Matrix Example.
Lt+1
1
2
3
t=0 populations
INPUTS
t = Generations.
1 ..n1(0) ..n1(t)
2 ..n2(0) ..n2(t)
3 ..n3(0) ..n3(t)
Lt+2
1
2
3
t+1 = Generations.
1 ..n1(t+1)
2 ..n2(t+1)
3 ..n3(t+1)
Here's an explicit example:
f1 = 1/3,
f2 = 2/3,
f3 = 2/3,
P1 = 0.5 and
P2 = 1.0.
You'll see these values in their appropriate slots in the 3x3 matrix (which is the matrix L) in the upper left of this JavaScript calculator.
There are inputs to this calculator, the initial populations of the 1, 2 and 3 year olds at t = 0 (they do not influence the powers of L). You enter those by clicking (or double clicking) on the indicated fields and typing in numerical values. (I haven't bothered to check for nonnumerical inputs, so if you have one you'll get a JavaScript error message.) So in this case w = 3, and all females over 3 years old have given up on breeding. Note that on average each season the 1, 2 and 3 year old females give birth to 1/3, 2/3 and 2/3 female spawn, respectively, that survive at least one year. Also, half of 1 year olds survive to 2, and all of 2 year olds survive to 3 (unrealistic, but we should expect survival rates to increase with age and experience at least to some extent).

The ouputs are the matrices Lt+1 and Lt+2, and the columns of populations n(t) and n(t+1) (these will depend on the 3 inputs). Ok, to start with try any 3 positive integers for n1(0), n2(0) and n3(0). Click through several (20 or so) generations with the "Take a Step" button. Observe what happens with the powers of L and the populations at subsequent t and t+1.

Then reset and try n1(0) = 200, n2(0) = 100, and n3(0) = 100. We'll discuss this on the next page.

Home. ..... Population Page 15. ..... Population Page 17.
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