1) Demography is the statistical study of factors that
affect population growth.
2) Life tables show how survival and reproduction vary with
age, size, or life cycle stage.
3) Life tables can be used to project the future structure, size,
and growth rate of a population.
4) All population models make assumptions.
Summarizes how survival and reproduction vary with the age
(or size or stage) of the organism.
A useful tool for organizing demographic information.
Cohort Life Table
Static Life Table
Fate of a group of individuals (cohort)
is followed from birth to death.
Determine survival and reproduction for a
group of individuals that vary in age.
Easiest for sessile organisms
(plants, inverts) that can be marked.
Must be able to estimate age
(or size, stage)
Difficult for long-lived organisms.
Assumes that cohort is typical;
although you can follow several
Assumes that age-specific survival and
fecundity rates have been constant
through time.
Simplest to use data on females only.
TypeI?
Specieswithparentalcare
(large)mammals,includinghumans
TypeII?
Somebirds,fish,turtles(rare)
TypeIII?
Invertebrates,plants,fungi
Age
Years
x N(x)
m(x)
l(x) =N(x)/N(0) l(x)m(x) l(x)m(x)x
0
500
0
1.0
0.0
1
400
2
0.8
1.6
2
200
3
0.4
1.2
3
50
1
0.1
0.1
4
0
0
0.0
0.0
l(x)m(x) = probability of survival from birth up to age(x) multiplied
by the average number of offspring per female of age(x).
Gives the average number of female offspring produced per female
discounted by the probability that a female survives to that age.
Age
Years
x N(x)
m(x)
l(x) =N(x)/N(0) l(x)m(x) l(x)m(x)x
0
500
0
1.0
0.0
1
400
2
0.8
1.6
2
200
3
0.4
1.2
3
50
1
0.1
0.1
4
0
0
0.0
0.0
R0 = 2.9
R0 = mean number of female offspring produced
per female over her lifetime.
Age
Years
x N(x)
m(x)
l(x) =N(x)/N(0) l(x)m(x) l(x)m(x)x
0
500
0
1.0
0.0
0.0
1
400
2
0.8
1.6
1.6
2
200
3
0.4
1.2
2.4
3
50
1
0.1
0.1
0.3
4
0
0
0.0
0.0
0.0
R0 = 2.9
4.3
G = 4.3 / 2.9 = 1.5 (years)
G = average age of the parents of all the offspring produced
by a single cohort (units = time).
If the proportion of females in each age class is stable over time:
λ ≈ R0 / G
λ =er or r=ln(λ)
r ≈ ln (R0 / G)
So In Our Cohort Life Table Example
Ro = 2.9
G = 1.5
λ = 2.9 / 1.5 = 1.93
Population is increasing by 93% each year!
MeasuringPopulationSize&Density
Mobile
Sessile
Wildebeast: Serengeti
(Kenya & Tanzania)
Sessile Marine Invertebrates:
Washington, USA
MeasuringPopulationSize&Density:Mobile
Lincoln–Peterson Method
N0 = (M X C) / R
N0 = population size estimate
M = Number of animals marked
C = Total number of animals captured
R = Number of animals recaptured with mark
Population size (N0) is equal to the number of
animals marked divided by the estimate of the
proportion that are marked.