10 11 phlox population growth rate dn = f (b, d, i, e) dt

1011

PHLOX

POPULATION GROWTH RATE

dN = f (B, D, I, E) dt

POPULATION GROWTH TRENDS

Figs. 11.3, 11. 6 in Molles 2008

Geometric Growth Exponential Growth

I) STEADILY INCREASING POPULATIONS

1) Pulsed Reproduction2) Non-Overlapping Generations3) Geometric Rate of Increase (

1) Continuous Reproduction2) Overlapping Generations3) Per Capita Rate of Increase (r)

λ)

UNLIMITED POPULATION GROWTH A:(Geometric Growth)

Fig. 11.3 in Molles 2008

• Pulsed Reproduction

• Non-Overlapping Generations

UNLIMITED POPULATION GROWTH A:(Geometric Growth: Ratio of Successive Population Size)

Fig. 11.3 in Molles 2008

N7 =___N6

N8 =___

N7

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 =

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)

Fig. 11.3 in Molles 2008

Nt = No λt

UNLIMITED POPULATION GROWTH B:(Exponential Growth)

Fig. 11.7 in Molles 2008

• Continuous Reproduction

• Overlapping Generations

dN

dT

dN___

dT=Rate

UNLIMITED POPULATION GROWTH BExponential Growth (Rate of Population Growth)

Fig. 11.6 in Molles 2006

EXPONENTIAL POPULATION GROWTH:Rate of Population Growth

dN___

dT

dN___

dT

dN___

dT

dN___

dT

N

Graph of dN/dT versus N (Exponential Growth)

1

0.5 rise

run

rise

rise

run

run

rmax =riserun

(= intrinsic rateof increase)

dN__dT

= rmax N

EXPONENTIAL POPULATION GROWTH:Rate of Population Growth

Intrinsic Rate of Increase

Population Size

Rate of Population Growth

rmax = b - d

Meaning of Intrinsic Rate of Increase (rmax)

rmax = individuals per individual per day

b = per capita birth rate (= births per individual per day)

d = per capita death rate (= deaths per individual per day)

= intrinsic rate of increase (r) during exponential growth

EXPONENTIAL POPULATION GROWTH:Predicting Population Size

dN__dT

= rmax N

Nt = No ermax t

(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) = 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 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

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

dN___

dT

N

Graph of dN/dT versus N (Logistic Growth)

rise

run

rise

run

rise

run

rise

run

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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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