Robert H. MacArthur

On Optimal Use of a Patchy Environment

A graphical method is discussed which allows a specification of the optimal diet of a predator in terms of the net amount of energy gained from a capture of prey as compared to the energy expended in searching for the prey. The method allows several predictions about changes in the degree of specialization of the diet as the numbers of different prey organisms change. For example, a more productive environment should lead to more restricted diet in numbers of different species eaten. In a patchy environment, however, this will not apply to predators that spend most of their time searching. Moreover, larger patches are used in a more specialized way than smaller patches.

THE LIMITING SIMILARITY, CONVERGENCE, AND DIVERGENCE OF COEXISTING SPECIES

1. There is a limit to the similarity (and hence to the number) of competing species which can coexist. The total number of species is proportional to the total range of the environment divided by the niche breadth of the species. The number is reduced by unequal abundance of resources but increased by adding to the dimensionality of the niche. Niche breadth is increased with increased environmental uncertainty and with decreased productivity. 2. There is a different evolutionary limit, L, to the similarity of two coexisting species such that a) If two species are more similar than L, a third intermediate species will converge toward the nearer of the pair. b) If two species are more different than L, a third intermediate species will diverge from either toward a phenotype intermediate between the two.

An equilibrium theory of insular zoogeography

As the area of sampling A increases in an ecologically uniform area, the number of plant and animal species s increases in an approximately logarithmic manner, or s = bAk, (1) where k < 1, as shown most recently in in the detailed analysis of Preston (1962). The same relationship holds for islands, where, as one of us has noted (Wilson, 1961), the parameters b and k vary among taxa. Thus, in the ponerine ants of Melanesia and the Moluccas, k (which might be called the faunal coefficient) is approximately 0.5 where area is measured in square miles; in the Carabidae and herpetofauna of the Greater Antilles and associated islands, 0.3; in the land and freshwater birds of Indonesia, 0.4; and in the islands of the Sahul Shelf (New Guinea and environs), 0.5.

POPULATION ECOLOGY OF SOME WARBLERS OF NORTHEASTERN CONIFEROUS FORESTS

Wahrscheinlichkeit-Rechnung. Proc. Tokyo Mathem. Phys. Soc., 2nd Ser., 8: 556-564. Miyasita, K. 1955. Some consideration on the population fluctuation of the rice stem borer. (In Japanese.) Bull. Nat. Inst. Agr. Sci., Japan, C, 5: 99-109. Schwerdtfeger, F. 1935. Uber die Populationsdichte von Bupalus piniarius, Panolis flammea, Dendrolin is pini, Sphinx pinastri und ihren zeitlichen Wechsel. Z. Forst-u. Jagdwesen, 67: 449-482, 513-540. . 1954. Grundsitzliches zur Populationsdynamik der Tiere, insbesondere der Insekten. Allgem. Forst-u. Jagdzeitung. 125: 200-209. Smith, H. S. 1935. The role of biotic factors in the determination of population densities. T. Econ. Ent., 28: 873-898.

PATTERNS OF SPECIES DIVERSITY

1. Species diversity is most simply measured by counting species. More complicated measures, which take into account the relative abundance of the species, have been derived from information theory or from parameters of statistical distributions fitted to the census data. The information theory formulae can also be used to measure habitat diversity and differences between communities or habitats. In this way, changes in the pattern of species diversity can be compared with changes in the environment.

Species packing and competitive equilibrium for many species.

It has always been interesting to some scientists to construct minimum principles for their science. These not only provide conceptual unification but also lead to some technical simplifications. Thus, for instance, in mechanics, a particle follows the path which will minimize the time integral of the difference between kinetic and potential energies (principle of least action) and the stable equilibrium positions of such a system are those for which the potential energy is at a minimum. The first example is a minimum principle for dynamics, the second only applies to the static, equilibrium, conditions. Here I attempt an ecological counterpart of the second, weaker, kind of minimum principle. I show that for some kinds of competition equations a quadratic expression is minimized, and I use this result to interpret species packing and competitive equilibria. The competition equations for n species are of the form

On the Relative Abundance of Species

1. A distinction is made between opportunistic and equilibrium species. 2. There is little ecological interest in the relative abundances of opportunistic species, but such species abundances should frequently have a log-normal distribution. 3. The relative abundances of equilibrium species are of considerable ecological interest and frequently can be deduced from the assumption that increase in one species population results in a roughly equal decrease in the populations of other species. To make the formulae well-defined it is necessary to assume that the census-taker has sampled a small area and thus achieved a certain sort of randomness. 4. For bird populations, at least, discrepancies between observations and predictions are negligible except when the censused area is compounded from different habitats. The discrepancy is then partly due to the fact that common species in one habitat are more likely to be present in adjacent habitats than are rate ones.

Density Compensation in Island Faunas

This paper analyzes factors determining the extent of density compensation on islands: i.e., is the summed population density of individuals of all species on islands equal to the summed mainland density as a result of niche expansions and higher abundances of island species compensating for the absence of many mainland species? In addition, a method is described for estimating bird population densities based on analysis of the time dependence or mist—netting yields. Puercos Island in the Pearl Archipelago off Panama has less than one—third as many resident birds species as comparable mainland habitats. Analysis of the Pearl avifauna suggests that about one—quarter of the island species may be relicts of the Pleistocene land bridge and that the remainder are subsequent over—water colonists. The successful colonists are a highly nonrandom sample of the mainland avifauna in such respects as family composition, social structure, and second—growth habitat origin. Song—based censuses and analysis of mist—netting show that Puercos has a slightly density of individuals than the mainland. Niche shifts between islands and mainland, or among different islands, include habitat expansions, wider ranges of vertical foraging strata, abundance increases checkerboard distribution patterns, and decreased morphological variability. Comparison of the present study with other studies shows that summed population densities on islands may be higher than, comparable to, or less than mainland levels, depending upon the particular island, habitat, and group of animals studied. Among factors affecting the extent of density colonists less appropriate to the vacated habitat, tending to lower island densities; and underrepresentation of large species on islands, tending to increase island population densities for a given biomass.

Competition among Fugitive Species in a Harlequin Environment

We examine the qualitative behavior of differential equations for the proportion of insular patches of each of two kinds of habitat occupied by each of two species with characteristics rates of migration between patches and of local extinction within a habitat. Certain migration and extinction rates result in stable coexistence, even of closely similar species; others lead to competitive exclusion, even when each species is competitively superior in one kind of habitat. For a community of many species in many habitats, we surmise qualitative limits to the subdivision of resources, and alternative stable communities. Our results extend to species that live in successional or ephemeral habitats. We therefore conjecture equilibrial theories for the number of patches of habitat occupied by insular species, fugitive plants and invertebrates, or infesting parasites.

On the Relation between Habitat Selection and Species Diversity

Breeding bird censuses were made in Puerto Rico, Panama, and temperate United States, and a profile of foliage density was made for each. Using information theory formulae both diversity indices and measurements of difference between censuses and difference between habitats can be made. Based on these, the following can be verified directly from the data: 1. Puerto Rico has nearly as many bird species per layer as Panama and the temperate regions, but the Puerto Rican species appear to recognize fewer layers and certainly subdivide habitats much less. Thus different habitats are likely to have quite similar species in Puerto Rico, unlike Panama and temperate United States.