10 11 PHLOX WHOOPING CRANES POPULATION SIZE N = f (B, D, I, E)

1011

PHLOX WHOOPING CRANES

POPULATION SIZE

N = f (B, D, I, E)

POPULATION GROWTH

STEADILY INCREASING POPULATIONS:Ecological Reality?

Figs. 11.5, 11.7 in Molles 2006

Figs. 11.3, 11. 6 in Molles 2007

Geometric Growth Exponential Growth

I) STEADILY INCREASING POPULATIONS

1) Pulsed Reproduction2) Non-Overlapping

Generations

1) Continuous Reproduction2) Overlapping Generations

GEOMETRIC GROWTH Exponential Growth

λ r

Geometric Growth

• Non-Overlapping Generations

• Reproduction is Pulsed

λ: Geometric Rate of Increase

λ < 1: λ = 1: λ > 1:

Exponential Growth

• Overlapping Generations

• Reproduction is Continuous

r: Per Capita Rate of Increase

r < 0: r = 0: r > 0:

Geometric Growth: Calculation of Geometric Rate of Increase (λ)

λ = Nt+1

______________

N t

Phlox drummondii

8

N0 = 996

N 1 = 2,408

λ =

Calculating Geometric Rate of Increase (λ)

Geometric Growth: Projecting Population Numbers

N0 = 996

Phlox drummondii

8 λ = 2.42

N2 =

N 1 = 2,408

N5 =

STEADILY INCREASING POPULATIONS Non-Continuous Reproduction (Geometric Growth)

Fig. 11.3 in Molles 2006

Nt = No λt

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?

UNLIMITED POPULATION GROWTH B:(Exponential Growth)

Fig. 11.7 in Molles 2006(e = 2.718)

dN

dT

UNLIMITED POPULATION GROWTH BExponential Growth (Rate of Population Growth)

dN___

dT=Rate

Fig. 11.6 in Molles 2006

EXPONENTIAL POPULATION GROWTH:Rate of Population Growth

dN___

dT

dN___

dT

dN___

dT

dN__dT

= rmax N

EXPONENTIAL POPULATION GROWTH:Rate of Population Growth

Intrinsic Rate of Increase

Population Size

Rate of Population Growth

r = bN - dN

Per Capita Rate of Increase

Per Capita Birth Rate

Per Capita Death Rate

Meaning of r

EXPONENTIAL POPULATION GROWTH:Predicting Population Size

dN__dT

= rmax N

Nt = No ermax t

(e = 2.718)

Problem D. Suppose that the worldwide population of whooping cranes, with initial population of 22 birds, is increasing exponentially with rmax = .0012 individuals per individual per year . How large will the population be after 100 years? After 1000 years?

Problem E. How many years will it take the whooping crane population described above to reach 1000 birds?

LN(AB) = LN(A) + LN(B) LN(A/B) = LN(A) – LN(B)

LN(AB) = B LN(A) LN(e) = 1-----------------------------------------------------------------------------------------------------------

Problem F. “Doubling Time” is the time it takes an increasing population to double. What is the doubling time for the whooping crane population described above?

Problem E. Refer to the whooping crane 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 whooping crane population when the rate of population change is 5 birds per year? When the rate of population change is 20 birds per year?

LOGISTIC GROWTH: Rate of Population Change

Fig. 11.11 in Molles 2006

N

T

Carrying Capacity (K):

Sigmoid Curve:

82

LOGISTIC GROWTH: Carrying Capacity

Figs. 11.11 in Molles 2006.

(Logistic Population Growth)

LOGISTIC GROWTH: Rate of Population Change

dN___

dT

LOGISTIC GROWTH: Rate of Population Change

dN____

dT

r max N= ( )1 - N

K

“Brake” Term

LOGISTIC GROWTH: Predicting Population Size

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2 http://www.bigantlers.com/dall15c.jpg

3 http://www.oilcrash.com/images/d_price3.gif

4 http://www.akcenter.org/images/programs/oceans/beluga/ Raw-Count-Graph.gif

5 http://csiwhalesalive.org/csi04404b.jpg

6 http://www.behav.org/00gallery/ecol/carni_isle_royal_graph_1.gif

7 http://mall.ballparks.com/images/AV75.jpg

8 http://www.sbs.utexas.edu/bio406d/images/pics/plm/Phlox% 20drummondii%20flws4.jpg

9 http://www.photobirder.com/Bird_Photos/whooping_crane_2.jpg

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

11 http://www.em.ca/garden/phlox_drummondii1.JPG

12 http://newsimg.bbc.co.uk/media/images/42096000/jpg/_42096628_ crowd_416_ap.jpg