Competition and Cooperation in Mathematical Ecology

One problem I want to examine arises in the systematic neglect of cooperative (or mutulaist) interactions and the correspondig privileging of competitive interactions evident throughout almost the entire history of mathematical ecology. When we ask practitioners in the field for an explanation of this historical disinterest in mutualist interactions, their response is usually one of puzzlement—not so much over the phenomenon as over the question. How else could it, realistically, be? Yes, of course, mutualist interactions occur in nature, but they are not only rare, they are necessarily secondary.

Often it is assumed that they are in the service of competition: such pheomena have at times actually been called "cooperative competition." Indeed, the expectation of most workers in the field that competition is both phenomenologically primary and logically prior is so deeply embedded that the very question has difficulty getting airspace: there is no place to put it. My question thus becomes, What are the factors responsible for the closing-off of that space?

Part of the difficulty in answering this question undoubtedly stems from the massive linguistic confusion in conventional use of the term competition. One central factor can be readily identified, however, and that is the recognition that, in the real world, resources are finite and hence ultimately scarce. To most minds, scarcity automatically implies competition, both in the sense of "causing" competitive behavior and in the sense of constituting, in itself, a kind of de facto competitio, independent of actual interactions between organisms. Indeed, so automatic is the association between scarcity and competition that, in modern ecological usage, competition has come to be defined as the simultaneous reliance of two individuals, or two species, on an essential resource that is in limited supply (see, e.g., Mayr 1963: 43). Since the scarcity of resources can itself hardly be questioned, such a definition lends to competition the same a priori status.

This technical definition of competition was probably first employed by Voltera, Lotka, and Gause in their early attempts to provide a mathematical representatation of the effects of scarcity on the population growth of "interacting" species, but it soon came to be embraced by a wider community of evolutionary biologists and ecologists—partly, at least, to neutralize the discourse and so bypass the charge of ideologically laden expectations about (usually animal) behavior, in fact freeing the discourse of any depen-

dence on how organisms actually behave in the face of scarcity. The term competition now covered apparently pacific behavior just as well as aggressive behavior, an absurdity in ordinary usage but protected by the stipulation of a technical meaning. As Ernst Mayr explains,

To certain authors eve since [Darwin], competition has meant physical combat, and, coversely, the absence of physical combat has been taken as an indication of the absence of competition. Such a view is erroneous. . . . The relatively rarity of overt manifestations of competition is proof not of the insignificance of competition, as asserted by some authors, but, on the contrary, of the high premium natural selection pays for the development of habits or preferences that reduce the severity of competition. (1963: 42–43)

Paul Colinvaux goes one step farther, suggesting that "peaceful coexistence" provides a better description than any "talk of struggles for survival." "Natural selection designs different kinds of animals and plants so that the avoid competition. A fit animal is not one that fights well, but one that avoids fighting altogether" (1978: 144).

But how neutral in practice is the ostensibly technical use of competition employed both by Mayr and Colinvaux? I suggest two ways in which, rather than bypassing ideological expectations, it actually preserves them, albeit in a less visible form—a form in which they enjoy effective immunity from criticism. so as not to be caught in the very trap I want to expose, let me henceforth denote competition in the technical sense as "Competition" and in the colloquial sense (of actual contest) as "competition."

The first way is relatively straightforward. The use of a term with established colloquial meaning in a technical context permits the simultaneous transfer and denial of its colloquial connotations. Let me offer just one example: Colinvaux's own description of Gause's original experiments that were designed to study the effect of scarcity on interspecific dynamics—historically, the experimental underpinning of the "competitive exclusion coexistence." He writes,

No matter how many times Gause tested [the paramecia] against each other, the outcome was always the same, complete extermination of one species. . . . Gause could see this deadly struggle going on before his eyes day after day and always with the same outcome. . . . what we [might have] expected to be a permanent struggling balance in fact became a pogrom. (142)

