WEBVTT

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Prof: Today we're going
to talk about inter-specific

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competition.

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And you will remember that last
time I was talking about

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intra-specific competition,
and we were looking a bit at

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the impact of density on
population growth.

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And I want you to remember that
if an individual is encountering

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increased population density,
during its life,

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as it grows from a zygote up
through an adult and reproduces,

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the effect of increasing
density will be to decrease its

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growth rate.

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It will be smaller when it
matures.

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It will have fewer babies.

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Often the babies will be of
lower quality,

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and the mortality rates in the
population will be higher.

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So that's the general impact of
intra-specific competition.

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However, animals don't live in
a world, and plants don't live

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in a world, where they only
encounter other members of their

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own species.

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They're often living in a
complex ecological community.

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And so what we want to do is
understand what happens to them

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in a complex community.

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And I'm going to do this by
showing you some classical

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descriptive patterns;
then move through to some

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experiments to demonstrate
competition;

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give you an abstract conceptual
framework in which to think

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about this;
and then return to the complex

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reality of competition,
at the end.

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Okay?

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So, a reminder that it's often
useful, when you're thinking

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about interactions between
species, to just use simple

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logic.

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You'll remember in an earlier
lecture I said,

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"Don't be afraid of using
simple logic in constructing

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your papers."

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This is the kind of thing that
could lay down a nice simple

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introductory logical framework
for something that you're

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dealing with.

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This particular one is about
biological interactions in

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communities.

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So if species' 1 effect on
species 2 is in this column,

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and species' 2 effect on
species 1 is in this column,

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and species 1 has a negative
effect on species 2,

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and species 2 has a negative
effect on species 1,

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then we've got competition.

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If species 1 has a positive
effect on species 2,

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and species 2 has a negative
effect on species 1,

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then species 1 is food,
and species 2 is eating it

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>

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, and you've got predation,
parasitism or grazing.

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If species 1 has a negative
effect on species 2,

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and species 2 has no effect on
species 1,

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we call that amensalism,
and you can contrast that with

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commensalism,
where the relationship is --0.

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So here, for example,
species 1 might be

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benefiting--its effect on
species 2 is positive.

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So species 2 is benefiting from
its presence,

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but there's no effect the other
way around.

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So basically what's going on
here is species 2 might be

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living in species 1,
but not impacting it otherwise.

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It might be very small or it
might not--it might just fit in,

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in a very comfortable way.

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So this kind of plus/minus
framework is a useful overall

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way to see what we're
concentrating on today,

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which is competition.

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And here are some of the
natural history patterns that

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suggested to ecologists that
inter-specific competition is

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important in Nature.

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This is one of Jared Diamond's
observations,

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from New Guinea.

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And this is a thrush.

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There are a couple of species
of thrush there.

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There are two species in the
same genus.

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Usually when two species are in
the same genus,

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they're ecologically pretty
similar, they tend to eat pretty

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similar things.

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And the interesting thing about
this pattern is that you're

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going up a mountainside,
and this species is getting

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more and more and more abundant,
and then suddenly it disappears.

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And if you're coming down from
the top of the mountain,

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this species is getting more
and more abundant,

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and then suddenly it
disappears, right here at about

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5500 feet elevation;
just about one mile high.

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So it looks like the two
species are butting into each

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other and they're excluding each
other right at the point where

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they're each doing really great.

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So that's a suggestive pattern.

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It doesn't demonstrate that the
reason for the border here is

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inter-specific competition.

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Anybody have an idea what else
might do that?

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They each carry a disease that
knocks out the other one.

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Okay?

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That'll do it.

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It could be that this one
actually can resist a predator

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that eats its eggs,
or something like that,

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and this one can't resist that
predator,

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and vice-versa.

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So it could be apparent
competition.

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Okay?

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Without an experiment,
you don't actually know what is

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making that sharp line.

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But it's suggestive,
it looks like it could be

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competition.

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Then Robert MacArthur did a lot
of work on warblers for his

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Ph.D.

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thesis.

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And the thing that you want to
concentrate on in this picture

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is the different parts of the
spruce tree that the different

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warblers use.

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So the Cape May--this is a
diagram of half a spruce tree,

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cut in half -- using the middle
and lower inner part.

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The Blackburnian warbler is
using the outer middle third

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about.

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The Bay-breasted warbler is
using about the upper outer

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third.

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The black-throated green
warbler is using some of the

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inner part here,
and the Myrtle warbler is down

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inside the tree,
about here, and then down close

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to the ground.

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So it looks like the warblers
of North America have taken the

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spruce tree and they've divided
it up so that they don't run

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into each other too much,
and they're each using a

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different part.

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That's an interesting
observation, because if you

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think about it,
what it means is that they're

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guaranteeing that they're going
to run into more intra-specific

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competition.

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They're avoiding inter,
but they're running into more

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intra-specific competition.

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So that if you say, "Hey,
this has been caused by

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competition,"
you're making an implicit

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assumption about how strong that
those relationships are.

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This one is saying
inter-specific has probably been

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more important than
intra-specific competition.

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Okay?

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So again a very suggestive
pattern, but not confirmed by

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experiment.

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Now, those sorts of patterns
led Evelyn Hutchinson to suggest

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this kind of view of why we find
so many species on the planet.

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He says basically over a long
period of time evolution will

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fill the world up with species,
and they will get better and

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better at exploiting the
resources they encounter,

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and competition will limit the
number of species you can pack

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onto the planet.

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At about the time that
Hutchinson was thinking about

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this,
various people,

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including Garrett Hardin,
were enunciating what's called

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the competitive exclusion
principle;

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that two species with very
similar resource needs in

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physiology can't co-exist in the
same place, at equilibrium.

