Transcript lecture7translated - College of Forestry, University of Guangxi

Population Ecology
and Interspecific Interactions
Lecture 7
Eben Goodale
College of Forestry
Guangxi University
Review
• What’s a population?
• What characteristics do populations have?
• What factors influence how a population
grows?
Review
• How does a population grow in the absence of
limiting factors（限制因子）?
Nt = Noλt
Geometric growth
When breeding is periodic
Nt = Noer(t)
Exponential growth
When breeding is continuous
N
Log N
Exponential/geometric growth
• When does this happen
in nature?
• Unlimited food (bacteria
in dish)
• Population released from
some restriction
(elephants after hunting
ban)
• Population colonizing
（殖民） new area
Review
• How do we include limitations（边界） into
models of population growth?
Why do you think this real example
doesn’t fit the model well?
Today, we’re going to look more
At this model with a time lag（时间间隔）.
And with two competing species.
Today’s class
• A little more population ecology
– Population cycles caused by delayed density
dependence.
– Extinctions in small populations
– Metapopulations.
• Species Interactions: competition
• Some time to think about exam
Fluctuations common in populations
• May be like sheep
example, K keeps
shifting up and down.
• Predators and prey also
can make each other’s
populations cycle. We
will explore this after
exam.
The logistic equation and time lags
The idea of “overshooting
（过辐射)” K
0 < rτ < 0.368
dN
 N (t  ) 
 rN 1 
dt
K 

Robert May (1976)
0.368 < rτ < 1.57
If a big lag (τ),
Or fast growth (r),
Can get oscillations
rτ > 1.57
The logistic equation and time lags
Nicholson 1957:
Negative effects of adult high densities
Only felt some time later,
when many fly larvae hatched
(all die because too many)
Fluctuations can be dangerous
in small populations
When λ goes up and down
(is variable – 变量), small
populations can go extinct.
Populati
on
Variabilit Extinctio
y (SD) of n after
λ
70 yrs
10
.2
0.3%
10
.4
17%
10
.8
53%
100
.8
29%
1000
.8
14%
10000
.8
6%
Other reasons for small populations
being extinction-prone
• Genetic drift:
– What is it and why is it
important in small
populations?
• Inbreeding
• The “Allee effect”: in
some populations λ gets
lower when population
is low.
– Animals can have
trouble finding mates
Metapopulation（集合种群）
theory
A large population is actually
broken into many small
populations, linked by dispersal (传播).
The small populations continually
go extinct or are colonize.
Some metapopulations are
successful and send out colonizers.
They are “sources（起源）”. Other
metapopulations are less successful
and are called “sinks（减少）”.
Metapopulation theory
• A model of metapopulations (Levin 1969,
1970)
dp
 cp 1  p   ep
dt
p = Proportion of habitat patches
occupied at time t
c = Patch colonization rate
e = Patch extinction rate
You don’t need to be able to solve this.
I just emphasize how equations can be
solved using 0’s.
dp/dt = the change in the amount of
patches over time.
What happens if this is 0?
0 = cp(1-p) – ep
ep = cp(1-p)
ep = cp – cp2
e = (cp – cp2) / p
e = c – cp
cp = c-e
p = (c-e)/c
p = 1 – e/c
If c > e, p is
positive and dp/dt
is positive.
But if e > c,
dp/dt is negative
and the metapopulation
will go extinct.
Metapopulation theory
• When forests are
fragmented（变成碎片）,
c gets less because it is
harder for animals to move
between patches.
• e also increases because the
patches are smaller and
cannot sustain large
populations.
• Hence e/c might become
greater than 1 and the
whole meta-population may
go extinct.
This argument has been used
to preserve forest from
fragmentation, especially in
the case of the northern
spotted owl.
Metapopulation theory
Patches that
are large and
nearby other
patches are
colonized first.
Today’s class
• A little more population ecology
– Population cycles caused by delayed density
dependence.
– Extinctions in small populations
– Metapopulations.
• Species Interactions: competition
• Some time to think about exam
Competition: a definition
• Competition occurs
between two individuals
that use the same resources.
• Resources（资源） are
anything that can be
depleted such as food,
water, light (because it can
be shaded), and space
(because it can be used up).
• Both individuals are harmed
(an - / - interaction)
Give an example of a + / - interaction.
A + / + interaction.
