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In der Abfullindustrie geht der Trend hin zur Selbstdiagnose, Optimierung und Qualitatsuberwachung der Prozesse. Ziel ist es, die Produktionsmengen zu erhohen und gleichzeitig die Qualitat zu steigern. Hierfur sind neue Konzepte in der Abfull- und Regelungstechnik notwendig. Fur diese Konzepte ist eine kontinuierliche Uberwachung des Abfullvorgangs Voraussetzung. In diesem Beitrag werden Algorithmen zur kontinuierlichen Fullprozessbewertung vorgestellt. Auf Basis von Referenzbildern wird die Full- und Schaumhohe bestimmt. Des Weiteren wird die Turbulenz der Flussigkeit bewertet

We present an approach for feature extraction in the context of condition monitoring of a bottling process. A special focus lies on the characterisation and evaluation of liquid textures. The approach will feed into a sensor and information fusion system to monitor a bottling process. Requirements like real-time capabilities, data reduction and resource limitations necessitate a fusion approach which capture physical effects of different sensors, extract appropriate features and combine them into one state for the complete filling process. Special attention is paid to the feature extraction of the visual sensor signals to monitor the filling level, the amount of foam and the degree of turbulence in the liquid.

The distribution of surface water affects herbivore–vegetation interactions in arid and semi-arid regions. Limited access to surface water typically results in the emergence of vegetation gradients around natural and artificial water sources. In particular, African elephants can create large-scale gradients of woody vegetation. Understanding the dynamics of these gradients is of particular importance for the conservation of other, less mobile herbivores that depend on woody vegetation in areas close to water. While rainfall is known to be a key determinant of herbivore–vegetation interactions in dry areas, we only have limited understanding on how it impacts woody vegetation gradients around waterholes. To address this problem, we developed a deterministic simulation model that describes the interplay of rainfall, elephants and woody vegetation in the vicinity of waterholes. The model is based on elephant telemetry data and the ecological conditions in Etosha National Park (ENP), Namibia. We found that decreasing amounts of rainfall led to an increased degradation of woody vegetation, which was particularly severe in areas close to water. Based on this result we conclude that low rainfall was an important driver of recently observed patterns of vegetation degradation in ENP. More generally, rainfall appears to be a key factor that determines elephant–vegetation interactions and thus dynamics of woody vegetation gradients around waterholes. Using long-term rainfall data from ENP, we also demonstrate that an increase in the number of water sources during periods of low rainfall can mitigate the destructive impact of elephants in areas close to water. However, more research is required to assess the sustainability and effectiveness of rainfall-adapted strategies of artificial water provisioning in more detail. In particular it is important to investigate potential effects on elephant population dynamics.

It is widely accepted that successful grazing management strategies in semiarid ecosystems need to be adapted to the highly temporal and spatially heterogeneous forage production. Nevertheless, a full understanding of the key factors and processes for sustainable adaptive management has yet to be reached. The investigation of existing, successful range management systems by simulation models may help to derive general understanding and basic principles. The semi-nomadic Himba in northern Namibia applied a sophisticated management system until the mid-1990s which combined season-dependent pasture use (resulting in rainy-season pastures and dry-season pastures), preservation of reserves for drought and sanctions for rule breaking. A stochastic ecological simulation model has been developed here which represents the main aspects of this management system. With this model we analyze (1) which components of the traditional Himba strategy are essential for sustainability and (2) what happens to the state of the rangeland system under socioeconomic changes. This study shows that temporally and spatially heterogeneous pasture use yields higher productivity and quality of a pasture area than the pressure of homogeneous permanent grazing. Two aspects are of importance: (1) intra-annual heterogeneous use (resting of the dry-season pastures during the rainy season) and (2) interannual heterogeneous use (spatial extension of grazing in years of drought). This management system leads to an effective build-up and use of a buffer in the system: the reserve biomass (the non-photosynthetic reserve organs of the plants), an indicator for grazing and management history. Analyzing purchase as one form of socioeconomic change, we demonstrate that easier market access to purchase livestock may lead to a decline in vegetation quality. However, cattle production increases as long as rest periods on parts of the pasture during the rainy season are granted. Methodologically, we emphasize that simulation models offer an excellent framework for analyzing and depicting basic principles in sustainable range management derived from local knowledge. They provide the opportunity of testing whether these basic principles are also valid under different ecological and socioeconomic settings.

Dispersal functions are an important tool for integrating dispersal into complex models of population and metapopulation dynamics. Most approaches in the literature are very simple, with the dispersal functions containing only one or two parameters which summarise all the effects of movement behaviour as for example different movement patterns or different perceptual abilities. The summarising nature of these parameters makes assessing the effect of one particular behavioural aspect difficult. We present a way of integrating movement behavioural parameters into a particular dispersal function in a simple way. Using a spatial individual-based simulation model for simulating different movement behaviours, we derive fitting functions for the functional relationship between the parameters of the dispersal function and several details of movement behaviour. This is done for three different movement patterns (loops, Archimedean spirals, random walk). Additionally, we provide measures which characterise the shape of the dispersal function and are interpretable in terms of landscape connectivity. This allows an ecological interpretation of the relationships found.

The worldwide loss of utilisable rangeland in (semi-) arid areas results in huge economic and social costs. Only adaptive management strategies are able to cope with these systems, which are mainly driven by unpredictable and stochastic rainfall. The aim of the study was to investigate the relevance of rest periods as part of the management scheme in these non-equilibrium rangeland systems. The starting point of the analysis is an approved management system – the Karakul sheep-breeding Gamis-Farm (Namibia). The farmer applies a flexible strategy, which combines short-term adaptation of the stocking rate to the available forage and long-term adaptation by resting a third of the paddocks in years with sufficient rainfall. We developed a simulation model that focuses on the key dynamics of this non-equilibrium system. Beginning with the strategy used by the Gamis-Farm, a set of alternative grazing strategies was defined, all adapted to the available forage but differing in whether and when resting is granted for a part of the pasture. The effectiveness of these strategies was compared according to the long-term productivity of the pasture and the farmer’s livelihood. Our results reveal ecological settings during which resting is essential for the recovery of the vegetation in a fluctuating environment, as well as those during which it is not. The growth rates of both the vegetation and of the livestock are demonstrated to be highly influential. Rests during wet years are crucial for the regeneration of the pasture. We conclude that even though a non-equilibrium rangeland system is assumed, the application of pure opportunistic strategies – destocking in times of drought and fast post-drought restocking – are not always adequate to maintain the long-term productivity of the pasture. Rest periods are indispensable when vegetation has a low regeneration potential. On an applied level, the study emphasises that improved farming conditions (supplementary feeding, unrestricted options to purchase livestock) may run the risk of ecological as well as economic damages.

