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Population Dynamics
Characteristics of Populations
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Population ecology is the study of populations
in relation to the environment, including
environmental influences on population density
and distribution, age structure, and population
size.
A population is a group of individuals of a
single species that live in the same general
area.
Members of a population rely on the same
resources, are influenced by similar
environmental factors, and have a high
likelihood of interacting with and breeding
with one another.
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Population Dynamics: change in
size, density dispersion and age
distribution in response to
environmental conditions.
Population Size: the number of
individuals in a population at a given
time.
Ways of Examining Population
1) density of a population is measured
as the number of individuals per unit
area or volume.
Ex: # of trees per acre
# of deer per square mile
# of Daphnia per liter of water
Difficulties in Measuring Density
- counting all of the individuals – nearly
impossible
- population counts are estimates based on
sampling techniques
Ex: For Plants and Sessile Organisms:
In a forest count the # of oak trees in many
different areas
Average the number and multiply by the
area of the habitat
- only accurate if the sample sizes are
the same and the area being
surveyed is homogenous which may
not be the case due to possible
variations in habitat that may make
it inhospitable and different social
interactions
For Animals: Mark and Recapture
- a certain area is used and a sample
of the population is caught and
marked – tags, electronic devices,
paint – and released
- later the same area is used and
more organisms are caught and
examined for markings
- based on the number of organisms
that have marks and don’t have
marks the actual population is
calculated
- The mark-recapture method assumes
that each marked individual has the
same probability of being trapped as
each unmarked individual.
- This may not be a safe assumption,
as trapped individuals may be more
or less likely to be trapped a second
time.
- Also affected by the changes in the
population
- birth (including all forms of
reproduction)
- immigration (the influx of new
individuals from other areas).
- death (mortality)
- emigration (the movement of
individuals out of a population).
- Immigration and emigration may
represent biologically significant
exchanges between populations
2) dispersion of a population is the pattern
of spacing among individuals within the
geographic boundaries.
Dispersion is clumped when individuals
aggregate in patches.
Plants and fungi are often clumped where
soil conditions favor germination and
growth.
Animals may clump in favorable
microenvironments (such as isopods
under a fallen log) or to facilitate mating
interactions.
Group living may increase the
effectiveness of certain predators, such
as a wolf pack.
Dispersion is uniform when individuals
are evenly spaced.
For example, some plants secrete
chemicals that inhibit the
germination and growth of nearby
competitors.
Animals often exhibit uniform
dispersion as a result of territoriality,
the defense of a bounded space
against encroachment by others.
In random dispersion, the position of
each individual is independent of the
others, and spacing is unpredictable.
Random dispersion occurs in the
absence of strong attraction or
repulsion among individuals in a
population, or when key physical or
chemical factors are relatively
homogeneously distributed.
For example, plants may grow where
windblown seeds land.
Random patterns are not common in
nature
Dispersion Patterns
Demography is the study of the vital
statistics of populations and how
they change over time.
Factors Influencing Demography:
1. Birth rates/Death Rates
2. Fecundity (fertility) of Organisms
3. Rate of Maturation to
Reproductive Capacity
4. Life Span
5. Reproductive Strategies
Often represented by a life table - an
age-specific summary of the survival
pattern of a population usually by
studying a group of individuals
(cohort) of the same age as they
proceed through life noting when
they die and calculating the survival
ratio of the group
Tables can also be represented as a
Survivorship Curve – Shows the
overall pattern of surviving members
of a population throughout the life of
the group of individuals.
Types of Survivorship Curves
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Type I curve is relatively flat at the
start, reflecting a low death rate in
early and middle life, and drops
steeply as death rates increase
among older age groups.
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Ex: humans, elephants
Indicates a high level of parental investment
in the raising of young. (Iteroparity)
Types of Survivorship Curves
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Type II curve is intermediate, with
constant mortality over an
organism’s life span.
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Ex: rodents, insects, annual plants
equal chance of dying at all times of life
Types of Survivorship Curves
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Type III curve drops quickly at the
start, reflecting very high death rates
early in life, then flattens out as
death rates decline for the few
individuals that survive to a critical
age.