Space can be a limiting resource
Intraspecies（种内） competition
Biomass
Young birch stand
# individuals
Self Thinning
Older stand
Intraspecific competition
# males
without
territories
# males with territories
# offspring
per female
# females
Juvenile
survival
# adults
Song Sparrow
2 different kinds of competition
Resource competition
Interference（干扰）
competition
All individuals get smaller
amount of common
Some individuals get
resource
resource and exclude (排除)
others from it
2 different kinds of competition
Resource competition
Interference competition
All individuals get smaller Some individuals get
amount of common
Resource and exclude others
resource
from it: tends to be
aggressive（好斗的）
Cattle grazing–
As more cattle all will be
thinner
Terrioriality（领土权） in birds –
Some get the territories, some don’t
Population
Intraspecific competition
Is controlling population
growth
And now we are starting to talk
about species interactions（种间
相互作用),
starting with interspecific（种间
的） competition.
Species
Population
The niche（生态位）
is a characteristic
Of the species
Intraspecific competition
Is controlling population
growth
The niche
The set of environmental requirements of the
species.
“N-dimensional hypervolume”
N = all the environmental variables
Important to survival and reprodution
Fundamental niche:
The abiotic environmental variables
G. Evelyn Hutchinson
Realized niche:
Actual niche where biotic interactions
are also considered.
What does this “N-dimensional
hypervolume” look like?
Ecologists then
Measure overlap（重叠）
In niches
Interspecific competition: competitive
exclusion（排斥） principle
• 2 species can not share the same niche
indefinitely
Gause’s 1934 experiments
Interspecific competition: competitive
exclusion principle
• 2 species can not share the same niche
indefinitely
Gause’s 1934 experiments:
P. aurelia and P. caudatum
eat the same resource and
one goes extinct.
P. bursaria eats a somwehat
different resource. Notice K
when 2 species co-exist is low.
Lotka-Volterra theory of
competition
• This model developed in the
1920’s by two scientists
independently.
• It looks at two populations that
are competing with each other,
and how they effect each
other’s population size.
• We will look at the model
graphically（生动的） and try
to understand it’s major ideas,
not the details.
A note on mathematics
• Ecology is mathematical in
nature, so presenting it
without math is not really
letting you see the science.
• My favorite experiences in
ecology have been in
understanding at a basic
level the idea of an
equation.
• Equations are valuable not
only for their conclusions,
but understanding
assumptions.
• Working with equations is
like reading a primary
literature paper: scary, but if
know tricks doable.
• Use “0”s and “1”s to simply
equations.
• Look at trends graphically
• I will be specific about what
you need to know for tests.
Adjusting the logistic equation for
interspecific competition
dN
= rmax (N) (1 -
dt
dN1
dt
=
rmax (N1) (K1 – N1)
K1
These are the growth rates
Of the two species.
We want to know: under
what conditions can the
two species co-exist?
N
)
K
dN2
dt
=
rmax (N2) (K2 – N2)
K2
Adjusting the logistic equation for
interspecific competition
dN
= rmax (N) (1 -
dt
dN1
=
dt
dN1
dt
=
N
)
K
rmax (N1) (K1 – N1)
K1
rmax (N1) (K1 – N1 – α12N2)
K1
dN2
dt
=
dN2
dt
=
Where α12 is the competitive effect of species 2 on 1,
and α21 is the competitive effect of species 1 on 2.
rmax (N2) (K2 – N2)
K2
rmax (N2) (K2 – N2 – α21N1)
K2
We are saying that the
population growth of one
species is dependent
on（取决于）
the other species.
Adjusting the logistic equation for
interspecific competition
dN
= rmax (N) (1 -
dt
dN1
=
dt
0
=
N
)
K
rmax (N1) (K1 – N1)
K1
rmax (N1) (K1 – N1 – α12N2)
K1
(K1 – N1 – α12N2) = 0
N1 = K1 - α12N2
dN2
dt
0
=
=
rmax (N2) (K2 – N2)
K2
rmax (N2) (K2 – N2 – α21N1)
K2
(K2 – N2 – α21N1) = 0
N2 = K2 – α21N1
Again notice we solve for 0. We are looking at conditions where growth is 0.
Drawing the isocline（等斜线）
K1/ α12
In these series of
graphs we are
looking at initial
numbers of N1 and N2.
Over time they change.
N2
N1 = K1 - α12N2
If N2 = 0, N1 =
If N2 = K1/ α12, N1 =
N1
Putting dN/dt on the graph
dN1
dt
=
rmax (N1) (K1 – N1 – α12N2)
K1
If N2 is 0, and N1 < K1
What happens?
dN1
dt
dN1
=
rmax (N1) (K1 – N1 – 0 ))
K1
N2
Is positive
dt
N1
Putting dN/dt on the graph
dN1
dt
rmax (N1) (K1 – N1 – α12N2)
=
K1
If N1 is 0, and N2 <
K1
α12
What happens?
X
Where X < K1
N2
α12
dN1
dt
=
rmax (N1) (K1 – 0 – X)
dN1
dt
K1
Is positive
Where X < K1
N1
Putting dN/dt on the graph
In fact, when the initial
conditions are to the left of
this line, N1 will increase.
