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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