MacArthur Model Research Articles

Relationship of Eastern Gulf of Mexico Reef-Fish Communities to the Species Equilibrium Theory of Insular Biogeography

A 1971 summer red tide (Gymnodinium breve Davis) and associated stress conditions resulted in mass mortalities and near extirpation of reef biotas from at least 1536 km2 of central West Florida Shelf. An estimated 77% of the resident fish species perished at shallow-water (12-18 m depths) reefs. Reef-fish colonization was monitored irregularly (1-6 month intervals) at two reefs for 3 years after the red tide. In addition, species censuses were taken 4 years after defaunation at one reef and 5 years later at both reefs. Since eastern Gulf of Mexico reefs occur as isolated patches, reef-fish coloniz- ation data were analysed in light of MacArthur and Wilson's species equilibrium model developed for insular biotas. Certain features of reef-fish colonization appeared consistent with the MacArthur-Wilson model: (1) an increasing convex colonization curve, (2) an observed immigration (colonization) rate de- creasing with time, (3) differences between colonization and decolonization (observed extinction) rate decreasing through time, and (4) attainment and maintenance of a rather stable species richness after 15 months colonization similar to the pre-defaunation level. However, other aspects of reef-fish coloniz- ation did not seemingly fulfil basic requirements of the model: (I) an erratic decolonization rate indicating no tendency to increase through time, (2) an observed species turnover rate considerably less than theoretical predictions, and (3) development of a compositionally stable community nearly identical with that existing prior to the red tide. It is proposed that eastern Gulf reef-fish communities develop according to well-defined successional rather than chance colonization processes. The eventual stability in species richness and composition probably represents attainment of a 'climax' community rather than a dynamic equilibrium resulting from continual species turnover. Possible reasons for failure of these communities to conform to the species equilibrium theory are presented.

Bayesian estimation of Shannon's index of diversity

SUMMARY This paper is concerned with methods of estimating Shannon's information measure, and with the sampling properties of those estimates. A Bayesian approach is used to suggest two possible classes of estimators, and their properties are compared with those of the usual Shannon measure of diversity. Particular attention is given to comparisons involving the MacArthur model of species abundances.

Glacial Migrations of Plants: Island Biogeographical Evidence

Analyses of the floras of the high north Andean habitat islands (paramos) and the Galápagos Islands show that plant species diversity conforms to the MacArthur and Wilson model of island biogeography but that immigration occurred primarily during glacial periods. Modern plant species diversity is more significantly correlated with area and distance measures of the glacial forms of the islands than with similar measures of the present-day islands.

Relative Abundance of Species and MacArthur's Model

MacAthur's model was derived to predict the relative abundance of species in adequately sampled sympatric associations in which niches are contiguous and nonoverlapping, the species are comparable in size and physiology and are maintained in equilibrium so that relative abundances are constant. The model is applicable only to homogeneously diverse biotopes in which the range of the environmental mosaic is small in relation to the requirements of the inhabitant species. These factors require that the niche arrangement be the outcome of competitive exclusion. Data are presented on the adequacy of the MacArthur model in describing the relative abundance of fish, ophiuroids, gastropods, pagurid crabs, and ciliates. In addition, summaries of previously reported tests are included. By comparing groups which are adequately and inadequately described by the MacArthur model, it is possible to examine the characteristics which may establish the equilibrium. It is hypothesized that characteristics of importance are length of life cycle, duration and frequency of reproduction, and relative (to generation time) constancy of environmental conditions. It is shown that when fish or gastropod species are tested, the goodness—of—fit to the model's predictions is related to the taxonomic affinity of the group being tested. Stable associations of species with high taxonomic affinity must be highly organized. A high degree of organization is required to maintain the random distribution of abundances. Density dependent competition for food is the most likely bases of this organization.