- Constructing A Stage Matrix Model For An Animal Species That Has Three Life Stages Juvenile Up To 1 Year Old Subadul 1 (153.75 KiB) Viewed 10 times
hello can someone please solve these questions step by step. thank you for your time and efforts!
Constructing a stage-matrix model for an animal species that has three life stages: juvenile (up to 1 year old), subadults and adult, like the dotted owls. Suppose the female adults give birth each year to an average of 12/11 female juveniles. Each year, -% 18% of the juveniles survive to become subadults, among the survived subadults % 91% stay 200 11 1000 11 400 subadults and % 36% become adults. Each year, 11 1000 = 11 %90% of the adults survive. For k ≥ 0, let Xk (jk, Sk, ak), where the entries in X are the numbers of female juveniles, female subadults, and female adults in year k. The stage-matrix A such that Xk+1 = A Xk for k ≥ 0 is 61 0 [0 2 A== 1 5 0 LO 2 51 11 As the largest eigenvalue of the stage-matrix A is more than one, the population of juvenile is growing. a. Compute the eventual growth rate of the population based on the determinant of A. [2 marks] b. Suppose that initially there are 6501 juveniles, 230 subadults and 2573 adults in the population. Write Xo [6501 230 2573] as a linear combination of v₁, v₂ and v3. That is solve the below linear system to obtain C₁, C₂ and C3, = [6501] 230 = C₁v₁ + C₂V₂ + C3V3. L2573] [3 marks] c. Calculate the population of juveniles, subadults and adults after 10 years. [3 marks] d. Deduce the number of total population and the ratio of juveniles to adults after 10 years. [2 marks]