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Reflect the production of large numbers of
offspring with little or no parental care.
(Semelparity)
Ex: long lived plants, sea turtles, marine
invertebrates, most fish.
Types of Survivorship Curves
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Many species fall somewhere
between these basic types of
survivorship curves or show more
complex curves.
Some invertebrates, such as crabs,
show a “stair-stepped” curve, with
increased mortality during molts.
POPULATION GROWTH
Population Growth
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Change in population size = Births - Deaths
- for a certain time period
Or
 N/t = (B − D) where B is the number of
births and D is the number of deaths.
 N represents population size, and t
represents time, then N is the change in
population size and t is the time interval.
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Ignores immigration and emigration
The per capita birth rate is the
number of offspring produced per
unit time by an average member of
the population.
If there are 34 births per year in a
population of 1,000 individuals, the
annual per capita birth rate is
34/1000, or 0.034 or 3.4%
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ESTIMATING DOUBLING TIME: Rule
of 70
- once a growth rate has been
determined the estimated time for
the population to double can be
determined by dividing 70 by the
rate as a percentage.
Ex: 70/3.4% = 20.6
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If we know the annual per capita birth
rate (expressed as b), we can use the
formula B = bN to calculate the expected
number of births per year in a population
of any size.
Similarly, the per capita death rate
(symbolized by m for mortality) allows us
to calculate the expected number of
deaths per unit time for a population of
any size. D = mN
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Population ecologists are most
interested in the differences between
the per capita birth rate and the per
capita death rate.
This difference is the per capita rate
of increase or r which equals
b−
m. r = b - m
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The value of r indicates whether a
population is growing (r > 0) or
declining (r < 0).
If r = 0, then there is zero
population growth (ZPG).
Births and deaths still occur, but they
balance exactly.
Population Growth Models
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1) Exponential: population growth in an
idealized, unlimited environment.
All populations have a tremendous
capacity for growth.
A hypothetical population living in an
ideal, unlimited environment.
Under these conditions, we may assume
the maximum growth rate for the
population (rmax), called the intrinsic rate
of increase.
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The size of a population that is growing
exponentially increases at a constant rate,
resulting in a J-shaped growth curve when
the population size is plotted over time.
J-shaped curves are characteristic of
populations that are introduced into a new
or unfilled environment or whose numbers
have been drastically reduced by a
catastrophic event and are rebounding.
Exponential Growth
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dN/dt = change in number over time
r = growth rate as a decimal
N = population size
EX: How many individuals will be added to a
population of 500 if the growth rate is 25%
per year?
EX: If 100 individuals are added to a
population in a year, what is the rate if the
original population was 400?
EX: If a population has a growth rate of 15%,
what is the original size of the population if
150 new individuals are added to the
population?
2) The logistic model of population growth
incorporates the concept of carrying
capacity.
 Typically, resources are limited.
 As population density increases, each
individual has access to an increasingly
smaller share of available resources.
 Ultimately, there is a limit to the number
of individuals that can occupy a habitat.
 Ecologists define carrying capacity (K) as
the maximum stable population size that a
particular environment can support
FACTORS DETERMINING CARRYING CAPACITY
Environmental Resistance – all the
factors acting jointly to limit the
growth of a population
1) Energy Limitation
2) Shelter and Breeding Sites
3) Predators
4) Soil Nutrients
5) Water
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If individuals cannot obtain sufficient
resources to reproduce, the per capita
birth rate b will decline.
If they cannot find and consume enough
energy to maintain themselves, the per
capita death rate m may increase.
the per capita rate of increase declines as
carrying capacity is reached
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Population growth is greatest when
the population is approximately half
of the carrying capacity.
At this population size, there are
many reproducing individuals but still
enough resources, and the per capita
rate of increase remains relatively
high.
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The logistic model of population growth
produces a sigmoid (S-shaped) growth
curve when N is plotted over time.
Population growth rate slows dramatically
as N approaches K.
In most natural populations, there is a lag
time before the negative effects of
increasing population are realized.
