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Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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Life Tables
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Page 1: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

Life Tables

Page 2: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

Grizzly Bears (Ursus arctos horribilis)

Page 3: 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)

Page 4: Life Tables. Grizzly Bears ( Ursus arctos horribilis)
Page 5: Life Tables. 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.

Page 6: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

Human age and sex structure

Page 7: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

Baby boom and social security

Page 8: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

Structured data• Known (or marked)

individuals

• Carcasses

• Age structure (how many of what age)

• Sex ratio (how many of what sex)

Page 9: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 10: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 11: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 12: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 13: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 14: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 15: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 16: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 17: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 18: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 19: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 20: Life Tables. Grizzly Bears ( Ursus arctos horribilis)
Page 21: Life Tables. Grizzly Bears ( Ursus arctos horribilis)
Page 22: Life Tables. Grizzly Bears ( Ursus arctos horribilis)
Page 23: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

Node-arc notation

0 1 2

3 ages or stagesAges – small bird

reproduces in its second year

Xantus' Murrelet Synthliboramphus hypoleucus

Page 24: Life Tables. Grizzly Bears ( Ursus arctos horribilis)
Page 25: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 26: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 27: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 28: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

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

Page 29: Life Tables. Grizzly Bears ( Ursus arctos horribilis)
Page 30: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

TEDs used in Australia

Page 31: Life Tables. Grizzly Bears ( Ursus arctos horribilis)

The end


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