Lecture 25

Topics

• Predation - the first observations

• The Lotka-Volterra model

Study Sources

• Chapters 7 and 23 in Ricklefs.

• Study Guide: Predation

The Main Points

• Ricklefs starts out Section 7.2 in Chap. 7, with nice discussion about the nature of predation, some fundamental observations and some case histories.

• In Section 23.2 and Fig. 23-2, Ricklefs opens the discussion of coupled oscillations (or linked cycles) and shows how these might work. (Read especially the story of Huffaker's experiments with orange mites that begins on p. 474. You really owe yourself a full reading of this marvelous paper. While not a classic in terms of terse scientific writing, it is a classic in terms of intuition and most of all, persistence).

• In 1925, A.J. Lotka and in 1926, V. Volterra, separately came to write models of the perceived coupled oscillations of predators and prey (pp.450-453; especially equations 23-1 and 23-2 and Figures 23-17, 23-18, 23-19, 23-20 and 23-22).

• The idea was that displaced from some joint equilibrium, the populations of prey and predator would oscillate continuously rather than returning to the equilibrium point. Their models incorporated several simplifying assumptions:
  1. The only control on the geometric growth potential of the prey was the removal by the predator.

  2. The only food source for the predator was the prey species.

  3. Prey was removed by the predator in proportion to the number of encounters between them (the product of the prey and predator population sizes).

  4. The predator has a constant death rate which imposed from outside the system (Ricklefs suggests the weather).

• The idea is that the prey is prevented from growing at its geometric potential by predator, which removes prey in proportion to the mutual densities. Since every potential enounter between the two species doesn't result in a prey being eaten, the number of encounters is modified by a constant which reflects the efficiency of predation.

• The predator is then allowed to grow in proportion to the energy received by eating prey. Since each prey eaten does not result in one predator being born, the predation efficiency is modified by a constant which reflects the efficiency of transformation of food into population growth of the predator.

• These relationships produce the "trajectories" of population growth of the two species which are represented in Figures 23-17 through 23-22. Make sure you understand how these are made. If you have trouble visualizing what is happening in these figures, pick population numbers off Figure 23-2 at different times (generations) and make a two species plot with the Prey on the X-axis and Predator on the Y-axis. Then you'll see how it works.

• The two-species models based as they were on a simple "grazing phenomenon" were not really satisfactory to address the complications of nature. While laboratory experiments indicated that the mechanics of the interaction were probably worth keeping, other factors needed to be considered in any expansion of predatory/prey theory.

• For one thing, the whole concept of cycles in nature brought up the problem of noise or stochasticity in understanding changes in population size. How much of the change in population sizes was actually due to the cause and effect of predation? Couldn't it be that the prey species is simply being regulated by its own environmental factors and that the predators were simply along for the ride and having relatively little effect on the prey populations? It was clear that a new way of thinking about this interaction was needed.

• In 1963, MacArthur and Rosensweig provided a new way of seeing the interaction. (Begin reading pp. 466-468 and study Figures 23-19 through 23-22).