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So the assumptions behind that
are that we're looking at an

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equilibrium that's established
after a long time;

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that the competitive exclusion
principle applies.

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That means two species cannot
occupy exactly the same niche--

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which is what it looks like is
going on with the warblers and

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the thrushes in New Guinea--
and that diversity is

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determined primarily by
competition rather than by

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predation or by disease or
something like that.

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So let's see to what extent
this kind of thinking has

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occasionally been confirmed in
Nature.

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And one of the first field
experiments, showing that

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competition was really quite
important, between two species,

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was done by Joe Connell.

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Joe Connell is much revered
Emeritus Professor at the

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University of California at
Santa Barbara now.

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He did his Ph.D.

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thesis at the University of
Edinburgh in Scotland,

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and he worked on barnacles that
were living in the rocky

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intertidal in Scotland.

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And in particular he contrasted
Balanus balanoides and

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Chthamalus stellatus;
and Balanus and is big and

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Chthamalus is small.

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And the pattern that he
found--and he confirmed this by

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doing manipulation experiments
in the field--

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is that the larvae of Balanus,
which is big,

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settle out over a big tidal
range.

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This is mean higher water;
this is mean lower spring water;

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this is mean lower normal tide
range.

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Okay?

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So once a month the tides get
this high, and at that point the

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larvae of Balanus can settle out
over the whole tidal range.

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However, Balanus is sensitive
to drying out,

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and so as these larvae grow up,
many of them die because

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they're getting desiccated,
and so the upper range of

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Balanus drops.

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However, it does just fine over
the whole tidal range below

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that.

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And down here,
the problem that Balanus is

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encountering is that primarily
there are other Balanus around

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crowding them out.

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And, by the way,
when two barnacles grow right

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up next to each other,
one of them can actually grow

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under the other and pry it off;
so it'll fall off.

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So you might think that
barnacles look like extremely

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boring,
slow moving rocks,

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but in fact they have a little
bit of direct competitive

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activity for space.

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Chthamalus is a little guy,
and what Chthamalus does

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basically is it gets a refuge up
in the dry part of the upper

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intertidal.

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Its larvae can actually settle
pretty high up,

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and it can survive up here,
where Balanus cannot.

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So its problem is primarily
getting scrunched by Balanus at

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lower tidal ranges.

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And by doing cage experiments
and removal experiments,

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where he actually took one type
or the other off the rock,

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and came back--and he actually
mapped them out,

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so he followed each
individual--Connell could show

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that this was what was going on.

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Another famous set of early
competition experiments were

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done by Gause.

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Gause was a Russian ecologist,
who became a Russian

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epidemiologist,
and he did some early work,

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back in the 1920s,
using Paramecia.

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And he used three species:
Aurelia, Caudatum and Bursaria.

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And what he showed basically is
that if you grow them alone,

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this is their density,
that you can measure,

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per milliliter;
and if you grow them together,

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that Aurelia will exclude
Caudatum completely;

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and that if you compete
Caudatum and Bursaria together,

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they can actually coexist.

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So from these early experiments
it did look--

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by the way, in this
circumstance they are both

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persisting at much lower
population densities than when

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they're alone.

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You can see that from the
y-axis.

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This goes up to 75;
that goes up to 200.

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So they are depressing each
other's densities.

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You can tell that they're
competing because of that

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observation.

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But they manage to coexist,
they don't go extinct.

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So it looked here like there
were two possible options.

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One wins and the other goes
extinct, or they co-exist.

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Now over the last fifty or
sixty years there have been a

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lot of competition experiments
done,

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and after Connell,
and then later Bob Payne,

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who was working more on
predators, did these removal and

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caging experiments,
people had a frenzy of

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experimentation out in Nature,
where they would remove one

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species and then see what
happened to another.

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Nelson Hairston did it with
salamanders,

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down in North Carolina,
on a huge scale in the

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Appalachian Mountains,
and managed to demonstrate that

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if you pull one salamander out,
the density of the other one

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increases,
and they grow faster and they

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have more babies.

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So you can--by removing one,
you can demonstrate that there

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is competition going on.

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In all those many experiments,
one of the important take-home

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points is that the results are
usually highly asymmetric.

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That means that the removal of
one of the competing species has

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a much bigger impact on the
other;

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species 1 having a big impact
on species 2,

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and removing species 2 often
doesn't have such a big impact

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on species 1.

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So asymmetric competition
appears to be fairly common.

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And it can get so asymmetric
that it may be amensalism rather

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than competition.

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So in some cases you get
removing one has no impact on

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the other, whereas you do it the
other way around and there's a

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big impact.

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Okay?

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So there's a continuum of these
kinds of cases.

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And often what's going on is
that competition for one

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resource is reducing the ability
of a species to compete for

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another.

13:20.649 --> 13:23.099
So, for example,
if plants are competing by

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shading each other out,
then the plant that's getting

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shaded is having a harder time
building roots,

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which is giving it difficulty
getting the water.

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So you can see there can be a
cascade of effects that

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inter-specific competition might
trigger.

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And just as a side note,
plants have developed an early

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warning system to indicate
whether they're coming into

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competition.

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They can't tell them whether
they're dealing with another

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species or not,
but if they're starting to get

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shaded by another species,
or by another plant,

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then the ratio of near-red to
far-red light,

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that's coming into their
chloroplasts,

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is getting shifted by being
shaded,

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and they actually produce a
hormone,

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that gives a signal to the
plant, oh,

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I'm getting shaded in that
direction,

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and they will grow a branch out
in the other direction;

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so they'll grow away from shade
and toward light,

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and they actually have an early
warning system that's detecting

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competitions.

