1. POPULATION SIZE
PHLOX 11
N = f (B, D, I, E) 10

2. POPULATION GROWTH TRENDS

3. 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, in Molles 2008

4. UNLIMITED POPULATION GROWTH A:
(Geometric Growth)
Fig in Molles 2008

5. Calculation of Geometric Rate of Increase (λ)
Geometric Growth:
Calculation of Geometric Rate of Increase (λ)
Nt+1
λ =
______________
N t

6. λ = N0 = 996 N 1 = 2,408 Calculating Geometric Rate of Increase (λ)
Phlox
drummondii
λ =

7. Projecting Population Numbers
Geometric Growth:
Projecting Population Numbers
N0 = 996
N 1 = 2,408 8
λ = 2.42
N2 =
Phlox
drummondii
N5 =

8. Nt = No λt STEADILY INCREASING POPULATIONS
Non-Continuous Reproduction (Geometric Growth)
Nt = No λt
Fig in Molles 2008

9. 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?

10. 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?

11. Problem C: For the plant population described
above, if the initial population is 500 plants,
after how many generations will the
population double?

12. UNLIMITED POPULATION GROWTH B:
(Exponential Growth)
Fig in Molles 2008

13. dN dT dN ___ dT = Rate UNLIMITED POPULATION GROWTH B
Exponential Growth (Rate of Population Growth) dN dT dN
___ =
Rate dT

14. EXPONENTIAL POPULATION GROWTH: Rate of Population GrowthdN
___ dT dN
___ dT dN
___ dT
Fig in Molles 2006

15. dN __ rmax N = dT Population Size Rate of Population Growth
EXPONENTIAL POPULATION GROWTH:
Rate of Population Growth
Population Size dN __
rmax N = dT
Rate of Population Growth
Per Capita Rate of Increase

16. rmax = b - d Meaning of r b = per capita bird rate
(= births per individual per day)
d = per capita death rate
(= deaths per individual per day)
rmax = per capita rate of increase
(individuals per individual per day)

17. EXPONENTIAL POPULATION GROWTH: Predicting Population SizedN __
rmax N = dT r t
Nt =
No e
max
(e = 2.718)

18. 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?

19. 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)

20. 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?

21. 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?

22. Problem F. How large is the Eurasian Collared
Dove population when the rate of population
change is 5 birds per year? When the rate of
population change is 20 birds per year?

23. LOGISTIC GROWTH: Rate of Population Change
Fig in Molles 2006

24. N T LOGISTIC GROWTH: Carrying Capacity 82 Carrying Capacity (K):
Sigmoid Curve:

25. dN ___ dT LOGISTIC GROWTH: Rate of Population Change
(Logistic Population Growth)
Figs in Molles 2006.

26. ) ( - 1 dN N r max N ____ = K dT “Brake” Term
LOGISTIC GROWTH: Rate of Population Change dN N )
r max N ( - 1
____ = K dT
“Brake” Term

27. Predicting Population Size
LOGISTIC GROWTH:
Predicting Population Size

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