American bison matrix?

The Leslie matrix for the American bison is given by

A =
2
4
0 0 0:42
0:60 0 0
0 0:75 0:95
3
5:

The population is divided into calves, yearlings, and adults (age two years or more).

We would like to see how the whole population and the individual classes (calves, yearlings, and adults) changes over time and how those results vary when we change the various parameters in the Leslie matrix for the bison population. Thus, if the matrix

x(0) =
2
4
x1
x2
x3
3
5

represents the American bison population at time t = 0, where x1 is the number of calves, x2 is the number of yearlings, and x3 is the number of adult bison, then

x(t) = Atx(0)

gives the bison population at time t. Suppose, at t = 0, there are 42 calves, 0 yearlings, and 95 adults.

Student Tasks

1. Using the Matlab skills you have learned in this Unit write an m-le (see Ap- pendix A for description of writing and running an m-le) that

(a) Find the number of calves, yearlings, and adults at times t = f1; 2; 3; 4; 5; 10; 20; 25; 50; 75g:

(b) Make a graph that has times t = 0 to 100 on the horizontal axis and population size along the vertical axis. Plot the calf, yearling, and adult population sizes for every time step between 0 and 100.

(c) Change the adult bison fecundity to 0.2, 0.42, 1.0, and 1.4. How do these changes aect the bison population equilibrium structure? Create one graph that has adult fecundity along the horizontal axis, and equilibrium population structure along the vertical axis with a data set plotted for each population class (calves, yearlings, and adults).

(d) Change the calf survival rate to 0.3, 0.5, 0.6, 0.7, and 0.85. How do these changes aect the the bison population equilibrium structure? Create one graph that has calf survival rate along the horizontal axis, and equilibrium population structure along the vertical axis with a data set plotted for each population class (calves, yearlings, and adults).

(e) Change the adult survival rate to 0, 0.3, 0.5, 0.75, 0.95, and 0.99. How do these changes aect the bison population equilibrium structure? Create one graph that has adult survival rate along the horizontal axis, and equi- librium population structure along the vertical axis with a data set plotted for each population class (calves, yearlings, and adults).

[Sven]

Quote:

"Student Tasks 1. Using the Matlab skills you have learned in this Unit..."

How can we follow the instructions for your tasks which you copied verbatim and answer the question when those instructions specifically say to use the skills *you've* learned? We haven't taken the unit, so it's much better if you're the one to do your own homework...

If you have a specific question on the other hand...

[Image Analyst]

Well you could have at least referred him to the American Bison Toolbox.

[Walter Roberson]

@Haley: I have reformatted your posting for you, but you really need to go through and correct the errors in the document scan. I don't think any of us know when time "75g" is, or have any idea how you can possibly get that A matrix that has colons as part of it.

I am almost certain that your equation x(t) = Atx(0) is wrong. It would be more understandable if it were x(t) = A^t * x(0) -- except that raising a matrix to a power requires a square matrix, which you do not appear to have.

@Image Analyst: Production of the American Bison Toolbox has been postponed until after finalization of the Moose Toolbox, as the moose are far more numerous, and tend to be closer to population areas than the American Bison are.

[Sven]

@Image Analyst: Oh, silly me, I completely forgot about the ABT! I've got an old version, but it must be the Australian Bison Toolbox (tm), because it's main function is:

function B = ABT(varargin), error('ABT:noneInOz','Missing Bison'), end

[Walter Roberson]

@Sven: http://www.abc.net.au/news/2011-07-21/australia27s-largest-bison-herd-up-for-sale/2803926

[Sven]

@Walter: Sorry, small typo... I meant the Australian _Native_ Bison Toolbox (tm), or ANBT for short. All the convenience of the ABT (tm) without the hassle of needing to account for the importation of massive animals from lands afar.