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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.

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.

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.

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.

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.

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.

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.

A classification of ecological models into two types is presented. Descriptive models condense field data into a concise form and can be used for predictions. Simulation models are constructed to provide an understanding. Very complex modelling exhibits several shortcomings. Models should concentrate on a specific goal and should be kept simple. These general ideas are exemplified by the power law for the species number-area relationship of island biogeography. Extinction and recolonization of populations are modelled with the inclusion of demographic and environmental noise. By including interspecific competition the power law is deduced. In addition, the species number-abundance distribution is found to be lognormal.

Periodically fluctuating environments occur in various ways in nature but have not, however, been studied in detail yet in the context of the color of environmental noise and extinction risk of populations. We use a stochastic model to simulate population dynamics with compensatory density regulation under four different patterns of periodically fluctuating environments. We found that extinction risk changes dramatically from what was known if the underlying environmental stochasticity driving population dynamics is periodically correlated rather than randomly correlated. Fluctuating environments with a very short period are found to decrease extinction risk over “white noise” fluctuations because a species is never in a bad environment for too long. Conversely, long periods increase extinction risk because species accumulate too much time in a bad environment. Moreover, we found the mean, variance, frequency distribution and especially the extensively studied noise color not to be sufficient for predicting extinction risk in periodically fluctuating environments. Rather, additional attributes of environmental noise have to be considered. The occurrence of monotonic trends within time series of environmental data (e.g. after ‘disturbance’ events), in combination with density regulation, may also affect extinction risk. Our study exemplifies that the investigation of periodically fluctuating environments leads to new insights into the interaction between environmental variation, population dynamics and the resulting extinction risk.

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.

A simple energy-balance model, relating energetic requirements of fish schools to food production, was used to predict shoal sizes. Lower limits to school size are unlikely to be set by food but rather by predation. Upper limits depend on both food and school behavior, being greater for schools that break up to feed than for schools that remain continuously cohesive. Faced with a decreasing food supply, a school could either break into smaller schools or change behavior, increasing the area available for foraging. The models suggest that environmental productivity needs to be considered when examining fishery statistics such as CPUE (catch per unit effort), where maximum catch may be limited by maximum school size.