Matrix, Life tables

Question 1

Why are life tables used?

Answer 1

Provides information for calculating survivorship curves and expectation of future life

b. When combined with age-specific fecundity then can:
i. Estimate the lifetime production of female offspring/female
ii. Either a direct or indirect estimate of population change
c. Age vs stage?
d. Generation length (discrete vs. overlapping generations)

Question 2

Nx

Answer 2

Number recorded alive

Question 3

lx

Answer 3

proportion of original individuals surviving to beginning of age class X.

Generally multiplied by 1000 to standardize.
Used to compare population ages

lx=(Nx/No)

Question 4

bx

Answer 4

age- specific fertility for females

Question 5

dx

Answer 5

number of individauls in age class dying during the age class
dx=lx-lx+1

Question 6

qx

Answer 6

force of mortality; age or stage specific mortality

qx=dx/lx

Question 7

kx

Answer 7

killing power

log10(Nx)-log10(Nx+1)

Question 8

Lx

Answer 8

number of individuals alive midway between two time periods

Lx=(lx+lx+1)/2

Question 9

Tx

Answer 9

cumulative sum of years lived by the cohort

∑Lx (done from bottom and work up)

Question 10

ex

Answer 10

expectation of future life

ex=Tx/lx

Question 11

Lxbx

Answer 11

contribution of offspring by each age class

Question 12

Ro

Answer 12

net reproductive rate (basic reproductive rate)

∑lxbx

Question 13

Ro - what type of generations?

Answer 13

Discrete generations: # females offspring/female life & multiplication rate/ generation

Only works well with non-overlapping generations

Question 14

Ro=1

Answer 14

then birth rates and death rates are equal

Question 15

High Ro means?

Answer 15

High reproductive capacity

- is found in small body organisms with high number of offspring

Question 16

Types of life tables

Answer 16

1. Cohort
2. time-specific
3. combined

Question 17

Cohort life table

Answer 17

i. Follow entire life (birth to death)

ii. Conditions of a specific group

Question 18

Time-specific

Answer 18

i. Sampled at a specific point in time (slice through time method)
ii. Age structure used to assess (lx and bx)

Question 19

Combined life table

Answer 19

i. Most common, takes benefits from both the cohort and the time specific

Question 20

Reproductive value (Vx) 
equation

Answer 20

Vx=bx+∑t=x+1((ltbt)/lx)

calculated by finding the left eignvector (v)

Question 21

Reproductive value (Vx) 
depends on:

Answer 21

i. Surviving to reproductive age
ii. Reproduction in current age
iii. All future reproduction in current age.
iv. All future reproduction, discounted by the probability of surviving to that age

Question 22

Stable age distribution

Answer 22

constant lx and bx and r>0

Question 23

Stationary age distribution

Answer 23

constant lx and bx by r=0

Question 24

Fitness

Answer 24

how many offsprings an individual has over a life time

Fails to account for years of reproduction, and age of 1st reproduction

Question 25

Goal of Leslie matrix?

Answer 25

calculate lambda

Question 26

Px (Leslie matrix)

Answer 26

Proportion of individuals that survive from one age class to the next
Px=lx+1/lx

Question 27

Fx (Leslie matrix - Post breeding)

Answer 27

Fx= Px*bx+1birth bulse , is included as a seperate class

Question 28

Fx (Leslie matrix - Pre breeding)

Answer 28

Fx=(po)(bx)

Question 29

Lefkovich Matrixdifferences from leslie matrix

Answer 29

• Described by classification other than age Individuals can stay within existing stage, transition forward or backward.
• Transitions can go in multiple direction
• See Px
• λ Is still calculated, but with Stable Stage Disturibution (SSD) attained.

Question 30

Px (Lefkovich matrix)

Answer 30

probability that an individual will survive and remain in the SAME stage or size class (differs from leslie)found on the middle diagonal

Question 31

Gx or Fx (Lefkovich)

Answer 31

probability that an individual will survive and move up to the next stage or size class in the next time unit

Question 32

Mortality (Lefkovich)

Answer 32

Mortality= 1- (Pi,j)-(Pi,i)-Pj,i 
Pi,j= Probability of transitioning to the next age/stage class
Pi,i= probability of remaining within the same age/stage class
Pj,i = probability of regressing to previous age/stage class.

Question 33

reproductive value is…

Answer 33

the weighted average of present and future generations