Life tables
• Were first used to estimate insurance risk in human populations– Divides the population into age specific
classes– Estimates the age-specific mortality risk in
each class
A life table for a town in the East Midlands
age pop death % death 1 death in
<1 2533 20 0.789578 127
1-4 11130 1 0.008985 11130
5-9 15519 2 0.012887 7760
10-14 16409 4 0.024377 4102
15-19 16133 9 0.055786 1793
20-24 21482 10 0.046551 2148
25-29 15997 22 0.137526 727
30-34 16026 35 0.218395 458
35-39 19800 34 0.171717 582
40-44 16076 39 0.242598 412
45-49 13404 59 0.440167 227
50-54 13027 108 0.829047 121
55-59 10051 136 1.353099 74
60-64 10220 176 1.722114 58
65-69 9190 320 3.482046 29
70-74 7427 445 5.991652 17
75-79 5231 414 7.914357 13
80-85 2884 355 12.30929 8
85+ 1840 347 18.8587 5
Assembling a life table
• Cohort or Dynamic life table• Assembled by following the fate of a cohort from
birth to death.
• Static life table• Assembled estimating the age specific death risks
from the age structure at a given time
age 1999 2000 2001 2002 survivorship lx
0 1000 1.00
1 400 0.40
2 100 0.10
3 20 0.02
estimated
age 1999 survivorship lx
0 1000 1.00
1 400 0.40
2 100 0.10
3 20 0.02
Dynamic life table
Static life table
estimated
age 1999original
population survivorship lx survivorship
0 1000 1000 1.00 1
1 400 1200 0.40 0.33
2 100 1400 0.10 0.07
3 20 1600 0.02 0.13
estimated
age 1999 survivorship lx
0 1000 1.00
1 400 0.40
2 100 0.10
3 20 0.02
However a static life table assumes the population is stable which is usually not true
Original estimates
But what if the population is decreasing?
Decreasing population
estimated
age 1999original
population survivorship lx survivorship
0 1000 1000 1.00 1
1 400 900 0.40 0.44
2 100 800 0.10 0.13
3 20 600 0.02 0.03
Population increasing
Phlox drummondii (annual phlox) is native to central and eastern Texas. It is a winter annual and grows abundantly in sandy fields and on roadside verges. It germinates in response to cool rainy weather.
qx=lx-lx+1
the proportion of individuals that have died over a time period =
the mortality rate.
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 50 100 150 200 250 300 350 400
time days
Average mortality rate per day
0.0001
0.001
0.01
0.1
1
0 50 100 150 200 250 300 350 400
time days
Average mortality rate per dayLog scale
Mortality analysis
Where bx seed=number of seed per plant (Bx/Nx)
0
1
2
3
4
5
6
7
8
9
10
290 300 310 320 330 340 350 360 370
Fecundity analysis
time days
Number of seed produced per plant
Diagrammatic dynamic life table for Phlox drummondii
Rectangles=stages in the life-cycle
Inverted triangles= transition probabilities
Diamond=seed production
A more complex diagrammatic life table of the biennial ragwort Senecio jacobea
Biennial lives for 2 years reproducing at the end of the second year
immigration
Seed bank dynamics
Dispersal
germination
establishment
Survivorship curves
Type I = Found where there are ample resources e.g. human population in developed countries
Type II = A constant risk of death throughout lifespan e.g. seeds in a buried seedbank
Type III = High early mortality e.g. many plants reproducing by seed
0
0.2
0.4
0.6
0.8
1
0 100 200 300 400
Survivorship curve for Phlox drummondii
Survivorship curves of Erophila verna at different densities
a=1-2
b=5-10
c=15-20
d=35-50
e=>50
1000s m-2
Survivorship curves for a species depend on a range of conditions
juveniles
immature
vegetative
generative
dead
In plants stage of development can be a more useful definition of progress than age. Data are for a perennial Ranunculus acris