13/01/2011
1
Population growth in ecology
EHJ351: January 13
Lecture 2
Remember to review
James Thomson BIO150
lecture slides and notes!
Headline of
National Geographic
article
(Jan. 2011) by Robert Kunzig:
"By 2045 global population is projected to
reach nine billion. Can the planet take the
strain?"
Population growth is an inherently
multiplicative process
•
Simplest case=Each individual within a species (or
some category within the species) has a probability
of birth and death
•
More individuals mean more net reproduction when
birth exceeds death, thus more individuals, more
birth.
...etc.
•
Leads to two basic models when all individuals are
similar r = b–d;
R = (B + 1)(1–D)
dN
dt
rN or N
t
1
RN
t
Time
Population
()
(0
)
( )
Nt
N Expr
t
r
is the instantaneous growth rate; its units are
numbers (or density) per unit time (
t
)
Exp(
rt
) is
e
to the
rt
power
where
e
is the base of the
natural logarithms
2.71828.
..
Any positive
r
means infinite growth!
Reducing
r
from x to 0.1x means that it will take ten
times longer to reach any given population size.
Human population growth is usually measured in %
per year:
1.It is a relatively small number; < 4% a year
2.The rate Ehrlich used in 1968 was about 2% a year
3.For low rates the exponential model with
r
= % in
decimal form N(t) = N(0)Exp(.02t)
4.N(t) = N(0)Exp[rt]
or N(0)R
t
(r=0.02 and R=1.02 are
almost equivalent
Doubling time approximately 70/(% growth per year)
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What is wrong with this model?
1. No resources or other factors that can be used up or
become scarce
2. No time lag in the effects of density (e.g., due to time
required to reach maximum reproductive rate)
3. No age structure, spatial structure, genetic variation,
or other structure (e.g., no sexes—female may be
assumed)
4. No predators or diseases
5. No culture or learning
•
It is possible that positive effects of higher population size
via #5 will cancel the probable net negative effects of 14
in humans
•
Over a short enough time interval, these modifying factors
usually won't change too much.
..
What is the impact of age
structure?
•
Obvious that distribution of individuals into
age classes matters if they have different b, d.
•
Numbers can always be calculated based on
life table, assuming constant per capita birth
and survival rates for each age; Life table gives
births at age x (m
x
), and probability of survival
from age x to x+1 (p
x
) ; survival from birth to
age x is l
x
= p
0
p
1
...p
x
‐
1
•
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 Spring '11
 PeterAbrams
 Demography, Population Ecology

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