Warm Up Record your group’s 4 matrices from Packet pg. 3 and your answer to the last question on a large whiteboard.

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Presentation transcript:

Warm Up Record your group’s 4 matrices from Packet pg. 3 and your answer to the last question on a large whiteboard

P. H. Leslie Worked in the Bureau of Animal Populations at Oxford University in Oxford, England Posed a problem in 1945 that explored the population growth of an imaginary species of small brown rats His work was expanded to model the growth rate of various animal populations over time It is important to note that during the time of his research no calculators or computers were available that could do the calculations necessary He did all his work by hand!

Brown Rat Example Age (months) BirthrateSurvival Rate 0 – – – – – – 1800 If the population started with 42 rats with the following age distribution… a. How many babies are born in each age group after 3 months? Age(months)0 – 33 – 66 – 99 – 1212 – 1515 – 18 Number

Brown Rat Example Age (months) BirthrateSurvival Rate 0 – – – – – – 1800 If the population started with 42 rats with the following age distribution… a. How many people survive to move to the next age group after 3 months? Age(months)0 – 33 – 66 – 99 – 1212 – 1515 – 18 Number

So… How many rats are in each age group after 3 months?

Practice Age Group0 – 44 – 88 – 1212 – 1616 – 2020 – 24 Birth Rate Survival The characteristics of the female population of a herd of small mammals are shown in the table above. Suppose the initial female population distribution is 22, 22, 18, 20, 7, and 2. a.Determine the number of new babies in the population after one cycle. b.Determine the population distribution after one cycle.

Turn in your book to pg. 134 Try #1

Homework: pg. 134 #1 a b.18.97, 9.96, 8.1, 7.29, 9.36, 2.4 c.56 d.9 months: , , 8.964, 7.29, 5.832, 5.616; months: 18.02, 10.99, 10.24, 8.06, 5.83, 3.5; 57 e. & f. growing slowly

Group Work With your group…attempt question #2 Record your findings to part d on a large whiteboard and bring it the front when done.

Developing the Leslie Matrix Based on your answers to question 2, develop a matrix that would allow you multiple the initial population row matrix by your matrix and the resulting matrix would be the new population distribution. Use the following example to test your conjecture. Age Group0 – 44 – 88 – 1212 – 1616 – 2020 – 24 Birth Rate Survival

The Leslie Matrix

Let’s Return to the Rodent Problem AgeBirthrateSurvival Rate 0 – – – – – – 1800 a.Write the Leslie Matrix b.Find the population distribution after one cycle. c.Find the population distribution after 5 cycles (15 months) What is the total population d.Find the population distribution and the total population 7 cycles (21months)

Homework: pg. 134 (2 – 4) 2. a b. The product is the number of newborn deer after 1 cycle. c. 30, 24, 21.6, 8.4 d.