Organisms at different life stages can have vastly different
reproduction and mortality rates:
Juveniles: often high mortality
risk and no reproduction
Mature adults: often low mortality
until old age, with reproduction
Some juveniles have
low mortality.
Age of first reproduction:
Mouse:
Rabbit:
Elephant:
5 weeks
5 months
5 years
Arabidopsis: 5 weeks
Scarlet Oak: 20 years
Bamboo:
100 years
Maximal life span:
Shrews:
1.5 years
Human:
122 years
Giant Tortoise:
177 years
Redwood tree:
2200 years
Litter/brood size:
Albatross:
songbirds:
Pheasants:
1 egg
2-5 eggs
8-18 eggs
Human:
gophers:
Lion:
Wolf
Pig:
1
1
3-4
4-6
10
Sea slug:
Saguaro
Coconut:
up to 500,000 eggs
10,000s of seeds
100 seeds
Life cycle of a fir
Life cycles can be quite complex:
diapause, pupation
larvae,
3rd instar
pupae
emergence
Sexual
adult
2nd molt
oviposition
larvae,
2nd instar
hatching
egg
1st molt
larvae,
1st instar
Life Tables:
Organize all relevant information about birth and death rates
as a function of age;
Provide the data for answering questions, like:
• What is the average number of offspring that an
organism produces in its life time?
• What is the average generation time of a population?
• What is the growth rate of the entire population?
What is Life Table Analysis used for?
Population management:
1. If the goal is to destroy a population, which life history
stage should we target to get the most bang for the
buck?
2. If the goal is to conserve a population at risk, which life
history stage should get the most protection?
3. If the goal is sustainable harvest: which life history
stages should be exempted from being killed?
Life Tables represent “life histories”
Life history: the timing of life cycle events, particularly as
relating to growth, fertility and death.
Life tables contain two sorts of data:
Fecundity schedules:
The average reproductive output of individuals as a
function of the age of an individual.
Survivorship schedules:
The probabilities of surviving from birth to all ages.
Two types of fecundity schedules:
Semelparous (in animals) or monocarpic (in plants) reproduction:
when organisms reproduce only once in their lifetime.
Marine salmon
Century plant
Iteroparous (in animals) or polycarpic (in plants) reproduction:
when organisms reproduce more than once in their lifetime.
Elephant
Cherry tree
Three types of survivorship schedules:
In plants we distinguish: annuals, biennials, perennials.
A biennial: spinach
An annual: sunflower
A perennial: sequoia
Three types of survivorship curves:
Type I: mammals with much parental care in
a low risk environment.
ln Survivorship
Type II: (rare) Individuals of
all ages have the same
probability of dying.
Type III: Species with many,
small and vulnerable young.
Age
How does one collect age-specific
survivorship and fecundity information
that is representative of an entire population?
HORIZONTAL METHOD:
• follow the fate of a group of individuals all born at the same time
(= a cohort)
• record all births and deaths until the last individual died
• equivalent to “longitudinal studies” in medical research
• preferred method but difficult to conduct
VERTICAL METHOD:
• examine the age and birth rate of a representative, random sample
of the population at one point in time
• reconstruct age-specific mortalities from age distributions
• equivalent to “cross-sectional studies” in medical research
• preferred method but difficult to conduct
Example of horizontal study:
At t0 : 1000 eggs
1 year later:
10 mature frogs
1 week later:
400 small tadpoles
2 weeks later:
200 large tadpoles
6 months later:
50 mature frogs
4 weeks later:
100 immature frogs
Book keeping:
(assuming post-breeding census)
S(x): the number of survivors at the beginning of age x
S(0)
S(1)
S(2)
S(3)
S(4)
x=2
x=3
x=4
S(5) = 0
Life history
interval
Age (x) x=0
BIRTH
x=1
x=5
DEATH OF OLDEST
INDIVIDUAL
Book keeping:
(assuming post-breeding census)
b(x): offspring produced per female during the interval from
x to x+1 and still alive at the end of the interval.