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Annie Schmitt,
up at Brown University,

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has done interesting work on
that.

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Now how to conceptualize all of
this?

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Well if we take those
observations we had,

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from the last lecture on
density dependence,

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this guy Verhulst,
who was a Belgian demographer,

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developed a simple modification
of the exponential equation that

14:42.860 --> 14:44.610
we were looking at.

14:44.610 --> 14:48.330
And the key idea there is that
as density goes up,

14:48.325 --> 14:52.415
the per capita rate of increase
is going to decline.

14:52.418 --> 14:55.908
So it's going to decline
linearly until it reaches 0 at

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K.

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And if you look at this,
right here--

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so if density goes up,
and when N = K,

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you have 1 minus 1,
which is 0, and that means that

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the rate of change of population
per unit time equals something

15:10.048 --> 15:10.848
times 0.

15:10.850 --> 15:11.590
Okay?

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So it levels out;
and that's what's going on

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right here.

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This is increasing,
but the rate at which it's

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increasing is being affected by
the density.

15:21.870 --> 15:24.490
So density is on this axis,
K is right here.

15:24.490 --> 15:27.820
And as you get that N closer
and closer to K,

15:27.815 --> 15:31.665
this part of it's getting
closer and closer to 0.

15:31.668 --> 15:34.658
So the multiplication rate is
dropping and it smoothes right

15:34.664 --> 15:34.974
out.

15:34.970 --> 15:40.050
In fact, in this simple model,
the maximum rate of increase is

15:40.048 --> 15:42.628
here, when N is equal to K/2.

15:42.629 --> 15:48.489


15:48.490 --> 15:54.500
These are the two guys that
extended that into multi-species

15:54.495 --> 15:59.175
competition: Alfred Lotka and
Vito Volterra.

15:59.178 --> 16:03.188
And Lotka was a demographer at
Johns Hopkins,

16:03.187 --> 16:08.377
and worked oh between about
1915 and about 1935 mostly.

16:08.379 --> 16:14.409
And Vito Volterra was a really
eminent Italian mathematician,

16:14.408 --> 16:18.518
who had a son-in-law who was
engaged in fisheries management

16:18.518 --> 16:21.578
in the Mediterranean,
and the son-in-law would

16:21.581 --> 16:24.481
occasionally have dinner with
the father-in-law,

16:24.480 --> 16:27.390
and would bring to the
father-in-law certain conceptual

16:27.389 --> 16:29.489
problems dealing with the
fisheries,

16:29.490 --> 16:32.210
like, "Well let's suppose
that we have two fish species

16:32.207 --> 16:33.957
that are competing with each
other,

16:33.960 --> 16:36.690
but we can conceive of the
fishing fleet being a predator

16:36.690 --> 16:39.000
acting on them;
how should we predict the

16:39.000 --> 16:39.950
dynamics?"

16:39.950 --> 16:43.110
And Volterra,
who really was a pretty

16:43.107 --> 16:47.337
profound mathematician,
found these problems amusing,

16:47.341 --> 16:51.581
and he tended to write down the
answers on napkins at dinner,

16:51.580 --> 16:53.010
and hand them to his son.

16:53.009 --> 16:57.969
So they were more or less
throwaway lines for him.

16:57.970 --> 17:02.490
Now the way that they--these
two guys, who came up with the

17:02.489 --> 17:06.769
same way of conceptualizing
these problems--the way they

17:06.773 --> 17:09.193
conceptualized it was this.

17:09.190 --> 17:11.640
This is the essence of it right
here.

17:11.640 --> 17:15.460
They've both decided that what
they would try to do is

17:15.458 --> 17:19.928
basically use the single species
framework and just convert the

17:19.925 --> 17:23.955
density of the other species
into an equivalent number of

17:23.961 --> 17:25.331
this species.

17:25.329 --> 17:26.249
Okay?

17:26.250 --> 17:30.200
And that's what these alpha
competition coefficients are

17:30.202 --> 17:31.212
going to do.

17:31.210 --> 17:35.760
And so they wrote down
differential equations that have

17:35.759 --> 17:38.449
a term up here,
that includes the

17:38.454 --> 17:40.734
inter-specific effects.

17:40.730 --> 17:44.900
And if you look at the logistic
equation,

17:44.900 --> 17:49.160
which had that nice smooth
approach to a saturation point,

17:49.160 --> 17:53.370
you'll notice that there is a
chunk of these equations that

17:53.365 --> 17:57.275
looks just like the chunk of the
logistic equation,

17:57.279 --> 17:59.649
except they've stuck in this
little term here.

17:59.650 --> 18:02.040
So what they're basically
saying here is this.

18:02.038 --> 18:03.828
I'll read it out to you in
English.

18:03.828 --> 18:07.328
"The rate of change of
species 1 is equal to the

18:07.333 --> 18:10.233
intrinsic rate of increase of
species 1,

18:10.230 --> 18:13.850
times the number of species 1,
which are present,

18:13.848 --> 18:19.408
times a factor that you're
using to account for

18:19.413 --> 18:21.353
density."

18:21.348 --> 18:24.148
And the way you account for
density is take the carrying

18:24.153 --> 18:25.963
capacity of species 1,
and you ask,

18:25.963 --> 18:28.683
"How far away from that
carrying capacity are we?"

18:28.680 --> 18:32.540
Well we have to subtract the
number of species 1 which are

18:32.538 --> 18:33.078
there.

18:33.079 --> 18:33.869
Okay?