Ecological theory suggests that environmental variability can promote coexistence, provided that species occupy differential niches. In this study, we focus on two questions: (1) Do allocation trade-offs provide a sufficient basis for niche differentiation in succulent plant communities? (2) What is the relative importance of different forms of environmental variability on species diversity and community composition? We approach these questions with a generic, individual-based simulation model. In our model, plants compete for water in a spatially explicit environment. Species differ in their size at maturity and in the allocation of carbon to roots, leaves and storage tissue. The model was fully specified with independent literature data. Model output was compared to characteristics of a species-rich community in the semi-arid Richtersveld (South Africa). The model reproduced the coexistence of plants with different sizes at maturity, the dominance of succulent shrubs, and the level of vegetation cover. We analyzed the effects of three forms of environmental variability: (a) temporal fluctuations in precipitation (rain and fog), (b) spatial heterogeneity of water supply due to run-on and run-off processes and (c) ‘rock pockets’ that limit root competition in space. The three types of variability had differential effects on diversity: diversity exhibited a strong hump-shaped response to temporal variation. Spatial variability increased diversity, with the strongest increase occurring at intermediate levels of temporal variability. Finally, rock pockets had the weakest effect, but contributed to diversity by providing refuges for small species, particularly at low temporal variability. The model thus shows that spatio-temporal variation of resource supply can maintain diversity over long time scales even in small systems, as is the case in the Richtersveld succulent communities. Trade-offs in allocation provide the basis for necessary niche differentiation. By describing resource competition between individual plants, our model provides a mechanistic basis for the link from species traits to community composition at given environmental conditions. It thereby contributes to an understanding of the forces shaping plant communities. Such an understanding is critical to reduce the threats environmental change poses to biodiversity and ecosystem services.

The intermediate disturbance hypothesis (IDH) predicts a hump-shaped relationship between regional diversity and the disturbance rate. We tested the IDH for the megabenthos inhabiting the Antarctic sea floor, which is disturbed by iceberg scouring. We used models based on the empirical knowledge of succession to calculate the IDH curve for this system and to extrapolate the presently observable range of the IDH curve to higher and lower disturbance rates. Although the hump-shaped relationship has been found for a purely theoretical (extremely large) disturbance range, within the feasible disturbance range (assumed as realistic in the Antarctic region under climate change), the regional diversity of successional stages due to iceberg scouring strongly decreases with lower disturbance rates but levels off only slowly with higher disturbance rates. The reason is the unevenness in the lifetimes of the successional stages, in that early stages are short-lived whereas late stages are long-lived. With such unevenness, increasing disturbances support the early stages without jeopardizing the later ones. Additionally, we converted this regional diversity of stages to the regional diversity of taxa using a transformation formula based on empirical knowledge of the number and mean abundance of taxa in the particular stages. Our results suggest that a decrease in iceberg scouring due to climate change would be more detrimental to the diversity of the Antarctic megabenthos than an increase.

Anisotropic clumped (patchy) dispersal of species is a widespread phenomenon in nature, however, its relevance for structuring communities and maintaining biodiversity is still a matter of debate. We used a spatially explicit simulation model to assess the effects of spatial aggregation through this dispersal strategy compared to isotropic clumped (local) dispersal on the diversity of a model community of sessile species. The species differed only in terms of their dispersal distance and no a priori trade-offs between dispersal and local competitive strength were assumed. We investigated spatially homogeneous and heterogeneous environments without and with temporally fluctuating reproduction success. In all cases patchy dispersal allowed the long-term coexistence of a variety of species—in contrast to local dispersal. In particular, patchy dispersal was found to decouple the mechanism of spatial aggregation from the dispersal distance. This supports species coexistence even in environments where local dispersal was a superior or inferior dispersal strategy. Thus, the specific way of spatial aggregation can be decisive for coexistence. Spatial aggregation independent of the dispersal distance is an attribute of dispersal offering new possibilities for trade-offs with life-history traits and with the dispersal distance itself.

Ecologists and economists both use models to help develop strategies for biodiversity management. The practical use of disciplinary models, however, can be limited because ecological models tend not to address the socioeconomic dimension of biodiversity management, whereas economic models tend to neglect the ecological dimension. Given these shortcomings of disciplinary models, there is a necessity to combine ecological and economic knowledge into ecological-economic models. It is insufficient if scientists work separately in their own disciplines and combine their knowledge only when it comes to formulating management recommendations. Such an approach does not capture feedback loops between the ecological and the socioeconomic systems. Furthermore, each discipline poses the management problem in its own way and comes up with its own most appropriate solution. These disciplinary solutions, however are likely to be so different that a combined solution considering aspects of both disciplines cannot be found. Preconditions for a successful model-based integration of ecology and economics include (1) an in-depth knowledge of the two disciplines, (2) the adequate identification and framing of the problem to be investigated, and (3) a common understanding between economists and ecologists of modeling and scale. To further advance ecological-economic modeling the development of common benchmarks, quality controls, and refereeing standards for ecological-economic models is desirable.

