Population ecology readings:
Ch 9 – population structure
Ch 10 – Life Tables, pp. 239-249
Ch 11- Exponential and Logistic Growth
DEF: Populations are individuals of the same species that
live together in time and space
POPULATION ECOLOGY
Why here and why now?
(1) Populations have emergent structures….
- Wolf packs; cooperative hunting, deferred reproduction
individuals
Are born and die
Disperse
populations
birth rates and mortality rates
immigration and emigration rates
Extinction
population structures (e.g., clumping)
Evolve
POPULATION ECOLOGY
Why here and why now?
(2) Many important processes related to, in particular, mortality
and reproduction are Density Dependent as opposed to being
Density Independent.
Abiotic forces are density independent:
Are these statements
always true?
- Fire kills irrespective of the number of trees
- Saguaros: Frost kills irrespective of the number of cacti
- Cold weather kills irrespective of the number of squirrels
Biotic forces are density dependent:
- Competition: your food availability depends on how many mouths there are
- Predation: predators seek food patches containing many prey
- Escaping predation depends on group defense
- Mutualisms: seed production depends on the number of pollinators
Hence, we want to characterize the number of individuals
Populations:
Abundance
( # individuals)
Survival of indivs:
Reproduction of indivs:
}
or
Density
(# individuals/area)
Project abundance/density
into the future  Growth Rate
Building Life Tables:
(1) Follow a population (or given group of indivs – a cohort)
from birth to death
(2) Follow a population of known-age indivs for a shorter period
of time and record deaths and births as a function of age
Terms:
X = Age (days, weeks, years) of individuals
NX = Number of individuals alive at the start of age X
lX = Proportion of the initial population that is alive at the
BEGINNING of age X. ****l0 = 1.0
mX = The number of daughters born to an average female
during the interval X to X+1.
Because only females contribute to population growth,
life tables only track female individuals
Age
#
X
0
1
2
3
4
NX
100
50
25
12
0
survivor maternity
lX
1.0
0.5
0.25
0.12
0
mX
0
1
3
2
0
What do we have?
(1) Maximum lifespan is 4 years
Age
#
survivor maternity
X
0
1
2
3
4
NX
100
50
25
12
0
lX
1.0
0.5
0.25
0.12
0
mX
0
1
3
2
0
(2) We can plot the natural logarithm of NX (or lX) versus age
to examine survivorship: (book plots Nx on a Log scale)
 Population experiences constant
survivorship with age: ~ ½ the
population dies at each interval
ln(NX)
age X
This is in contrast with populations that senesce:
E.g., Humans,
whales
ln(NX)
age X
or, experience greatest mortality early in life
E.g., Most insects,
many plants
ln(NX)
age X
Age
#
X
0
1
2
3
4
NX
100
50
25
12
0
survivor maternity
lX
1.0
0.5
0.25
0.12
0
mX
0
1
3
2
0
(3) Reproductive effort (per individual) is greatest at midlife
But even better, we can calculate a population growth rate
and determine whether the population is increasing or declining
Age
#
X
0
1
2
3
4
NX
100
50
25
12
0
survivor maternity
lX
1.0
0.5
0.25
0.12
0
mX
0
1
3
2
0
lXmX
0
0.5
0.75
0.24
0
lXmX = the number of daughters each initial female can expect
to give birth to during the interval X to X+1.
Age
#
X
0
1
2
3
4
NX
100
50
25
12
0
survivor maternity
lX
1.0
0.5
0.25
0.12
0
mX
0
1
3
2
0
lXmX
0
0.5
0.75
0.24
0
The difference between lXmX and mX is the former accounts
for mortality. E.g., m2 = 3 and L3m3 = 0.75.
0.75 < 3 because 75% of females die before the age of 2
lXmX
0
0.5
0.75
0.24
0
Expected # daughters between ages 0 – 1
Expected # daughters between ages 1 – 2
Expected # daughters between ages 2 – 3
Expected # daughters between ages 3 - 4
If we add all these up, we get the expected number of
daughters over a females lifetime
That sounds Useful !!!
And IT IS
The sum of lXmX is called the Net Reproductive Rate, R0
R0 =  (lXmX) is the expected number of daughters born to
each female during her lifetime.
It is true that many females do not reproduce, those that do have
many daughters in their lifetime – what we are examining is
the reproductive output of the average female.
Given that each female dies in her lifetime (-1 female) if
R0 = 1 daughter, then she exactly replaces herself in her lifetime
Has the population therefore grown or declined??
If R0 = 1 the population is neither growing or declining,
rather population size is stable.
If, however, R0 > 1 the population is growing
And, if R0 < 1 the population is declining
R0 = 1.25 = 25% population increase/generation **
R0 = 0.67 = 33% population decrease/generation **
** True in special circumstances (e.g., annual plants)
Why are Life Tables Useful??
We can tell at a glance: (1) patterns of survivorship,
(2) at what age reproductive potential is “stored”,
(3) The direction and magnitude of population change
Furthermore, we can understand the effects of changes in
age-specific death or maternity whether by accidental or
by design.
Peter and Rosemary
Grant’s study of
Darwin’s Finches
Life Tables – the COHORT approach
The
STATIC
approach
Percentage of finches
See Fig. 10.19
in your text
50 1983
Bottom-heavy
Increasing
populations
drought
1977
25
0
1 2 3 4 5 6 7 8 9 10 11
50 1987
La Niña
25
0
Top-heavy
declining
populations
droughts
1 2 3 4 5 6 7 8 9 10 11
Age in years
X
0
1
2
3
4
5
6
NX
100
50
25
13
6
3
0
lX
1.0
0.5
0.25
0.13
0.06
0.03
0
mX
Constant mortality
0
rate with age and
1.0
reproductive
3.0
senescence
1.0
0.5
0
0 R0 = 1.41
-------------------------------------------------------X
0
1
2
3
4
5
6
NX
100
50
10
5
3
1
0
lX
1.0
0.5
0.1
0.05
0.03
0.01
0
mX
0
1.0
3.0
1.0
0.5
0
0
R0 = 0.865
Hunters target young adults
X
0
1
2
3
4
NX
100
50
25
13
0
lX
1.0
0.5
0.25
0.13
0
mX
0
1.0
3.0
1.0
0.5
R0 = 1.38
Hunters target old adults
X
0
1
2
3
4
5
6
NX
100
20
10
5
2
1
0
lX
1.0
0.20
0.10
0.05
0.02
0.01
0
mX
Constant mortality (50%)
0
rate with age and
0
increasing reproductive
2.5
2.5
output with age
3.0
3.0
0 R0 = 0.465
-------------------------------------------------------X
0
1
2
3
4
5
6
NX
100
40
20
10
5
2
0
lX
1.0
0.4
0.2
0.1
0.05
0.02
0
mX
0
0
2.5
2.5
3.0
3.0
0
R0 = 0.96
Increase survival of hatchlings
X
0
1
2
3
4
5
6
NX
100
20
15
11
8
6
0
lX
1.0
0.20
0.15
0.11
0.08
0.06
0
mX
0
0
2.5
2.5
3.0
3.0
0
R0 = 1.07
Increase survival of adults
The Niche concept place in a Population Framework
Realized Niche
R0 < 1.0
predation
R0 > 1.0
competition
Factor One
Factor Two
Fundamental Niche