Interactions between Two Species

  • Alan A. Berryman
Part of the Population Ecology book series (POPE)


Populations of two different species that coexist within the same geographic area may be viewed as two separate population systems which interact with each other through their common environment. In this way, the numbers of one population modify the favorability of the environment for the other (Figure 4.1). This interaction creates an additional feedback loop, shown as a bold line in the figure, which passes through both population systems. This loop may be positive or negative depending on the signs of the interspecific interactions.


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  1. 4.1.
    A number of classifications have been proposed for interactions between two species, resulting in a sometimes confusing proliferation of terms. Eugene Odum, in his classic text Fundamentals of Ecology (p. 211 in the 3rd ed.; W. B. Saunders Co., Philadelphia, 1971), identifies nine kinds of interactions by splitting competition into direct and indirect types, separating predation from parasitism, and dividing symbiosis into obligatory and nonobligatory forms. However, in keeping with the nature of this present book, I have tended to lump together rather than to split apart in an attempt to retain an elemental simplicity. We hope to see that particular types of interactions are the evolutionary result of species interacting in the three basic ways.Google Scholar
  2. 4.3.
    It is very important to understand the concept of superimposed reproduction planes, and so the student is encouraged to perform the following exercise with cooperative, competitive, and predator-prey interactions: First draw the equilibrium lines for each species on separate sheets of paper, or better still, clear acetate. Then manipulate one or both sheets until species A occupies the abscissa and species B the ordinate and the origin A = B = 0 is in the lower left hand corner. These manipulations are illustrated for the cooperative interaction in Figure 4.23. The reproduction planes can now be superimposed by drawing B’s on top of A’, and labeling each equilibrium line, their intercepts, and their zones of population growth and decline.Google Scholar
  3. It is also important for the student to compute several population trajectories on each superimposed plane. To do this start at any point A,B in the graph’s phase space and put arrows for the expected direction each species will Move; e.g., if A’s sign is positive at this point it will move horizontally to the right and if B’s is negative it will move vertically downwards. The distance moved by each species will depend on their positions relative to their respective zero axes and to their equilibrium lines; i.e., population change over the time increment will be smallest close to these lines and greatest in between (see Chapter 3). The distance and direction moved on the reproduction plane will be the resultant of these two vectors (see Figure 4.2C). For purposes of simplicity it is best to assume that the approach to equilibrium is asymptotic. However, we should remain aware that the stability qualities of each system are governed by the slope of the reproduction curve in the immediate vicinity of the equilibrium line as well as time delays in the negative feedback loops. These qualities have been suppressed in our simplified two-dimensional graphical model. However, the rules of feedback specify that if either species is unstable by itself, or exhibits cyclic dynamics, then this effect will be transferred to the two species interaction (see Chapter 6).Google Scholar
  4. 4.5.
    M. E. Gilpin and F. J. Ayala [Proceedings of the National Academy of Science (U.S.A.) vol. 70, p. 3590, 1973] have analyzed the interaction between two speceis of Drosophila competing for a fixed quantity of food in culture bottles and found equilibrium systems of the type shown in Figure 4.9C,D. Their model explains the nonlinearities in the intraspecific competitive process. However, an equally tenable argument is that the interspecific interaction is nonlinear or, for that matter, that both processes have nonlinear components.Google Scholar
  5. 4.6.
    An interesting review of the rise and fall of various herring, sardine, anchovy, and pilchard fisheries is given by G. I. Murphy in the book Fish Population Dynamics (edited by J. A. Gulland, John Wiley and Sons, New York, 1977). Some of these fisheries have collapsed dramatically under heavy exploitation and, in some instances, the collapse seems permanent. However, there is considerable evidence that other similar species have increased dramatically following the collapse of the original fishery (see Figure 4. 11 ).Google Scholar
  6. As an expatriate Cornishman I am keenly aware of the collapse and virtual extinction of the Cornish pilchard schools, and of the current heavy exploitation of mackerel stocks—perhaps these were the competitors that replaced the pilchards? The lessons from competition theory and past experience seem plain and, yet, little seems to be done to rectify these problems.Google Scholar
  7. 4.7.
    Strong competitors are often referred to, following the ideas of Robert MacArthur and others, as K-strategists. The K-strategy aims at maintaining a high but consistent population close to the saturation density (carrying capacity) and is usually most successful when organisms inhabit rather stable environments. K-strategists usually have low maximum rates of increase and fast-acting regulating mechanisms and, therefore, show high degrees of temporal stability.Google Scholar
  8. Opportunists, on the other hand, are called r-strategists, because they have high maximum rates of increase, inhabit variable or temporary environments, and tend to have low temporal stability. Although, for a number of reasons I have avoided these terms in this book, the following references are provided for those who wish to pursue this subject: The Theory of Island Biogeography, by R. H. MacArthur and E. O. Wilson (Princeton University Press, 1967 ) and T. R. E. Southwood’s contribution in Theoretical Ecology Principles and Applications, edited by R. M. May (W. B. Saunders and Co., Philadelphia, 1976 ).Google Scholar
  9. 4.8.