18:33.868 --> 18:36.958
So we might be a long away from
carrying capacity,

18:36.959 --> 18:39.229
because we have some of species
1;

18:39.230 --> 18:44.800
and we convert species 2 into a
number that's equivalent to a

18:44.798 --> 18:46.838
number of species 1.

18:46.838 --> 18:49.698
And we do the same thing over
here.

18:49.700 --> 18:54.210
So this is very similar to K -
N/K.

18:54.210 --> 19:02.740
And you'll see that basically
when this number here,

19:02.740 --> 19:08.930
N1 alpha 1,2 N2 = K1,
we have K1 - K1,

19:08.929 --> 19:11.939
which is 0/K1.

19:11.940 --> 19:15.980
So as this gets larger and
larger, the rate of increase is

19:15.982 --> 19:17.972
going to smoothly go to 0.

19:17.970 --> 19:21.730
So they did posit what is
probably the simplest way to

19:21.729 --> 19:26.269
make that one species situation
into a two species situation,

19:26.269 --> 19:29.759
and they did it by assuming
that you could just convert one

19:29.762 --> 19:32.712
species into the other,
in terms of its impact on

19:32.711 --> 19:34.261
inter-specific competition.

19:34.259 --> 19:37.779


19:37.779 --> 19:42.209
Now, let me go back there for a
minute.

19:42.210 --> 19:47.330


19:47.328 --> 19:50.638
These differential equations
are not easy to solve;

19:50.640 --> 19:56.120
and in fact it's a system of
differential equations that are

19:56.115 --> 19:58.245
linked to each other.

19:58.250 --> 20:02.060
But there are some simple
tricks that you can use to get

20:02.063 --> 20:06.503
some insight into the dynamic
behavior of a system like this,

20:06.500 --> 20:11.230
whether you have a numerical
solution or not.

20:11.230 --> 20:13.380
And so I'm now going to show
you that simple trick,

20:13.384 --> 20:14.984
and we'll practice it a little
bit.

20:14.980 --> 20:18.480


20:18.480 --> 20:22.740
So here we have plots of N1
versus N2.

20:22.740 --> 20:26.370
So what we have done is we've
created a phase space.

20:26.368 --> 20:29.868
And it's important to realize
what I'm talking about now.

20:29.868 --> 20:33.298
I am not talking about an axis
in which we are plotting the

20:33.295 --> 20:36.185
population density of the
species against time.

20:36.190 --> 20:39.840
I'm talking about axes where we
have the population density of

20:39.839 --> 20:43.549
one species plotted against the
population density of the other

20:43.550 --> 20:44.270
species.

20:44.269 --> 20:46.899
And time has disappeared,
for the moment,

20:46.904 --> 20:49.874
from our consideration,
when we look at it.

20:49.868 --> 20:57.078
So this is the zero-growth
isocline, and basically what

20:57.084 --> 21:04.574
this line here is expressing,
at what points is species 1

21:04.566 --> 21:06.566
increasing?

21:06.568 --> 21:10.208
And the answer is that if there
aren't any species 2 present--

21:10.210 --> 21:12.680
so we're down at 0,
on the y-axis,

21:12.682 --> 21:16.282
no species 2 present--
it reverts to the simple

21:16.278 --> 21:17.478
logistic model.

21:17.480 --> 21:22.640
And species 1 will increase up
to the point where it hits its

21:22.641 --> 21:24.621
carrying capacity,
K.

21:24.618 --> 21:28.398
If it goes over that carrying
capacity, it will decrease until

21:28.397 --> 21:30.377
it hits the carrying capacity.

21:30.380 --> 21:32.320
That's the assumption of the
model.

21:32.318 --> 21:39.298
The species 2 isocline
intersects the y-axis--

21:39.298 --> 21:43.158
not the x-axis but the
y-axis--at the carrying capacity

21:43.156 --> 21:46.046
of species 2,
and if there are no species 1

21:46.047 --> 21:48.167
present,
then we're just down to this

21:48.172 --> 21:50.682
one axis,
and species 2 will increase

21:50.680 --> 21:54.290
until it hits its carrying
capacity of species 1,

21:54.288 --> 21:57.588
and species 2 will decrease if
it's over that carrying

21:57.594 --> 21:58.284
capacity.

21:58.279 --> 22:02.169
What the isocline does is it
gives you the effects of

22:02.167 --> 22:06.277
converting the other species
into equivalent competition

22:06.280 --> 22:08.300
units for this species.

22:08.298 --> 22:11.778
So if you're looking here at
the species 1 situation,

22:11.778 --> 22:14.508
and you start adding in some
species 2,

22:14.509 --> 22:19.629
then it will hit its
zero-growth point,

22:19.630 --> 22:23.500
its carrying capacity,
at a lower and lower density of

22:23.500 --> 22:26.040
species 1,
because there's some species 2

22:26.044 --> 22:27.974
there,
that are competing with it.

22:27.970 --> 22:30.360
And this line tells you exactly
where that will happen.

22:30.358 --> 22:35.868
Everywhere along this line
species 1 has a zero growth

22:35.872 --> 22:36.602
rate.

22:36.599 --> 22:38.479
Similarly, for species 2.

22:38.480 --> 22:41.840
What this line is doing is
telling you what the impact of

22:41.835 --> 22:44.225
competition, coming in from
species 1 is,

22:44.230 --> 22:45.250
on species 2.

22:45.250 --> 22:49.670
And as you add in species 1,
by increasing the numbers out

22:49.669 --> 22:52.399
here,
it is reducing the density at

22:52.403 --> 22:56.563
which species 2 reaches its
carrying capacity and its zero

22:56.556 --> 22:59.006
growth rate;
which is why this line is

22:59.005 --> 23:01.765
pointing down here,
this line is pointing up here.

