Phenomenal and rapid increase of population in a short period is called

$I.$ Population evolve to maximise their reproductive fitness, also called Darwinian reproductive fitness (higher $r$ value), in the habitat in which they live

$II.$ The population growth rate $r$ is inversely related to generation time

$III.$ The housefly, which has a short life span and produces a large number of eggs, could be considered as a ' $K$ ' selected species

$IV.$ Under a particular set of selection pressures, organisms evolve towards the most efficient reproductive strategies

$V.$ Life history traits of organisms have evolved in relation to the constraints imposed by biotic and abiotic factors in their habitat Select the combination of correct statements

A biologist studied the population of rats in a barn. He found that the average natality was $250$, average mortality $240$, immigration $20$ and emigration $30$. The net increase in population is

Maximum survival and reproductive capacity shown by a population under optimal environmental conditions is called

In a population, unrestricted reproductive capacity is called

If natality is represented by $-B$

If mortality is represented by $-D$

If immigration is represented by $-I$

If emigration is represented by $-E$

If population density is represented by $-N$

Then population density at time $t+1$ is represented by