Question

Please compare the Matrix formulation of the Fibonacci's rabbits model (Lecture 9) with the two-tree forest ecosystem model (Lecture 14) and the Frameshift mutation model (Lecture 14). How these models similar and different? In particular, how assumptions of matrix models similar to Fibonacci's and Leslie Models (Lecture 9) are different from the assumptions of Markov chain models (Lecture 14)?

Answer 1

Frame shift mutation	Fibonacci's rabbits mdel	two-tree ecosystem model
A frameshift mutation is a genetic mutation caused by a deletion or insertion in a DNA sequence that shifts the way the sequence is read.	Rabbits are able to mate at the age of one month, and pregnancy takes one month. Thus, at the end of its second month, a female can produce another pair of rabbits.	A characteristic feature of European, particularly Central European, forest and ecosystem management is the concept of integration.
Frameshift mutations arise when the normal sequence of codons is disrupted by the insertion or deletion of one or more nucleotides, provided that the number of nucleotides added or removed is not a multiple of three	Rabbits never die, and a mating pair always produces one new pair (one male, one female) every month from the second month on.	The first, very early phase that in Europe persisted until the 17th century is characterized by multiple use forestry: hunting, bee-keeping, grazing in forests, forest assortment, wood felling and timber use.
frameshift mutations result in abnormal protein products with an incorrect amino acid sequence that can be either longer or shorter than the normal protein.	The puzzle that Fibonacci posed was: if we start with a new pair from birth, how many pairs will there be in one year?
	To solve Fibonacci's problem, we'll let f(n) be the number of pairs during month n. By convention, f(0) = 0. f(1) = 1 for our new first pair. f(2) = 1 as well, as conception just occurred. The new pair is born at the end of month 2, so during month 3, f(3) = 2. Only the initial pair produces offspring in month 3, so f(4) = 3. In month 4, the initial pair and the month 2 pair breed, so f(5) = 5. We can proceed this way, presenting the results in a table. At the end of a year, Fibonacci has 144 pairs of rabbits.