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Ecology: Study of interactions among organisms (biotic factors) and
their physical environment (abiotic factors).
(Solomon et. al. 1999)
Jaguar in Brazilian rain forest
Community
Population
Organism
Raven & Johnson 1999
Ecosystem
Populations as Units of Structure and Function
•The population has unique, discernable properties and is an
important unit of biological investigation.
•Interests of population ecologists include
•to understand how and why population sizes change.
•to understand populations as functional subunits of communities.
•The population is an important level of organization for the study
of evolution
•a population has common gene pool
•evolutionary change happens to populations
Population ecology has important applications:
•Conservation biology - predicting extinction risk, managing
populations
•Understanding, predicting human population growth
Density and Dispersion
Population Density Number of
conspecific individuals per unit area or
volume at a given time
Clumped
Dispersion Distribution, or spacing
of individuals relative to each other
Uniform
Random
Uniform dispersion: Individuals are dispersed more evenly than
expected from random occurrence of a habitat. Explanations
include:
•uniform territory sizes in relatively homogenous environments (e.g. penguins)
•allelopathy -- production of toxins that inhibit growth of nearby plants (e.g.
desert creosote bush and saltbush)
Campbell 1993
(Solomon et. al. 1999)
Campbell 1993
Sunbathers in Sydney, Australia Humans often exhibit uniform distribution
Clumped dispersion (aggregation) by far most common in nature.
•Environmental conditions seldom uniform throughout even relatively small area.
•Reproductive patterns including sexual attraction, often favor clumping
•Behavior patterns often lead to active congregation in loose groups or in more
organized colonies, schools, flocks, or herds
Population Dynamics; Changes in population size and
demographics over time
Mathematical modeling is an important and widely-used
approach to studying population dynamics
• Using equations to simulate population dynamics over time
•Illuminate complex processes and guide further research
•Vary in predictive ability; rarely are perfect approximations
Life Table of the 1978 Cohort
of Ground Finches on Isla
Daphne
•Mortality high during first year of
life; mortality then dropped for
several years, followed by a
general increase
•Some of the fluctuation between
years was probably related to
annual rainfall; survival is related
to seed production, which is
closely correlated with rainfall
In drought years on the archipelago, seed
production is low, nesting is low (most adults
don’t breed), and adult survival is low
In years of heavy rainfall, seed production is
high, most birds breed several times, and
adult survival is high
http://cervid.forsci.ualberta.ca/library/taxonomy/cervus_elaphus.htm
•Deer live up to 16, and
females can breed at 4
•Type I survival curve
indicates a relatively
consistent increase in the
risk of mortality with age
•The growth rate for most
populations is strongly
dependent on age
structure
Raven and Johnson 1999
Raven and Johnson 1999
Life table for Red Deer on island of Rhum, Scotland.
•All species have potential for explosive, exponential growth;
absent resource limitations, growth would be exponential
•Biotic potential (rmax) is the maximum rate at which a
population could increase under ideal conditions
•Exponential growth has been demonstrated experimentally
in bacterial and protist cultures and in some insects.
•At some point, environmental resisitance will curtail
exponential growth; environmental limitations cause
decreases in birth rates and increases in death rates
Population Size
Biotic Potential and the Exponential Growth Model
Time
Raven & Johnson 1999
Solomon et al 1999
Example of rapidly increasing population. European
loosestrife is now naturalized over thousands of square miles of
North American wetlands. Introduced in 1860, it has had a
negative effect on may native plant and animal species
Exponential growth in bacteria. Bacteria,
dividing every 20 minutes, experience
exponential population growth
Biotic potential and the Exponential Growth Model
•Rate of increase steadily accelerates,
population increases exponentially.
Population Size
dN = (bN-dN)
dt
b=per capita birth rate
d=per capita death rate
Think about (bN-dN) ...
•difference between births and
deaths in absolute numbers
•determines if population will
grow, be stable, or decline
dt
Time
Keeton & Gould 1993
(b-d) is the per capita growth rate. It is
the net rate of population change per
individual
factor N out on right side of equation
dN = (b-d)N
dt
Population Size
divide both sides by N to “see” the per
capita growth rate (b-d)
dN
dt = (b-d)
----N
back to...
dN = (b-d)N
dt
Time
(Keeton & Gould 1993)
dN = (b-d)N
dt
substitute r for b-d
dN = (r)N
dt
r = b-d = net rate of population change
per individual at a given moment
Population Size
Under these conditions of maximum
birth rate and minimum death rate r is
designated rmax
dN = rmaxN
dt
(Keeton & Gould 1993)
Time
• rmax represents the intrinsic rate
of increase, or biotic potential of
the population
• rmax varies widely among
species
dN = rmaxN
dt
Rate of population growth is a function of r and N;
N is related to the number of breeders
Population Size
N increases with each generation; therefore so
does the rate of increase -- dN/ d t
Its due to this accelerating rate of increase that
the slope of the curve becomes steeper and
steeper
Time
(Keeton & Gould 1993)
•All other things being equal, a
population with a higher intrinsic rate of
increase will grow faster than one with a
lower rate of increase
•The value of rmax for a population is
influenced by life history features, such
as
•age at onset of reproductive
capability
•number of young produced
Population growth predicted by the exponential model.