Metapopulation models are frequently used for analysing species–landscape interactions and their effect on structure and dynamic of populations in fragmented landscapes. They especially support a better understanding of the viability of metapopulations. In such models, the processes determining metapopulation viability are often modelled in a simple way. Animals’ dispersal between habitat fragments is mostly taken into account by using a simple dispersal function that assumes the underlying process of dispersal to be random movement. Species-specific dispersal behaviour such as a systematic search for habitat patches is likely to influence the viability of a metapopulation. Using a model for metapopulation viability analysis, we investigate whether such specific dispersal behaviour affects the predictions of ranking orders among alternative landscape configurations rated regarding their ability to carry viable metapopulations. To incorporate dispersal behaviour in the model, we use a submodel for the colonisation rates which allows different movement patterns to be considered (uncorrelated random walk, correlated random walk with various degrees of correlation, and loops). For each movement pattern, the landscape order is determined by comparing the resulting mean metapopulation lifetime Tm of different landscape configurations. Results show that landscape orders can change considerably between different movement patterns. We analyse whether and under what circumstances dispersal behaviour influences the ranking orders of landscapes. We find that the ‘competition between patches for migrants’ – i.e. the fact that dispersers immigrating into one patch are not longer available as colonisers for other patches – is an important factor driving the change in landscape ranks. The implications of our results for metapopulation modelling, planning and conservation are discussed.

This essay develops the “concept of stocks” — a conceptual notion designed to enable a clearer understanding of the interaction between the dynamics of ecosystems and the economy. The notion of stocks is formulated in a general manner based on set theory. The central attribute of a stock is its temporal durability. Seen thus, stocks are suitable for depicting the influences a system's history has on its present — and hence for analysing temporal developments. Since permanency is a temporal attribute, the concept of stocks is not specifically limited to individual scientific disciplines and is suitable for interdisciplinary analysis. The notion is applied to economic and ecological examples and generalised for stochastic sets. The hierarchical structure of actual ecological-economic systems can be analysed by distinguishing the stock perspective from a system view. A theory of stocks may be a building block for the conceptual foundations of ecological economics.

Dispersal has been shown to be a key determinant of spatially structured populations. One crucial aspect is predicting patch accessibility: the probability rij of a certain patch j being reached by individuals starting at another patch i. Patch accessibility rij depends on both the landscape structure and the individuals’ dispersal behaviour. To investigate the effects of these factors on rij, we developed a simulation model focusing on animal dispersal. Our model analyses show that there is an important intrinsic effect of the interplay between landscape structure and dispersal behaviour on patch accessibility: the competition between patches for migrants. We derive a formula for patch accessibility. This formula is very simple because it just takes distances into account: not only the distance between start patch and target patch, but also between the start patch and all the other patches in the landscape. Despite its simplicity, the formula is able to cover effects such as the competition for migrants. The formula was found to have high predictive power for a variety of movement behaviours (random walk with various degrees of correlation, Archimedean spirals and loops) in any given landscape. The formula can be interpreted as a generic function for patch accessibility for further population dynamics analyses. It also delivers insights into the consequences of dispersal in fragmented landscapes.

Without humans, large areas of central Europe would be covered by forests dominated by beech (Fagus silvatica). The spatiotemporal dynamics of natural beech forests are hence a subject of interest for both forest management and conservation. However, since in most regions there are no longer any natural beech forests, their structure and dynamics cannot routinely be analysed and compared to managed forests. The forest model BEech FOREst (BEFORE) is therefore, designed to reconstruct the spatiotemporal dynamics of natural beech forests. BEFORE is a grid-based and partly individual-based model which divides beeches into four different height classes. Changes to the forest structure due to growth, mortality and storm disturbances are entirely described by empirical ‘if-then’ rules. BEFORE is capable of reproducing two patterns which have been observed in remnants of natural beech forests: beech forests consist of a mosaic pattern of small areas (on average 0.3 ha) which are at different developmental stages; at the scale of these small areas, a cyclic succession of three developmental stages occurs, which are characterised by different vertical structures. One typical feature of natural beech forests is hence their very high structural diversity. Gaps in the canopy induce a local pulse of vitality and growth for younger beech trees. These pulses are spread into the vicinity by two mechanisms. Firstly, windfalls affect not only the site of the tree knocked over itself but also neighbouring sites due to the damage caused by the tree falling over. Moreover, since the light is diffuse and oblique, canopy gaps affect also vitality and growth in the neighbourhood of a gap. The results obtained with BEFORE show that natural beech forests achieve quasi-stationary dynamics, demonstrating considerable fluctuations in the forest structure. For example, the percentage of forest area at the optimal stage, which is characterised by a closed canopy and almost no understorey, varies between 10 and 40%, and after extreme storm events even between 0 and 60%. Beech forests with an inner area larger than 40 ha (corresponding to a total area of 70 ha) develop spatiotemporal dynamics which do not differ qualitatively or quantitatively from larger forests, but even very small natural beech forests would exhibit very high temporal and structural diversity. Thus, even small ‘islands’ of unmanaged stands within larger, managed forests would contribute significantly to providing structures typical of natural beech forests.

Analysing the persistence and viability of small populations is a key issue in extinction theory and population viability analysis. However, there is still no consensus on how to quantify persistence and viability. We present an approach to evaluate any simulation model concerned with extinction. The approach is devised from general Markov models of stochastic population dynamics. From these models, we distil insights into the general mathematical structure of the risk of extinction by time t, P 0 (t). From this mathematical structure, we devise a simple but effective protocol - the ln(1-P 0 )-plot - which is applicable for situations including environmental noise or catastrophes. This plot delivers two quantities which are fundamental to the assessment of persistence and viability: the intrinsic mean time to extinction, T m , and the probability c 1 of the population reaching the established phase. The established phase is characterized by typical fluctuations of the population's state variable which can be described by quasi-stationary probability distributions. The risk of extinction in the established phase is constant and given by 1/T m . We show that T m is the basic currency for the assessment of persistence and viability because T m is independent of initial conditions and allows the risk of extinction to be calculated for any time horizon. For situations where initial conditions are important, additionally c 1 has to be considered.

