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1997 Symposium

This symposium will be presented at the 1997 annual meeting of the Ecological Society of America, to be held in Albuquerque, NM, 11-14 August 1997.


Organized by: Peter Turchin, Department of Ecology and Evolutionary Biology, University of Connecticut, Storrs, CT 06269-3042, (860) 486-3603 (phone), (860) 486-4320 (fax),

Spatial dynamics of populations and ecosystems is one of the fastest developing areas in ecology. New ideas and results from patch and metapopulation dynamics and lansdcape ecology induced a decisive shift from aspatial “balance of nature” paradigms that dominated in the past, to approaches emphasizing effects of spatial heterogeneity and non-equilibrium nature of ecological systems. Explicitly spatial approaches generate a lot of enthusiasm both in academic ecology (for example, the National Center for Ecological Analysis and Synthesis in Santa Barbara chose spatio-temporal dynamics as one of its two focus areas), and in applications such as natural resource management and conservation (witness, for example, the current controversy over the importance of wildlife movement corridors).

Spatial population dynamics are driven by complex mechanisms involving both temporal and spatial dimensions. Because of this complexity, mathematical methods have to be a key ingredient in investigating spatial dynamics. We are lucky in that we have a well-developed general theory for population dynamics in space. However, most of the theory is very abstract and, until very recently, had little impact on empirical investigations. In an exciting recent development, a number of investigators have begun bridging the gap between theory and data, by developing models rooted in general theory, but with parameter estimates and sometimes even functional forms based on observational and experimental data. Such models can be (and are) rigorously tested by comparing their predictions to independent data. Of necessity, these empirically-based models have to be closely tied to particular systems; yet, it is becoming clear that general insights will result from a systematic application of this approach to a number of systems.

The goal of the proposed symposium is to present a progress report on our successes (and failures?) – current studies addressing tough questions that can not be resolved using purely theoretical or purely empirical approaches.

List of Planned Presentations

Doak Using spatial models to address the monitoring and management of rare species.

Grünbaum Foraging ecology in spatially heterogeneous environments.

Hanski Spatial dynamics in highly fragmented landscapes: the incidence function approach.

Kobe et al. Forest models defined by field measurements.

Turchin et al. Reaction-diffusion dynamics in a host tree-bark beetle-clerid predator system.

van den Bosch and Metz Focus expansion in plant epidemics.

Wilson et al. Spatial pattern formation in a host-parasitoid system.

Abstracts of the Presentations:


A variety of spatial and pseudospatial models have been applied to questions of endangered species protection. I will discuss the problem of choosing the optimal model complexity given species-specific behavior, the time-scales and impacts of concern, and the quality of available data. To illustrate some of the trade-offs involved in modeling populations of large, rare, and difficult to see vertebrates, I will present results of models designed to assess alternative monitoring strategies for populations of grizzly bears subjected to ongoing habitat conversion and degradation. Results of these simple models provide pessimistic predictions of our ability to safely monitor populations subjected to on-going habitat conversion. However, they also suggest various concrete improvements in monitoring strategies for grizzly bears and other species. As these results show, models can be highly useful for conservation planning of species such as bears, even when they are largely untestable in the short-term. I will discuss this contradiction in light of how best to balance model complexity with the limited data available — or even collectable — for many rare vertebrate species.

2. Grünbaum, Danny. University of Utah, Salt Lake City, UT 84112 USA. FORAGING ECOLOGY IN SPATIALLY HETEROGENEOUS ENVIRONMENTS.

Spatial heterogeneity of resources is increasingly recognized as fundamental to the dynamics of ecological dynamics. Organisms ranging from bacteria to higher vertebrates exploit spatial variability in their environments with foraging strategies such as taxis, area-restricted search, and other biased random walk behaviors. Central to these behaviors is the dependence of movement on internal state variables (physiological condition, memory, signal transduction mechanics, etc.) which mediate responses to changing conditions. Mathematical models of biased random walks are essential for translating observations of individual movements into predictions of the resulting population distributions. However, two principal limitations have restricted models’ capacity to assess how heterogeneity affects populations and which empirical approaches best characterize spatial dynamics. First, existing models omit meaningful internal state dynamics, and are therefore too simplistic to reflect behavioral ecologists’ concepts of foraging strategies. Second, population-level descriptions have not been translated into digestible summary statistics relevant to foraging theory. I address these limitations by presenting an approach for predicting movements of populations in which foraging behavior depends explicitly on internal state variables. I then derive ecologically relevant statistical assessments of forager performance, that quantify the suitability of specific behaviors to particular resource distributions. The performance statistics identify which spatial features of resource distributions are most important in determining habitat quality to foragers. The performance assessments also enable qualitative and quantitative predictions of spatial dynamics of multi-species predator-prey systems.


Many species living in highly fragmented landscapes have high turnover rate of local populations. The extinction rate is typically an increasing function of the size of the habitat patch, whereas the colonization rate is primarily a function of isolation. Based on these first-order effects of habitat patch size and isolation, a simple stochastic model can be constructed for the incidence of habitat patch occupancy. This model can be parameterized with data on patch occupancy and, if available, on turnover events. The model can be used to predict the transient dynamics, metapopulation-level quasi-equilibrium and expected time to metapopulation extinction in fragmented landscapes. Because the model is spatially realistic, it can be used to study the formation of spatially correlated patterns in species distributions. Additional environmental factors can be included in the model, though experience suggests that often the effects of habitat patch area on extinction and isolation on colonization are so dominant that other factors make only a minor contribution. The incidence function approach has been applied with considerable success to real metapopulations of birds, mammals and butterflies living in highly fragmented landscapes. This talk will describe these applications.