The exponential growth model predicts unlimited
populations increase under conditions of unlimited
resources. This graph compares growth in populations with
two different values of rmax:1.0 and 0.5
(Solomon et al 1999)
Human population growth. During the last 1000 years, the human population
(globally) has been growing nearly exponentially
No population can continue to
increase exponentially indefinitely
Environmental resistance:
•Environment imposes limits on population
growth
•Food; water; disease; shelter from
elements, predators…...
Carrying capacity (K):
•Theoretical maximum population size that
can be maintained indefinitely (assumes
unchanging environment)
•In reality, K changes with changes in
environmental conditions
Logistic population growth:
•Populations can be modeled taking
carrying capacity of environment into
account using the “logistic growth equation”
•dN/dt = rN [(K-N)/K]
The term (K-N)/K causes growth
in the simulated population to
respond to environmental
resistance
•When N is small compared to K,
[(K-N)/K] is close to 1 and growth is
nearly exponential
•When N is large compared to K,
[(K-N)/K] approaches 0, as does
population growth
Time
Some assumptions and simplifications
of the logistic model that either are not
true for most populations or do not
apply equally to all populations
•Each individual added to a population at a low
level (N) has the same negative effect on
population growth rate at low population at a
high level (N)
•Each individual exerts its negative effects
immediately at birth
•All individuals have equal effect on the
population
•Populations approach carrying capacity
smoothly – don’t overshoot it
•Carrying capacity is constant
How well does the logistic growth model fit the growth of real populations?
Experimental populations (bacteria, yeast, Paramecia…)
•Some show sigmoidal growth fairly well, but conditions do not approximate nature
(predators, competitors lacking).
•Some, not all, experimental populations stabilize at some carrying capacity, and
most experimental populations deviate unpredictably from a smooth sigmoidal
curve
Natural populations
•Introduced populations and decimated, recovering populations show growth
patterns that generally support the concept of carrying capacity that underlies
logistic population growth
Logistic Population Growth
http://www.pinnipeds.fsnet.co.uk/species/species.htm
Raven & Johnson 1999
Raven & Johnson 1999
A fur seal population on St. Paul Island, Alaska The numbers of male fur seals with
harems were reduced to very low numbers due to huntin untill 1911. After hunting was
banned, the population increased diramatically and now oscillates around an equilibrium
number, presumably the islands carrying capacity for this species
(Campbell 2000)
Logistic Population Growth
– Overshooting K
•Lag time in many populations before
negative effects of increasing
population are realized
•Hypothetical example: food becomes
limiting, but birthrate not immediately
affected because females use energy
reserves to continue producing eggs
for a period; population may then
overshoot carrying capacity
(Keeton & Gould 1993)
•Real life: In many of the populations
that show sigmoidal-type growth, they
oscillate around K, or at least
overshoot it the first time
Growth curve of the sheep population of Australia.
Smooth curve is the hypothetical curve about which real
curve fluctuates
Population Growth & Life Histories*
•Conditions of high population density may favor
life history traits different from those favored at low
population density
•High population size and life history
•High population size; limited resources, slow
or zero population growth
•Traits favored may be those that enable
organisms to survive and reproduce with few
resources
•Competitive ability and high efficiency at
resource use may be favored in populations
that tend to remain at or near their carrying
capacity
•Low population size and life history
* Life history
•Low population size; abundant resources,
rapid population growth
•Life history of an organism includes
birth, growth to reproductive
maturity, reproduction, and death
•Traits favored may be those that promote
rapid reproduction; ie high fecundity, early
maturity; efficiency of resource use not as
important
•“Life history traits” are
characteristics that affect an
organisms schedule of reproduction
and death.