    The predator parameters can also be viewed at a more basic physiological level using the approach of Andrew Gutierrez and his co-workers (e.g., see the article by A. P. Gutierrez in the EPPO Bulletin vol. 9, p. 265, 1979). From this perspective we consider predator reproduction and survival to be a function of stored energy, which is supplied by eating prey, and physiological time, or aging. If we set the time scale equal to the life span of the predator, then the energy available for reproduction is S — D m where S is the energy supply, in terms of prey eaten, and Dm is the energy demand for basic metabolic processes in order to keep the predator alive (Dm can be viewed as the number of prey required to meet the basic metabolic demands of the predator). We can see that the predator will starve if m while if S Dm there is surplus energy which can be used for reproduction. Given an energy supply in excess of the basic survival demands, then the number of offspring produced will be proportional to the supply/demand ratio, so that when S/D m is large, reproduction will be close to its intrinsic maximum while reproduction will decrease to zero as the limit S/D m = 1 is approached. We now see that the predator parameter P a is the prey density at which one predator can just gather enough to supply its basic metabolic needs; i.e., where S/D m = 1. However, the supply obtained from a given density of prey is also dependent on the efficiency of the particular predator in searching out and capturing its prey; i.e., S will be higher for a more efficient predator under equal prey density levels and, therefore, S must be related to the hunting efficiency of the predator.Google Scholar
  10. 4.10.
    The effects of interference between insect parasitoids (mostly small wasps and flies which attack and lay eggs on or in other insects) on their efficiency during their search for prey has been studied intensively by M. P. Hassell. He has recently summarized this work in his book The Dynamics of Arthropod Predator-Prey Systems (see Note 4.9 for complete reference).Google Scholar
  11. 4.11.
    M. E. Solomon (Journal of Animal Ecology vol. 18, p. 1, 1949) was apparently the first to coin the term “functional response” to describe the changes in numbers of prey attacked by individual predators as the density of the prey population changes. However, it was C. S. Holling [Canadian Entomologist vol. 91, p. 385, 1959; Memoirs of the Entomological Society of Canada nos. 45 (1965) and 48 (1966); and subsequent contributions] who investigated the functional response and its components in great detail. Holling also identified the three basic types of functional responses (see Figure 4.19 for review).Google Scholar
  12. 4.13.
    Holling originally proposed the type III functional response for animals with learning abilities, particularly birds and mammals (see Note 4.11 for references). These general predators learn that a particular prey species is available and palatable when they encounter it fairly frequently. They then tend to search for that species in preference to others and their rate of attack on it increases; that is, they switch to the more abundant species in their prey repertoire. However, as Hassell points out in the Journal of Animal Ecology (vol. 35, p. 65, 1966), specific invertebrate predators with type II responses, but which can only attack prey after they reach a certain density, may produce comparable effects. In addition, S-shaped responses have been observed in other invertebrate predators (e.g., D. G. Embree in the Canadian Entomologist vol. 98, p. 1159, 1966), which suggests that they may be more common in nature than meets the casual eye.Google Scholar
  13. 4.15
    An interesting demonstration of the effect of the prey’s saturation density, K a on the stability of a predator-prey system can be found in J. Maynard Smith’s book Models in Ecology published by Cambridge University Press, 1974. On pages 33 to 35 he discusses experiments performed by L. S. Luckinbill with Paramecium (prey) and Didinium (predator). Luckinbill was able to stabilize an otherwise unstable interaction by cutting the prey’s food supply in half. This operation reduced K a to less than one-half of its previous level and probably had little effect on P5.Google Scholar
  14. For those interested in a more analytical approach to the problem of predator-prey interactions which, nevertheless, arrives at much the same conclusions as we do, Maynard Smith’s book is recommended. and its predator Didinium (see Note 4.4 for reference), and C. B. Huffaker’s beautiful series of experiments with predator and prey mites (Hilgardia, vol. 27, 1958). Huffaker was also able to show that hampering the predators or facilitating the prey’s escape tended to stabilize the interaction (see Figure 4. 22 ).Google Scholar
  15. Unstable predator-prey interactions are also seen in nature, particularly in highly simplified agro-ecosystems. An example of an unstable interaction between mite predators and their prey in Washington apple orchards is documented by S. C. Hoyt (Journal of Economic Entomology vol. 62, p. 74, 1969). However, this interaction was more stable when alternative food, in the form of different species of mites, was available for the predators.Google Scholar
  16. 4.17.
    The idea that natural selection may act on groups of organisms, or populations, as well as on individuals is another subject of controversy amonst biologists. The principal proponent of group selection is V. C. Wynne-Edwards, and those interested in this fascinating subject should consult his works (e.g., Nature, vol. 200, p. 623, 1963). He has also summarized his ideas in the book Natural Regulation of Animal Populations (edited by I. A. McLaren, Atherton Press, New York, 1971 ). Also in this book is an article by D. Pimentai on the co-evolution of predator-prey systems. Pimentai argues, and presents data to support his arguments, that predator-prey systems evolve stable interactions via genetic feedback which produces adjustments in the efficiency of the predator, the vulnerability of the prey, and/or their reproductive potentials.Google Scholar

Copyright information

© Alan A. Berryman 1981

Authors and Affiliations

  • Alan A. Berryman
    • 1
  1. 1.Washington State UniversityPullmanUSA

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