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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
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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
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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
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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
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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
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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
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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.
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qx=lx-lx+1
the proportion of individuals that have died over a time period =
the mortality rate.
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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
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Where bx seed=number of seed per plant (Bx/Nx)
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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
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Diagrammatic dynamic life table for Phlox drummondii
Rectangles=stages in the life-cycle
Inverted triangles= transition probabilities
Diamond=seed production
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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
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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
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0
0.2
0.4
0.6
0.8
1
0 100 200 300 400
Survivorship curve for Phlox drummondii
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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
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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