Lecture 9:

Competition

What is competition?
!! An interaction that occurs when a number of
organisms of the same (intraspecific) or different (interspecific) species utilize common resources

!! General types of competition: !! Exploitation competition - organisms compete for resources

that exist in a limited supply

!! Interference competition - organisms compete aggressively

for a resource, with the possibility of competitors being harmed or killed. In this case, the resource need not necessarily be in short supply.

!! Pre-emptive competition - organisms compete for space as a

limiting resource.

Competition in Hypothetical Space

K for two different species may be different, such that a single area may accommodate more individuals of one species than another In resource competition, each species may fill a particular area at a different rate, regardless of species density

Lotka-Volterra equations
!! We have already seen an equation for population
growth that considers carrying capacity:

dN/dt = rN((K-N)/K)
!! We can now consider this equation for two different

species, and how to incorporate competition between the two species in the equation

dN1/dt = r1N1 ((K1-N1)/K1) & dN2/dt = r2N2 ((K2-N2)/K2)

!! How do we combine these two equations?

Species Conversion Factors

!! As each species potentially has a different resource
demand, we need to find a conversion rate between species. In this case we use:

!N2 = equivalent # of species 1 individuals

!! Where ! is a conversion factor for expressing species
2 in units of species 1

!! This is a very simple assumption, that there is a

constant conversion factor between competitors, but it allows us to incorporate the competitor species into our equation:

dN1/dt = r1N1 ((K1-N1-!N2)/K1)

What does this model predict?

What about species 2?

!! For species 2 we can take the same approach. First,
find a conversion factor:

"N1 = equivalent # of species 2 individuals

!! And include this expression into our equation for
species 2: dN2/dt = r2N2 ((K2-N2-"N1)/K2)

!! We can then represent this graphically with a similar

equilibrium isocline

Species 2 equilibrium

So if we put these two species together, what happens?

!! One of three things:

!! Both species coexist !! Species 1 goes extinct !! Species 2 goes extinct

!! How do we predict which of these outcomes is most

likely?

!! Solve the following simultaneous equations at

equilibrium:

dN1/dt =0=dN2/dt
!! We can do this by vector additions with our isocline
graphs..

So if we put these two species together, what happens?

So if we put these two species together, what happens?

So if we put these two species together, what happens?

So if we put these two species together, what happens?

Outcome of Lotka-Volterra models

!! No equilibrium unless the isoclines cross !! If the isoclines do cross, the equilibrium point
represented by the crossing can be stable or unstable

!! We can make predictions of outcomes based on the

values of !, ", K1 and K2

Outcome of Lotka-Volterra models

!! While they provide fairly explicit predictions, the L-V
models are based solely on outcomes; no mechanisms for competition are incorporated in the models

!! In response to this perceived shortfall, Tilman

presented mathematical models of competition based on resource use

Tilmans Model
!! Tilmans model is based on resource use and
limitation, the actual mechanisms through which competition may take place decrease for a single species based on the availability of two different resources that the species requires in varying levels

!! First, Tilmans model presents a zone of increase or

Competition in Tilmans Model

!! We can repeat this analysis for a second species and
superimpose the two zero growth isoclines

!! We can then determine how the two species will

interact when competing for the considered resources (stable or unstable) are possible

!! Much like the L-V models, extinction or equilibrium

Mathematical models of competition

!! From the Lotka-Volterra and Tilman models three
important ideas about the competitive interactions of two species have arisen !! Competition can lead to one species winning and one
going extinct !! Some competitive interactions can lead to coexistence !! We can understand competitive interactions only by knowing the resources involved and the mechanisms by which species compete

dN1/dt = r1N1 ((K1-N1-!N2)/K1)

dN2/dt = r2N2 ((K2-N2-"N1)/K2)

dN1/dt =0=dN2/dt

Competition in Natural Populations

!! Gause (and others) suggested that competition
would prevent two species with very similar niches from coexisting Gause to be implied by the Lotka-Volterra models

!! the Competitive Exclusion Principle was assumed by

!! As we have discussed before:

!! competition alters the relationship of an organism to

its environment !! While the cumulative environmental tolerances of a
species define its fundamental niche !! Competition limits the distribution of a species further, to what is know as its realized niche

Competition in Natural Populations

!! Does competitive exclusion prevent the simultaneous
occupancy of a niche by two species?