Populations may overshoot their carrying
capacity before settling down to a
relatively stable density.
Logistic Growth
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dN/dt = rmaxN ((K-N)/K)
dN/dt = growth of the population
(number of new individuals added)
rmax = growth rate as a decimal
K = carrying capacity population
N = number of individuals in the
population
If N < K then r > 0, if N = K then r =
0, and if N > K then r < 0
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Ex: If a population of 200 is at half
the carrying capacity and growing at
a rate of 20 individuals per year,
what is the growth rate of the
population?
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If a population of 500 is at its
carrying capacity, what is the growth
rate?
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A population exhibits logistic growth.
If the carrying capacity is 200 for a
given area. If the growth rate is 2%
at the carrying capacity, what is the
maximum growth rate?
(Hint: the population at the
maximum growth rate is half the
population at carrying capacity or N
at rmax = K/2)
How Does Population Density
Affect Population Growth?
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Density-independent population
controls affect a population size
regardless of its density.
Ex: floods, hurricanes,
earthquakes, landslides, drought,
fire, habitat destruction,
pesticide spraying
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Density-dependent population
controls have a greater effect on a
population as the population size
increases
Ex: competition for resources
(Intraspecific or Interspecific),
territory. Health, predation,
parasitism, disease
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Dense populations have lower birth
rates, higher death rates.
Ex: In mice, overcrowding causes
hormonal changes that inhibit sexual
activity, lower sexual activity, reduced
milk production. Stress from
overcrowding reduces the number of
offspring produced (spontaneous
abortion). May also lead to cannibalism
and killing of the young.
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Population Change Curves
(Population Cycles)
Stable – population fluctuates slightly
above and below its carrying capacity
Irruptive
population occasionally explodes
(irrupts) to a high peak and then
crashes to a very low level.
caused by some factor that temporarily
increases the carrying capacity Ex:
increase in rain = increased growth of
seeds  increase in mice
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Cyclic – boom-bust cycles; poorly
understood and involve a number of
factors.
Factors Influencing Population Growth
Life Histories - the traits that affect
an organism’s schedule of
reproduction and survival
Factors Affecting Life Histories
1) when reproduction begins
2) how often the organism
reproduces
3) the number of offspring are
produced during each
reproductive episode.
Types of Life Histories:
1) Semelparity: big-bang
reproduction - an individual
produces a large number of
offspring and then dies.
2) Iteroparity: Repeated
reproduction - some organisms
produce only a few offspring
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Semeparity vs Iteroparity is
determined by the survival rate of the
offspring.
When the survival of offspring is low, as
in highly variable or unpredictable
environments, big-bang reproduction
(semelparity) is favored.
Repeated reproduction (iteroparity) is
favored in dependable environments
where competition for resources is
intense.
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However, all reproductive attempts are
limited by the resources available.
Ex: Plants and animals whose young are
subject to high mortality rates often
produce large numbers of relatively
small offspring.
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Plants that colonize disturbed environments
usually produce many small seeds, only a few of
which reach suitable habitat.
Smaller seed size may increase the chance of
seedling establishment by enabling seeds to be
carried longer distances to a broader range of
habitats.
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In other organisms, extra investment
on the part of the parent greatly
increases the offspring’s chances of
survival.
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Oak, walnut, and coconut trees all have
large seeds with a large store of energy and
nutrients to help the seedlings become
established.
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However, a small population is not always
beneficial for reproductive rates
Some populations show an Allee effect,
in which individuals may have a more
difficult time surviving or reproducing if
the population is too small.
Animals may not be able to find mates in
the breeding season in small population
sizes.
A plant may be protected in a clump of
individuals but vulnerable to excessive
wind if it stands alone.
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Selection for life history traits that are
sensitive to population density is known
as K-selection, or density-dependent
selection.