We summarise the contributions of empiricists, modellers, and practitioners in this issue of Biodiversity and Conservation, and highlight the most important areas for fu- ture research on species survival in fragmented landscapes. Under the theme 'uncertainty in research and management', we highlight five areas for future research. First, we know little about the effects of density dependence on the viability of metapopulations, a requirement for fragmented landscapes. Second, successful early attempts suggest that it is worth developing more rigorous calibration methods for population viability analysis with spatially explicit, individual-based models. In particular, the balance between model complexity, ease of calibra- tion, and precision, needs to be addressed. Third, we need to improve methods to discriminate between models, including alternatives to time-series approaches. Fourth, when our ability to reduce model uncertainty is weak, we need to incorporate this uncertainty in population viability analysis. Fifth, population viability analysis and decision analysis can be integrated to make uncertainty an explicit part of the decision process. An important future direction is extending the decision framework to adaptive management. Under the theme 'tools for quantifying risk and predicting species sensitivity to fragmentation', we highlight three areas for future research. First, we need to develop tools to support comparative approaches to pop- ulation viability analysis. Second, population modelling can be used to find rules of thumb to support conservation decisions when very little is known about a species. Rules of thumb need to be extended to the problem of managing for multiple species. Third, species' traits might be useful for predicting sensitivity but predictions could be further refined by considering the relative importance of population processes at different scales. Under the theme 'tools for reassembling fragmented landscapes', we consider the 'focal species' approach, and highlight aspects of the approach that require more rigorous testing. Finally, we highlight two important areas for future research not presented in the previous themes or papers in this volume. First

The major tools used to make population viability analyses (PVA) quantitative are stochastic models of population dynamics. Since a specially tailored model cannot be developed for every threatened population, generic models have been designed which can be parameterised and analysed by non-modellers. These generic models compromise on detail so that they can be used for a wide range of species. However, generic models have been criticised because they can be employed without the user being fully aware of the concepts, methods, potentials, and limitations of PVA. Here, we present the conception of a new generic software package for metapopulation viability analysis, META-X. This conception is based on three elements, which take into account the criticism of earlier generic PVA models: (1) comparative simulation experiments; (2) an occupancy-type model structure which ignores details of local population dynamics (these details are integrated in external submodels); and (3) a unifying currency to quantify persistence and viability, the ‘intrinsic mean time to extinction’. The rationale behind these three elements is explained and demonstrated by exemplary applications of META-X in the three fields for which META-X has been designed: teaching, risk assessment in the field, and planning. The conception of META-X is based on the notion that PVA is a tool to deal with rather than to overcome uncertainty. The purpose of PVA is to produce relative, not absolute, assessments of extinction risk which support, but do not supplant, management decisions.

We present a brief introduction to current attempts to understand and mitigate the effects of fragmentation on species survival. We provide a short overview of the contributions of empiricists, modellers, and practitioners in this issue of Biodiversity and Conservation, which were initiated during a workshop held in Australia in February 2002 on the topic ‘Species Survival in Fragmented Landscapes: Where are we now?’. These contributions address the themes ‘uncertainty in research and management’, ‘tools for quantifying risk and predicting species sensitivity to fragmentation’, and ‘tools for reassembling fragmented landscapes’. A final contribution provides a synthesis across the contributions and highlights the most important areas for future research on species survival in fragmented landscapes.

Viability analyses of large metapopulations are often hampered by difficulties in the parameter estimation. This leads to high uncertainty in parameter values and model outputs and complicates the formulation of clear recommendations for conservation management. We present a comprehensive procedure that is able to process spatiotemporal patterns of metapopulation occupancy to rank management scenarios. The first step of the procedure involves the formulation of the stochastic metapopulation model and the estimation of parameter values with a Bayesian approach, using a Markov chain Monte Carlo algorithm. In the second step, the model is used to predict the effects of different management actions, taking into account the uncertainty in the parameter estimates. Finally, in the third step, decision analysis is used to evaluate and aggregate the results of the previous step into a simple rank order of management scenarios. The procedure was applied to a metapopulation of the Glanville fritillary, Melitaea cinxia. Although the amount of available occupancy data was considerable, the uncertainty in the estimated model parameter values was so large that a precise estimate of the extinction risk of the metapopulation could not be made. However, the procedure was able to produce a rank order of management scenarios that was extraordinarily robust to the uncertainty. Application of the procedure to two other case studies revealed that, even though robust rankings cannot always be obtained, the results of the procedure are helpful in assessing the degree of uncertainty in the ranking and pointing to those factors most responsible for the lack of robustness. The results of this paper demonstrate very clearly, by way of example, both the limitations and the possibilities of model-based metapopulation viability analysis.

A general rule of thumb for biological conservation obtained from simple models of hypothetical species is that for populations with strong environmental noise moderate increases in habitat size or quality do not substantially reduce extinction risk. However, whether this rule also holds for real species with complex behavior, such as social species with breeding units and reproductive suppression, is uncertain. Here we present a population viability analysis of the alpine marmot Marmota marmota, which displays marked social behavior, i.e. it lives in social groups of up to twenty individuals. Our analysis is based on a long-term field study carried out in the Bavarian Alps since 1982. During the first fifteen years of this study, 687 marmots were individually marked and the movements and fate of 98 dispersing marmots were recorded with radio-telemetry. Thus, in contrast to most other viability analyses of spatially structured populations, good data about dispersal exist. A model was constructed which is individual-based, spatially explicit at the scale of clusters of neighbouring territories, and spatially implicit at larger scales. The decisive aspect of marmot life history, winter mortality, is described by logistic regression where mortality is increased by age and the severity of winter, and decreased by the number of subdominant individuals present in a group. Model predictions of group size distribution are in good agreement with the results of the field study. The model shows that the effect of sociality on winter mortality is very effective in buffering environmental harshness and fluctuations. This underpins theoretical results stating that the appropriate measure of the strength of environmental noise is the ratio between the variance of population growth rate and the intrinsic rate of increase. The lessons from our study for biological conservation are that simple, unstructured models may not be sufficient to assess the viability of species with complex behavioral traits, and that even moderate increases in habitat capacity may substantially reduce extinction risk even if environmental fluctuations seem high.