Just to set the record straight, these are not "killer" paramecia but perfectly ordinary paramecia—minding their own business, eating and dividing, or not, perhaps even starving. The terms extermination, deadly struggle , and program refer merely to the simultaneous dependence of two species on a common resource. If, by chance, you should have misinter-

preted and taken them literally, to refer to overt combat, you would be told that you had missed the point. The Lotka-Volterra equations make no such claims; strictly speaking, they are incompatible with an assumption of overt combat; the competitive exclusion principle merely implies an avoidance of conflict. And yet the description of such a situation, only competitive in the technical sense, slips smoothly from "Competition" to genocide—much as we saw our neo-Tennysonians slip from inpersonality to heartless rejection.

The point of this example is not to single out Colinvaux (which would surely be unfair) but to provide an illustration of what is, in fact, a rather widespread investment of an ostensibly neutral technical term with a quite different set of connotations associated with its colloquial meaning. The colloquial connotations lead plausibly to one set of inferences and close off others, while the technical meaning stands ready to disclaim responsibility if challenged.^[4]

The second and more serious route by which the apparently a priori status of competition is secured can be explored through an inquiry into the implicit assumptions about resource consumption that are here presupposed and the aspects of resource consumptions that are excluded. The first presupposition is that a resource can be defined and quantitatively assessed independent of the organism itself; and the second is that each organism's utilization of this resource is independent of other organisms. In short, resource consumption is here represented as a zerosum game. Such a representation might be said to correspond to the absolutely minimal constraint possible on the autonomy of each individual, but it is a constraint that has precisely the effect of establishing a necessary link between self-interest and competition. With these assumptions, apparently autonomous individuals are in fact bound by a zerosum daynamic that guarantees not quite an absence of interaction but the inevitability of a purely competitive interaction. In a world in which one organism's dinner necessarily means another's starvation, the mere consumption of resources has a kind of de facto equivalence to murder: individual organisms are locked into a life and death struggle not by virtue of their direct interactions but merely by virture of their existence in the same place and time.

It is worth noting that the very same (Lotka-Volterra) equations readily accommodate the replacement of competitive interactions by cooperative ones and even yield a stable solution. This fact was actually noted by Gause himself as early as 1935 (Gause and Witt 1935) and has been occasionally rediscovered since then, only to be, each time, reforgotten by the community of mathematical ecologists. The full reasons for such amnesia are unclear, but it suggests a strong prior commitment to the representation of resource consumption as a zero-sum dynamic—a

representation that would be fatally undermined by the substitution (or even addition) of cooperative interactions.

Left out of this representation are not only cooperative interactions but any interactions between organisms that affect the individual's need and utilization of resources. Also omitted are all those interactions between organism and environment which interfere with the identification and measurement of a resource independently of the properties of the organism. Richard Lewontin (1982) has argued that organisms "determine what is relevant" in their environment—what, for example, is a resource—and actually "construct" their environment. But such interations, either between organisms or between organism and environment, lead to pay-off matrices necessarily more complex than those prescribed by a zero-sum dynamic—pay-off matrices that, inturn, considerably complicate the presumed relation between self-interest and competition, if they do not altogether undermine the very meaning of self-interest.

Perhaps the simplest example is provided by the "prisoner's dilemma." But even here, where the original meaning of self-interest is most closely preserved, Robert Axelrod has shown that under conditions of indefinite reiterations, a ("tit-for-tat") strategy is generally better suited to self-interest than are more primitive competitive strategies.

Interactions that effectively generate new resources, or either increase the efficiency of resource utilization or reduce absolute requirement, are more directly damaging to the very principle of self-interest. These are exactly the kinds of interactions that are generally categorized as special cases: as "mutualist," "cooperative," or "symobiotic" interactions. Finally, interactions that affect the birth rate in ways not mediated by scarcity of resources, for example, sexual reproduction, are also excluded by this representation. Perhaps the most important of these omissions for intraspecific dynamics, I would point to sexual reproduction, a fact of life that potentially undermines the core assumptions of radical individualism. In the last few years, there has been a new wave of interest in mutualism among not only dissident but even a few mainstream biologists, and numerous authors are hard at work redressing the neglect of previous years.^[5] But in the sixty years in which the Lotka-Volterra equations have reigned as the principal, if not the only, model of interspecific population dynamics—even in the more genial climate of recent years—the omission of sexual reproduction from this model has sacrcely been noted.

