Lecture 12 – Interspecific competition (cont.)

(Updated: Wed. 3/3/99. This Lecture 12 is for Tuesday (3/2/99) and Thursday(3/5/99))
There is the "add-on" at the End and change in table indicated in red

Review from last lecture:

For species 1 in competition with species 2

dN1/dt = r1N1 [K1-(N1+ a 1,2 N2)]/K1

dN1/dt = 0 when N1=K1 - a 1,2 N2

when N1=0, N2= K1/ a 1,2 and N2 =0, N1=K1

For species 2 in competition with species 1

dN2/dt = r2N2 [K2- (N2+ a 2,1 N1)]/K2

dN2/dt = 0 when N2=K2- a 2,1 N1

when N2=0, N1= K2/ a 2,1 and N1 =0, N2=K2

Now to evaluate the outcome of the interaction we can superimpose the two graphs for N2 and N1.

To do this we will use vectors – they will represent the average of the joint movement of population sizes for species 1 and 2.

e.g.

­

sp 2

¯

¬ sp 1®

joint movement will be at 45o angle

There are four possible outcomes:

  1. species 1 wins
  2. species 2 wins
  3. either species 1 or 2 wins
  4. coexistence
  1. Species 1 wins (see Fig.1)

    2. Here the zero isocline of dN1/dt = 0 lies outside the dN2/dt line.

    This says that the effect of species 2 is smaller on species 1 than species 1 is on itself. Interspecific competition (sp. 2 on sp. 1) < intraspecific (sp. 1 on sp. 1) but the effects of sp. 1 on 2 is greater than sp. 2 is on itself.

    interspecific (1on 2) > intraspecific (1 on 1)

    That is, K1/ a 1,2> K2 = K1 > a 1,2 K2

    intra inter

    (1 on 1) (2 on 1)

    and, K1> K2/ a 2,1 = K1 a 2,1 > K2

    inter intra

    (1 on 1) (2 on 2)

  2. Species 2 wins (See Fig. 2)

    3. Results are identical to case 1 but species 2 wins.

    Here K2 > K1/a 1,2 and K2/ a 2,1 > K1

    K2/a 1,2 > K1 and K2 > K1 /a 2,1

    Inter 2 on 1 intra 1 on 1 intra 2 on 2 inter 1 on 2

  3. Either species 1 or 2 wins (See Figure 3)

    4. Three equilibrium points exist – where they cross however is not stable since shifts away from central stable point lead to populations moving to either extreme.

    Now, K2 > K1/a 1,2

    K2/a 1,2 > K1 ß

    species 2 wins

    OR

    K1> K2/ a 2,1

    K1 a 2,1 > K2

    ß

    species 2 wins

    What are the biological conditions under which this might occur? Difficult to envision since each species must be superior to the other in a predominantly intraspecific environment (i.e. more species 1 for species one to win and vice versa).

    Could occur if each species is inhibited by the release of toxic chemicals (allelopathy) - the species at initially higher density would have the competitive edge, i.e. it would be reduced less quickly.

  4. Species 1 and 2 coexist, both species are weak competitors. (See Fig 4)

Stable coexistence is possible because intraspecific competition is greater than interspecific competition.

Here, K1/a 1,2 > K2 /a 1,2

K1 > K2a 1,2

intra 1 on 1 inter 2 on 1

And

K2/a 1,2 > K1

K2 > K1a 2,1

intra 2 on 2 inter 1 on 2

Bottom line – coexistence is mathematically unstable unless intraspecific competition is stronger than interspecific competition.

This is not to say that when coexistence occurs species will not have an effect on one another, rather their interactions do not exclude one another because they are limiting themselves just as rapidly as they interferring with the other species.

From the Lotka –Volterra equation, if we know certain parameter values we can estimate the effect of competition between two species.

Let’s take the case of 2 species that coexist. At equilibrium (i.e. dN/dt = 0) N1=100 and N2 =700, and we know that a 1,2 and a 1,2 both equal 0.7.

