topic 6

Question 1

why do we need age structure models

Answer 1

geometric, exponential, and logistic models assume no (or stable) age structure 
Many pops are structured (age specific vital rates) and do not have stable age class distributions 
Structural models needed to make pop, projections

Question 2

age structure pop growth models - life cycle diagram

Answer 2

• Life cycle diagram - break down into age classes
§ Age specific survival: Px or Pi
Age specific birth rates (fertility or fecundity) Fx or Fi

Question 3

notation used in age life cycle vs life table

Answer 3

Different notation than that used in life tables
Age = x or i
Px=gx
Age-specific per capita survival rate (probability that an
individual of age x will survive to age X+1
Fx=bx)
Age-specific per capita birth rate (# offspring born per
individual of age x)

Question 4

practice predicting N in future

Answer 4

ok

Question 5

leslie matrices

Answer 5

Leslie matrices 
• Top row: age-specific fertility (Fx) 
• Sub-diagonal: age-specific survival (PX) 
• All other values = 0 
Always square, e.g., 
4 age classes = 4x4 
5 age classes = 5x5 
Number of rows and columns always based on age class numbers

Question 6

what info is contained in leslie matrix

Answer 6

age specific fertility + age specific survival 
F1 F2 F3 G4 
P1 0   0    0
 0  P2 0   0
0   0  P3  0

Question 7

leslie matrix - pop vector

Answer 7

Initial population vector
— Initial age structure in I-dimensional
column matrix (vector)
— E.g., # individuals in age class 1, 2, 3, & 4
in first time period (t)
multiply to find resultant fecotr

Question 8

time specific growth rate ( λt)

Answer 8

λt = Nt+1/Nt
subscript t = specific time period
Growth rate for time specific - ONLY for that time period

Question 9

asymptotic (geometric growth rate)

Answer 9

read thru lab

growth rate once pop has reached stable age distribution - will eventually occur if vital rates are constant

Question 10

stage structure - complication

Answer 10

• Vital rates might depend more on size or developmental stage (than age)
• Can adapt methods to handle stage - structured pops
Added complication: some individuals will remain in the same stage even after time has elapsed

Question 11

stage structure life cycle variables

Answer 11

PX = probability that an individual will survive & remain in same stage after
one time interval
Gx = probability that an individual will survive & move into next stage after
one time interval
Fx = fertility (same as age-based model)

Question 12

lefkovitch stage class pop matrix variables

Answer 12

PX = probability that an individual will survive & remain in the same stage in the next
time unit
Gx = probability Of surviving & moving on into the next stage after 1 time interal
Fx = age-specific fertility

Question 13

look at the matrix

Answer 13

ok