General Ecology: Lecture 12

Competition 1

Reading: Ch. 14. I will cover everything except “Differential resource utilization” on pp. 255-256. I will cover some sections more extensively than others. Use the outline to guide your reading.

  1. Types of species interactions
  2. Chart (Table 14.1)
  3. Brief explanation of amensalism as a “special case” of competition.
  4. Interspecific competition: overview
  5. Exploitative competition

a)Definition: Both species use the same limited resource. Each makes the resource scarcer for the other species.

b)Results: Reduced growth of members of both species.

Impact on each species willdiffer depending upon how efficiently each uses the resource

  1. Interference competition:

a)Definition: Species directly interact and interfere with access to a resource that may or may not be limiting.

May involve aggressive behavior.

  1. NOTE: These definitions differ somewhat from the same terms used to describe intraspecific competition.
  1. Interspecific competition: Lotka-Volterra model
  2. Introduction
  3. Derived independently by these two researchers in the 1920s.
  4. Based on the logistic growth equation
  5. Four key assumptions of the Lotka-Volterra model
  6. The environment is homogenous and stable, without any fluctuations
  7. Migration is unimportant (i.e. model takes only “r”, or b-d, into account, just as for the other equations we have covered)
  8. The effects of competition are instantaneous
  9. Coexistence requires a stable equilibrium (you’ll see what this means…)
  10. The equations (see p. 243 in text to double-check.)
  11. Species 1: dN1/dt = ______

a)State in words, going through each term.

b)In the absence of interspecific competition, the equation is reduced to the logistic growth equation.

  1. Species 2: dN2/dt = ______
  1. Focus: thecompetition coefficients(α and β terms)
  2. Used to convert the numbers of one species into the “equivalent” number of the other species. So ifspecies 1 uses 3 times the quantity of the limiting resource as Species 2, then α = 3.

a)100 of Species 2 individuals  growth rate is “docked” by 300 individuals. So 300 fewer individuals of Species 1 can be produced before K1 is reached, even though there are only 100 “actual” individuals of species 2 added.

What effect does Species 2 have on the ability of Species 1 to reach it carrying capacity?

  1. An equivalent equation exists for the population growth of Species 2 in the presence of Species 1 (note  term)
  1. Species 1: Zero-growth isocline and intercepts.
  2. At “zero growth” for species 1, what does dN/dt equal?
  3. Replace this value in the equation to get the zero-growth isocline (a line) that indicates the equilibrium population size for Species 1.

a)Should get N1 = K1 -N2. This equation tells you what your equilibrium population size for Species 1 is, for a particular pop. size of Species 2

Do the math for a case in which K1 =1000, N2 = 100 and  = 0, 1 or 3. What is the equilibrium pop. size for N1 be in each case?

Note how a larger  leads to a smaller equilibrium pop. size.

b)NOTE: Book has an error on p. 244, 2nd column, line 13. The  term is left out! Similar error on line 12, -term left out of parallel equation.

  1. Solve for the extremes to get the intercepts for the line

a)If N1 = 0, you get the y-intercept (value for N2):

N2 = ? (solve it!)

b)If N2 = 0, you get the x-intercept (value for N1):

N1 = ?

HINT: This result makes intuitive sense: If Species 2 is absent, then the population should reach its carrying capacity!

  1. Graph this result on a phase plane diagram that describes the changes in Species 1 as affected by competition with Species 2 [Fig. 14.1a]

a)x-axis: Population size of Species 1; y-axis: population size of Species 2

b)Diagonal line: dN1/dt = 0, the “zero growth isocline” for Species 1

The x and y intercepts are what you just calculated (III.E.3)

Vectors: Species 1 grows if the population sizes of Species 1 and 2 are left of the isocline, and shrinks if they are to the right of it.

  1. Repeat the process for Species 2. Note that species 1 is always plotted on x-axis, Species 2 is always plotted on the y-axis. (Do not reverse!)
  2. Create the equation for the “zero growth isocline” for Population 2 (dN2/dt = 0)
  3. Solve for the extremes…
  4. Graph the results on a similar phase plane diagram as for population 1

a)Understand the direction (and size) of the vectors!

  1. Solve for both equilibria at once: dN1//dt = 0; dN2/dt = 0
  2. We will do “by hand” (but see also Fig. 14.1 c-f; but they did not do the vectors as clearly…)

a)Combine graphs for individual equations.

  1. 4 possible combinations: Show these and determine who wins (or if an equilibrium is reached, what type and what it means for the populations.)

a)x-axis limits: K1> K2/β; y-axis limits: K1/α > K2

b)x-axis limits: K1< K2/β; y-axis limits: K1/α < K2

c)x-axis limits: K1 > K2/β; y-axis limits: K2 > K1/α

d)x-axis limits: K1 < K2/β; y-axis limits: K2 < K1/α

e)NOTE: You will have to work these out for real numbers, without calculators…

  1. Two species may compete differently in locations with different environmental conditions/resource availability
  2. Example: Competition between two seed-eating species of birds [Fig. 14.2]

a)Scenario: Overlap in seed sizes eaten, but difference in preferred size

Species 1 eats somewhat smaller seeds than Species 2

b)Changes in K, α and β

Under which conditions will K1and β be relatively high? Under which conditions will K2and αbe relatively high?

c)Results

Where small seeds prevail, species __ wins

Where large seeds prevail, species __ wins

Under what conditions do the two co-exist?

NOTE: Be sure you understand shifts in positions of isoclines!

