# Project #52298 - Linear Algebra Final Project

1 Introduction

MAT2580 - Project

The Wildlife Conservation Society1 (WCS) is an organization dedicated to helping wildlife around the world. Based out of New York City, WCS manages hundreds of conservation projects in an attempt to protect the world’s biodiversity. In this project, we will analyze the New York City robin population using data gathered by WCS.

Figure 1: Typical American robin.

The goal of this project is two-fold:

1. To develop a matrix model that describes the population/age distribution of robins in New York City.

2. To examine the long-term population/age distribution of robins in New York City if current trends persist.

2 Data

The table below (Table 1) represents the average 2-year birth and survival rates for dierent age groups of robins. For example, the 39.1% in row 2, column 4 means that, on average over the course of 2 years, 39.1% of all robins aged 6-7 survived to age 8-9.

1 http://www.wcs.org

1

 0-1 2-3 4-5 6-7 8-9 10-11 Birth Rate 5.2% 25.4% 46.7% 64.3% 32.6% 10.3% Survival Rate 78.4% 67.8% 65.5% 39.1% 12.6% 0%

Table 1: Average robin population survival and birth rates per age group.

The following table (Table 2) gives a count of the total number of robins (by age group) observed in May of 2014.

Table 2: Robin population per age group observed in May of 2014.

3 Task

In this project, you will work in groups of 3 to 4 on a technical report. Using the data given above, your goals are to:

 0-1 2-3 4-5 6-7 8-9 10-11 405 343 332 210 157 120

4

Construct a matrix model
that describes the population/age distribution of robins in New York City over time.

Use any methods from class to determine the number of expected robins in each age group in 20 years and decide if any immediate action is needed to prevent their disappearance from the New York City area.

Report Template

xn =Axn1,forn1,

Reports should be double-spaced in 11 pt New Times Roman font. Outside of the cover sheet and abstract (see below), the report should not exceed 3 pages.

Your report should contain each of the following sections:

• Cover Page - The cover page should include the names of the people in your group as well as the title of the project report.

• Abstract - The abstract should appear on its own page. This should be a one-paragraph summary of the paper. It should state the problem you are studying, the methodology used to solve it, and the end results.

• Introduction - Briefly introduce the problem. What are you looking to solve? What is the point of your paper?

• Assumptions and Definitions - List any assumptions you make on the given data and explain why they are reasonable. Also, include any definitions you need (including mathematical definitions) for the next section.

2

• Analysis - Explain what methods you used to solve the problem mathematically. You do not have to show every step in your computation, but you should explain what you did to arrive at your result.

Example: “Using MATLAB, we computed the eigenvectors of A to be...”

• Interpretation and Conclusion - This section should summarize your results and address all

questions posed. Explain what your results mean and what you can conclude from them.

5 Grading

The report is due DECEMBER 17. Grades will be assigned out of 50 points using the following criteria:

• (25 points) Mathematical content - This includes appropriate methods and computations.

• (5 points) Assumptions - This includes making reasonable and necessary assumptions for your

matrix model.

• (10 points) Conclusion - This includes how you answer the questions posed and whether or not they are reasonable based on your computations.

• (10 points) Organization - This includes making sure that the template was followed, neatness, and appropriate grammar.

 Subject Mathematics Due By (Pacific Time) 12/16/2014 11:59 pm
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