Using the same arguments,
when initial conditions are
to the right of this line, N1 will
decrease.
N2
N1
Putting dN/dt on the graph
Now we could make
a similar graph for N2
Putting dN/dt on the graph
Things get really complicated
When we put both dN1/dt
and dN2/dt on the same
graph
But let’s take a point
In the lower left corner
What’s dN1/dt doing?
What’s dN2/dt doing?
We can combine their motion
like this
Putting dN/dt on the graph
Now let’s take a point
In between the lines
What’s dN1/dt doing?
What’s dN2/dt doing?
We can combine their motion
like this
Putting dN/dt on the graph
Finally, pick a pint in
upper right corner
What’s dN1/dt doing?
What’s dN2/dt doing?
We can combine their motion
like this
Putting dN/dt on the graph
The whole
picture looks
like this
What does
this mean?
In this case,
N2 will go extinct
Putting dN/dt on the graph
There are other
scenarios, too
Note that now
N2’s isocline
is on top of N1’s
What’s the
outcome here?
In this case,
N1 will go extinct
Putting dN/dt on the graph
A third scenario（方案）
Compare to
the first we did
What’s the
outcome here?
In this case,
N1 or N2
will go extinct,
depending on the
initial numbers
Putting dN/dt on the graph
And a fourth scenario
Compare to
the third…
What’s the
outcome here?
In this case,
the two
populations
can co-exist
What does this mean
The only situation
When these 2
Species can
Co-exist（共存) when:
Also note that the point
of equilibrium（平衡点） for species
is smaller than K1 and K2.
K1 /α12 > K2
That means α12 is small
At the same time
K2 /α21 > K1
So α21 is small, too
Overall when the effects of the interspecific competition are less than
intraspecific competition, two species can co-exist
Lotka-Volterra theory of
competition
• In most cases in which two
species compete, one will go
extinct.
• But an equilibrium can be
reached when interspecific
competition is low (niches are
somewhat different)
• And at that equilibrium the
carrying capacity for both
species is lower than when they
are by themselves: same as
Gause’s results.
But does competition happen in real
communities?
• Review articles（综述） show
that competition was found in
most cases in the field.
• For example, Schoener (1983)
looked at 164 papers studying
390 species and 76% of
species showed some effect of
competition.
• Let’s look at some examples…
Barnacles（藤壶） in the
intertidal zone（潮间带）
Joseph Connell removed Balanus and looked at response of Chthamalus.
Chthamalus moved down, proving that it is not in this area due to
competition with Balanus.
Barnacles in the intertidal zone
Rodents（啮齿动物）
in the desert
Brown and colleagues
And competition can even be between
very different kinds of organisms
How to avoid competition
• Organisms can avoid
competition by having
different niches.
• Sometimes an inferior
competitor can persist
because it tolerates
disturbance（干扰）.
• Sometimes an inferior
competitor can persist
because predators or
herbivores don’t like it.
This sea palm only lives in areas
where waves remove musssels
frequently. Otherwise it is outcompeted.
The “ghosts（幽灵） of competition past”:
Character displacement（性状替换）
• Often two species are
not competing with
each other now, but
may have had before
• Character
displacement: species
are more different
when they live in the
same place
Today’s class
• A little more population ecology
– Population cycles caused by delayed density
dependence.
– Extinctions in small populations
– Metapopulations.
• Species Interactions: competition
• Some time to think about exam
Key concepts
• Population fluctuations can
be caused by time delays in
the effect of densitydependent factors.
• Small populations are more
vulnerable to extinction for
several reasons.
• Large populations can
actually be thought of as a
collection of small
populations, that go extinct
and are re-colonized.
• Interspecific competition
occurs when individuals of
different species both
deplete a resource.
• If the species’ exact
resource requirements
(niches) are the same they
can not coexist, but they
can coexist with some niche
overlap.
• Evidence of interspecific
competition has been found
commonly by ecologists.
Tuesday’s exam
• What to bring:
1) calculator (phone OK)
2) Pen or pencil
3) One A4 piece of paper with your notes (can
be front and back).
• One thing about studying: for lectures 4-7
please check FINAL version on web.
What kinds of questions to expect
• Multiple answer questions (A, B, C, D).
• Short answer questions
• One essay question on the primary literature
readings (3 choices). For those literature
readings, read carefully titles, abstracts and
figures, and any more of the article necessary
to get the general idea of a) what they did and
b) what they concluded.
Review questions posted today on
website
• Vocabulary words (underlined in notes or in
red in readings) are fair game. Know what
these words mean and the ideas associated
with them.
• The review questions will highlight important
ideas.
• I will be at the classroom at 2:00, and
between 2:00 and 3:00 will answer any
questions. The exam will start at 3:00 and last
to 5:00.