard may only be able to get within 50 m or even 100 m before the gazelle will sense their presence.

 
4.5 Simulating the Chase 
We will estimate the position of both the predator and the prey every 0.1 seconds for the duration of the hunt and store these positions and times in arrays. These arrays (that should have the same number of elements) must have enough elements to accommodate the chase until the predator would give up (say, enough elements to accommodate a chase that lasts as long as 7 × tts of the predator). 
The position of the mammal at each time step is given by the following equation: 
New position = Current position + Current speed × 0.1 s 
For example, if a cheetah has a position after 3 seconds of 100 m and a current speed of 20 m ·s−1then the position after 3.1 seconds is given by: 
New position = 100 m + 20 m · s−1 × 0.1 s 
= 100 m + 2 m 
= 102 m 
The cheetah is now at 102 m after 3.1 s. 

4.6 Displaying the chase 
Graphical information is a good way to display information about the chase. For example, a patron will benefit from seeing a graph showing the distances of the predator and prey from the predator’s starting position as a function of time. They will find it exciting to see a graph showing the distance between the predator and prey as a function of time. 

5 Specifications for deliverable (D1) 
Deliverable (D1) is an interactive Python program which models the process of predators chasing down prey. 
1. The museum staff have supplied a flow chart describing how the program should run. It is included on Page 7 of this document. Your code must be an implementation of the flow chart provided. 
2. The museum staff have specified that, if the predator catches the prey, any display of information should not show what happens after the predator catches the prey (this is considered too gruesome for some museum patrons). This means that you will need to explicitly specify the limits of the x-axis in your plot. This can be done by using the command xlim(xmin, xmax) immediately before the show() command. 
3. All messages to the user, including prompts to enter data, should communicate in a manner appropriate for the level of patron and should serve the purpose of the program. You may write different messages for patrons at different levels when you think it is appropriate to do so. You may indicate reasonable ranges for data entry when prompting the user. Writing appropriate messages is a way that you can demonstrate your communication skills. 
4. You should use units appropriately in your communication with the user. 
5. Any graphs that you display should be appropriately labeled, and may be accompanied by explanatory text. Pro viding a well-labelled graph is a way that you can demonstrate your communication skills. 
6. Patrons will be able to enter data using a number keypad only, so all input will be numerical (the user can access only digits, the negative sign, a decimal point and the ENTER key). 
7. You should use comments in your code to help the museum staff who may need to maintain and modify the code. Writing good documentation in your code is a way that you can demonstrate your communication skills. 
8. Museum staff have a beginner’s level of experience using Python, which you may regard as the equivalent of a student who has taken SCIE1000. If you write code that goes beyond that covered in SCIE1000, you must provide comments that explain the code sufficiently well that museum staff can maintain it. 
9. Museum staff are familiar with the library pylab, but they are not familiar with and have not installed other libraries. If you decide to include other libraries, you should include comments in the code to justify this choice and provide instructions for how staff at the museum can download the libraries. 
10. You should provide a bibliography. This should be printed to the screen at the end of the program as part of the farewell message. Any standard referencing style is acceptable. The aim is to provide enough information to effectively acknowledge your sources. For example, you may refer to this task sheet as: 
SCIE1000 Python and Communication Task Sheet (2020). Faculty of Science, University of Queensland. 
11. Museum staff have identified several functions that they think will be useful in possible modifications and exten sions of the code. You must define these functions in your code, with the exact names specified below and so that they take the same arguments in the order specified. You should call these functions in your code as appropriate. You may define other new functions as you think appropriate. 
(a) You must define a function called 
MRS_mammal 
which takes one argument, representing the mass of a mammal (in kg), and returns the the maximal running speed of the mammal (in km· h−1) as predicted by the model in [4]. 
5
(b) You must define a function called 
time_to_top_speed 
which takes one argument, representing the mass of a mammal (in kg) and returns the time (in s) taken for that mammal to reach its top speed. 
(c) You must define a function called 
speed_of_predator 
which takes three arguments, representing the top speed of the predator (in m · s−1), the time taken for the predator to reach top speed (in s) and the time since the chase started (in s), and returns the current speed of the predator (in m · s−1). 
(d) You must define a function called 
speed_of_prey 
which takes three arguments, representing the top speed of the prey (in m · s−1), the time taken for the prey to reach top speed (in s) and the time since the chase started (in s), and returns the current speed of the prey (in m · s−1). 
(e) You must define a function called 
kph_2_mps 
which takes one argument, a speed in kilometers per hour, and returns the equivalent speed in meters per second. 
 

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