Arid savannas are regarded as one of the ecosystems most likely to be affected by climate change. In these dry conditions, even top predators like raptors are affected by water availability and precipitation. However, few research initiatives have addressed the question of how climate change will affect population dynamics and extinction risk of particular species in arid ecosystems. Here, we use an individual-oriented modeling approach to conduct experiments on the population dynamics of long lived raptors. We investigate the potential impact of precipitation variation caused by climate change on raptors in arid savanna using the tawny eagle (Aquila rapax) in the southern Kalahari as a case study. We simulated various modifications of precipitation scenarios predicted for climate change, such as lowered annual precipitation mean, increased inter-annual variation and increased auto-correlation in precipitation. We found a high impact of these modifications on extinction risk of tawny eagles, with reduced population persistence in most cases. Decreased mean annual precipitation and increased inter-annual variation both caused dramatic decreases in population persistence. Increased auto-correlation in precipitation led only to slightly accelerated extinction of simulated populations. Finally, for various patterns of periodically fluctuating precipitation, we found both increased and decreased population persistence. In summary, our results suggest that the impacts on raptor population dynamics and survival caused by climate change in arid savannas will be great. We emphasize that even if under climate change the mean annual precipitation remains constant but the inter-annual variation increases the persistence of raptor populations in arid savannas will decrease considerably. This suggests a new dimension of climate change driven impacts on population persistence and consequently on biodiversity. However, more investigations on particular species and/or species groups are needed to increase our understanding of how climate change will impact population dynamics and how this will influence species diversity and biodiversity.

1. A spatially explicit, rule-based model for three co-occurring Banksia species was developed to investigate coexistence mediating processes in a fire-prone shrubland in western Australia. Fecundity, recruitment, mortality and other biological data for two non-sprouting (B. hookeriana, B. prionotes) and one resprouting (B. attenuata) species were available from 15 years of empirical field studies. 2. Without interspecific competition, each species could persist for a wide range of fire intervals (10 to > 20 years). The resprouting species performed better under shorter fire intervals (10-13 years), while both non-sprouting species were favoured by longer (15 to > 20 years) fire intervals. These results conform with those obtained from single-species, non-spatial population models. 3. When interspecific competition for space was included in the model, all three species exhibited optima at shorter fire intervals and with a narrower range than in isolation. The three species did not co-occur under any fire regime. At intermediate fire frequencies (11-13 years), B. hookeriana excluded the other species, while for longer intervals between fires B. prionotes became dominant. 4. The introduction of temporal (stochastic) variability in fire intervals (drawn from a normal distribution) failed to produce coexistence, unless spatial variability as a spatial ignition gradient was also included. The spatial arrangement of the non-sprouters observed in the field was then reproduced. 5. Observed patterns of coexistence and spatial distributions of all species occurred when a spatial establishment gradient for the resprouter species was included in the model (individuals of B. attenuata are known to produce more seeds in swales than on dune crests and recruit seedlings here more frequently). 6. Coexistence appears to be highly dependent upon the mean interfire period in combination with subtle gradients associated with fire propagation and recruitment conditions. Variation around the mean fire interval is less critical. When the system is modelled over a long time period (1500 years) coexistence is most strongly favoured for a narrow window of mean fire intervals (12-14 years).

We present a formula for the mean lifetime of metapopulations in heterogeneous landscapes. This formula provides new insights into the effect of the spatial structure of habitat networks on metapopulation survival, with consequences for modeling, landscape evaluation, and metapopulation management. In the whole study, the spatially realistic metapopulation model of Frank and Wissel is taken as a basis. First, as a key result on the way toward the desired formula, it is shown that a simple nonspatial (Levins-type) model is able to reproduce the behavior of the complex spatial model considered regarding the mean lifetime, provided its parameters appropriately summarize all the relevant details of spatial heterogeneity. Second, the formula presented reveals how data from species and landscape have to be combined to estimate the survival chance of a metapopulation without having to run any simulation or to solve numerically any model equation. Third, by taking the formula as a basis, landscape measures are derived that allow dissimilar habitat networks to be evaluated, compared, and ranked in terms of their effect on metapopulation survival. Fourth, a combination of analytical, nonlinear regression as well as aggregation techniques was used to deduce the formula presented. The potential of these techniques for simplifying (meta)population models that are complex due to spatial heterogeneity is discussed.

Naturnahe Nutzung von Buchenwaldern erfordert detaillierte Kenntnis des ungenutzten, naturlichen Zustandes der Walder. So ist es nicht nur fur die Waldforschung, sondern gerade auch fur den Waldbau notwendig, den Urwaldzustand charakterisieren zu konnen. Das Simulationsmodell BEFORE bietet die Moglichkeit, einen fiktiven Buchenurwald uber lange Zeitraume hinweg auf verschiedenen raumlichen Skalen zu analysieren. Dabei erwies sich die bisher in der Forstwissenschaft ubliche Charkterisierung des Urwaldes durch die Flachenanteile der Entwicklungsstadien als unzureichend, da diese — bedingt durch Sturmstorungen — starken zeitlichen Schwankungen unterliegen. Zeitlich invariant und somit charakteristisch fur den hier untersuchten Modell-Urwald sind vielmehr: (1) Bezuglich der Altersverteilung die Differenzierung der Altersverteilung in den Kronenschichten schon auf kleinster Skala und die daraus folgende hohe Diversitat und charakteristische Altersverteilung auf groser Skala. (2) Bezuglich der Verteilung der „Riesen“ (Baume alter als 300 Jahre oder maximal grose Baume) im Wald der konstante mittlere minimale Abstand der Riesen untereinander von ca. 30 Metern und dass 80% aller Riesen in ca. 40 Meter Entfernung einen Nachbarn desselben Typs haben. Alle diese Charakteristiken sind — ab einer Mindestgrose von ca. 20 ha Innenflache — unabhangig von der Waldgrose.

