Christian Wissel

On the application of stability concepts in ecology

Abstract Using the example of stability properties, this paper demonstrates the problem of defining and characterizing ‘emergent properties’ in ecology. The debate about stability in ecological theory is marked by a frightful confusion of terms and concepts. Judgements about stability properties are often far too general. In fact, stability concepts can only be applied in clearly defined ecological situations. The features of an ecological situation determine the domain of validity of statements about stability. We have compiled these features into an “ecological checklist” aimed at making statements on stability complete and more useful as a result. The checklist is also a tool for identifying gaps in previous ecological research on stability. A model is provided to demonstrate that approaches other than local stability analysis (here the “Linear Response Theory”) can help close these gaps.

Modelling the mosaic cycle of a Middle European beech forest

Abstract A stochastic model is introduced which provides the temporal and spatial pattern of a Middle European beech forest ( Fagus sylvatica ). Starting from a cyclic succession which is known from field observations the effect of solar radiation on beech trees is modelled in a simple manner. The computer simulation shows the formation of spatial patterns. These consist of a mosaic of patches each containing trees of one species and one age class only. The cyclic succession occurs in every patch, but the cycles are desynchronized. The results of the model show that the stability of this ecosystem depends on the spatial and temporal scale under consideration. The reaction of the system to disturbances is investigated. The results of this model can be generalized to other forests.

Metastability, a consequence of stochastics in multiple stable population dynamics

Abstract A seminumerical method is introduced which solves the equations of population dynamics with environmental or demographic stochastic influences. By this method it is shown that random influences on population dynamics showing multiple stability change the deterministic results completely. A metastable state showing temporal constancy for a finite period is found. This shows some relationship to both the deterministic result and the final stochastic state. The ecological consequences of metastability are discussed.

Interdependence of ecological risk and economic profit in the exploitation of renewable resources

Abstract A new stochastic optimal control approach is introduced which quantifies the risk of extinction of a population associated with its optimal exploitation. In addition the maximization of the profit can be performed subject to the constraint that the mentioned risk does not exceed a given limit. As a first example for this general method an exponentially growing population is investigated. The interdependence of the risk and the profit is discussed. This model reveals the possibility of reducing the risk considerably without a substantial decrease of profit.

Scenarios and Experiments

You will spend most of your time working with META-X specifying scenarios and experiments, i.e. with translating your real-world or theoretical problems into parameter sets for the generic metapopulation model which is implemented in META-X. Most elements of how to specify scenarios and experiments are described in the Guided Tour and will not be repeated here in detail; in particular, the Screenshots are not repeated. Instead, this chapter gives an overview of: The structure and elements of the Experiment Wizard. The structure and elements of the Scenario Wizard. The specification and purpose of ‘homogeneous’ parameters. The hierarchy of model parameters in META-X which allows you to create ‘user-defined’ scenarios.

The Landscape Editor

The right-hand part of the META-X window contains the Landscape Editor which is designed to visualize the landscape of a scenario, to modify existing scenarios via a graphical interface, and to create new scenarios with this graphical interface. Once a scenario has been selected in the Project Tree by a double-click or by choosing EditorpLoad Scenario in the menu, the Landscape Editor will indicate: 1. Whether the scenario is completely specified or some parameters regarding patches, dispersal range or correlation length are still missing. 2. The position of the patches and if a patch is occupied by a subpopulation. 3. The scales of the scenario, i.e. the basic scale of the map, dispersal range and correlation length. 4. If a so-called ‘Local Aspect’ is chosen, different aspects of the patches, i.e. the mean time to extinction, number of emigrants produced or number of immigrants needed to establish a new subpopulations (with 50% probability). 5. The connections between patches, i.e. all pairs of patches which can recolonize each other via dispersal.

The Project Tree

The Project Tree in the left half of the META-X screen is designed to organize your projects: It hierarchically lists the experiments of a project, the scenarios of an experiment and the parameters and evaluations of experiments and scenarios. The most important procedures of META-X (scenario, experiment and simulation wizard) can be started directly from the Project Tree. Scenarios may be selected to be displayed in the Landscape Editor. You can copy (or cut) and paste existing experiments and scenarios. Experiments and scenarios can be deleted or renamed. You can modify the sequence of scenarios in the experiment.

Parameterizing META-X

One main task when working with META-X is to translate questions regarding hypothetical or real metapopulations into parameterizations of the META-X model. To be able to do this, you need to know the model and exactly what its parameters mean (Chap. 14). The next step is to compile all the relevant empirical information available and to extract the model parameters. To give you an idea of how to do this, we briefly describe some general concepts of parameterizing META-X (or any other PVA model) in this chapter. However, this is not the place for a complete introduction into the problem of parameterizing (meta-)population models. There is a whole body of literature on, for example, obtaining demographic or dispersal data from mark/recapture studies (Moilanen et al. 1998, Henle et al 1999, Moilanen 1999, Hanski et al. 2000). In general, if you want to learn how to parameterize PVA models, you will need to scan the PVA literature (see suggested readings at the end of Chap. 13) and assemble your own tool chest.

Import, Export and Report

META-X has four ways to communicate with ‘the rest of the (computer) world’: Import of model parameters. This is useful if you want to import model parameters from other programs, for example programs which calculate ‘Patch characteristics’ (mean time to extinction, etc.). The format of the import files is thus an interface between all kinds of sources which produce model parameters for all kinds of species and landscapes, and META-X. Export of simulation results. Raw data from the simulations may be exported and analyzed with other programs. Export of graphs. Some of the diagrams of META-X and the entire window of the Landscape Editor can be exported to other programs via the clipboard, or sent directly to the printer. Reports. You can generate reports of scenarios and whole experiments which contain all the information and parameters specified by you, and all evaluations. Reports are HTML format and can thus easily be imported into wordprocessing programs, printed and modified.

Goals, Methods, and Concepts of PVA

META-X has been developed as a tool for education and for practical use by specialists such as field ecologists, conservation biologists, managers of natural resources, and environmental decision-makers. Working with META-X requires no programming and — at least at the level of the metapopulation — no modelling, and is therefore easy to use by non-experts. However, as with any tool, even nonexperts have to know the purpose of the tool and its basic function if they want to use it appropriately. Moreover, META-X is not a fully ‘canned’ PVA software because external sub-models, for example of local population dynamics, are needed to parameterize META-X for actual species and landscapes. Therefore, to work with META-X you need to be familiar with the basics of PVA. In this chapter we briefly introduce the goals, methods and concepts of population viability analysis (PVA). In particular, we explain in detail how to quantify the persistence and viability of populations (and metapopulations), since this is usually not explained in PVA literature. For those needing a full introduction into PVA, we strongly recommend consulting the literature listed at the end of this chapter.