POPULATION GROWTH RATE. PHLOX. 10. 11. N = f (B, D, I, E). POPULATION GROWTH TRENDS. I) STEADILY INCREASING POPULATIONS. Geometric Growth. Exponential Growth. 1) Pulsed Reproduction 2) NonOverlapping Generations 3) Geometric Rate of Increase (. 1) Continuous Reproduction
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POPULATION GROWTH RATE
PHLOX
10
11
N = f (B, D, I, E)
POPULATION GROWTH TRENDS
I) STEADILY INCREASING POPULATIONS
Geometric Growth
Exponential Growth
1) Pulsed Reproduction
2) NonOverlapping
Generations
3) Geometric Rate of Increase (
1) Continuous Reproduction
2) Overlapping Generations
3) Per Capita Rate of Increase (r)
λ
)
Figs. 11.3, 11. 6 in Molles 2008
UNLIMITED POPULATION GROWTH A:
(Geometric Growth)
Fig. 11.3 in Molles 2008
UNLIMITED POPULATION GROWTH A:
(Geometric Growth: Ratio of Successive Population Size)
N7
___
=
N6
N8
___
=
N7
Fig. 11.3 in Molles 2008
Geometric Growth:
Calculation of Geometric Rate of Increase (λ)
Nt+1
λ =
______________
N t
Calculating Geometric Rate of Increase (λ)
N0 = 996
8
N 1 = 2,408
Phlox
drummondii
λ =
Geometric Growth:
Projecting Population Numbers
N0 = 996
N 1 = 2,408
8
λ = 2.42
N2 =
Phlox
drummondii
N5 =
Problem A: The initial population of
an annual plant is 500. If, after one
round of seed production, the
population increases to 1,200 plants,
what is the value of λ?
Problem B. For the plant population described
in Problem A, if the initial population is
500, how large will be population be after
six consecutive rounds of seed production?
Problem C: For the plant population described
above, if the initial population is 500 plants,
after how many generations will the
population double?
STEADILY INCREASING POPULATIONS
(Geometric Growth: Rate of Population Growth)
Nt = Noλt
Fig. 11.3 in Molles 2008
UNLIMITED POPULATION GROWTH B:
(Exponential Growth)
Fig. 11.7 in Molles 2008
UNLIMITED POPULATION GROWTH B
Exponential Growth (Rate of Population Growth)
dN
dT
dN
___
=
Rate
dT
EXPONENTIAL POPULATION GROWTH:
Rate of Population Growth
dN
___
dT
dN
___
dT
dN
___
dT
Fig. 11.6 in Molles 2006
Graph of dN/dT versus N (Exponential Growth)
(= rmax)
1
dN
___
0.5
dT
(rmax = intrinsic rate of increase)
N
EXPONENTIAL POPULATION GROWTH:
Rate of Population Growth
Population Size
dN
__
rmax N
=
dT
Rate of Population Growth
Per Capita Rate of Increase
Meaning of Intrinsic Rate of Increase (rmax)
rmax = b  d
= per capita rate of increase (r) during
exponential growth
b = per capita birth rate
(= births per individual per day)
d = per capita death rate
(= deaths per individual per day)
rmax = individuals per individual per day
EXPONENTIAL POPULATION GROWTH:
Predicting Population Size
dN
__
rmax N
=
dT
r
t
Nt =
No e
max
(e = 2.718)
Problem D. Suppose that the Silver City
population of Eurasian Collared Doves,
with initial population of 22 birds, is increasing
exponentially with rmax = .20 individuals per
individual per year . How large will the
population be after 10 years? After 100
years?
Problem E. How many years will it take the
Eurasian Collared Dove population described
above to reach 1000 birds?

LN(AB) = B LN(A)
LN(e) = 1
LN(AB) = LN(A) + LN(B)
LN(A/B) = LN(A) – LN(B)
Problem F. “Doubling Time” is the time
it takes an increasing population to double.
What is the doubling time for the Eurasian
Collared Dove population described above?
Problem E. Refer to the Eurasian Collared
Dove population described earlier. How fast
is the population increasing when the population
is 100 birds? How fast is the population
increasing once the population reaches
500 birds?
Problem F.How large is the Eurasian Collared
Dove population when the rate of population
change (dN/dt) is 5 birds per year? When the
rate of population change (dN/dt) is 20 birds
per year?
LOGISTIC GROWTH: Rate of Population Change
Fig. 11.11 in Molles 2006
LOGISTIC GROWTH: Carrying Capacity
Carrying Capacity (K):
82
N
T
Sigmoid Curve:
LOGISTIC GROWTH: Rate of Population Change
dN
___
dT
(Logistic Population Growth)
Figs. 11.11 in Molles 2006.
Graph of dN/dT versus N (Logistic Growth)
(= rmax)
1
dN
___
(rmax = intrinsic rate of increase)
0.5
dT
N
LOGISTIC GROWTH: Rate of Population Change
dN
N
)
(
r max N

1
____
=
K
dT
“Brake” Term
LOGISTIC GROWTH:
Predicting Population Size
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