This omission, once recognized, takes us beyond the question of selective biases in admissible or relevant interactions between organisms. It calls into question the first and most basic assumption for the methodology of individualism in evolutionary theory, namely, that in-

trinsic properties of individual organisms are primary to any description of evolutionary phenomena.^[6] To examine this argument, let us turn from mathematical ecology to population genetics, that branch of evolutionary theory that promises to avoid the practical difficulties of selective focus on certain interactions by excluding the entire question of competitive or cooperative interactions from its domain. In other workds, traditional population genetics addresses neither interactions betwee organisms nor limitations in resources; it effectively assumes populations at low density with infinite resources.

However, one last problem with the language of competition must be noted lest it carry over int our discussion of individual autonomy in population genetics: the widespread tendency to extend the sense of "competition" to include not only the two situations we distinguished earlier (i.e., conflict and reliance on a common resource) but also a third situation^[7] where there is no interaction at all, where "competition" denotes an operation of comparison between organisms (or species) that requires no juxtaposition in nature, only in the biologist's own mind. This extention, where "competition" can cover all possible circumstances of relative viability and reproductivity, brings with it, then, the tendency to equate competition with natural selection itself.

Darwin's own rhetorical equation between natural selection and the Malthusian struggle for existence surely bears some responsibility for this tendency. But contemporary readers of Darwin like to point out that he did try to correct the misreading his rhetoric invited by explaining that he meant the term struggle in "a large and metaphoric sense," including, for example, that of the plant on the edge of the desert: competition was only one of the many meanings of struggle for Darwin. Others have been even more explicit on this issue, repeatedly noting the importance of distinguishing natural selection from "a Malthusian dynamic." Lewontin, for one, has written.

Thus, although Darwin came to the idea of natural selection from consideration of Malthus' essay on overpopulation, the element of competition between organisms for a resource in short supply is not integral to the argument. Natural selection occurs even when two bacterial strains are growing logarithmcally in an excess of nutrient broth if they have different division times. (1970: 1)

However, such attempts—by Lewontin, and earlier and more comprehensively, by L.C. Birch (1957)—to clarify the distinction between natural section and competition (what Engels called "Darwin's mistake") have done little to stem the underlying conviction that the two are somehow the same. In a recent attempt to define the logical essence of "the Darwinian dynamic," Bernstein et al. (1983) freely translate Darwin's

"struggle for survival" to "competition through resource limitation" (192), thereby claiming for competition the status of a "basic component" of natural selection. Even more recently, George Williams (1986) describes a classic example of natural selection in the laboratory as a "competition experiment," a "contest" between a mutant and normal allele, in which he cites differential fecundity as an example of "the competitive interactions among individual organisms" that cause the relative increase in one population (114–115).

At issue is not whether overtly competitive behavior or more basic ecological scarcity is the rule in the natural world; rather, it is whether or not such a question can even be asked. To the extent that distinctions between competition and scarcity, on the one hand, and between scarcity and natural selection, on the other, are obliterated from our language and thought, the question itself becomes foreclosed. As long as the theory of natural selection is understood as a theory of competition, confirmation of one is taken to be confirmation of the other, despite their logical (and biological) difference.

While this clearly raises problems about the meaning of confirmation, my principal concern is with the dynamics by which such an oversight or confusion is sustained in the theory and practice of working biologists—with the internal conventions that render it effectively resistant to correction. Dynamics similar to those in the language of competition can also be seen in the language of reproductive autonomy, especially as employed in the theory and practice of population biology.