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Population Ecology
Introduction
All populations of organisms are dynamic.
Many factors, such as predation, available resources,
or environmental changes, influence the changes
in a species’ population.
Population dynamics is the study of the long term
changes in population sizes and the factors that
cause a change.
History of Population
Dynamics
Thomas Malthus proposed
the first mathematical
equation to characterize
human population
growth over 200 years
ago.
This lead to the
development of many
equations for the various
kinds of population
growth, some of which
we will cover in this unit.
There are four factors that affect a population’s growth:
1)
2)
3)
4)
Births (natality) (B)
Deaths (mortality) (D)
Immigration (I)
Emigration (E)
These factors can be put into a simple equation to summarize
the changes in a population from one moment in time
(N0) to another (N1):
N1 = N0 + (B – D) + (I – E)
Population Density
Population Density is a measure of how many
individuals of a given species are found in a given
area.
There are two types of density:
1) Crude density is the total number of individuals
divided by the total area of the entire habitat.
2) Ecological density is the total number of
individuals divided by the total useable area in the
habitat.
The equation for population density (D) is:
D = N (population size)/S (area)
Population Dispersion
Population dispersion is how individuals of a species are
arranged in their environment. There are three kinds.
Clumped dispersion is
usually due to a species
being concentrated in areas
most favourable for survival
(ex. Cattails in wet soils
lining ponds or lakes) or
social behaviour (ex. fish in
schools) for protection from
predators
Uniform dispersion is
when the individuals
of a species are
spaced equally
throughout a habitat.
This usually occurs
with territorial
organisms (ex.
penguins).
Random dispersion is
when organisms are
spread throughout a
habitat in an
unpredictable and
patternless way
Measuring Populations
Population density is found
differently depending on
whether the species being
studied is mobile or
stationary.
Quadrat studies are used for
non-mobile populations such
as plants.
Mark-Recapture studies are used
for mobile populations such
as animals.
Quadrat Studies
A quadrat is a small sample frame (usually a square) that is
placed randomly throughout a larger ecosystem in order
to estimate the population density (D).
All the individuals counted in the quadrats
are added together in the following
equation:
Estimated density = total number of
sampled individuals / total sample area
The population size (N) can then be
estimated:
N = (estimated density)(total area of
studied habitat)
Example Calculations
A student wants to estimate the population of ragweed plants in a large
field which measures 100 m x 100 m. She randomly places three
2.0 m x 2.0 m quadrats in the field. Estimate the population density
and size if she finds 18, 11, and 24 plants in her three quadrats.
average sample density = total number of individuals
total sample area
=
18 + 11 + 24
(4.0m)² + (4.0m)² + (4.0m)²
= 4.4 ragweed plants/m²
estimated population size = (estimated population density) (total size of study area)
= (4.4 plants/m²) x (10 000m²)
= 44 000 plants
Mark-Recapture Method
To start, traps are laid out in the
study area and any subjects that
are captured are marked and
returned to the environment.
A short time later the traps are set
again and individuals are
captured.
This time it is noted how many
individuals were recaptures and
how many were new captures.
All this data can be plugged into
an equation to estimate
population density.
The equation is:
M (total # marked on 1st day) = m (# of recaptures)
N (total estimated population) n (total # captured on 2nd day)
Example Calculation
Consider a fish population of unknown size where 26 individuals
are randomly captured, marked, and released. Some time later,
21 individuals are captured and three of those appear to
already have been marked. What is the estimated population
size?
total # marked individuals in population  26
= 3  # marked in 2nd sample
estimated population size  N 21  size of 2nd sample
N = 26 x 21
N = 182
3
Therefore, the estimated population size is 182.
Homework
Page 659, # 3, 4, 5, 6
Measuring and Modelling
Population Change
Fecundity is the potential for a
species to produce offspring in
one lifetime. This relates to the
species’ ability to increase
population rapidly or over a long
period of time.
High fecundity is when a female of a
species can produce large numbers
of offspring (ex. star fish lay over
1 million eggs per year).
Low fecundity is when a female can
produce a much more limited
number of offspring in their
lifetime (ex. a hippopotamus
could produce maybe 20 young
over an average life of 45 years).
Carrying capacity is the maximum
number of organisms that can
be sustained by the available
resources of a habitat over a
given period of time. It is
always changing as the resource
levels are never constant and
depend on the changing abiotic
elements of habitat (ex.
climate).
Biotic potential is the maximum
rate a population could increase
under ideal conditions. It is
represented mathematically by
r.
Survivorship Patterns
Biologists recognize three general patterns of
survivorship among species.
Type I Curve
- Low mortality rate until they
are past their reproductive age
- Long life expectancy
- Slow to reach sexual maturity
and produce low numbers of
offspring
- Ex. humans
Type II Curve
-Intermediate between types
I and III
-Have a uniform risk of
mortality over their lifetime
Type III Curve
-Very high mortality rate when
young
-Those that reach sexual
maturity have a greatly reduced
mortality rate
-Very low average life
expectancy
-Ex. Green Sea Turtle
Population Change
Population change (%) = [(birth+immigration)–(deaths+emigration)] x 100
initial population size (n)
A negative result means population is declining.
A positive result means population is growing.
In an open population all four factors come into play. In a closed
population, normally an island, only births and deaths are a
factor.
Types of Population Growth
Geometric growth is a pattern where organisms
reproduce at fixed intervals at a constant rate.
Exponential growth is a pattern where
organisms reproduce continuously at a
constant rate.
Logistic growth is a pattern where growth levels
off as the size of the population reaches the
carrying capacity of their environment.