23:01.769 --> 23:09.199


23:09.200 --> 23:11.870
I'm now going to show you the
four possible outcomes,

23:11.868 --> 23:15.268
of putting these things
together, but before I do it,

23:15.269 --> 23:19.609
I'd like you to take a moment
and turn to your colleague,

23:19.608 --> 23:23.888
and explain to them what these
axes mean and why the arrows

23:23.892 --> 23:25.962
point in those directions.

23:25.960 --> 23:28.420
And then I'd like to take any
questions about somebody that

23:28.423 --> 23:30.653
doesn't understand this,
because when I show you the

23:30.650 --> 23:32.720
next picture,
if you haven't got that clear

23:32.719 --> 23:35.159
in your mind,
the next picture is just going

23:35.161 --> 23:36.901
to be a little hard to digest.

23:36.900 --> 23:39.210
So take a minute and try to
explain this to each other,

23:39.208 --> 23:41.258
and then ask me questions if
you don't get it.

23:41.259 --> 25:30.909
<<Students confer with
one another>>

25:30.910 --> 25:36.510
Prof: Okay.

25:36.509 --> 25:39.859
We have the opportunity for an
immediate quiz on how well you

25:39.861 --> 25:41.901
got it,
because when I show you the

25:41.898 --> 25:44.608
four possible outcomes,
I can ask you to explain why

25:44.606 --> 25:46.896
the vectors move in the
direction that they do.

25:46.900 --> 25:50.150
These are the four possible
outcomes of competition between

25:50.145 --> 25:50.925
two species.

25:50.930 --> 25:54.220
The first one is that species 1
wins.

25:54.220 --> 25:58.710
And that species 1 here is
always indicated in red,

25:58.710 --> 26:03.120
and you can always tell which
isocline belongs to which

26:03.118 --> 26:08.018
species by looking at where the
isocline is intersecting,

26:08.019 --> 26:09.259
and how it's labeled.

26:09.259 --> 26:09.939
Okay?

26:09.940 --> 26:13.680
So we know that this isocline
belongs to species 1,

26:13.681 --> 26:16.301
because the K1 is on the N1
axis.

26:16.298 --> 26:20.568
And what you see here is that
species 1 is able to grow at

26:20.565 --> 26:23.775
higher densities,
across the entire range of

26:23.782 --> 26:27.452
densities of both species,
than is species 2.

26:27.450 --> 26:30.100
In this intermediate area,
between the two lines,

26:30.097 --> 26:33.517
species 2 is above its carrying
capacity and it's dying out.

26:33.519 --> 26:38.559
So basically this is a case
where species 1 excludes species

26:38.556 --> 26:40.686
2, completely;
it wins.

26:40.690 --> 26:44.540
It was that first case we saw
in Gause's Paramecia

26:44.538 --> 26:45.638
experiments.

26:45.640 --> 26:47.860
The other case is where species
2 wins.

26:47.858 --> 26:50.068
The black isocline belongs to
species 2.

26:50.068 --> 26:55.298
We can tell that by remembering
to look for which axis has the

26:55.297 --> 26:56.237
K2 on it.

26:56.240 --> 26:57.210
Okay?

26:57.210 --> 27:02.120
K2 is corresponding to N2 here,
and it is above the isocline

27:02.115 --> 27:04.715
for species 1,
over the entire range of

27:04.723 --> 27:07.763
possible combinations,
of mixtures of both species.

27:07.759 --> 27:12.019
And what basically that means
is that species 2 can grow at

27:12.021 --> 27:15.991
densities where species 1 is
declining, and it excludes

27:15.990 --> 27:17.020
species 1.

27:17.019 --> 27:20.669
The more complex,
and therefore more interesting

27:20.672 --> 27:22.462
cases, are down here.

27:22.460 --> 27:26.610
This case is an unstable
equilibrium.

27:26.608 --> 27:29.568
Above the isoclines,
both species are declining.

27:29.568 --> 27:32.318
Below the isoclines,
both species are increasing.

27:32.318 --> 27:34.638
If they happen to be at this
point,

27:34.640 --> 27:37.370
it's an unstable point,
because if they just get a

27:37.371 --> 27:40.911
little bit off of it,
the system wanders off in this

27:40.913 --> 27:44.593
direction and ends up going to
be only species 2.

27:44.588 --> 27:47.138
And if it wanders a little way
off, down here,

27:47.144 --> 27:50.554
it goes off in this direction
and ends up being species 1.

27:50.548 --> 27:56.458
And over here you have the
interesting case that you have

27:56.461 --> 27:59.991
co-existence,
and that's where intra-specific

27:59.988 --> 28:03.368
competition is stronger than
inter-specific competition.

28:03.368 --> 28:07.348
And above the isoclines they
both decrease,

28:07.348 --> 28:09.128
and below the isoclines they
both increase,

28:09.130 --> 28:12.890
and that means that the
critical thing to focus on is

28:12.885 --> 28:16.855
what's going on in these
intermediate triangles here.

28:16.858 --> 28:20.818
And if you look at where the
carrying capacities are for the

28:20.821 --> 28:23.661
individual species,
you can see that carrying

28:23.656 --> 28:25.646
capacity for 1,
in this case,

28:25.646 --> 28:29.256
is below the intersection for
2, over here.

28:29.259 --> 28:33.009
And that means that above this
point,

28:33.009 --> 28:35.699
1 is decreasing and 2 is
increasing,

28:35.700 --> 28:38.400
and that means that if you plot
the change in both of them,

28:38.400 --> 28:41.540
you get a vector that points up
and to the left.