b(0)
b(1)
b(2)
b(3)
b(4)
newborns
S(0)
S(1)
S(2)
S(3)
S(4)
x=2
x=3
x=4
S(5) = 0
Life history
interval
Age (x) x=0
x=1
x=5
Life Table:
x
S(x)
b(x)
0
1000
0
1
800
2
2
400
3
3
100
1
4
0
0
Life Table:
Step 1: Calculate survivorship at the beginning of each age:
l ( x) 
x
S(x)
b(x)
l(x)
0
1000
0
1
1
800
2
0.8
2
400
3
0.4
3
100
1
0.1
4
0
0
0
S ( x)
S (0)
Life Table:
Step 2: Calculate survivorship from one age class to the next:
g ( x) 
S ( x  1)
S ( x)
x
S(x)
b(x)
l(x)
g(x)
0
1000
0
1
0.8
1
800
2
0.8
0.5
2
400
3
0.4
0.25
3
100
1
0.1
0
4
0
0
0
Life Table:
Step 3: Calculate the net reproductive rate of an
individual over its lifetime:
R0  l ( x)b( x)
x
S(x)
b(x)
l(x)
g(x)
l(x)b(x)
0
1000
0
1
0.8
0
1
800
2
0.8
0.5
1.6
2
400
3
0.4
0.25
1.2
3
100
1
0.1
0
0.1
4
0
0
0
S= 2.9
R0 = 2.9
Definition of Reproductive Value:
The average contribution of an individual to the future
generation.
Partitioning overall population growth rates into
contributions made by members of specific age classes
is very useful for purposes of population genetics and
population management.
Life Table:
Step 3: Calculate the net reproductive rate of an
individual over its lifetime:
R0  l ( x)b( x)
x
S(x)
b(x)
l(x)
g(x)
l(x)b(x)
0
1000
0
1
0.8
0
1
800
2
0.8
0.5
1.6
2
400
3
0.4
0.25
1.2
3
100
1
0.1
0
0.1
4
0
0
0
S= 2.9
R0 = 2.9
Life Table:
Step 4: Calculate the generation time:
l ( x )b ( x ) x

G
 l ( x )b ( x )
l(x)b(x) l(x)b(x)x
x
S(x)
b(x)
l(x)
g(x)
0
1000
0
1
0.8
0
0
1
800
2
0.8
0.5
1.6
1.6
2
400
3
0.4
0.25
1.2
2.4
3
100
1
0.1
0
0.1
0.3
4
0
0
0
S= 2.9 S= 4.3
R0 = 2.9
G = 1.48 yrs
Definition of Generation Time:
The average age of breeding females (e.g. of newborn’s mothers)
It is the average length of time between successive
generations.
Life Table:
Step 5: Estimate the population growth rate:
ln( R0 )
r
G
l(x)b(x) l(x)b(x)x
x
S(x)
b(x)
l(x)
g(x)
0
1000
0
1
0.8
0
0
1
800
2
0.8
0.5
1.6
1.6
2
400
3
0.4
0.25
1.2
2.4
3
100
1
0.1
0
0.1
0.3
4
0
0
0
S= 2.9 S= 4.3
R0 = 2.9
G = 1.48 yrs
r = 0.72 yrs-1
Plug & Play
Excel Worksheets:
• A life table
Life Table Analysis makes many assumptions:
1. Mortality and fecundity depend only on the age of the
organism.
2. Age-specific mortality and fecundity are constant
through time.
3. To determine the population growth rate a very
specific age structure must be assumed: the stable
age distribution.
Definition of Age Structure:
The age structure of a population refers to the way a
population is divided among different age classes.
The age structure is often represented in an age structure
pyramid. is is often It is the average length of time between
successive generations.
Definition of Stable Age Structure:
It is a relative age distribution of a population that will not
change over time.
The growth rate of a population can be estimated by life table
analysis only if the population has a stable age structure.
Life Table for feral cats in San Marcos
age
1. Determine the population’s
r-value
Individuals
(years)
left in cohort
b(x)
0
1000
0
1
200
3
2
150
6
3
120
6
4
70
4
5
50
2
6
0
0
l(x)
l(x)b(x)
l(x)b(x)x
2. Assume that a spay/neuter
program prevents 50% of
cat pregnancies. What
would the r be?
3. What is the likely long-term
consequence of the
spay/neuter program?
Summary:
1. Life tables organize information about fecundity and mortality
schedules for populations. They usually only track females.
2. There are mathematical fomulae that one can use to calculate,
based on life tables,




stable age distributions of populations
population growth rates
the average generation times
the reproductive values of females of a certain age.
3. This analysis has application in virtually any task of population
control, including the protection of endangered species or the
control of invasive species, and is basic to understand the
evolution of life history strategies.