4. Kobe, Richard K.*, Charles D. Canham, Steven W. Pacala, and John A. Silander, JR. Michigan State University, E. Lansing, MI 48824 USA, Institute of Ecosystem Studies, Millbrook, NY 12545 USA, Princeton University, Princeton, NJ 08544 USA, and University of Connecticut, Storrs, CT 06269 USA. FOREST MODELS DEFINED BY FIELD MEASUREMENTS.

To scale from short-term, individual-tree interactions to long-term, community-level dynamics, we developed a forest model (SORTIE) that is spatial and mechanistically based on field-calibrated and species-specific submodels. Three submodels characterize individual performance: seedling dispersal and recruitment, light-dependent growth, and survival as a function of recent growth. The fourth submodel is attenuation of local light availability by tree crowns (“effect” competition). Based upon these individual-level processes, SORTIE closely predicts community-level attributes (e.g. species succession, accrual of basal area). We identified interspecific trade-offs in performance that are critical to this community’s dynamics; i.e. species that grow fast in high light tend to disperse offspring widely, survive poorly under low light, and cast relatively light shade. To examine landscape variation, sapling growth and mortality submodels were developed for different communities; SORTIE simulations showed that among-site variation in these submodels was sufficient to predict dominant species in different sites. Current study foci include: incorporating N and water into SORTIE and a full SORTIE calibration for interior cedar-hemlock forests (northwestern British Columbia). Initial results from B.C. point to the generality of this approach and species trade-offs structuring forest communities.

5. Turchin, Peter*, Richard T. Wilkins, John D. Reeve, and James T. Cronin. University of Connecticut, Storrs, CT 06269 USA, Southern Research Station, Pineville, LA 71360 USA, and Bucknell University, Lewisburg, PA 17837 USA. REACTION-DIFFUSION DYNAMICS IN A HOST TREE-BARK BEETLE-CLERID PREDATOR SYSTEM.

A central question in spatial ecological theory is what mechanisms are responsible for generating and maintaining spatial patterns in the distribution of organisms, or what are the origins of patchiness. One particularly interesting biological mechanism for pattern formation arises in reaction-diffusion theory. This theory suggests that an interplay between consumer-resource interactions and movement can lead to patchy distribution of both species in originally homogeneous environment. We have developed an empirically-based model for the interaction between southern pine beetles, its host trees, and one of its arthropod predators, a clerid beetle. The system is characterized by a very discontinuos pattern of bark beetle attack, since most trees are killed in localized outbreaks, or “spots”. The highly contagious distribution of attack is partly due to congregative movement of bark beetles coupled with the presence of attack thresholds (it takes approximately 2,000 beetles to overwhelm defenses of a healthy pine). However, our model suggests that clerid predators play a key role in maintaining spatial cohesiveness of beetle spots. The mechanism underlying this effect is a variation on the theme of pattern formation by diffusive instability. Field experiments to test this theory are in progress.

6. van den Bosch, Frank* and J. A. J. Metz. Agricultural University, Dreijenlaan 4, 6703 HA Wageningen, the Netherlands, and Institute of Evolutionary and Ecological Sciences, 2300 RA Leiden, the Netherlands. FOCUS EXPANSION IN PLANT EPIDEMICS.

Many fungal plant diseases develop so-called foci. A focus originates from a single infected plant. From this centre of infection the disease expands in a circular pattern. Focus expansion is a phenomenon at the population level brought about by the life-history characteristics at the individual level. The relevant life-history characteristics are the production of new infections by an infection and the dispersal of individual spores inside the canopy. It is shown how the velocity of focus expansion can be calculated from the life history characteristics. To test the model Professor Jan Carel Zadoks provided ideal data sets on stripe rust (Puccinis striiformis) on wheat and downy mildew (Peronospora farinosa) on spinach. Model predictions are in reasonable quantitative agreement with the data. From the model we derive the testable hypothesis: In a mixture of susceptible and resistant plants the velocity of focus expansion increases linearly with the logarithm of the proportion susceptible plants. The hypothesis was tested using yellow rust on wheat. A further test was done by Dr. H. Assefa in Ethiopia using bean rust (Uromyces appendiculatus) on common bean.

7. Wilson, William G.*, Susan P. Harrison, and Alan M. Hastings. Duke University, Durham, NC 27708, University of California, Davis, CA 95616, and University of California, Davis, CA 95616. SPATIAL PATTERN FORMATION IN A HOST-PARASITOID SYSTEM.

The tussock moth Orgyia vetusta undergoes intense yet spatially localized outbreaks within large, evidently habitable regions of its resource, Lupinus arboreus. Wingless females imply low mobility for these moths, which have widely dispersing egg and larval parasitoids, Telenomus californicus and Tachinomyia similis. These dispersal features suggest the conditions for diffusive instabilities, which might explain the localized aspect of the outbreaks. Other features of the natural system include: 1) resource limitation at high moth densities; 2) a highly resilient host plant; and 3) generalist predation on immature moths (e.g. by the ant Formica lasiodes). Stable pattern formation has been the subject of much theory, yet there are few empirical ecological examples. We present preliminary modeling results using individual-based simulations and population-level partial differential equations that demonstrate the possibility of stable pattern formation in this natural system.

last updated March 5, 1997

Alan R. Johnson

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