  1. Laboratory studies of competition
  2. Gause’s experiments on competition in Paramecium
  3. With P. aurelia and P. caudatum, competitive exclusion
  4. With P. caudatum and P bursaria, he was able to get a stable equilibrium. Why the difference?

a)Gause’s hypothesis: “As a result of competition, two similar species scarcely ever occupy similar niches, but displace each other in such a manner that each takes possession of certainly particular kinds of food and modes of life in which it has an advantage over its competitor.”

b)In essence, they had somewhat separate niches…

  1. Field studies of competition
  2. What evidence is required to show that competition is responsible for a particular pattern of distribution?
  3. The distribution of the two species is inversely correlated; where one is abundant, the other is not.

a)Is this alone sufficient to show competition?

  1. The two species have been demonstrated to require the same limited resource and/or one has been shown to interfere with the other’s ability to acquire resources
  2. If the presumed “superior” competitor is removed, the “inferior” competitor will then expand its range into that where the “superior” competitor inhabited.
  3. It is really the presumed competitor that is responsible for the exclusion (and not some other factor also altered in the experiment…).

a)So an actual mechanism of competition has been demonstrated.

  1. Good example: Barnacle zonation: Joe Connell, 1961. (Not in the book…)
  2. Basics

a)The range of larval settlement for Chthamalus(“little gray barnacle”) and Semibalanus(“rock barnacle”)overlaps in the higher zone

b)AdultChthamalus are found in a band above Semibalanus in the intertidal (true for Scotland, New England, Pacific coast)

c)Connell et al. experiments on Semibalanus and Chthamalus.

Removal of SemibalanusChthamalus moves lower, into the space occupied by Semibalanus.

Removal of Chthamalus has no effect on the position of Semibalanus? Why not?

  • Shading experiments show that abiotic factors (which ones?) are responsible for the upper limit of Semibalanus.
  1. Are the four conditions for competition satisfied? (Reason through each.)
  1. Another example: Mallards vs. black ducks in wetlands [Fig. 14.7]
  2. Basics of example

a)The “realm” of black ducks is in wetlands of the northeast, whereas the realm of mallards has traditionally been more to the south and west

b)In the region where the two overlap, mallards have been increasing while black ducks have been decreasing

c)When present in the overlap area, the black ducks occupy less fertile wetlands (i.e. more marginal habitat.)

  1. Are the four conditions for competition satisfied? (Reason through each.)

Study questions

  1. Describe the different types of interactions possible between two species. Be sure to note how each of the species is affected by each type of interactions (i.e. +, - or 0)
  1. List each of the four assumptions of the Lotka-Volterra model. Then, discuss (1-2 sentences each) whether each of the assumptions is realistic for a)most populations or b) some populations? To the extent that these assumptions are not realistic, why bother with this model in the first place?
  1. The basic competition equations
  2. Write out the Lotka-Volterra competition equations from memory
  3. Define/explain each of the key terms in the equation.
  4. Compare this equation with the logistic growth equation, and point out specifically what is different and why.
  1. State, in words, what it means to have a β value of 2. State, in words, what it means to have an α value of 0.5.
  1. Be able to calculate the limits for each of the two phase-plane diagrams (i.e., the x and y intercepts for each.) For the mathematically disinclined, memorizing them will help, but for “full credit” you should understand the calculation that gets you there.
  1. Understand the diagonal linesof the Lotka-Volterra phase-plane diagrams. For example, what, mathematically, does the line represent? What, in words, does that line represent?
  1. Be able to draw the vector arrows for each graph individually, and for the graphs when combined. This will help you with the next question.
  1. Be able to sketch each of the four different phase-plane diagrams for competition between two species, complete with vectors, and indicate which species wins and/or whether there is a stable or unstable equilibrium.
  1. What is the difference between a stable and unstable equilibrium, ecologically speaking?
  1. For each of the following situations, determine whether Species 1 wins, Species 2 wins, a stable equilibrium is reached or an unstable equilibrium is reached. To solve, create phase-plane diagrams for each of the six situations. (HINT: Answers for part a can be found in your reading-look carefully! Answers for part b provided at a later date…)
  2. For α = β = 0.5 and

Trial 1: K1 = 225 and K2 = 75

Trial 2: K1 = 150 and K2 = 150

Trial 3: K1 = 75 and K2 = 225

  1. For =2 and =1and

Trial 4: K1 = 225 and K2 = 75

Trial 5: K1 = 150 and K2 = 150

Trial 6: K1 = 75 and K2 = 225

  1. Understand the key concepts demonstrated in Fig. 14.2. Be able to explain all graphs in the figure and understand how they are related.
  1. Explain how figures 14.4 and figure 14.5 (Gause and Tilman studies) show evidence of competition in the laboratory. What is the limiting resource in each of these cases. Which of the Lotka-Volterra situations best explains the results of each of these experiments? (NOTE: We did not go through Tilman in class, but you should be able to understand…)
  1. How did Gause’s results differ when he combined P. aurelia and P. caudatum together vs. when he combined P. caudatum with P. bursaria? How did Gause explain this difference in results? What is Gause’s hypothesis of competitive exclusion.
  1. What four conditions must be satisfied to show that competition is one factor responsible for the particular pattern of distribution and abundance seen?
  1. Of these four conditions, which is most often used as evidence of competition in natural populations? Why is this condition used as evidence when it is clearly not sufficient?
  1. Explain how Joe Connell’s studies of competition between the two barnacle genera, Chthamalus and Balanus, satisfy all of these conditions. You must be clear about which aspect of his observations/experiments satisfy which of the conditions.
  1. Given unlimited resources and permits to manipulate the mallard and black duck populations at will, explain how you could show that the mallards had indeed outcompeted the black ducks in their regions of overlap.

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