Alan Hastings

Weak trophic interactions and the balance of nature

Ecological models show that complexity usually destabilizes food webs,, predicting that food webs should not amass the large numbers of interacting species that are in fact found in nature. Here, using nonlinear models, we study the influence of interaction strength (likelihood of consumption of one species by another) on food-web dynamics away from equilibrium. Consistent with previous suggestions,, our results show that weak to intermediate strength links are important in promoting community persistence and stability. Weak links act to dampen oscillations between consumers and resources. This tends to maintain population densities further away from zero, decreasing the statistical chance that a population will become extinct (lower population densities are more prone to such chances). Data on interaction strengths in natural food webs indicate that food-web interaction strengths are indeed characterized by many weak interactions and a few strong interactions.

Approaching a state shift in Earth’s biosphere

Localized ecological systems are known to shift abruptly and irreversibly from one state to another when they are forced across critical thresholds. Here we review evidence that the global ecosystem as a whole can react in the same way and is approaching a planetary-scale critical transition as a result of human influence. The plausibility of a planetary-scale ‘tipping point’ highlights the need to improve biological forecasting by detecting early warning signs of critical transitions on global as well as local scales, and by detecting feedbacks that promote such transitions. It is also necessary to address root causes of how humans are forcing biological changes.

Chaos in a Three‐Species Food Chain

A continuous time model of a food chain incorporating nonlinear functional (and numerical) responses exhibits chaotic dynamics in long-term behavior when biolog- ically reasonable parameter values are chosen. The appearance of chaos in this model suggests that chaotic dynamics may be common in natural food webs.

Thresholds and the resilience of Caribbean coral reefs

The deteriorating health of the world’s coral reefs threatens global biodiversity, ecosystem function, and the livelihoods of millions of people living in tropical coastal regions. Reefs in the Caribbean are among the most heavily affected, having experienced mass disease-induced mortality of the herbivorous urchin Diadema antillarum in 1983 and two framework-building species of coral. Declining reef health is characterized by increases in macroalgae. A critical question is whether the observed macroalgal bloom on Caribbean reefs is easily reversible. To answer this question, we must resolve whether algal-dominated reefs are an alternative stable state of the ecosystem or simply the readily reversible result of a phase change along a gradient of some environmental or ecological parameter. Here, using a fully parameterized simulation model in combination with a simple analytical model, we show that Caribbean reefs became susceptible to alternative stable states once the urchin mortality event of 1983 confined the majority of grazing to parrotfishes. We reveal dramatic hysteresis in a natural system and define critical thresholds of grazing and coral cover beyond which resilience is lost. Most grazing thresholds lie near the upper level observed for parrotfishes in nature, suggesting that reefs are highly sensitive to parrotfish exploitation. Ecosystem thresholds can be combined with stochastic models of disturbance to identify targets for the restoration of ecosystem processes. We illustrate this principle by estimating the relationship between current reef state (coral cover and grazing) and the probability that the reef will withstand moderate hurricane intensity for two decades without becoming entrained in a shift towards a stable macroalgal-dominated state. Such targets may help reef managers face the challenge of addressing global disturbance at local scales.

Disturbance, coexistence, history, and competition for space

A simple model to elucidate the effect of disturbance on a large number of competitors that compete for space and exhibit a competitive hierarchy is developed. Conditions are derived that determine presence of species, and diversity is calculated as a function of percentage cover. The model is compared to data from coral reefs collected by J. W. Porter (1974, Science 186, 543–545). Using parameter values in the model that allow a fit to Porters data, the response of an individual species to changes in disturbance becomes quite complex, depending on the position (odd or even) of the species in the competitive hierarchy. For these same parameter values, the system is interactive: the existence of a particular species may effect the presence of another. Different parameter values would lead to a noninteractive system.

Complex Interactions Between Dispersal and Dynamics: Lessons From Coupled Logistic Equations

A study of one of the simplest systems incorporating both dispersal and local dynamics, coupling two discrete time logistic equations, demonstrates several surprising features. Passive dispersal can cause chaotic dynamics to be replaced by simple periodic dynamics. Thus passive movement can be stabilizing, even in a deterministic model without underlying spatial variation in the dynamics. The boundary between initial conditions leading to qualitatively different dynamics can be a fractal, so it is essentially impossible to specify the asymptotic behavior in terms of the initial conditions. In accord with several recent studies of arthropods and earlier theoretical work, density dependence may only be detectable at a small enough spatial scale, so efforts to uncover density dependence must include investigations of movement. 26 refs., 6 figs.

