Question

1. Describe this equation and what does it mean? When it would be used by an ecologist?

dN/dt = rN

2. Describe this equation and what does it mean? When it would be used by an ecologist?

dN/dt = r N (1 - N/K)

3 . Describe this equation and what does it mean? When would it be used by an ecologist?

N_t = N_o e^rt

4. Distinguish between exponential and logistic population growth. Give the equations for each.

5. What is carrying capacity? Why do populations fluctuate around some estimated value

of K?

6. A population of Spotted Fritillary butterflies exhibits logistic growth. If the carrying

capacity is 500 butterflies and r = 0.1 individuals/(individuals x month), what is the

maximum population growth rate for the population?

What you need to know: maximum population growth rate occurs when N = K/2).

In the question you're given the following information:

K = 500,   r = 0.1, maximum population growth at K/2.  

What formula would you use to calculate the answer, from the formulae supplied above?

What is the answer?

Answer 1

1) dN/dt=rN is an equation used in population dynamics study when the population growth is continuous exponential type. it is used when growth is being studied in an environment where resources are unlimited and it is a density independent growth. in this equation, N as a function of time i.e. rate of change in the no. of organisms with time.

r= growth rate or can also be given as (r=birth-death) thus, is also the internal carrying capacity.

2) dN/dt=rN (1-N/K) is an equation used in population dynamics study when the population growth is logistic type where K stands for carrying capacity. used in density dependent enviroment when resources are also limited.

3) N_o= initial number of individuals; N_t= number of individuals after time t; r is same as above

4) Exponential growth is seen when resources are infinite and can be representated by the population dynamic equation given in answer 1

however, according to the theory of life given by darwin, there is alwaz limited resource and thus, struggle for survival. thus, this is logical reasoning and logistic model of population growth and uses the equation in answer no. 2 where there is a finite carrying capacity K for an ecology.

5) carrying capacity denoted by K is the ability of an ecology to carry a population size. it is affected when resources are limited and only a maximum size of population can be sustained within an environment. since limited resources are presnt the struggle to survive will cause the population to fluctuate around the calculated K value.

6) will use eq: dN/dt=rN (1-N/K)

since mentioned, N=K/2 thus, N=500/2 N=250 (maximum no. of individuals)

thus, dN/dt=rN(1-N/K)

=0.1X250 (1-250/500)

=25X0.5= 12.5 individuals/month