### Population Growth

```Population
Growth
Factors Affecting Population
Growth
 Populations
grow and shrink in response to
abiotic and biotic factors.


Abiotic – physical & chemical factors such
as water & light availability, soil structure,
salinity, pH, etc.
Biotic – factors having to do with living
organisms, like competition & predation.
Population Growth Models
 We
can study the way populations grow
by using models.


What happens when resources are
unlimited?
What limits population growth?
Example – Waterhemp
 Waterhemp
populations can grow
quickly. When it
occurs in soybean
fields, it can reduce
the crop of soybeans
available to harvest.
Geometric Growth
 When
there are plenty
of resources, the
population can grow
very rapidly.

As the population
grows, there are more
individuals available to
reproduce, so it grows
faster.
Geometric Growth
 If
the estimated
growth rate is 2.0,
each individual will
produce 2 offspring
each year.

2,4,8,16,32,64 etc
Geometric Growth

A simple measure of
population growth is
the ratio of the
population size at
one time (Nt+1) to the
population size in the
previous time step
(Nt). This is known as
the finite rate of
increase, denoted
by lambda (λ).
Geometric Growth
 The
geometric
population growth
model:


Nt = N0λt
Population that
reproduce all at
once sometimes
follow this growth
model.
 Sockeye
salmon
Exponential Growth
 Some
organisms can reproduce multiple
times throughout the year.

We need to adjust our growth equation.
 r=lnλ
Exponential Growth
 dN/dt
= rN
 N= population size
 t = time
 r = intrinsic rate of increase
 So, change in population size over time is
the population size times r.
 Populations grow increasing fast due to
increase in reproductive individuals.

Positive feedback
Exponential Growth
 When
conditions
are optimal, with
unlimited
resources, the
population can
grow at its
maximum rate.
 rmax
Exponential Growth
 The
human
population is
growing
exponentially.
Logistic Growth
 In
reality,
populations usually
can not sustain
exponential growth
for long.

Resources
become limiting.
Logistic Growth
 Carrying
Capacity (K) – the number of
individuals the environment can support.

The population grows exponentially, then
levels off as K is reached and resources start
to run low.
Logistic Growth
 Example:
sheep in
Tasmania (southern
Australia)



Introduced in 1810
Reached carrying
capacity around 1860
Fluctuates around
carrying capacity
Logistic Growth Equation
 Adds
a carrying
capacity
component to the
exponential growth
equation:

dN/dt = rN (1-N/K)
Factors that Affect Population
Growth
 Density
dependent factors will affect
population growth more when there are
more individuals in a given area.





Disease / parasites
Food
Light
Space
Predation
Factors that Affect Population
Growth
 Density
independent factors affect
population size in the same way
regardless of population density.



Storms
Falling trees
Natural disasters
Example - Aphids
 Aphid
populations will increase until they
reach the carrying capacity.


This is determined by limited resources –
soybean leaves for example.
When the population nears the carrying
capacity, some individuals will get enough
food to survive & reproduce, some get
enough to just survive, and some will starve.
Aphids
 Is
food limitation an example of a densitydependent factor or a densityindependent factor?


Density-dependent
Density-independent
Dispersal and
Metapopulations
Growth Rate
 Growth
rate = births – deaths
 We
must also account for immigration
and emigration.
 Growth
rate = births – deaths +
immigration – emigration

r = b-d + i-e
Immigration
 If
a habitat patch is
small, it may not be
able to permanently
support a population.

Immigrants from other
patches can come in
and rescue the
population periodically.
Source-Sink Populations
 Immigrants
usually come
from a neighboring
population. If there is a
large population
surrounded by smaller
populations, the small
ones may be constantly
re-populated by
immigrants from the
large one.
Source-Sink Populations

Population size and distance
between ponds affects the
probability of California tiger
salamanders colonizing one
pond from another in a system
of ponds in Monterey County,
CA. Trenham and colleagues
estimated how far rescue
effects from source ponds
extend to other ponds that
might be sinks, based on
dispersal patterns and pond
characteristics. Dispersal
estimates are shown by arrows.
Ponds with many emigrants,
such as LC, are sources, while
ponds that primarily have
immigrants but not emigrants,
such as CRP, are sinks.
Dispersal
 Dispersal
is important to help small
populations avoid extinction.


Allows organisms to escape competition,
find mates, find new resources, etc.
Take advantage of new space opened up
after a landslide etc.
Metapopulations

A metapopulation is a set
of subpopulations
connected via dispersal. A
metapopulation inhabits a
shifting set of occupied
and empty patches that
together sustain the
metapopulation for much
longer than any one
patch sustains a
subpopulation.
Variability in Populations
 Environmental
stochasticity - refers to
seemingly random variability in resource
availability, ecological community
composition, predation pressure, weather
events, etc., which often causes
fluctuations in a population's growth rate.
Variability in Populations
 Demographic
Stochasticity - Population
growth rate is determined by birth and
death rates. By chance, there could be
many births in a row, leading to a higher
population growth than you would
expect. Or by chance, there could be a
number of deaths in a row, leading to
unexpected extinction.
Variability in Populations

The Allee effect
occurs when
populations
reproduce at a
slower rate than
expected at low
population densities.

Meerkats form social
groups where only
one pair reproduces.
Variability in Populations
 All
of these sources of variability can
make modeling and predicting
population dynamics challenging.
```