Matrix, Life tables Flashcards
Why are life tables used?
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)
Nx
Number recorded alive
lx
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)
bx
age- specific fertility for females
dx
number of individauls in age class dying during the age class dx=lx-lx+1
qx
force of mortality; age or stage specific mortality
qx=dx/lx
kx
killing power
log10(Nx)-log10(Nx+1)
Lx
number of individuals alive midway between two time periods
Lx=(lx+lx+1)/2
Tx
cumulative sum of years lived by the cohort
∑Lx (done from bottom and work up)
ex
expectation of future life
ex=Tx/lx
Lxbx
contribution of offspring by each age class
Ro
net reproductive rate (basic reproductive rate)
∑lxbx
Ro - what type of generations?
Discrete generations: # females offspring/female life & multiplication rate/ generation
Only works well with non-overlapping generations
Ro=1
then birth rates and death rates are equal
High Ro means?
High reproductive capacity
- is found in small body organisms with high number of offspring
Types of life tables
- Cohort
- time-specific
- combined
Cohort life table
i. Follow entire life (birth to death)
ii. Conditions of a specific group
Time-specific
i. Sampled at a specific point in time (slice through time method)
ii. Age structure used to assess (lx and bx)
Combined life table
i. Most common, takes benefits from both the cohort and the time specific
Reproductive value (Vx) equation
Vx=bx+∑t=x+1((ltbt)/lx)
calculated by finding the left eignvector (v)
Reproductive value (Vx) depends on:
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
Stable age distribution
constant lx and bx and r>0
Stationary age distribution
constant lx and bx by r=0
Fitness
how many offsprings an individual has over a life time
Fails to account for years of reproduction, and age of 1st reproduction
Goal of Leslie matrix?
calculate lambda
Px (Leslie matrix)
Proportion of individuals that survive from one age class to the next Px=lx+1/lx
Fx (Leslie matrix - Post breeding)
Fx= Px*bx+1birth bulse , is included as a seperate class
Fx (Leslie matrix - Pre breeding)
Fx=(po)(bx)
Lefkovich Matrixdifferences from leslie matrix
- 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.
Px (Lefkovich matrix)
probability that an individual will survive and remain in the SAME stage or size class (differs from leslie)found on the middle diagonal
Gx or Fx (Lefkovich)
probability that an individual will survive and move up to the next stage or size class in the next time unit
Mortality (Lefkovich)
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.
reproductive value is…
the weighted average of present and future generations
