There are four variables which govern changes in population size.

A population gains individuals by birth and immigration and loses individuals by death and emigration.

Biotic Potential
Populations vary in their capacity to grow. The maximum rate at which a
population can increase when resources are unlimited and environmental
conditions are ideal is termed the population’s biotic potential. Each
species will have a different biotic potential due to variations in
the species’ reproductive span (how long an individual is capable of reproducing)
the frequency of reproduction (how often an individual can reproduce)
“litter size” (how many offspring are born each time)
survival rate (how many offspring survive to reproductive age)

There are always limits to population growth in nature. Populations
cannot grow exponentially indefinitely. Exploding populations always
reach a size limit imposed by the shortage of one or more factors such
as water, space, and nutrients or by adverse conditions such as disease,
drought and temperature extremes. The factors which act jointly to
limit a population’s growth are termed the environmental resistance. The interplay of biotic potential and density-dependent environmental resistance keeps a population in balance.
Carrying Capacity
For a given region, carrying capacity is the maximum number of
individuals of a given species that an area’s resources can sustain
indefinitely without significantly depleting or degrading those
resources. Determining the carrying capacities for most organisms is
fairly straightforward. For humans carrying capacity is much more
complicated. The definition is expanded to include not degrading our
cultural and social environments and not harming the physical
environment in ways that would adversely affect future generations.

For populations which grow exponentially, growth starts out slowly,
enters a rapid growth phase and then levels off when the carrying
capacity for that species has been reached. The size of the population
then fluctuates slightly above or below the carrying capacity.
Reproductive lag time may cause the population to overshoot the carrying
capacity temporarily. Reproductive lag time is the time required for
the birth rate to decline and the death rate to increase in response to
resource limits. In this scenario, the population will suffer a crash
or dieback to a lower level near the carrying capacity unless a large
number of individuals can emigrate to an area with more favorable
conditions. An area’s carrying capacity is not static. The carrying
capacity may be lowered by resource destruction and degradation during
an overshoot period or extended through technological and social

An example of dieback occurred in Ireland after a fungus infection
destroyed the potato crop in 1845. During this potato famine
approximately 1 million people died and 3 million people emigrated to
other countries. Increased food production due to improved agricultural
practices, control of many diseases by modern medicine and the use of
energy to make historically uninhabitable areas of Earth inhabitable are
examples of things which can extend carrying capacity. The question is
how long will we be able to keep increasing our population on a planet
with finite size and resources?