Question

1. A petri dish is inoculated with a single bacterium and the intrinsic rate of increase for the species is 0.5.

a. What will the size of the population be after 10 generations?

b. How often will the population double, if the rate of increase remains constant?

c. If the petri dish can hold one million bacteria, what will the rate of increase be after 25 generations?

d. The rate of resource use by the first species is 2 units/individual. A second species is added to the petri dish that uses resources at a rate of 3 units/individual and has a carrying capacity of 750,000. What will be the end result of adding in the second species of bacteria (i.e., will one species out-compete the other or will they co-exist)?

Answer 1

a. The size of population after 10 generations will be 2^10= 1024 cells.

b. The size of population can be found by equation : Nt = No*e^rt where, Nt = population size at time t; No = original population size, r = intrinsic rate of increase and t = time

Nt= 2 No, r=2, t=?

putting values of each in equation we get:

log_e 2= r*t

log_e 2=0.5*t

t= 0.693/0.5

t=1.386hours

Doubling time is 83minutes.

c. The rate of increase after 25 generations is zero as the holding capacity of plate is one million which will be formed by 20 generations. This can be calculated by equation 2^(number of generations)= number of cells.

d. It will totally depend upon the metabolism of the species whether one will species out compete the other or they will co-exist, because after some time when the population of both species will rise there will be less availability of food, which might trigger formation of secondary metabolites in the species which could serve the purpose of antibiotic to another species.