28:41.538 --> 28:45.008
Similarly here,
the vectors are pointing down

28:45.009 --> 28:47.929
to the right,
because 2 is decreasing,

28:47.926 --> 28:50.876
but 1 is increasing;
1 is increasing in this

28:50.878 --> 28:53.228
direction, and 2 is decreasing
in this direction,

28:53.230 --> 28:55.800
and that yields a vector that
points like this,

28:55.798 --> 28:58.248
which leads you to a stable
equilibrium point.

28:58.250 --> 29:00.710
And if you look at the
relationship of where the

29:00.709 --> 29:04.519
intercepts are on the axes,
basically you see that this is

29:04.519 --> 29:08.769
a situation in which species 1
is being limited by its own

29:08.773 --> 29:11.443
density,
below the point at which it is

29:11.441 --> 29:14.041
being limited by the density of
species 2,

29:14.038 --> 29:17.378
and species 2 is being limited
by its own density,

29:17.380 --> 29:20.520
below the point at which it
would be limited by the density

29:20.518 --> 29:21.328
of species 1.

29:21.328 --> 29:24.788
And that tells us that this is
a situation in which

29:24.792 --> 29:28.742
intra-specific competition is
stronger than inter-specific

29:28.740 --> 29:29.850
competition.

29:29.849 --> 29:31.459
Okay?

29:31.460 --> 29:41.970
Now if you were faced with that
issue on an exam,

29:41.970 --> 29:47.250
and I plotted N1,
N2, and I just put down two

29:47.250 --> 29:53.460
lines like this,
and I drew K1 here,

29:53.458 --> 29:59.268
and I drew K2 here,
which of the three cases do we

29:59.266 --> 29:59.556
have?

29:59.559 --> 30:03.169


30:03.170 --> 30:04.610
Student:  Number two.

30:04.609 --> 30:05.529
Prof: Which one?

30:05.529 --> 30:06.659
Student:  Number two.

30:06.660 --> 30:09.300
Prof: We have this one;
that's right.

30:09.298 --> 30:12.458
And the thing that you
immediately want to focus on is

30:12.461 --> 30:15.921
what is the relationship of the
intercept for itself to the

30:15.922 --> 30:18.072
intercept for the other species?

30:18.068 --> 30:21.428
And if the intercept for itself
is above that of the other

30:21.430 --> 30:24.690
species, you have unstable;
and if it's below that of the

30:24.691 --> 30:26.351
other species you have stable.

30:26.348 --> 30:36.098
Now do any of you feel
confident that you know why this

30:36.098 --> 30:39.348
looks like that?

30:39.348 --> 30:41.518
If you were up here at the
board with me,

30:41.522 --> 30:44.842
how would you convince me that
I should draw the arrow in that

30:44.838 --> 30:45.598
direction?

30:45.599 --> 30:49.239


30:49.240 --> 30:50.440
Yes?

30:50.440 --> 30:53.240
Student:  You could
break it down as a vector,

30:53.240 --> 30:55.610
and you know that K2 has to be
going down.

30:55.608 --> 30:57.888
Prof: Okay,
so you could just make a sketch

30:57.890 --> 30:59.750
and say, "Oh,
I know K2's going like

30:59.750 --> 31:00.450
that."

31:00.450 --> 31:03.340
Student:  And then K1 is
going to the right.

31:03.338 --> 31:05.168
Prof: Right,
because at this point it's

31:05.173 --> 31:06.643
still below its carrying
capacity.

31:06.640 --> 31:07.310
Student:  Right.

31:07.308 --> 31:10.198
Prof: So you would go
like that, and that's how you

31:10.201 --> 31:11.421
would get that vector.

31:11.420 --> 31:14.810
Very good.

31:14.809 --> 31:18.339
Okay.

31:18.338 --> 31:20.548
So the take-home points from
this--

31:20.548 --> 31:22.708
and by the way,
I don't think the important

31:22.708 --> 31:25.688
thing about the Lotka-Volterra
equations is that they're an

31:25.689 --> 31:27.539
accurate description of reality.

31:27.539 --> 31:28.729
>

31:28.730 --> 31:32.250
Reality is a lot messier than
those equations.

31:32.250 --> 31:35.830
What they are is a good
analytical tool that helps you

31:35.827 --> 31:38.557
to realize that hey,
we're probably dealing with

31:38.560 --> 31:40.830
four cases,
and there are some nice

31:40.827 --> 31:45.397
qualitative ways to simplify the
analysis of complex systems of

31:45.403 --> 31:49.683
differential equations so that
you don't have to do all the

31:49.682 --> 31:51.752
numerical calculations.

31:51.750 --> 31:55.360
And if you put those equations
into something like Mathematica,

31:55.358 --> 31:57.988
on the computer,
you can draw out the vector

31:57.988 --> 32:00.038
fields,
over the entire phase space,

32:00.038 --> 32:03.118
and you'll get arrows pointing
in all possible directions,

32:03.118 --> 32:06.818
and they'll be pretty and
they'll look nice.

32:06.818 --> 32:12.458
But the essential thing is not
that pretty picture,

32:12.460 --> 32:14.810
but the general qualitative
result,

32:14.808 --> 32:17.798
and to know where things are
generally going in each parts of

32:17.801 --> 32:18.701
the phase space.

32:18.700 --> 32:20.030
Okay?

32:20.028 --> 32:23.358
So on the one hand it's a
method of simplifying a complex

32:23.355 --> 32:26.975
reality, and on the other hand
it's a neat analytical tool;

32:26.980 --> 32:28.810
and that's why I present it to
you.

