POPULATION GROWTH RATE
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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) Non-Overlapping 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) Non-Overlapping

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)

  • Pulsed Reproduction

  • Non-Overlapping

  • Generations

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)

  • Continuous Reproduction

  • Overlapping Generations

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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10 http://www.learner.org/jnorth/images/graphics/c/crane_Sp04_020.jpg

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12 http://newsimg.bbc.co.uk/media/images/42096000/jpg/_42096628_

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