K-selection tends to maximize population
size and operates in populations living at a
density near K (carrying capacity)
Characteristics of K-selected Populations:
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- fewer, larger offspring
- high parental care of offspring
- later reproductive age
- larger adults
- adapted to climate and
environmental conditions
- lower population growth rate (r)
- stable population size– near
carrying capacity
- high ability to compete for resources
- late successional species
Ex:
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Selection for life history traits that
maximize reproductive success at low
densities is known as r-selection, or
density-independent selection.
r-selection tends to maximize r, the rate of
increase, and occurs in environments in
which population densities fluctuate
well below K, or when individuals face
little competition.
Characteristics of r-selected Populations
- many small offspring
- little to no parental care of
offspring
- early reproductive age
- most offspring die before
reaching reproductive age
- small adults
- adapted to unstable climates and
environmental conditions
- high population growth rate
- population size fluctuates wildly
and below carrying capacity
- low ability to compete
- early successional species
Ex:
The Human Population
Human Population Growth
1. The human population has been
growing almost exponentially for
three centuries but cannot do so
indefinitely.
How Have Humans Modified Natural
Ecosystems?
Global population = > 7 billion people
Increasing by about 73 million each
year
Or 201,000 people each day.
Population ecologists predict a population of
7.3–8.4 billion people on Earth by the year
2025.
Each color represents 1 billion
people.
White areas is where 98% of
the Australian population lives
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Although the global population is still
growing, the rate of growth began to
slow approximately 50 years ago.
The rate of increase in the global
population peaked at 2.19% in 1962.
By 2011, it had declined to 1.17%.
Current Growth Rates
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Current models project a decline in overall
growth rate to just over 0.4% by 2050.
In the developed nations, populations are
near equilibrium, with reproductive rates
near the replacement level.
Most population growth is concentrated in
developing countries, where 80% of the
world’s people live.
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Examining Human Population
Growth:
Population growth seen in Age
structures - the proportion of
individuals in each age group in a
population.
prereproductive
reproductive
postreproductive
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A population with a large percentage
of its individuals in the
prereproductive and reproductive
categories has a high potential for
growth
Age structure is shown as a pyramid
showing the percentage of the
population at each age.
Significant Shapes of Age
Structures
1. Pyramid: developing country – high
birth rate, but low life expectancy
2. Narrow at Top, but even below:
developed country with a fairly
stable population
3. Narrow Top and Bottom: Usually a
developed country – reproductive
rates have fallen below replacement
rates
Changes Due to Economic
Growth
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Demographic Transition Model
Demographic Transition Model
Changes that occur as a population
moves from a LDC to a HDC.
Stage 1: Pre-industrial – LDC
- high birth and death rate
- low life expectancy
- lack of sanitation and medicine
- agricultural subsistence
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Demographic Transition Model
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Stage 2: Transitional Stage
• Movement toward industrialization
• Increase in sanitation and medicine and
reliable food supply
• Birth rate still high but death rate is
lower = increase in population rate
• LDC-HDC
Demographic Transition Model
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Stage 3: Industrial Stage
• Sanitation and medicine readily
available
• Higher levels of education
• Birthrate begins to lower = population
rate declines
• MDC-HDC
Demographic Transition Model
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Stage 4: Post-industrial
• High levels of :
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Education
Sanitation
Medicine
Food
• Smaller families
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Low birth rate and death rate
Population Growth Rate is low, at ZPG or
even declining
Impact of A Large Human Population:
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Fragmenting and degrading habitat
Simplifying natural ecosystems
Strengthening some populations of
pest species and disease-causing
bacteria by speeding up natural
selection
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Eliminating some predators
Deliberately or accidentally
introducing new species
Overharvesting potentially renewable
resources
Interfering with the normal chemical
cycling and energy flows in
ecosystems
SOLUTIONS: how can we rehabilitate
and restore damaged ecosystems?
 Prevention strategy – reduce and
minimize the damage we do to nature
 Restoration ecology – renew, repair or
reconstruct damaged ecosystems
• Natural restoration – an abandoned damaged
ecosystem will eventually partially recover
through secondary ecological succession
• Rehabilitation – human intervention to make
degraded land productive again through
stopping soil erosion, etc.
• Active Restoration – take a degraded site and
reestablish a diverse, dynamic community of
organisms consistent with the climate and soil
of an area.