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Population growth is exponential.

Nt = N0 x ert


Nt = number of individuals at time t

N0 = initial number of individuals

e= base of natural logs (2.718)

r= average individual contribution to population growth

So population increases exponentially with time.

With the short generation time of insects and their large reproductive rate, this can lead to enormous numbers.

e.g. If a grain beetle population starts at 100 individuals, has no growth restraints and has an r of 0.75 individuals/week, how many beetles will there be after x weeks?

N3= 100 e (0.75x3) = 949

N20 > 3 x108

N82 6.1 x 1028

If each beetle weighs 10mg, than after 82 weeks the population of beetles will weigh 6.1 x 1021 tonnes, which is the weight of the earth.

Obviously there is not unrestrained growth because food shortages, disease, overcrowding etc will occur. Therefore, the individual's reproductive contribution, (r), varies with population size.

Where r decreases linearly as N increases, the population number will stabilise at a carrying capacity, K.

With variation over time of weather, seasons, food resurces, etc., the growth curve would not be smooth. The next figure shows these irregulatities of population growth toward the carrying capacity.

The rate of population increase (r), can also be looked at as

r = b-d


b = birth rate

d = death rate

Birth rate is dependant upon

Death rate is dependant upon

Population size is also dependant upon movement of individuals

Nt = N0e(b-d) - Et + It

Where :

Et = emigration

It = immigration

This takes into account spread and dispersal/migration

Spread is the movement of individuals in searching for food, shelter etc. It is restricted to areas that are favourable and increases the size of a single area populated by a species.

Dispersal is removal of a variable % of individuals to other areas. These new places may not be favourable.

Migration is mass dispersal, often seasonal, of an entire population to a new area.

For example, Bogong moths. Adults emerge in early summer in pasture and legume regions in NSW and Qld. They migrate to alpine areas and return in autumn to mate and lay eggs. The species thus avoids the annual occurrence of harsh climate.


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