PRINCIPLES FOR THE DESIGN OF MARINE RESERVES

The theory underlying the design of marine reserves, whether the goal is to preserve biodiversity or to manage fisheries, is still in its infancy. For both of these goals, there is a need for general principles on which to base marine reserve design, and because of the paucity of empirical experience, these principles must be based on models. However, most of the theoretical studies to date have been specific to a single situation, with few attempts to deduce general principles. Here we attempt to distill existing results into general principles useful to designers of marine reserves. To answer the question of how fishery management using reserves compares to conventional management, we provide two prin- ciples: (1) the effect of reserves on yield per recruit is similar to increasing the age of first capture, and (2) the effect of reserves on yield is similar to reducing effort. Another two principles answer the question of how to design reserve configurations so that species with movement in various stages will be sustainable: (3) higher juvenile and adult movement lowers sustainability of reserves for biodiversity, but an intermediate level of adult move- ment is required for reserves for fishery management, and (4) longer larval dispersal distance requires larger reserves for sustainability. These principles provide general guidelines for design, and attention to them will allow more rapid progress in future modeling studies. Whether populations or communities will persist under any specific reserve design is un- certain, and we suggest ways of dealing with that uncertainty.

POPULATION MODELS FOR MARINE RESERVE DESIGN: A RETROSPECTIVE AND PROSPECTIVE SYNTHESIS

We synthesize results from existing models of marine reserves to identify key theoretical issues that appear to be well understood, as well as issues in need of further exploration. Models of marine reserves are relatively new in the scientific literature; 32 of the 34 theoretical papers we reviewed were published after 1990. These models have focused primarily on questions concerning fishery management at the expense of other objectives such as conservation, scientific understanding, recreation, education, and tourism. Roughly one-third of the models analyze effects on cohorts while the remaining models have some form of complete population dynamics. Few models explicitly include larval dispersal. In a fisheries context, the primary conclusion drawn by many of the complete population models is that reserves increase yield when populations would otherwise be overfished. A second conclusion, resulting primarily from single-cohort models, is that reserves will provide fewer benefits for species with greater adult rates of movement. Although some models are beginning to yield information on the spatial configurations of reserves required for populations with specific dispersal distances to persist, it remains an aspect of reserve design in need of further analysis. Other outstanding issues include the effects of (1) particular forms of density dependence, (2) multispecies interactions, (3) fisher behavior, and (4) effects of concentrated fishing on habitat. Model results indicate that marine reserves could play a beneficial role in the protection of marine systems against overfishing. Additional modeling and analysis will greatly improve prospects for a better understanding of the potential of marine reserves for conserving biodiversity.

Re-evaluating the omnivory–stability relationship in food webs

Under equilibrium conditions, previous theory has shown that the presence of omnivory destabilizes food webs. Correspondingly, omnivory ought to be rare in real food webs. Although, early food web data appeared to verify this, recently many ecologists have found omnivory to be ubiquitous in food web data gathered at a high taxonomic resolution. In this paper, we re–investigate the role of omnivory in food webs using a non–equilibrium perspective. We find that the addition of omnivory to a simple food chain model (thus a simple food web) locally stabilizes the food web in a very complete way. First, non–equilibrium dynamics (e.g. chaos) tend to be eliminated or bounded further away from zero via period–doubling reversals invoked by the omnivorous trophic link. Second, food chains without interior attractors tend to gain a stable interior attractor with moderate amounts of omnivory.

Can spatial variation alone lead to selection for dispersal

Abstract The question of selection on dispersal rates in a spatially varying, temporally constant environment is studied using an evolutionarily stable strategy approach. Dispersal is modelled as passive diffusion. For any dynamics leading to an equilibrium which does exhibit spatial variation, dispersal will be selected against. Hence, selection for dispersal must include other factors. Other biological implications of the results are discussed.