Life tables Were first used to estimate insurance risk in human populations –Divides the...

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