A major problem in ecological modelling is finding the appropriate level of resolution when describing the processes and structures of ecological systems. When modelling basic ecological questions, as a rule the best approach is to ignore as much detail as possible in order to obtain general insights. However, for applied problems focusing in particular on ecological systems, there are no clear guidelines for identifying the most appropriate resolution in space, time and the detail of description. Spatially explicit modelling thus has to mainly rely on trial and error in scaling-up from modelling at the local scale to exploration of the model at the global scale. We demonstrate here a modelling strategy that takes the opposite approach: starting at the global scale, with a strategic model of minimum resolution, we proceed step by step to a model addressing applied questions. The strategic model is designed to reproduce a certain pattern observed in nature. As an example, we use the wave-like spreading pattern of rabies. The applied model addresses the question of whether rabies might persist in areas with a high proportion of foxes immunized by oral vaccination. As a consequence of our scaling-down strategy, the resolution of the applied model is not chosen a priori, but emerges from the step by step modelling strategy. During each step of model refinement, one module of the preceding model is described with a slightly increased resolution. This stepwise approach allows both a backward reference to the pattern reproduced by the strategic model and a cross-reference between the coarser and finer version of the module refined. The main potential of the scaling-down strategy is that it leads to efficient models in an efficient way, but since scaling-down is a complement to scaling-up approaches, it might also help to bridge the gap between theoretical and applied ecological modelling.

Fluctuations of population sizes affecting the risk of extinction may have different causes. The effects of environmental noise are well-known from different population models. Environmental noise results in fluctuating population sizes and an enlarged extinction risk. We present a stochastic simulation model investigating a different mechanism leading to such fluctuations. It is constructed for a consumer-resource population system. Explicit use of resources leads to fluctuations of the population size because the birth rates of the consumers depend on the amount of food available and thus vary with time. A different type of noise is created, denoted as internal noise. The effects of internal and environmental noise on the extinction risk are compared. We find that despite internal noise the mean lifetime of a population grows rapidly with capacity, whereas strong environmental noise causes a much slower growth of the mean lifetime. The implications of these findings for nature conservation are discussed. We argue that mere time-series of fluctuating populations provide an inadequate basis for population viability analysis, and that knowledge of the source of the fluctuations is required if the best conservation strategy is to be found.

1 A comprehensive data set on age, survival and reproduction for the non-sprouting (fire-killed) shrub Banksia hookeriana, encompassing 13 years of measurements at 15 sites in south-western Australia, and including 10 fires, was used to parameterize a computer model to investigate optimum plant life-history strategies in a fire-prone environment. Parameter ranges encompassed life-history information for other nonsprouting Banksia species from the same region. 2 The relationship between fire interval and level of canopy seed storage (serotiny) was analysed to identify the circumstances under which serotiny is favoured, and what degree of serotiny maximizes potential population growth rate. In addition to deterministic versions of the model, stochasticity in fire interval and conditions for recruitment were analysed. 3 The deterministic model indicated a maximum finite rate of natural increase (λ = 1.15) when the fire interval was 16 years and all seeds were retained on the plant until fire occurred. Although the model failed to predict the intermediate degrees of serotiny present in nature, it supported the optimum fire interval predicted from canopy seed bank dynamics. 4 Changes to biological attributes associated with timing of reproduction and longevity shifted the optimum fire interval and estimated rate of population growth, but did not alter the conclusions concerning serotiny. Although shorter seed longevity and increased rates of predation and/or decay reduced the value of serotiny, even very low levels of canopy seed storage increased species fitness under intermediate fire frequencies (10-20 years). 5 If the probability of inter-fire recruitment and survival was increased, optimum growth shifted from strong serotiny under a regime of frequent fire ( 40 year interval). 6 Stochasticity around mean fire interval resulted in intermediate to strong (but not complete) serotiny being predicted as optimal once the CV for fire interval approached 100%. This result is interpreted as a bet-hedging strategy whereby spontaneous release of some seeds during the inter-fire period permits recruitment on rare occasions where fire interval approaches or exceeds the species longevity.

The two main approaches in theoretical population ecology-the classical approach using differential equations and the approach using individual-based modeling-seem to be incompatible. Linked to these two approaches are two different timescales: population dynamics and behavior or physiology. Thus, the question of the relationship between classical and individual-based approaches is related to the question of the mutual relationship between processes on the population and the behavioral timescales. We present a simple protocol that allows the two different approaches to be reconciled by making explicit use of the fact that processes operating on two different timescales can be treated separately. Using an individual-based model of nomadic birds as an example, we extract the population growth rate by deactivating all demographic processes-in other words, the individuals behave but do not age, die, or reproduce. The growth rate closely matches the logistic growth rate for a wide range of parameters. The implications of this result and the conditions for applying the protocol to other individual-based models are discussed. Since in physics the technique of separating timescales is linked to some concepts of self-organization, we believe that the protocol will also help to develop concepts of self-organization in ecology.

Nomadic larks in the semi-arid Nama-Karoo, South Africa, depend on patches of temporally suitable habitat for breeding. These patches occur where rain has recently fallen, where there has been growth and seeding of grasses, and where invertebrates are locally abundant. They are also attractive to domestic livestock which may constitute a threat to successful breeding by the larks. Since rainfall in the Nama-Karoo is unpredictable in time and space on a regional scale, it is difficult a priori to select protected areas for such nomadic birds. As a first approach, we present a spatio-temporal model for estimating the survival of flocks in relation to different configurations of protected areas. The results show that neither one large protected area nor a high number of small protected areas provide the optimal solution. This is due to the impact of various spatial effects which affect the probability of a flock finding a suitable breeding area. These effects are identified and discussed. Furthermore, we are able to reproduce and explain the present spatial abundance of the larks on a regional scale with our model. The model is intended to complement and define the field studies needed to determine practical parameters more precisely.

The role of spatial configuration for metapopulation survival is analyzed by using a stochastic metapopulation model. This model reveals conditions which must be satisfied by the species' ecology and the landscape settings before a metapopulation can persist over a long term. Taking this as a basis, initial rules of thumb for landscape management are deduced. The following results are highlighted: (1) the critical correlation length dc of the extinction processes determines a spatial scale of the metapopulation dynamics. (2) Only species with a dispersal range dr above the correlation length dc are able to benefit from landscape management at all. (3) A certain metapopulation can only persist over a long term if no patch is inside the range of correlation of another one. (4) There is a hierarchy of importance in the characteristics of a spatial configuration (scale and type) and, hence, in the scopes of landscape management. To conclude, some general consequences for supporting species survival by management are discussed. Some prospects concerning the use of models for decision support in landscape planning are discussed.