32:28.808 --> 32:32.768
It's not necessarily the way
Nature actually works;

32:32.769 --> 32:34.119
that's another issue.

32:34.119 --> 32:36.009
That's why we do experiments.

32:36.009 --> 32:40.259
Okay, so you don't really have
to be able to solve numerically

32:40.262 --> 32:43.962
a differential equation to
understand its outcomes.

32:43.960 --> 32:47.160
There are four outcomes in this
case: one wins,

32:47.157 --> 32:50.147
two wins, or there's an
unstable or a stable

32:50.146 --> 32:51.256
equilibrium.

32:51.259 --> 32:55.029
And even the very simplest
analysis of competition shows

32:55.025 --> 32:59.055
that coexistence is possible
when intra-specific competition

32:59.064 --> 33:02.354
is stronger than inter-specific
competition.

33:02.348 --> 33:04.838
I'll give you an example of a
system where that works.

33:04.838 --> 33:08.618
Go to Panama,
look around on the floor of the

33:08.615 --> 33:10.585
rainforest in Panama.

33:10.588 --> 33:12.678
Often you'll find yourself
under a fig tree;

33:12.680 --> 33:15.430
fig trees are very important in
rainforests.

33:15.430 --> 33:21.210
Each time a fig tree drops to
the ground, it is colonized by a

33:21.212 --> 33:23.112
fruit fly species.

33:23.108 --> 33:28.048
If a fruit fly arrives first,
at the fig, it will start to

33:28.048 --> 33:31.338
display, and then mating will go
on;

33:31.338 --> 33:35.048
it will attract other members
of its own species to that fig.

33:35.048 --> 33:39.528
However, different individual
figs, just by random chance,

33:39.529 --> 33:42.909
will attract different fruit
fly species;

33:42.910 --> 33:45.350
you're just bumbling along
through the forest,

33:45.348 --> 33:47.358
buzz buzz buzz buzz,
and you hit a fig,

33:47.359 --> 33:49.919
and then you say, "Hey,
I found some places for our

33:49.917 --> 33:50.717
babies to grow up.

33:50.720 --> 33:52.260
Come over here and mate with
me."

33:52.259 --> 33:54.009
And so, that's what happens.

33:54.009 --> 33:57.689
And because the resources are
discrete and they're scattered

33:57.685 --> 34:00.735
across the floor of the
Panamanian rainforest,

34:00.740 --> 34:05.600
what you have is a
concentration of intra-specific

34:05.602 --> 34:08.582
competition within each fig.

34:08.579 --> 34:11.339
The mating behavior attracts
more of your own species to the

34:11.342 --> 34:13.592
place where your larvae are
going to grow up,

34:13.590 --> 34:15.060
and the larvae are competing
with each other.

34:15.059 --> 34:15.849
Okay?

34:15.849 --> 34:20.659
So this process generates a
situation in which you get

34:20.655 --> 34:22.555
stable coexistence.

34:22.559 --> 34:27.969
And there are about 17 species
of fruit flies that can live on

34:27.967 --> 34:31.197
the same fig tree;
the same fruit from the same

34:31.197 --> 34:33.277
fig tree,
in Panama, and it's very

34:33.284 --> 34:36.444
probably because the process
I've just described is

34:36.443 --> 34:40.233
guaranteeing that intra-specific
competition will be stronger

34:40.233 --> 34:42.573
than inter-specific competition.

34:42.570 --> 34:45.320
So you can see that the
analysis of the Lotka-Volterra

34:45.320 --> 34:48.330
model is giving us kind of a key
criterion to look for,

34:48.329 --> 34:53.559
that in fact is reflected in a
very complex natural situation;

34:53.559 --> 34:57.389
and it might not have occurred
to us if we hadn't been through

34:57.393 --> 35:00.413
the simplicity of the
Lotka-Volterra analysis.

35:00.409 --> 35:03.329
So now I'd like to go back to
the field.

35:03.329 --> 35:05.449
And this is a habitat that I
like a lot.

35:05.449 --> 35:07.499
This is the Alpine habitat.

35:07.500 --> 35:09.450
This is probably the first week
of July.

35:09.449 --> 35:12.129
You're looking at a flowering
meadow.

35:12.130 --> 35:14.210
It's a complicated environment.

35:14.210 --> 35:16.680
You've got grasses,
you've got flowering plants.

35:16.679 --> 35:20.209
There are orchids coming up in
here.

35:20.210 --> 35:24.880
In ten square meters you might
have 50 or 100 species.

35:24.880 --> 35:28.450
Below the surface there are
mycorrhizae down in the soil.

35:28.449 --> 35:31.739
There are earthworms that are
splitting up the subsurface

35:31.744 --> 35:34.454
habitat into three or four
different niches;

35:34.449 --> 35:36.839
all kinds of stuff is going on
here.

35:36.840 --> 35:39.070
It's complicated.

35:39.070 --> 35:42.810
There's a very interesting
result from plant competition

35:42.806 --> 35:46.406
experiments that have been done
by taking seeds off of

35:46.409 --> 35:49.399
individual plants in a meadow
like that.

35:49.400 --> 35:53.010
If you go in and you determine
which are the next door

35:53.012 --> 35:56.952
neighbors of a particular plant,
in that meadow--so you take one

35:56.945 --> 35:59.595
individual plant and you ask,
"Is it next to species 1,

35:59.599 --> 36:01.079
species 2, species 3?"

36:01.079 --> 36:04.089
Normally it's not going to have
more than three or four

36:04.090 --> 36:04.760
neighbors.

