POPULATION GROWTH I Predicting Future Population Size Nt1

POPULATION GROWTH

I) Predicting Future Population Size Nt+1 = f (Nt, B, D, I, E)

II) Estimating Rates of Population Change d. N = f (B, D, I, E) dt

I) STEADILY INCREASING POPULATIONS Geometric Growth Exponential Growth 1) Pulsed Reproduction 1) Continuous Reproduction 2) Non-Overlapping 2) Overlapping Generations 3) Per Capita Rate of Increase (r) 3) Geometric Rate of Increase ( 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 2013

UNLIMITED POPULATION GROWTH A: (Geometric Rate of Increase ( ) : Ratio of Successive Population Size) N 7 ___ = N 6 N 8 ___ = N 7 Fig. 11. 3 in Molles 2013

Geometric Growth: Calculation of Geometric Rate of Increase (λ) λ= Nt+1 _______ Nt

Calculating Geometric Rate of Increase (λ) N 0 = 996 8 N 1 = 2, 408 Phlox drummondii λ=

Geometric Growth: Projecting Population Numbers N 0 = 996 N 1 = 2, 408 λ = 2. 42 8 Phlox drummondii N 2 = N 3 = N 4 = N 10 =

STEADILY INCREASING POPULATIONS (Geometric Growth: Rate of Population Growth) Nt = N o Fig. 11. 3 in Molles 2008 t λ

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) • Continuous Reproduction • Overlapping Generations Fig. 11. 7 in Molles 2008

UNLIMITED POPULATION GROWTH B Exponential Growth (Rate of Population Growth) d. N d. T Rate = d. T d. N ___ d. T

Graph of d. N/d. T versus N (Exponential Growth) 1 d. N ___ d. T rise run rise 0. 5 run rise rmax = run (= intrinsic rate of increase) rise run N

EXPONENTIAL POPULATION GROWTH: Rate of Population Growth Population Size d. N __ = r N d. T max Intrinsic Rate of Increase Rate of Population Growth • rmax = maximum value of r

EXPONENTIAL POPULATION GROWTH: Predicting Population Size d. N __ = r N d. T max Nt = No e (e = 2. 718) r max t

Problem D. Suppose that the Silver City population of Eurasian Collared Doves, with initial population of 22 birds, is increasing exponentially with rmax =. 2 individuals per individual per year. How large will the population be after 10 years?

Problem E. How many years will it take the Eurasian Collared Dove population described above (initial population size: 22 birds) 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 (d. N/dt) is 5 birds per year? When the rate of population change (d. N/dt) is 20 birds per year?

LOGISTIC GROWTH: Rate of Population Change Fig. 11 in Molles 2006

LOGISTIC GROWTH: Carrying Capacity 82 N Sigmoid Curve: T

LOGISTIC GROWTH: Rate of Population Change d. N ___ d. T (Logistic Population Growth) Figs. 11 in Molles 2006.

Graph of d. N/d. T versus N (Logistic Growth) rise d. N ___ d. T rise run N

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

LOGISTIC GROWTH: Predicting Population Size