For species 1:

N1 = K1 - a 1,2 N2

100 = K1 - 0.7(700)

K1 = 590 (100 vs 590 potential)

For species 2

N2= K1 - a 2,1 N1

700 = K2 - 0.7 (100)

K2 = 770 (700 vs 770 potential)

 

Question is what is the potential carrying capacity of sp. 1 and sp. 2? Which species is more effected by the interaction?

What do the curves look like?

K2/a 2,1 > K1 770/0.7 = 1100 K1= 590

K1/a 1,2 > K2 590/0.7 = 842 K2=770

See Fig. 5

How well does the Lotka-Volterra describe the outcome of natural populations?

Gause’s microcosm experiments:

Series of three experiments

Started with two yeast species, provided with nutrient culture.

1st experiment: Alone species 1 grew faster than species 2. Together both showed reduced growth rate. Here however the two populations became limited by not by resources but rather the production of toxic by-product – EtOH. Coexistence possible because of substrate inhibition and not limiting resources.

 

 

2nd experiments, Gause grew two species of Paramecium , P. caudatum and P. aurelia.

P. caudatum usually went extinct when the two were grown together. P. aurelia was able to outcompete P. caudatum by using resources faster but also produced toxins lethal to P. caudatum. a ’s changed through time as toxin level increased.

3rd experiment

compared P. caudatum and P. bursaria alone and together.

Coexistence resulted because Gause found that while P. caudatum feed on suspended yeast, P. bursaria fed on bacteria at the bottom of the container when density of yeast decreased. In other words, it shifted to alternative source of food but P. caudatum did not.

Use of resources diverged Þ Resources were partitioned.

Results of Gause’s experiments were widely accepted and the "competitive exclusion paradigm" became widely accepted as dogma.

However 15 years later, Thomas Park showed that the competitive exclusion principle may not be simple, widespread rule.

Park’s experiments – two species of flour beetles (Tribolium) were pitted in competition experiments but here the environment was not held constant. Park found that the outcome of competition was variable and dependent on several factors, mainly temperature and moisture.

Proportion present at end of experiment

 

Temp C ®

34o

29o

24o

Tribolium confuseum

wet

0

0.14

0.7

 

dry

0.9

0.87

1

Tribolium castaneum

 

 

 

 

 

wet

1.0

0.86

0.3

 

dry

0.1

0.13

0

Conclusions: Tribolium confuseum wins when conditions are dry and when temperature are 24 C and wet.

Tribolium castaneum wins when condition are wet and when temperatures are above 24 C.

Explanation for outcome: Genetic differences between species resulting in changes in a ’s and r’s as a function of environmental conditions.

Independently Park’s experiments were repeated and found to lack consistency, particularly at intermediate temperatures?

Two explanations –

    1. genetic diversity – some individuals of

      2. Tribolium castaneum do well in warm-dry environments and some Tribolium castaneum

      do well in hot, wet environments. Founder

      effect’ important in determining outcome. Inbreed lines yielded more consistent experiment. (1960’s and ‘70’s).

    2. random changes in population size. One

species more common simply by chance. More common types have competitive advantage (reached K first) – referred to as demographic stochasticity (i.e. chance). From 1976 experiment.

These results do not necessarily dispute Lotka-Volterra results but add complexity to the model. Use of resoures can be affected by environment (i.e. a and r not always constant in the environment).

Lecture 12(cont.)

What about evidence in support of the "competitive exclusion" principle from field studies?

IF competitive exclusion is the general result of competitor interactions, may be difficult to find evidence since most assemblages of species would have sorted their interactions into – exclusion or partitioning.

In part, this problem can be circumvented by examining species interactions between introduced species (i.e. species that were previously separated.

Example: Aphytis – several species of parasitic

wasps.

Red scale – resource

In 1900 orange groves in southern California became infested over a large area with an introduced wasp – A. chrysomphali. (derived from Mediterranean)

48 years later – Aphytis lingnanensis (China) excluded A. chrysomphali but only from areas of high tree density.

Few years later A. melinus resulted in excluding others from hot and dry areas – dominated inland.

Lab experiments conducted showed exclusions resulted from competitive interaction.