bio lec 5
what is the density of a population
it is the number of individuals / area
why are pop models imp
tp predict pop in the future with the nmbers we have availible now for :
natural resource allocation and reserve,
monitior human pop
health
extinction of species
who was malthus and why was he important
he was imp as he said that no pop can grow exponentially and grow more than the reasources can support it as there are only a fintine number of resources and food.
what are the differences between the differential and difference equations and what are their cons
the difference also known as discrete time equation is used to mark the growth of indivuduals who have specific times for their reproduction like annual or seasonal they do not reproduce constantly or continuously whenever they want. the exponential growth is for smooth continous growth
what are the disadvatages of the exponential growth models
they are completely density independant and dont accounf for any density dependant factor, they also leave of emmigration and immigration to simplify the model. learn the shape of both the curves the discrete time kind of has step not smooth curve fully
what are the formulas for both
geometric is esentially supp to be
Nt+1= Nt * lambda
can also be writted as
Nt=lamda^t * N0
the lambda is the finite rate of increase ans it is supp to be the per capita birth - per capita death
if lambda = 1 pop stays the same
if labda > 1 pop grows
if lambda <1 pop dec
exponential
dN/dT= rN
Nt=N0* e^rt
what is the relation be lamda and r
ln(lambda) =r
one form of density dep
adding K which makes the
dN/dt= rN *(1-N/K)
in terms of r what is the pop growth
r>0 pop grows
r=0 pop same
r<0 pop dec