Quiz 10, last of the class :’(

Please place your name(s) in the upper-right corner.

1. What is a population projection matrix?
   A. A matrix of population sizes at \(N_t\).
   B. A matrix of population sizes at \(N_{t+1}\).
   C. A matrix with population sizes for each age class from \(t = 0\) to \(t = T\), given \(T\) is the amount of steps for which the population sizes are projected.
   D. A matrix with fecundities and probabilities of survival for each age class.
   E. A dystopian future in which humanity is unknowingly trapped inside a simulated reality.

2. For the given population projection matrix \[\begin{gather}\begin{bmatrix} x_0(t+1) \\ x_1(t+1) \end{bmatrix} = \begin{bmatrix} 0 & f_1 \\ p_{10} & 0 \end{bmatrix}\begin{bmatrix} x_0(t) \\ x_1(t) \end{bmatrix}\end{gather}\] please define each element in each vector and matrix (including the zeros).
   
   
   
   
   
   
   
   
   
   

3. For the same population projection matrix above, if \(f_1 = 2\), \(p_{10} = 0.5\), \(x_0(0) = 20\), and \(x_1 = 15\), what would be the total population size at the next time step, \(t+1\)?
   
   
   
   
   
   
   
   
   

4. How about at the following time step, \(t+2\)?

5. Please write out two population projection matrices for an age-structured population: one for a species with 3 age classes and one for a species with 9 age classes.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

6. Please write out a population projection matrix with \(n\) rows and columns for a size-structured population assuming that all size classes could move from one to another.