A model analysis of the extinction of metapopulations is presented, based on a general model which explicitly considers essential population dynamical factors, such as environmental fluctuations and dispersal of individuals. The model is used to evaluate the influences of three plausible management options on the viability of a metapopulation. These are the increase of the capacity and the number of patches and the improvement of their connectivity. We find that the effects of these management options depend on the specific environmental conditions, such as environmental variability and the patch capacities. We generate a set of scenarios which cover a wide range of different environmental situations. For each scenario the influences of the management options are evaluated. The results are used to compare local management of subpopulations with the establishment of a habitat network.

Usually extinction risk due to environmental stochasticity is estimated under the assumption of white environmental noise. This holds for a sufficiently short correlation time τ c of the fluctuations compared to the internal time scale of population growth r −1 ( τ c / r −1 ⪡1). Using a time-discrete simulation model we investigate when the white noise approximation is misleading. Environmental fluctuations are related to fluctuations of the birth and death rates of the species and the temporal correlation of these fluctuations (coloured noise) is described by a first-order autoregressive process. We found that extinction risk increases rapidly with correlation time τ c if the strength of noise is large. In this case the white noise approximation underestimates extinction risk essentially unless temporal correlation is very small ( τ c / r −1 ⪡0.1). Extinction risk increases only slowly with correlation time if the strength of noise is small. Then the white noise approximation may be used even for stronger temporal correlations ( τ c / r −1 ⩾0.1). Thus, the estimation of extinction risk on the basis of white or coloured noise must be justified by time scale and strength of the fluctuations. Especially for species that are sensitive to environmental fluctuations the applicability of the white noise approximation should be carefully checked.

Understanding of large-scale spatial pattern formation is a key to successful management in ecology and epidemiology. Neighbourhood interactions between local units are known to contribute to large-scale patterns, but how much do they contribute and what is the role of regional interactions caused by long-distance processes? How much long-distance dispersal do we need to explain the patterns that we observe in nature? There seems to be no way to answer these questions empirically. Therefore, we present a modelling approach that is a combination of a grid-based model describing local interactions and an individual-based model describing dispersal. Applying our approach to the spread of rabies, we show that in addition to local rabies dynamics, one long-distance infection per 14000 km2 per year is sufficient to reproduce the wave-like spread of this disease. We conclude that even rare ecological events that couple local dynamics on a regional scale may have profound impacts on large-scale patterns and, in turn, dynamics. Furthermore, the following results emerge: (i) Both neighbourhood infection and long-distance infection are needed to generate the wave-like dispersal pattern of rabies; (ii) randomly walking rabid foxes are not sufficient to generate the wave pattern; and (iii) on a scale of less than 100 km x 100 km, temporal oscillations emerge that are independent from long-distance dispersal.

We present an inventory and analysis of discussions of ecological stability, considering 163 definitions of 70 different stability concepts. Our aim is to derive a strategy that can help to dispel the existing "confusion of tongues" on the subject of "stability" and prevent its future recurrence. The strategy consists of three questions that should be kept in mind when communicating about stability properties. These three questions should overcome the three main sources of confusion in terminology. Firstly, which stability properties are being addressed in the stability statement? Our analysis shows that the general term "stability" is so ambiguous as to be useless.It can be replaced by the stability properties "staying essentially unchanged" (constancy), "returning to the reference state (or dynamic) after a temporary disturbance" (resilience), and "persistence through time of an ecological system" (persistence). Second, to what ecological situation does the statement refer? An ecological situation is defined by a set of features that, taken as a whole, determine the domain of validity of a stability statement. The six most important features form the "ecological checklist", which serves to classify ecological situations and thereby provides a system of coordinates for communication. The six points are: variable of interest, level of description, reference state, disturbance, spatial scale and temporal scale. Thirdly, is the statement anchored in the situation in question, or is there unacceptable generalisation by inferring "stability" of the whole system from a certain stability property in a certain ecological ecological situation? This question separates the scientifically valuable content of a statement from the desire for general statements which is often projected through stability statements.

Many models of metapopulations describe the regional dynamics of local extinction and recolonization separately from the local dynamics within the habitat patches. A strict justification of this approach has not been given yet. In this work we systematically derive the processes of extinction and colonization from the local dynamics and the dispersal of the individuals. We show that local and regional dynamics can be described separately only if the variances of environmental fluctuations and the rates of dispersal (emigration and immigration) are below particular bounds. If environmental fluctuations and dispersal satisfy these conditions the local dynamics have a much faster time scale than the regional dynamics and extinction and recolonization can each be described by a single rate which depends on the parameters of the local dynamics and dispersal.

In many riverine marginal wetlands water management is a main goal for nature conservation. However, sediments contaminated by organic chemicals and heavy metals often pose a potential risk for the ecosystem. The framework for our study is the wetlands of the rivers Weise Elster and Parthe near Leipzig (Germany). We developed a conceptual model that links processes of sediment transport and biodegradation. The hydrological processes are described by a simplified advection-diffusion equation. The submodel for biodegradation includes a logistic equation and a Michaelis-Menten-like approach. It characterizes the growth of heterotrophic bacteria populations degrading contaminants. Hydrological parameters greatly affect the growth of the bacteria as well as the spatial distribution of accumulated contaminants. The spatial pattern of the metabolites differs significantly from that of the contaminants. As metabolites are also suspected to be toxic, they cannot be neglected. We discuss strategies to minimize negative impacts of contaminated sediments influencing the spatial arrangement of the overall risk potential.

