Suppose the population of a particular endangered bird changes on a yearly basis asa discrete dynamic system. Suppose that initially there are 60 juvenile chicks and 3060breeding adults, that is xo =[800]Suppose also that the yearly transition matrix is30[0 1.25]A=where s is the proportion of chicks that survive to become adults (note9S0.5that 0≤ s≤ 1 must be true because of what this number represents).(a) Which entry in the transition matrix gives the annual birthrate of chicks per adult?(b) Scientists are concerned that the species may become extinct. Explain why if 0 ≤s < 0.4 the species will become extinct.(c) If s = 0.4, the population will stabilise at a fixed size in the long term. What willthis size be?

Given: Initial counting: x0=6030 Yearly transition matrix: A=01.25s0.5 As 0≤s≤1 To find: Which…

Suppose the population of a particular endangered bird changes on a yearly basis as a discrete dynamic system. Suppose that initially there are 60 juvenile chicks and 30 [60 breeding adults, that is xo Suppose also that the yearly transition matrix is . 30] = [0 1.25] S 0.5' where s is the proportion of chicks that survive to become adults (note that 0 ≤ s ≤ 1 must be true because of what this number represents). (a) Which entry in the transition matrix gives the annual birthrate of chicks per adult? (b) Scientists are concerned that the species may become extinct. Explain why if 0 ≤ s < 0.4 the species will become extinct. (c) If s = 0.4, the population will stabilise at a fixed size in the long term. What will this size be?

Suppose the population of a particular endangered bird changes on a yearly basis as a discrete dynamic system. Suppose that initially there are 60 juvenile chicks and 30 [60 breeding adults, that is xo Suppose also that the yearly transition matrix is . 30] = [0 1.25] S 0.5' where s is the proportion of chicks that survive to become adults (note that 0 ≤ s ≤ 1 must be true because of what this number represents). (a) Which entry in the transition matrix gives the annual birthrate of chicks per adult? (b) Scientists are concerned that the species may become extinct. Explain why if 0 ≤ s < 0.4 the species will become extinct. (c) If s = 0.4, the population will stabilise at a fixed size in the long term. What will this size be?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 14EQ

See similar textbooks