March 18 , 2014
Biology 3SS3: Population Ecology
Competition
InterSpecies Interactions
Competition: interaction hurts (decreases the per capita growth rate of) both
species
Exploitation: interaction is good for one species but bad for the
Mutualism: interaction is good for both species
Commensalism: interaction is good for one species, and close to neutral for the
other
() helps neutral hurts
helps mutualism commensal exploitation
neutral neutral ???
hurts competition
Resource Competition
Resource competition occurs when two species both depend on the same
resource(s)
Other forms: apparent competition [via shared exploiters]; interference
competition [direct interaction]
Each species growth rate is reduced by the other’s presence
What aspsects of a species life history could be affected by competition?
• Survival growth, producing offspring
• Species may be very similar, or very different
• Oaks and maples competing for light
• Ants and deer competing for leaves
• Mussels and algae competing for space in the intertidal zone
Competition in Ecology
What factors determine which species survive in which habitats?
What factors determine how many similar species can coexist?
Why do similar species coexist at all?
Flour Beetles
Model species: ecology in the laboratory
There is a series of experiments where researchers allow two species of flour
beetles (Tribolium) to compete in different laboratory environments
The larger species survives better in drier conditions, and the smaller species
reproduces faster in moister conditions
What are the possible outcomes of such experiment?
• Each species wins when conditions are better for it
What if we tune the conditions to something in between (neither species always
does better than the other)? • The species could both survive together
• Whichever species get a head start might exlude the others
Outcomes of Competition
In a given stable environment, we generally expect the competitive interaction
between two species to have one of the following results
Dominance: one species wins every time
Coexistence: if both species are present, they will both persist
Founder control: whichever species gets established first will exclude the other
Model
We modeled a single species using the equation: dN/dt = (b(N) – d(N))N
We wan to modify this for a species which is competing with another species
dN 1dt = ?
The amount of competition seen by species 1 is N = N +a N1 1 21 2
How should our equation change?
• dN = (b (~N ) – d (~N ))N
1 1 1 1 1 1
• dN 2= (b )2~N ) 2 d (~2 ))N 2 2
• ~N = N + a N
2 2 12 1
Carrying Capacity
For this unit, we will mostly ignore Allee effect
Therefore, we expect each species to have a carrying capacity K (or K and K )
1 2
If the species is alone, the carrying capacity is that species’ stable equilibrium,
defined by: b(K) = d(K)
Carrying Capacity with Competition
dN 1= (b (1N ) 1 d (~N1))N 1 1
How can this population be at equilibrium?
~N 1 K : 1he species has the right amount of competitive pressure to make R = 1
N 1= 0 : the species is not present
K i
A 12
N 1= 1000, N =02
N 1 750, N =2500
N 1 000, N = 200
th
March 20 ,2014
Equal Competition
If the as are both equal to one, we have equal competition
This means that the competitive effect of an individual from either species is the
same
The total populations is N = N + N 1 2
Our equations are now: dN 1
=(b (1)−d (N))1 1
dt
dN 2
=(b (2)−d (N))2 2
dt
What happens in this case?
• The population with the higher value of K is going to dominate
• No coexistence (ignore K = 1 ) 2
Competitive Exclusion
Why does one species always win in equal competitions?
Competition is mediated by only one quantity, N
Whichever species can reproduce up to a higher value of N is going to win; there
is no basis for a tradeoff
Reminder:
dN 1
=(b (1)−d (N))1 1
dt
dN
2=(b (2)−d (N))2 2
dt
If K >K , then species 1 can always increase when species 2 can; and sometimes
1 2
when it can’t
Dominance (Dynamics vs. Time)
Dominance (Phase Plane) Dominance (Comparison)
Dominance (Multiple Starting Points)
Dominance Reversed
Units of a
N 1= N 1 a N21 2
N 2= N 2 a N12 1
A 21easures the strength of the competitive effect of individuals of species 2 on
the growth rate of species 1
What are the units of a 21
• Individuals of sp1/individuals of sp/2
Equal competition (both species have the same effect on each other) is a special
case of balanced competition (both species have the same relative effect on each
other)
Balanced Competition Example
Two plants, compete with each other for water. A is 4 i21ividuals of
sp1/individuals of sp2 Which species is bigger?
• Species 2 individuals use as much water as 4 species 1 individuals
If they’re only competing for water, what’s the value of a ? 12
• A 12 1 individuals of sp2/4 individual of sp1
• In some sense this means the same thing; the larger plant has four times as
much impact as the smaller one
What result do we expect from balanced competition?
• It seems like the bigger species should win
• But that’s not always the case
Balanced competition works just like equal competition
• Both species experience total density in the same way
• So the species with the higher carrying capacity (compared using the same
units) will dominate
Balanced competition means (exactly) no tendency for founder control or for
coexistence
K = K a ([sp1/sp2])
1 2 21
K 2= K a1 12
A 12 1/a 21
Measuring Competitive effects
It makes sense that we have a range of parameters that give use balanced
competition, because we know qualitative changes in dynamics are explained by
unitless parameters
What’s the unitless parameter here: C = a a 21 12
C measures the relative effect of betweenspecies and within species competition
C = 1 means competition is balanced
C<1 means there is more intraspecific competition (within species: tendency for
coexistence)
C>1 means there is more interspecific competition (between species: tendency for
founder control)
Neutral Competition
Competition is balanced, and neither species dominates: neutral competition
No tendency for either species to win
No tendency for founder control or for coexistence
If there’s any small difference between the species, one may dominate
Even if there’s no difference, one should win eventually by random drift (genetic
drift)
March 21 , 2014
Unbalanced Competition
If two species are competing by using a simple resource, we expect competition to
be balanced
Both as measure the relative ef
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