•“r-Selected populations”
likely to be found in variable
environments in which
population densities
fluctuate, or in “open”
habitats where individuals
likely to face little
competition
•“K-selected populations”
likely to be living at a
density near the limit
imposed by their resources
•Life history traits do often
vary in ways shown in table
•No demonstration of direct
relationship between
population growth rate and
specific life history traits;
concepts of r and K
selection are mainly useful
as hypothetical models
Population ecology and the evolution
of life history traits
•Because of the varying pressures of natural
selection, life histories show high variability
•among species and higher taxa
•among populations within species
•even among individuals within a
population
•Patterns exist in the way in which life history
traits vary
•Life histories often vary in parallel with
environmental patterns
•Life histories often vary with respect to
each other (eg, delayed maturity & high
parental investment tend to correlate with
low fecundity and low mortality)
Relationship between adult mortality and annual
fecundity in 14 bird species Birds with high
probability of dying during any given year usually
raise more offspring each year than those with a low
probability of dying. Wandering albatross; lowest
fecundity (~.2 offspring/yr – single surviving offspring
every 5 yrs) & lowest mortality. Tree sparrow; >50%
chance of dying from one breeding season to another,
produces average of 6 offspring per year
Organisms have finite resources to
invest in components of their life
history; Trade-offs between
investments in reproduction and
survival are a consequence
•Selection favors (heritable) life history
traits that allow individuals to maximize
lifetime reproductive success; these traits
will become more common in a population
•Natural selection can not simultaneously
“maximize” all the life history traits that can
potentially contribute to the greatest lifetime
reproductive output, because organisms
have finite resources to invest; this
mandates trade-offs. eg few, wellprovisioned offspring vs many offspring,
each with little chance of survival.
•Trade-offs have been demonstrated:
•between investing in current
reproduction and survival (eg seed
beetles)
•between investing in current
reproduction and future reproduction
Manipulating fecundity
of female seed beetles
by denying access to
males or egg-laying
sites causes a trade off
in adult longevity and
fecundity
Manipulating clutch
size in collared
flycatchers (add or
remove eggs) results in
direct trade off between
number of chicks
raised that year and the
next year’s fecundity
(no effect of current
fecundity on adult
survival in this study)
Population Regulation: Two categories of factors affect population size
Density-independent factors
•Any environmental factor that affects population size, but its effect is
not influenced by population size
Density-dependent factors
•Any environmental factor that affects population size and its effect is
influenced by population size
Density-independent factors
(Solomon et. al. 1999)
Typically abiotic, often weatherrelated
•e.g. in insects, winters kill off all
individuals except eggs and
dormant larvae
Often random (unpredictable)
•e.g., blizzard, flood, fire
Effects may be indirectly related
to density
•e.g., social animals often able to
endure weather by collective
behavior -- sheep huddling in
snow storm
Density dependent factors
Important density dependent factors
•Competition, predation, disease
Effects are proportional to population size
•Density-dependent factors exert stronger effect as
population increases
•12 Bahamian islands; all
islands have native spider
populations, 4 have lizards, 8
do not have lizards
•Lizards introduced in
enclosures on 4 islands
without native lizard
populations.
•After 7 years, spider densities
were higher in lizard-free
islands (enclosures).
Effect of lizard presence on spider density.
Tropical islands with lizards typically have few
spiders. Spiller and Schoener (UC-Davis) tested
the effect of presence of lizards on spider
population density on Bahamian Islands
•Species diversity of spiders
was also greater on lizard free
islands.
•Due to predation (lizards eat
spiders), or competition
(lizards and spiders compete
for insect food)?
Solomon et. al. 1999
Age
interval
(in
months)
Number
alive at
beginning
of age
interval
Proportion
alive at
beginning
of age
interval
Number
dying
during
age
interval
•Age-specific demographics for 9-12 month cohort
•death rate = 172/316=.544
•per capita birth rate = 430
Death
rate for
age
interval
No. seeds
produced
per ind.
during
age
interval
Age
interval
(in
months)
Number
alive at
beginning
of age
interval
Proportion
alive at
beginning
of age
interval
Number
dying
during
age
interval
Death
rate for
age
interval
•Cohort members began reproducing after 3 months of age;
•Then reproduced throughout life; all dead by 2 years of age
•Probability of age-specific survival decreases with age
•Can calculate age-specific birth rates and death rates
No. seeds
produced
per ind.
during
age
interval
Population Size
factor N out on right side of equation
N
t N
Time
= (b-d)
…and dividing both sides by N gives
the per capita growth rate (b-d)...
(Keeton & Gould 1993)
N = rN
t
Under these conditions of maximum birth rate
and minimum death rate:
Population Size
r is designated rmax
rmax represents the intrinsic rate of increase, or
biotic potential of the population
rmax varies widely among species
Time
(Keeton & Gould 1993)
N = rmaxN
t
Population Size
Under these conditions of maximum
birth rate and minimum death rate:
r is designated rmax
rmax represents the intrinsic rate of
increase, or biotic potential of the
population
Time
rmax varies widely among species
(Keeton & Gould 1993)