Transcript in population size

Population Ecology
Solomon et. al. 1999
Jaguar in Brazilian rain forest
Freeman 2002
Humans on a crowded urban street
Ecology is the study of interactions among organisms (biotic factors) and
their physical environment (abiotic factors).
Population
Organism
Raven & Johnson 1999
Ecosystem
Community
Population refers to individuals within a species living in the same
place at the same time
Populations as Units of Structure
and Function
Solomon et al 2002)
•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
Population of Mexican poppies (Eschscholzia
mexiana) blooming in the desert after the winter rains
Density and Dispersion are
important attributes of
populations
Species Range Geographic
extent of the occurrence of
individuals in a species
Population Individuals within a
species living in the same place
at the same time;
Species consist of populations of
varying size and number, with
varying degrees of proximity and
connectedness (think gene flow)
Population Density Number of
conspecific individuals per unit
area or volume at a given time
Dispersion Distribution, or
spacing of individuals within a
population, relative to each other
Aerial census for African Buffalo (Syncerus caffer) in the
Serengeti of East Africa. (Campbell 2002)
Clumped dispersion Many fishes, including these
butterfly fish, often clump in schools. Adaptive
function may relate to hydrodynamic efficiency of
swimming, decreased predation risk, increased
feeding efficiency. Within a school, individuals are
fairly evenly spaced
Clumped
Uniform dispersion Not common in general, but is not
uncommon among birds nesting on small islands. This
is a breeding colony of King Penguins on South Georgia
Island in the South Atlantic Ocean.
Random dispersion Populations of trees in tropical
rain forests are often randomly dispersed, but in
general, this dispersion pattern is rather rare in
nature
Patterns of dispersion of individuals in
a population
Uniform dispersion: Individuals are dispersed more evenly than expected
from random occurrence in 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
Clumped dispersion (aggregation) by far most common
in nature.
•Environmental conditions seldom uniform throughout
even relatively small area. Clumping of individuals often a
response to clumping of resources
Clumped distribution of “Microhabitats” often explains
clumping; local soil moisture, rotting log, limestone
outrcrop…
•Reproductive behavior patterns including sexual
attraction, often favor clumping
•Nonreproductive behavior patterns often lead to active
congregation in loose groups or in more organized colonies,
schools, flocks, or herds
Population demographics affect increase (growth) or
decrease (decline) in population size
Demography; study of changes in size and structure of
populations
Important demographic variables include:
•Sex Ratio
•Age structure (cohort=individuals of same age, age
class)
•Age specific fecundity (birth) rate and mortality (death)
rate
Ecologists assemble such demographic data in life tables,
then use the life tables as the basis for further analysis of
population dynamics
Population Dynamics; Changes in population size and
demographics over time
Populations size changes in response to births and deaths, and
to the movement of individuals into (immigration) our out of
(emigration) the population
N1=N0 + B - D + I - E
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
Survivorship curves are
graphical representations of agespecific survivorship
Survivorship = 1-mortality, =
percent of cohort surviving to a
given age
Top left figure shows generalized,
hypothetical survivorship curves
across a range of possibilities, and
that are recurring in nature
Curve I characterizes humans,
other large mammals, that have
high parental care but produce
relatively few young
Curve III characterizes some
species with low parental care,
large number of young (eg many
fishes, marine invertebrates
Curve II Individuals roughly equally
likely to die at any age.
Characterizes some annual plants,
some invertebrates (eg Hydra),
some lizards, rodents, birds…
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.
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
•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 (slope of the curve) steadily
accelerates, population increases exponentially.
Population Size
dN = (bN-dN)
dt
dN/dt = rate of change in size of population
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 are either 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 hunting until 1911. After hunting was
banned, the population increased dramatically 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.
Life History
•Life history of an organism includes birth,
growth to reproductive maturity, reproduction,
and death
•“Life history traits” are characteristics that affect
an organisms schedule of reproduction and
death.
•Life history of any individual will include these
traits;
-size & energy supply at birth
-rate and pattern of growth and
development
-number and timing of dispersal events
-number and timing of reproductive events
-number, size and sex ratio of offspring
-age at death
Flowering stalks of century plants (Agave
shawii). Copyright G. J. James/BPS.
•Life History varies among organisms, lineages,
based on variation in the allocation of time,
effort, energy, etc, to activities and stages from
birth, growth to maturity, reproduction, death
•Consider the importance of life history traits in
explaining demographic populations
statistics…age-specific fecundity, mortality…
Salmon spawning. Chugack National Forest,
AK. Copyright J. Robert Stottlemyer/BPS.
•“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
•among individuals within a population
•within individuals, depending on
environmental conditions, availability of
mates; consider the adaptiveness of
plasticity in life history traits
•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); such
relationships between life history traits
often reflect “trade-offs”…
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 tradeoffs.
•Trade-offs occur between:
-number & size of young;
-number of young & parental care per young;
-reproduction and growth;
-reproduction and survival;
-current reproduction and future reproduction
--between investing in current reproduction and
future reproduction
Experimental manipulation demonstrates
trade-off between investing in current
reproduction and survival Manipulating
fecundity of female seed beetles by denying
access to males or egg-laying sites causes a
trade off in adult longevity and fecundity
Experimental manipulation
demonstrates trade-off between
investing in current reproduction and
survival 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)
Populations dynamics may be influenced by factors operating independent of
population density, or in a manner that is dependent on population density.
Density-independent factors Factors that affect per capita birth rate (b) or per capita death
rate (d), with the degree of the effect not influenced by (dependent on), population density
•Typically abiotic, often weather-related; 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 Factors that affect the per capita birth rate (b) or per capita death
rate (d), with the degree of the effect influenced by (dependent on), population density
•Important density dependent factors; Competition,
predation, disease
(Solomon et. al. 1999)
-increasing density may attract predators (more
successful, efficient, hunting prey at high density)
-increasing density may increase foster spread of
contagious disease
-increasing density may lead to depleted food
supplies
Effects are proportional to population density; Densitydependent factors exert stronger effect as population
increases
Fire may constitute a densityindependent factor for some populations
•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
Hypothetical population
dynamics in regulated
population. In these
models, if birth or death rates
or both are density
dependent, population
responds to increases or
decreases in density by
returning toward equilbrium
density (zero positive or
negative growth
Population “Regulation” and Reality
A regulated population is one whose dynamics are influenced primarily
by density-dependent factors
Regulated populations experience interactions between density and
carrying capacity
In reality, many populations are probably affected by both densitydependent and density-independent factors
Number of song sparrows
on Mandarte Island (B.C.)
is a consequence of
density-independent
(winter weather) and
density dependent factors
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)