An Alternative Model Based on Random Distributions for Density-dependent Regulation in Host-parasite Systems

The distribution patterns of adult female Lernaea cyprinacea (Copepoda, Lernaeidae) among the goldfish and centrarchids of North Pond, Kelleys Island, Ohio, were studied. In contrast to predictions based on a model proposed by Crofton, the distributions appeared random rather than clumped, and the parasite did not demonstrably harm infested hosts. An alternative model, based upon the assumptions that Lernaea cyprinacea causes host mortality only when penetrating vital organs and that parasites are randomly distributed among their hosts, is presented to determine whether Lernaea-induced host mortality serves as a density-dependent regulatory mechanism. According to this model, regulation of the parasite is density-dependent, whereas regulation of the host is not. INTRODUCTION Although density-dependent regulation among free-living organisms has been extensively studied for many years, host-parasite systems have been considered only relatively recently. Crofton (1971a,b) proposed a model to explain how parasiteinduced host mortality may serve as a density-dependent regulatory mechanism. Three essential features of his model are that (1) the distribution of the parasite is clumped; (2) the parasite distribution can be predicted by the negative binomial, and (3) heavily parasitized hosts are adversely affected. A clumped distribution, like the negative binomial, is conducive to stable host and parasite populations since it counterbalances the reproductive and death rates of both populations. Despite the flaws inherent in Crofton's model (May, 1977), it has proven useful because it has stimulated analysis of the observed parasite distributions within individual hosts. In many cases, the observed distribution is clumped and is characterized by a low value of "K," the inverse measure of the degree of clumping used in generating a negative binomial distribution (see Anderson and May, 1978, Table 2). In the articles analyzed by Anderson and May, the value of "K" ranged from 0.04 to 10, indicating a considerable degree of clumping in many of the host-parasite systems examined. Not all observed distributions are clumped. Stromberg and Crites (1974) document a random distribution of Cammalanus oxycephalus among young gizzard shad Dorosoma cepedianum. Anderson and May (1978) suggest that in cases like these, random patterns may be observed during the initial invasion of a host population. They also propose that even random distributions of parasites may lead to globally stable equilibria if the rate of parasite-induced host mortalities follows an exponential function, rather than being linearly related to parasite burden. In 1975, I began a study of the population ecology of the anchor worm Lernaea cyprinacea (Copepoda, Lernaeidae) among the goldfish and centrarchids of North Pond, Kelleys Island, Ohio. My intent was to determine whether Lernaea matches the features of the model outlined by Crofton (1971a) and by Anderson and May (1978) for a species capable of regulating its hosts. Lernaea cyprinacea is an ectoparasite of freshwater fishes. The adult female stage causes most damage to the host. The female anchor worm, so named because of its cephalic horns, penetrates the body of the host and causes a local inflammation characterized by the proliferation of fibrous connective tissue (Joy and Jones, 1973). A large dermoid tumor is formed, through which the posterior half of the parasite protrudes. Other symptoms caused by the adult parasite are an increase of monocytes and