NET REPRODUCTIVE RATE (Ro) AND GEOMETRIC RATE OF INCREASE (L) An annual plant po

Question

NET REPRODUCTIVE RATE (Ro) AND GEOMETRIC RATE OF INCREASE (L)

An annual plant population in Utah has 100 individuals and an R0 (net reproductive rate per lifetime) of 1.5.

a) What will be the size of the population in 5 years?

b) Estimate geometric growth rate (L) from the ratio of the population sizes. What is the relationship between net reproductive rate Ro and geometric growth rate L

c) Would R0 and L have the same relationship in a perennial species? Why?

d)What if L values over 5 successive years fluctuate, from 1.5, 1.2, 1.0, 0.8, and 0.7? What will be the population size in each year over this period?

Explanation / Answer

a)

we know that Nt=R0tN0

where Nt is the size of the population after t generations,

N0 is the initial size of the population and
R0t is the net reproductive rate.

so,here we have R0=1.5, t=5 year and N0=100

i.e Nt=R0tN0

         =(1.55)100

      =759.375

b) geometric growth rate(L)=Nt/N0

                                                  =759.375/100

                                     =7.59375

so,geometric growth rate(L) is greater than reproductive rate R0 by (7.59375-1.5)=6.09375

c) NO,because in perennial species time interval is more than two year.

d)since, geometric growth rate(L)=Nt/N0

so,Nt=LN0

For L=1.5

     Nt=(1.5)100=150

For L=1.2

      Nt=(1.2)150=180

For L=1.0

      Nt=(1)180=180

For L=0.8

     Nt=(0.8)180=144

For L=0.7

     Nt=(0.7)144=100.8

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