Ecological modelling should take its orientation more from real patterns observed in nature, than has been the case up to now, to overcome the deficiencies of the present strategies. Firstly, the orientation towards patterns provides guidelines about the manner and extent of the aggregation of biological information in the model. Modelling thereby loses much of its arbitrariness; secondly, pattern-oriented models are not ‘scale-free’, i.e. they relate explicitly to spatial and temporal scales; and finally, they produce comparative predictions which are better suited for testing than the predictions achieved by models, which are only either complex or generalizing. To demonstrate the strategy of pattern-oriented modelling and its advantages, three examples from population ecology are presented: (1) In a model concerning density dependence and individual variability, the orientation towards a pattern in weight distributions requires explicit inclusion of the within-generation time scale in the model. (2) Orientation towards a pattern in the dispersal capabilities of small organisms leads to a metapopulation model, where environmental correlations about certain distances are taken into account. The survival of the metapopulation depends mainly on the ratio of the correlation distance to the range of dispersal of the organisms. (3) The wave-like pattern of the spread of rabies is reproduced by an extremely simple one-dimensional model, which is based on an extended cellular automaton approach. From this basic model, a description on finer spatial and temporal scales can be developed with the aim of constructing a model which allows for the investigation of spatial barriers against the spread of rabies. A comparison of the three example models shows that the main features of pattern-oriented models are generic. In producing comparative predictions which are related explicitly to scales, pattern-oriented modelling seems to be a strategy well suited to the ‘scaling up’ from population ecology to community and ecosystem ecology.

Plant community dynamics in semiarid regions appear to be event-driven. The aim of our model is to attain an understanding of the main processes determining the spatial and temporal dynamics of a shrub community in the semiarid Karoo on a large temporal scale and to identify the significant events that drive this shrub community. Vegetation at the study site covers 15-20% of the soil surface and is dominated by five shrubs : Brownanthus ciliatus (Mesembryanthemoideae), Ruschia spinosa (Ruschioideae), Galenia fruticosa (Aizoaceae), Pteronia pallens (Asteraceae), and Osteospermum sinuatum (Asteraceae). Grasses and annuals play little part in the dynamics of this vegetation. The model is based on detailed life history data for the five dominant species and on monthly long-term rainfall data for this region. The method of dynamic automata is employed to model individual plants. Growth, death, seed production, germination, and seedling establishment are modelled over long time scales in annual time steps under the influence of the stochastic and unpredictable rainfall in ungrazed rangeland. In the absence of grazing, survival of seedlings depends on their competitive ability during the seedling stage and their ability to compete with established plants in neighboring cells. The model shows that the dynamics of this shrub community are typified by episodic and discontinuous changes in species composition with intervening quasistable phases lasting some decades. The reason for this episodic behavior is that both recruitment and mortality of plants depend on particular conditions. Using 93 complete data sets with monthly rainfall data taken at the weather station in Prince Albert we show that rainfall is only sufficient for seedling recruitment in 44% of all years for B. ciliatus and in

A model of stochastic birth and death processes which includes demographic and environmental stochasticity is used to determine the chance of survival of small populations with overlapping generations. Mean life times dependent on the present size of the population and the probability of recovery are calculated. It is shown how the mean life time is related to the concept of minimum viable population. For moderate environmental noise, a critical individual number is found above which a population is relatively safe against extinction. The overwhelming importance of the environmental noise is demonstrated. It is shown that the mean life times increases with increasing capacity K in a way which is determined by the environmental noise. The smaller this noise the stronger is this increase.

A model is introduced which determines the dynamics of a pest population with respect to control by the sterile insect technique (SIT). Random spreading of the population is described by diffusion. The model determines the conditions for stopping an invasion of the pest population by a barrier. The optimization with respect to the costs of the barrier is discussed. There is a conflict between costs and safety of a barrier. We give a proposal which mitigates this conflict.

So far models describe host-parasitoid interaction in a phenomenological way. We discovered that the parasitoid behaviour of searching and laying eggs is essential for the question of stability. Therefore, we model the searching of parasitoids in a spatial and temporal inhomogeneous environment. Temporal inhomogeneity results in seasonal patterns of the distribution of hosts and parasitoids. We find that a slight temporal desynchronization between the emergence of hosts and parasitoids is an effective mechanism leading to stability. In the case of inhomogeneous space we solve some as yet unresolved problems. The existing host-parasitoid models are confined to very special cases because they use a constant spatial distribution of parasitoids and hosts from generation to generation. We show that variation in this distribution can appear and is important for coexistence.

Modelling problems of forest ecosystems is a difficult task because of their long-term dynamics and the influences of spatial aspects. Nevertheless the importance of theoretical investigations of phenomena like forest dieback is evident. We present a type of model called “dynamical automata model” that is a specification of the so-called “cellular automata models”. Basing our approach on a theory deduced from field data enables us to keep the model understandable and testable. We discuss the importance of stochastical influences on the long-term dynamics of monospecific forests and the resulting spatial patterns. Additionally we investigate some examples of natural dieback in different parts of the world.

We analyse the stochastic dynamics of a population with non-overlapping generations by a Markov chain model with discrete time steps. It is demonstrated that one can calculate mean lifetimes and colonization probabilities from the elements of the corresponding transition matrix. Our model includes demographic as well as environmental noise. An important contribution to demographic noise comes from sexual reproduction which our model takes into account. Introducing comparatively low mating probabilities results in an Allee effect which has a great influence on the mean lifetimes and colonization abilities of small populations. The non-overlapping of generations allows us to reduce the two-dimensional model including both sexes to the one-dimensional case. If there is no environmental stochasticity we find that the long mean lifetimes of asexual populations are extremely reduced in models with two sexes. But the stronger the environmental variations are, the more the large difference between sexual and asexual models disappears. Another important result is that the mean lifetime grows very fast (exponentially) with the capacity if we assume slight environmental variations (or exclude them totally), but only slowly (linearly) if we include them. These trends are supported by the findings from models with overlapping generations that exist in the literature.

Fish do not need a leader or external stimuli for their school organization. The model presented shows that the group movement of a school can be maintained by interactions in which each individual controls its movement in relation to its neighbours. Our three-dimensional simulations reproduce the typical characteristics of real schools, if the behaviour of the single fish is based on four patterns: attraction, repulsion, parallel orientation and averaging the influences of at least four neighbours. The results of our simulations agree with experimental data in many points, as is demonstrated here for the polarization, nearest neighbour distance and internal dynamics.

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.