Question

Consider two species A and B, with natural growth rates rA = 1 and rB = 4 respectively, and natural carrying capacities MA = 300 and MB = 15, respectively.

Suppose the species interact so that eA = 0.5 and eB = 0.1.

(a) If the species interact according to competition: (Give your answers correct to at least two decimal places.) The interesting equilibrium occurs when A = ____________and B =____________ .

If the initial populations are A(0) = 2 and B(0) = 1, one of the two species eventually dominates. Which one?

Species A

Species B

What is the long-term population of this dominant species? (Give your answer correct to the nearest integer.) ___________

(b) If the species interact according to symbiosis: (Give your answers correct to the nearest integer.)

The interesting equilibrium occurs when A =___________ and B = _________________.

Answer 1

Explanation:

Consider two species A and B, with natural growth rates

rA = 1

and

rB = 4

respectively, and natural carrying capacities

MA = 300

and

MB = 15,

respectively. Suppose the species interact so that

eA = 0.5

and

eB = 0.1.

(a) If the species interact according to competition:

(Give your answers correct to at least two decimal places.)

The interesting equilibrium occurs when

A =

and

B = .

If the initial populations are

A(0) = 2

and

B(0) = 1,

one of the two species eventually dominates. Which one?

Species A Species B    

What is the long-term population of this dominant species? (Give your answer correct to the nearest integer.)

(b) If the species interact according to symbiosis:

(Give your answers correct to the nearest integer.)

The interesting equilibrium occurs when

A =

and

B = .

If the initial populations are

A(0) = 39

and

B(0) = 2,

what happens?

one species dies off both species die off     both species survive

(c) If the species interact according to commensalism:

(Give your answers correct to the nearest integer.)

The interesting equilibrium occurs when

A =

and

B = .

What do you notice about the equilibria?

The presence of species A dramatically decreases the equilibrium population for species B. The presence of species A somewhat decreases the equilibrium population for species B.     The equilibrium population for species B is the same whether or not species A is present. The presence of species A somewhat increases the equilibrium population for species B. The presence of species A dramatically increases the equilibrium population for species B.