Geometric Growth
Deaths occur at a relatively constant rate over
time but births are restricted to a specific
breeding period. These populations increase
rapidly during breeding season and decline
slowly the rest of the year.
Appears
continuous
In reality…
Their growth rate is a constant (λ) and can be determined
using the following equation:
λ = N (t + 1)
N(t)
– λ is the fixed growth rate (from one year to the next)
– N is the population size at year (t+1) or (t)
To find the population size at any given year, the formula is:
N(t) = N(0)λt
– N(0) is the initial population size
Sample Problem
The initial Puffin population on Gull Island, Newfoundland is 88 000. Over the
course of the year they have 33 000 births and 20 000 deaths.
a) What is their growth rate?
ANSWER
a) N (0) = 88 000
N (1) =101 000
λ = N(t + 1) = 101 000 = 1.15
N(t)
88 000
Therefore the growth rate is 1.15.
b) What will the population size be in 10 years at this current growth rate?
ANSWER: From a) growth rate, or λ = 1.15
N(10) = N(0)λ10
* Remember BEDMAS!
= 88 000 (1.15)10 = 356 009
Therefore the population size will be 356 009 in 10 years.
Practice Question
Exponential Growth
Many species, such as humans, are not limited to a breeding season. These
species can reproduce at a continuous rate throughout the year.
Since they grow continuously, biologists are able to determine the
instantaneous growth rate, or intrinsic (per capita) growth rate, r.
(r = b (births per capita) – d (deaths per capita))
Population growth rate is given by:
Instantaneous
growth rate
dN = rN r is growth rate per capita and N is population size
dt
To find the time it takes a population that is reproducing
exponentially to double, we use the equation:
td = 0.69
r
Example Calculations
A population of 2500 yeast cells in a culture tube is growing exponentially. If the intrinsic
growth rate is 0.030 per hour, calculate:
a) the initial instantaneous growth rate of the yeast population.
b) the time it will take for the population to double in size.
c) the population size after four doubling periods.
a) r = 0.030 per hour and N = 2500
dN = rN
dt
= 0.030 x 2500
= 75 per hour
When the population size is 2500 the instantaneous growth rate is 75 per hour.
b) r = 0.030
td = 0.69
= 0.69
= 23 hours
r
0.030
The yeast population will double in size every 23 hours.
c)
Doubling Time
0
1
2
3
4
Time (hours)
0
23
46
69
92
Population Size
2500
5000
10 000
20 000
40 000
After 4 doubling periods, the population of the yeast culture is 40 000 cells.
Logisitc Growth
The previous two models assume an unlimited resource supply, which is never the
case in the real world.
However, when a population is just starting out, resources are plentiful and the
population grows rapidly.
As the population grows, resources are being used up and the population nears the
ecosystem's carrying capacity. The growth rate drops and a stable equilibrium
exists between births and deaths. The population size is now the carrying
capacity (K).
This is known as a sigmoidal curve.
A: Population small, increasing
slowly
B: Population goes through largest
increase
C: Dynamic equilibrium (at carrying
capacity), b=d, no net population
increase
Logistic Growth, continued.
Logistic growth represents the effect of carrying capacity on the growth of a
population. It is the most common growth pattern in nature.
Population size
at given time
Population
growth at a
given time
dN = rmaxN (K – N)
dt
K
Carrying
capacity
Max intrinsic
growth rate
Notice if the population size is close to the carrying capacity, there is virtually no
growth (K-N = 0), thus the equation takes into account declining resources as
the population increases.
Sample Problem
A population of humans on a deserted island is growing continuously. The carrying
capacity of that island is 1000 individuals and the maximum growth rate is 0.50.
a) Determine the population growth rates over 5 years if the initial population size is 200.
b) Describe the relationship between population size and growth rate.
Answer
a)
Population size, N
rmax
(K-N)
K
Population growth
rate
0.50
200
800/ 1000
80
0.50
500
500/1000
125
0.50
900
100/1000
45
0.50
990
10/1000
4.95
0.50
1000
0
0
b) When the population is small the rate of growth is slow. The rate of growth increases
as the population gets larger and then, as it approaches carrying capacity, the growth rate
declines and levels off.
Factors Affecting Population
Change
There are many things that can alter a population size.
Density-independent factors limit population growth no matter
what the population size (ex. natural disaster, human
intervention, etc).
Density-dependent
factors limit population
growth and intensify as
the population increases
in size (ex. competition
for resources, disease,
etc).
Density-dependent Factors
Intraspecific competition is when individuals of the same
species compete for resources. If this is high then the
population will have a low growth rate.
Predation is a densitydependent factor. If
there is more prey
available they will be
chosen more by
predators.
Illness/disease spreads
faster when a population
has a higher density.
Allee Effect
Warder Allee found that some density-dependent
factors reduce population growth when the
population is at a low density rather than high
density.
This is known as the Allee effect.
For example, at times when a population has such a
low density it is harder for individuals to find a
mate and successfully reproduce thus lowering the
growth rate of the species.
Small populations also may go
through inbreeding depression
which reduces the
populations’ genetic
variability and may prevent
successful population growth.
The minimum viable population
size is the smallest number of
individuals that ensures the
population will persist for a
certain period of time. It is
different for different species.
Allows biologists to
determine whether a species is
endangered.
Density-independent Factors
The resource in the ecosystem
that is in the shortest supply is
known as the limiting factor
since it is preventing massive
population growth.
Often times these are based on
human influences on the
ecosystem (ex. pollution, urban
sprawl, etc.) but it could also
be related to changes in climate
(ex. a dry season that growth of
plants for food) or natural
disasters.