Question

Giant pandas are a vulnerable species famous for their consumption of large amounts of bamboo. Write a discrete-time matrix model of a giant panda population using the following assumptions. We are modeling only the female population. – Pandas have three life stages: cubs, subadults, and reproductively mature adults. – Cubs remain cubs for only one year. They have a mortality rate of 17%. – Pandas remain subadults for three years. Thus, about 33% of subadults mature into adults each year. – 28% of subadults die each year. – On average, adults give birth to 0.5 female cubs each year. – 97.7% of adults survive from one year to the next.

Answer 1

Our Model will be:

`\left[\begin{array}{ccc}C+1\\S+1\\A+1\end{array}\right] =\left[\begin{array}{ccc}0&0&0.5\\0.83&0.39&0\\0&0.33&0.977\end{array}\right] *\left[\begin{array}{ccc}C\\S\\A\end{array}\right]`

Explanation:

As we know while making a discrete time matrix model we look at how much of a state contributes to the next state thus let following be the variables which shows the present state and the next state:

Pandas have three life stages: cubs, sub adults, and re-productively mature adults So,

C = Cubs

S = Sub Adults

A = Mature Adults

Now,

Next Level Contribution of C Contribution of S Contribution of A

C+1 0 (since cubs only 0 (Since no sub 0.5 (Since adults give

remain cubs for a adults will become birth to 0.5 females

year.) cubs next year.) each year.)

S+1 0.83 (since all cubs 0.39 (Those who 0 (Since no adults

will become sub-adults remain sub-adults will become

accept those who die. after those who sub-adults next

`1-0.17=0.83` ) matured or died. year.)

`1-0.33-0.28=0.39`)

A+1 0 (Since no cubs 0.33 (Since about 33% 0.977 (Since 97.7%

will become adults of sub adults mature of adults will survive

next year. into adults each year.) through next year.)

Thus, The model becomes:

`\left[\begin{array}{ccc}C+1\\S+1\\A+1\end{array}\right] =\left[\begin{array}{ccc}0&0&0.5\\0.83&0.39&0\\0&0.33&0.977\end{array}\right] *\left[\begin{array}{ccc}C\\S\\A\end{array}\right]`