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Populations
• Population- the number of individuals of a species that
inhabit a particular area.
• Population structure- the density and spacing of
individuals within a landscape.
• Structuring features of populations:
1. Spacing- how individuals are distributed across the
landscape.
2. Geographic distribution – a species’ range; the
range can change with changing population
dynamics.
3. Population dynamics- population changes over
time.
Population Spacing
• Spacing refers to the dispersion pattern of
individuals in a population.
• Types:
1. Clumped- individuals are clustered in
groups.
2. Random- no spacing pattern is apparent.
3. Spaced- individuals are regularly spaced
across a landscape.
Factors Controlling Distributions
• Physiological tolerances- based on the internal functioning of the body.
• Ecological tolerances- based on the such factors as the habitat needs of a
species.
• Dispersal ability- the ability of a species to colonize new areas.
• Population pressure- when a population grows beyond an area’s ability to
support it, individuals tend to invade new areas.
In eastern Connecticut,
The Black-capped
Chickadee’s moves its
geographic range south
in winter (summer left,
winter right; darker
colors are denser
populations) because its
physiological need for a
warmer climate is
better met there.
Population Dispersal
• The way that populations distribute themselves
is potentially due to a number of factors.
• Models that attempt to explain dispersal patterns
include:
1. Metapopulation
2. Source-sink
3. Ideal free distribution
4. Landscape
Metapopulations
• Metapopulations are sets of
geographically isolated
populations that occupy
patches of suitable habitat.
• Metapopulations maintain
contact with each other, to a
greater or lesser extent, by
dispersal of individuals (or
seeds) from one to another.
• The green areas in the aerial
infrared photo at right are
metapopulations of the marsh
plant Scirpus. Blue areas are
metapopulations of Acorus.
Source-sink Dispersal
• This model assumes that habitats differ in quality,
and that higher quality habitats produce more
offspring of species than the habitat can support-
these are Source habitat.
• Poorer habitats do not produce enough offspring
to maintain populations, so they are instead
maintained by immigration from source habitats-
these are Sink habitat.
• Typically, larger habitat patches are thought to be
higher in quality than smaller habitats.
Ideal Free Distribution
• As with the source-sink model, this model asserts that
individuals disperse from high to low quality habitats.
• The expectation is that the highest quality habitats are
colonized first, and the lowest quality habitats are colonized
last.
• It also asserts that as populations grow within a habitat patch,
the quality of that patch declines as resources like food are used
up. This happens, for example, when large deer populations
damage their habitats through excessive browsing.
Landscape Model
• The landscape model asserts that the quality of a habitat
can be altered by the nature of nearby habitats, thereby
influencing populations within the habitat.
• For example a low intensity use power line right-of-way
affects an adjacent forest differently than a higher intensity
use farm field adjacent to forest.
Population Dynamics
• Demography- the study of population
growth.
• Populations often grow multiplicatively.
For example, one yeast cell divides into
two; these each divide producing four
cells and, in turn, each of these divides,
producing a total of eight cells.
Exponential Population Growth
• An exponential pattern of Population Growth
growth is often followed by
1200
populations that have recently
Population Size
1000
colonized an area. 800
600
• Exponential growth is 400
characterized by a continually 200
0
accelerating rate of growth.
1 2 3 4 5 6 7 8 9 10 11
• An equation of the form y = axn Day
describes exponential growth
and produces a graph like that
at right:
Exponential Equations
• The exponential population
growth equation is usually
written in this form (right):
• The slope of this equation,
known in Calculus as its
derivative, is (right):
• An equation like this that tells
how a variable changes over
time is called a differential
equation. This one tells us the
rate of population growth at
any point in time.
Deriving dN/dt = rN Birth
rate:
• Make a flow diagram (right) bN
showing the influence of all
factors on population growth Number
rates: of individuals:
N
• Express the diagram in words:
a change in numbers (N) over Death
time is the difference of the rate:
effects of birth (b) and death dN
(d) rates on the population • Rearrange and replace:
(assume these rates are
constant). (b – d) with the symbol r,
which stands for the overall
• Express the words as symbols:
dN/dt = bN – dN rate of population growth as
influenced by birth and
• Simplify through factoring:
death rates:
dN/dt = N(b – d) dN/dt = rN.
Logistic Growth
Population Growth
• Population growth does not 70
60
Population Size
remain exponential. Eventually it 50
---------------------------------------------------------------------------------- K
slows down as the habitat’s 40
30
carrying capacity (K: the ability 20
10
of the habitat to support 0
individuals) is reached (right). 0 5
Day
10 15
• The equation that relates the rate
of population growth to carrying
capacity (the derivative, or
instantaneous slope equation) is:
• It is the same as the exponential
slope equation except that an
additional term (in red) for
reduction in growth rate is added.
Deriving dN/dt = rN(1-N/K) I
• Assume that a population’s
reproductive factor R (the
number of surviving
individuals/ parent) declines
linearly (graph at right):
• The growth rate r is
maximized when population
size is near zero and
minimized when carrying • Write this relationship as a
capacity K is reached. linear equation (y = mx + b,
• At K, each individual in the or y = (rise/run)x + y
population just replaces itself intercept):
(R = 1). R = – (r/K)N + (1 + r)
slope y intercept
Deriving dN/dt = rN(1-N/K) II
• To calculate the change in • Substituting the formula
population over time (dN/dt), we for R into this, – (r/K)N
subtract the number at some + (1 + r), gives:
future time N(t), from the dN/dt = N[– (r/K)N + 1 + r
starting population N:
– 1]
dN/dt = N(t) – N • Combining terms gives:
• N(t) also may be expressed as dN/dt = N (– rN/K +r)
the product of the reproductive • Factoring and
factor R and the starting
population N: rearranging yields:
dN/dt = rN(1 – N/K)
N(t) = RN
• Substituting into dN/dt, we get:
dN/dt = RN – N = N(R – 1)
factoring
Population Age Structure
• Age structure- the number of
individuals in each of a
population’s age classes.
• Population growth rate
depends on age structure.
• Example: The red-spotted
newt (salamander) has two
clearly distinguishable age
classes, the yellow and tan
aquatic adult, and the bright
orange terrestrial juvenile
(lower left).
Life Tables
• Life tables provide a method for calculating population
change over time.
• To compute population change, information on
survivorship and fecundity (birth rate) in age classes
are required.
• Age classes for animals like the snapping turtle
typically are measured in years. Snapping turtles can
live to be nearly fifty years old. Other animals, like the
meadow jumping mouse (upper right), generally do not
live more than a year.
Life Table Calculations
The table below shows life table calculations for a
hypothetical population of eastern cottontail rabbits:
1 2 3 4 5 6
Age class Total population % Survivorship # surviving Fecundity # of offspring Total population
(years) -beginning to next year (young/adult) -ending
(time = 0) (time = t)
(1 x 2) (3 x 4)
0 20 0.5 0 74 Sum of 5
1 10 0.8 10 1 10 10 3
2 40 0.5 8 3 24 8 3
3 30 0 20 2 40 20 3
4 0 0 0 0 0 0
Sum 100 38 74 112
Population Regulation
• Density-dependent factors- as a population
grows, certain factors begin to limit growth.
These include disease and availability of food
and living space. As populations increase,
mortality tends to increase and fecundity tends
to decline.
• Density-independent factors- other factors
influence populations regardless of their size.
These include storms, geologic events,
minimum winter temperatures and snowfall
amounts.