36:04.760 --> 36:08.310
And you take its seeds back,
and you test it against a

36:08.307 --> 36:11.587
random selection of species,
in the greenhouse.

36:11.590 --> 36:14.310
So you take its seeds,
and you ask,

36:14.309 --> 36:17.249
"Are these seeds doing the
best against the neighbors I

36:17.253 --> 36:19.983
found out there in Nature,
or just a random selection that

36:19.976 --> 36:21.496
I took out of the same
meadow?"

36:21.500 --> 36:23.080
Okay?

36:23.079 --> 36:26.029
And what you find is that they
do better in competition with

36:26.030 --> 36:28.980
the neighbors than with the
average of the larger collection

36:28.980 --> 36:30.630
of all species in the meadow.

36:30.630 --> 36:32.790
And you ask yourself,
"Well how could that

36:32.786 --> 36:33.486
happen?"

36:33.489 --> 36:37.489
That is something that's really
a rather remarkable pattern,

36:37.489 --> 36:42.609
because it's almost as though
they had been selected to do

36:42.606 --> 36:45.566
better against those neighbors.

36:45.570 --> 36:46.950
But what process could do that?

36:46.949 --> 36:50.099
Well the answer is that there's
a seed bank,

36:50.099 --> 36:54.669
and that there are seeds of
many individuals,

36:54.670 --> 36:57.220
from many different species,
that are in the soil,

36:57.219 --> 36:59.449
all over that meadow,
and in the spring when they

36:59.449 --> 37:01.269
sprout out,
there's selection,

37:01.268 --> 37:04.388
and that selection is mediated
by competition,

37:04.389 --> 37:07.139
and it's acting on seedlings in
juvenile stages,

37:07.139 --> 37:09.909
and both intra- and
inter-specific competition are

37:09.911 --> 37:12.911
interacting to determine who
survives to be adults.

37:12.909 --> 37:15.479
And the ones that we see as
adults are the ones that have

37:15.478 --> 37:17.448
made it through that competition
screen,

37:17.449 --> 37:21.869
and if there were twenty or
thirty or fifty possible

37:21.871 --> 37:26.351
seedlings that were staring up,
to yield just one plant,

37:26.346 --> 37:29.206
surviving,
you can see how that pattern

37:29.210 --> 37:30.710
would be generated.

37:30.710 --> 37:34.380
And so in every generation,
out in a meadow,

37:34.380 --> 37:38.880
inter-specific competition is
mediating the distribution of

37:38.880 --> 37:42.910
the plants that we see,
and the fact that selection is

37:42.911 --> 37:46.531
effective is an indicator that
there's a lot of genetic

37:46.532 --> 37:50.962
variation within each of those
species for competitive ability.

37:50.960 --> 37:53.650
This selection couldn't work
unless there were genetic

37:53.646 --> 37:55.976
variation among individuals in
each species.

37:55.980 --> 37:59.910
So that each species consists
of a whole variety of possible

37:59.913 --> 38:01.583
competitive mechanisms.

38:01.579 --> 38:03.779
Some of them do well against
one neighbor,

38:03.777 --> 38:05.867
some of them do well against
another;

38:05.869 --> 38:08.869
as a result of which you get
the maintenance of quite a few

38:08.867 --> 38:11.757
different species in the meadow
and quite a few different

38:11.764 --> 38:15.314
genotypes,
within a species, both.

38:15.309 --> 38:19.489
Okay, so to sum up
inter-specific competition.

38:19.489 --> 38:23.289


38:23.289 --> 38:25.929
It really does occur.

38:25.929 --> 38:28.429
It does help to shape
communities in Nature;

38:28.429 --> 38:31.149
it's not the only thing shaping
communities in Nature,

38:31.153 --> 38:33.523
but it's one of the things that
shapes them.

38:33.519 --> 38:35.889
And it is often asymmetric.

38:35.889 --> 38:41.009
So often you have a situation
where the bully wins.

38:41.010 --> 38:43.220
It's frequently been
demonstrated,

38:43.219 --> 38:45.869
both in field and in lab,
and the best way to demonstrate

38:45.871 --> 38:48.861
it in the field is to remove one
species and see what happens to

38:48.856 --> 38:49.516
the other.

38:49.519 --> 38:52.849


38:52.849 --> 38:55.319
There is an analytical
framework called the

38:55.318 --> 38:58.198
Lotka-Volterra model,
that helps us to understand and

38:58.197 --> 39:00.517
pull together the results of
these experiments,

39:00.518 --> 39:04.518
and it points us to a key
conclusion.

39:04.518 --> 39:10.528
And the key conclusion is that
you'll get coexistence when

39:10.530 --> 39:16.540
intra-specific competition is
stronger than inter-specific

39:16.541 --> 39:18.231
competition.

39:18.230 --> 39:20.930
This kind of model,
and others, predict that both

39:20.927 --> 39:23.847
competitive exclusion and
competitive coexistence are

39:23.849 --> 39:26.379
possible, depending on the
circumstances.

39:26.380 --> 39:29.470
And so it was probably a
mistake to enunciate the

39:29.467 --> 39:33.457
competitive exclusion principle
as something that must apply at

39:33.456 --> 39:36.026
all times in all places in
ecology,

39:36.030 --> 39:39.300
because under the particular
circumstance of strong

39:39.304 --> 39:43.634
intra-specific competition,
coexistence is possible;

39:43.630 --> 39:47.370
exclusion is not the only
logical outcome.

39:47.369 --> 39:50.289
Okay, next time predation,
disease;

39:50.289 --> 39:52.359
and I'm going to be very
interested to see what you do

39:52.358 --> 39:52.748
with it.

39:52.750 --> 39:58.000