Question

explain population growth in terms of ode

Answer 1

In the population growth model for any species either its human being or any microorgansims,it is assumed that the rate of growth of population is always greater than rate of death which is much more practical and is proportional to the number of population present at that time.This is called exponential growth model but the main flaw with this equation is that it conveys population will tend to infinite after long time which is somewhat true for human being but not for any species.Also it doesn't consider the population density of the species and available resources,population distribution, etc. the combined effect of which will decide the growth and decay of the species. So in order to overcome this problem the per capita growth of the population is modeled in terms of some parameters which takes into account the population density and available resources which will generate a competition for other species for their growth.This is called Logistic growth model.

In the parametric term for per capita Logistic growth model ,'K is a measure of threshold" that means it gives some sort of idea that how much population can be accomodated by the environment or habitat of the species such that it can have some positive growth.If the resource is not abundant (ie. K) and population is large (i.e. N) then [N/K becomes greater than 1] there will be some sort of intraspecific competition within the species and that is modelled by multiplicative factor (1-N/K) in equation 2.Also the ratio of N/K is dimensionless quantities.Therefor K is a measure of how much population density that can be supported by the available resources.And this way there will be an optimum K where the equilibrium may lie.