!! Hutchison (1958) suggested some conditions under which

competitive exclusion might not lead to extinction !! Unstable environments that never reach equilibrium and are
occupied by colonizing species !! Environments in which species do not compete for resources !! Fluctuating environments that reverse the direction of competition before extinction is possible

!! How can we explain the apparent coexistence of large

numbers of species in field communities? !! Perhaps competition in nature is actually somewhat rare !! Perhaps competition is common, and has resulted in similar
species having adaptations that serve to minimize competition

How can we determine whether competitive exclusion will occur?

!! A species will not be excluded from a habitat if it can still
invade under non-ideal circumstances !! When abundance is close to 0 and competitor abundance is close to K !! If per capita growth rate is still positive under these conditions then the species can invade. dN1/dtN1 = r1((K1-N1-!N2)/K1) !!!! if K1/K2 > !, then Sp. 1 can invade

The Ghost of Competition Past

!! The apparent coexistence of a number of species led
Connell (1980) to suggest that the current distribution of species resulted from a past in which competitive exclusion was a significant selective force

!! Competition between species in the evolutionary past

has led to a current state where species with very similar niches have either: !! 1) experienced extinctions or !! 2) evolved differences in behavior, diet, phenology or
distribution that now minimize competition

Character Displacement & Speciation

!! Character displacement takes place when competing
species evolve to be more distinct from one another in some attribute so as to minimize competition a population that can ultimately bring about speciation

!! Intraspecific competition can select for differences within

MacAurthurs Warblers

Character Displacement & Speciation

!! Resource partitioning in terns: a
and the size of fish they tend to consume case of character displacement?

!! Species differ in their overall size, !! Two species (Sooty and Brown

Noddy) have similar prey size distributions, but search for prey in very different habitats

Character displacement in finch beak size

! Comparison of 5 islands where Geospiz fortis and G. fuliginosa occur

Testing competition using replacement Series Experiments

!! Pioneered in the 1960s,

these experiments allow for the manipulation of the distribution of plant species in a common garden. !! Similar to common garden experiments across experimental plots, but the distribution of the study species is altered.

!! Density is held constant

Competition and Facilitation

!! Interactions between species need not always be a
lose-lose situation

!! For some species, the presence of another species !! Sometime both species in an interaction are

improves growth, leading to a phenomenon know as facilitation facilitated; in other cases one species benefits while the other experiences a net loss

Competition, Facilitation & Effect Size

!! Gurevitch and colleagues (1992) tabulated the results of
218 competition experiments and arrived at the following results:

!! Thus, for different groups, the mean effect of competition

is quite different

!! This is calculated through mean effect size:

!! Xc= mean biomass of the control group (w/ competition) !! Xe= mean biomass of the experimental group (w/o
competition) !! s = standard deviation of both groups pooled

(Xe-Xc)/s

The Paradox of Plankton

!! Plant communities in many ways compete more
directly than animal species, as they generally have more similar needs: !! nutrient, water and light--necessities for survival despite the similarity in niches of the species

!! Phytoplankton communities are often quite diverse, !! Hutchinson suggested that the phytoplankton
community might serve as an exception to competitive exclusion, due to climatic and seasonal variation in aquatic (freshwater and marine) habitats equilibrium and allows a large number of species to coexist

!! This variability prevents the system from attaining

!! Types of IGP

Intraguild predation When neighbors attack!!

!! Symmetrical both species prey upon each other. !! Asymmetrical one species preys upon the other !! Age-structured Predator and prey roles are usually
determined by an age or size !! Juveniles and small individuals become the prey.

!! Additional term added to the equations for

population growth. Predator - dN1/dt = r1N1 ((K1-N1-!N2)/K1)+#N1N2 Prey dN2/dt = r2N2 ((K2-N2-!N1)/K1)+$N1N2

Intraguild predation
!! How will IGP influence influence our zero-growth
isoclines?