Life Tables. Grizzly Bears ( Ursus arctos horribilis)

Life Tables

Grizzly Bears (Ursus arctos horribilis)

– Yellowstone grizzly population was declining

– Age-structured models

– survival of mothers was most important to the population

– Legislation resulting from his findings got tourists out of areas with mothers and cubs

– Yellowstone grizzlies began to recover

Grizzly Bears (Ursus arctos horribilis)

Population structure• Sex (gender)• Age• Size (better for plants)• Birth, death and movement rates vary in different sex, age, or size categories.

Human age and sex structure

Baby boom and social security

Structured data• Known (or marked)

individuals

• Carcasses

• Age structure (how many of what age)

• Sex ratio (how many of what sex)

Life tablesCohort (dynamic): follow all

individuals born in one time interval (e.g. year) until they die

Cross-sectional (static): take a snap-shot of the current age-structure

Composite: data taken from multiple years

Notationx = age of the individual

nx = number of individuals of age x

lx = number (or %) of individuals alive at age x

mx = fecundity rate

average # of female offspring produced per female per time period

--------------------------------------------------------------------------------------------------

px = survival rate

probability of surviving from age x to x+1

qx = mortality rate

probability of dying between age x and x+1

Aphids Aphidoidea Age, days Number of survivals Mean offspring per parent

0 1000 01 900 02 820 03 750 04 680 05 620 06 550 17 500 28 450 59 400 10

10 350 1211 300 1012 250 813 200 614 100 315 50 116 0 0

Excel data sheet – start with 1000

Cohort study

Survival – px

px – the probability of surviving from x to x+1

px = Nx+1/Nx

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

Age (days)

Px

Survivorship, lx

lx – survival to age x - survivorship lx = Nx/N0

Three types of survivorship curves – plotted on a semi-log plot

Survivorship of Aphids

0.01

0.1

1

0 5 10 15 20

Age (days)

log l

x

Looks like Type I – lab conditions

Survivorship, lx

lx – survival to age x - survivorship

N0= 1000

lx = Nx/N0

Survivorship of Aphids

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12 14 16

Age (days)

lx

Fecundity table (mx)Usually recorded as # of females

produced per female of age x

Can be interpreted as the probability that a female of age x will give birth to a daughter during that time interval

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Age (days)

mx

Aphids

R0: the mean number of female offspring produced by a female during her lifetime.

R0 < 1 population is decliningR0 > 1 increasing populationR0 = 1 indicates a stationary population

If lx is a proportion:

Net reproductive number

xxmlR0

Generation Time, TT – average generation time, is the average age a female gives birth to one offspring

0

0R

mxlT

n

x

x x

T=183.85/18.55 = 9.11

An average female Aphid gives birth to one offspring at 9.11 days

Net Reproductive Number or

Note that does not equal R0

is a rate per time step = N t+1/Nt

R0 is a rate per lifetime/generation.

xxmlR0

Age (x) lx mx

0.00 1.00 0.00 1.00 0.85 0.05

2.00 0.82 0.39

3.00 0.80 0.47

4.00 0.76 0.48

5.00 0.70 0.55

6.00 0.63 0.54

7.00 0.53 0.50

8.00 0.42 0.47

9.00 0.29 0.46

10.00 0.16 0.43

11.00 0.06 0.42

Domestic Sheep (Ovis aries)

0.00

0.20

0.40

0.60

0.80

1.00

1 2 3 4 5 6 7 8 9 10 11 12

Age Class (years)

mx

0.00

0.20

0.40

0.60

0.80

1.00

1 2 3 4 5 6 7 8 9 10 11 12Age Class (years)

lx

Caughley, 1967

Node-arc notation

0 1 2

3 ages or stagesAges – small bird

reproduces in its second year

Xantus' Murrelet Synthliboramphus hypoleucus

Node-arc notation3 ages or stagesStages – plant which can hang out in a vegetative state or progress to a reproductive state

0 1 2

Prickly lettuce Lactuca serriola

Why is age-structure useful?• Life-expectancy calculations

– Life insurance companies like it– Planning for future funds (politics)

• Harvesting – When are fish going to be big enough

to eat?– What is the population turnover?

• Conservation/Control issues– Which age is most susceptible to

mortality– If females aren’t surviving to

reproduce, then no point in saving the babies

Turtle Excluding Devices (TEDs)

• The loggerhead turtle (Caretta caretta)

– Very high egg loss due to beaches being developed, eggs poached

– Also very high early juvenile loss due to predation – as they disperse into the ocean

• Turtle conservation in the 1980s focused on protecting eggs and beaches

Turtle Excluding Devices (TEDs)1987 – Crouse et al. - programs

focusing on preserving turtle eggs may be least effective; late juvenile/ early adult survival is more important• Often caught in fish nets – huge source

of mortality

• Create TEDs to prevent turtles and other large by-catch species drowning

• 1997 – Grand and Beissinger – move the eggs and the picture changes – we must protect eggs on beaches AND use TEDs

TEDs used in Australia

The end