Life Tables
Grasshopper life table: (page 114 Bush)
A
B
Life
stage
Number at
start (n x)
Egg
Inst. 1
Inst. 2
Inst. 3
Inst. 4
Adult
44000
3513
2529
1922
1461
1300
C
D
E
F
G
Proportion dying
in stage (d x)
Mortality rate
in stage (q x)
Proportion alive
in stage (L x)
Life expectancy
(Ex)
0.057
0.044
0.033
0.030
0.014
0.010
0.004
0.030
0.240
0.240
0.110
0.051
0.038
0.031
2.352
1.937
1.390
0
0
Proportion
surviving at start
(lx)
Eggs produced
Column A: Age stages
Column B: Actual number alive at the beginning of each stage (nx)
Column C: Proportion of the initial number that is still alive at the beginning of the stage (lx)
= 1.0 for the first interval, otherwise = nx/n0
Column D: Proportion that die during the stage (dx)
= lx – lx+1 for stage
Column E: Rate of mortality during the stage (qx)
= proportion dying/proportion alive at beginning
= dx/lx
Column F: Average proportion alive during stage (Lx)
= (lx + lx+1)/2
Column G: Life expectancy for individuals in that stage (Ex)
= sum (Lx:Ln) /lx
Questions:
1.
When is the mortality rate highest?
2.
Why is mortality rate = 1 for adults?
3.
What does a life expectancy of 2.553 mean, in words?
4.
Why is the life expectancy for adults (the last life stage) 0.5?
5.
How can we estimate the fitness of the population?
6.
Why are the stages chosen in 5 groups?
22617
Incorporating age specific birth rate
Example: Consider a plant population whose members live up to 3 years of age. Each year, 3/4 of the
population dies. Those who live to be 1 year old produce only 2 viable seeds between the ages of 1 and 2.
Those who live to be 2 years of age produce 10 viable seeds.
Age stage
Age (x)
Proportion
units= years surviving at
start (l x)
0-1
0
1-2
1
2-3
2
3-4
3
Birth rate (b x)
units= indv/indv
Birth rate in stageaccounting for
mortality (l xbx)
Ro =
Age*previous column
(x l x bx)
Life
expectancy
(Ex)
offspring/plant
G=
years
bx = fecundity schedule = average number of offspring/parent within a particular age class
R0 = net reproductive rate = reproductive potential of an individual during its entire lifetime, adjusted for
mortality. (average fitness)
k
R0   l x bx
x 0
G = generation time = average age of the parents of all the offspring produced by a single cohort.
k
G
l b x
x 0
x x
R0
r = intrinsic growth rate: the finite rate of increase of a population (increases as a function of absolute time)
r
ln( R0 )
G
Population Trajectory: If we start with 100 seeds, how will the population change through time?
Generation
1
2
3
4
5
6
7
8
9
10
[0 to 1)
100
0
50
62.50
25.00
62.50
51.56
46.88
64.84
55.66
[1 to 2)
0
25
0
12.50
15.63
6.25
15.63
12.89
11.72
16.21
[2 to 3)
0
0
6.25
0.00
3.13
3.91
1.56
3.91
3.22
2.93
[3 to 4]
0
0
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
….need to carry out further…..then plot Total Population vs. Time
total
100
25
56.25
75.00
43.75
72.66
68.75
63.67
79.79
74.80