Richard Levins

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.

Coexistence in a Variable Environment

A community which would not reach a stable equilibrium may nevertheless persist if there is temporal variation and nonlinear dynamics. A procedure is introduced for taking time averages of the rates of change. Since the average of a nonlinear function is not the function of the average, higher terms such as the variances of resources or covariances among species and environmental factors enter into the coexistence conditions. These measures behave as if they were resources. Therefore the number of consumer species cannot exceed the number of resources plus distinct nonlinearities. The nonlinearities arise from predator saturation, learning, group hunting, multiple nutritional requirements, or seasonally variable feeding rates. It is shown that there is no long term correlation between the abundance of a species and its rates of increase.

Theory of Fitness in a Heterogeneous Environment. I. The Fitness Set and Adaptive Function

A method is presented for representing the fitness of populations in a heterogeneous environment in terms of their fitness in the various niches taken separately, and the distribution of the niches in space and time. The characteristics of the optimal population can be found for each environmental pattern, and conditions determined in which the optimum is specialized or generalized, mono- or polymorphic, differentiated into discrete races or gradually along clines. These results are shown in table 1. The next paper in this series will extend the model and discuss experimental approaches for testing the theory.

Thermal Acclimation and Heat Resistance in Drosophila Species

Physiological and developmental acclimation to dry heat as measured by survival at 38⚬ C was studied in several species of Drosophila. Physiological acclimation occurs rapidly (about half-completed in 12 hr), is quickly lost, and does not depend on water uptake. In broad-niched species, and especially in D. melanogaster, adaptation to different climates depends mostly on individual flexibility and less on genetic differences among populations. None of the narrow-niched species acclimate. The D. willistoni, a moderately broad-niched species, does not acclimate nor show much genetic variation. It is suggested that this species avoids desiccation stress behaviorally.

DISCUSSION PAPER: THE QUALITATIVE ANALYSIS OF PARTIALLY SPECIFIED SYSTEMS

The most difficult general problem of contemporary science is how to deal with complex systems as wholes. Most of the training of scientists, especially in the United States and Great Britain, is in the opposite direction. We are taught to isolate parts of a problem and to answer the question “What is this system?” by telling what it is made of. The dramatic advances in science in our generation have almost all been in areas where such an approach is practicable. The notable stagnations have been in areas of complex systems approached in pieces. I t is now a commonplace, a t least in ecology, that systems are complex and that the one-step linear causality is a poor predictor of ultimate outcome. Consider, for example, the problem of providing more food for hungry people. Since insects destroy a significant portion of the world’s crops, and since insecticides can be shown in the laboratory to kill insect pests, it is a plausible inference that the use of insecticides will control insects and increase food available to the hungry. Furthermore, to avoid side effects, laboratory tests may show that insecticides such as heptachlor are relatively nontoxic to mammals. Therefore, it is reasonable t o expect that the use of such insecticides would reduce insect pests, increase yields, and alleviate hunger. But often it does not work that way. First, the application of insecticide does not necessarily control the insect pest, for a t least three reasons: 1. Any insect killed by insecticide is that much less food for the predators of the pest. This in itself reduces the predator population, so that the end result is a shift in the cause of death of the pest-more are poisoned, fewer are eaten-but not in the numbers. 2. The insecticide directly reduces the predators of the pest. 3. Natural selection in the target population rapidly builds up resistance t o the insecticide. In general, an insecticide is physiologically effective for two to ten years. The side effects may also behave in unexpected ways. The relatively safe heptarhlor may be transformed into highly toxic substances under field conditions where the action of sunlight in the presence of a vast ensemble of organic and inorganic substances promotes reactions that d o not occur in the simple laboratory test. Finally, even the obvious expectation that increased food production alleviates hunger proves false. The whole domain of agricultural economics, grain prices, trade agreements, credits for farmers, land concentration, and speculation intervenes between the harvesting of a crop and its consumption. Similar problems of complex interactions have arisen in ecology, medicine, economics, administration, and other disciplines. This has led t o an interest in complexity per se and the exploration of strategies t o deal with complexity. Three general approaches have emerged. 1. Statistical-biometrical. Here the system is treated as a black box, and its

An Hypothesis to Explain the Incidence of Monophagy

An insects choice of food plant is assumed to be based on a simple decision rule that maximizes the expected production of offspring. Monphagy or polyphagy may be favored, depending on the proportion of an extended diet that would be unsuitable if chosen, versus the difficulty in finding the most suitable food. See full-text article at JSTOR

Dialectics and Reductionism in Ecology

The philosophical debates which have accompanied the development of science have often been expressed in terms of dichotomous choices between opposing viewpoints about the structure of nature, the explanation of natural processes, and the appropriate methods for research:

Toward an Ecosocial View of Health

The changing patterns of health in the United States justify both celebration and dismay. We can celebrate declining mortality rates, increased life expectancy, and improvements in diagnostic and therapeutic technologies. But public health was caught by surprise by the return of infectious disease; the gap in health outcomes between rich and poor and between whites and blacks increases; there is a growing discrepancy between what is technically possible and the actual health status; and despite its greater expenditures on health, the United States lags behind the other developed countries in health outcomes. The authors examine four reasons for this: we do not buy more health care, only pay more for it; we receive more health care, but much of it inappropriate, ineffective, or harmful; only some of us get more health care; and we have created a way of life that makes us sick, then spend more to repair the damage. Major failures arise when problems are understood too narrowly. An ecosocial perspective attempts to look at the whole. It rejects as false the dichotomies social/biological, physical/psychological, genetic/environmental, lifestyle/environment, examining their interrelations rather than assigning them relative weights. In addition to looking at average differences among populations, the authors examine patterns of variability in health outcomes.

The Maintenance of Genetic Polymorphism in a Spatially Heterogeneous Environment: Variations on a Theme by Howard Levene

1) Levenes model of polymorphism in a patchy environment is generalized and extended to include different patch structures and inbreeding. 2) Starting with heterosis in each patch, as the fitness of the heterozygote decreases we pass through regions of average heterosis providing stable polymorphism, then one satisfying Levenes condition for polymorphism, then a region of alternative equilibria (one polymorphic, one monomorphic), and finally fixation of one allele. Variation in inbreeding, patch abundance, and patchiness can have similar effects. Any of these can result in a discontinuity in the population structure along a continuous cline in environment.

Biogeography of the Puerto Rican Bank: Species‐Turnover on a Small Cay, Cayo Ahogado

The equilibrium species—number of plants on Cayo Ahogado, a small sand cay east of Puerto Rico, is 11.2 if all species are considered, and 6.8 if only established species are counted. Establishment is defined in terms of reproductive success and presence on the island for at least two consecutive visits. There were only five species in the permanent flora. Species—turnover rates of plants were high, migration being on the average 14.4 species/year (all species), or 1.6 species/year (established species only). Extinction rates were 17.2 and 0.8 species/year for total species and established species respectively. Immigration is chiefly by flotation, particularly of propagules released by flood waters in Puerto Rico; extinction is caused by failure to find suitable habitat, wave erosion, and hurricanes. Nine individuals of three species of lizard arrived, probably by flotsam as time of arrival correlated with flooding in Puerto Rico, and persisted for varying times up to 5 months. No reproduction occurred. Species turnover of invertebrates was high. Eighty—one species (77 terrestrial, 1 marine water strider, and 3 semiterrestrial crustacea) were recorded from the cay. Equilibrium number was 9.8 for established species and 14.2 for total species. Direct flight was probably the most imporrant mode of immigration for the entire fauna because of the large number of strong fliers among the ephemerals. If only established species are considered, flotsam transport becomes important. Human transport and passive dispersal by wind were relatively insignificant. Trophic structure of the fauna remained relatively constant although taxonomic structure varied. It is postulated that species—numbers on small cays are determined in part by the type of trophic structure which can be built upon available energy reserves, and that establishment of immigrants is influenced by whether they fit into the trophic scheme.