>>Department of Ecological Modelling >> Personal homepage Thorsten Wiegand >>  Abstracts

A simulation model for a shrub ecosystem in the semiarid Karoo, South Africa

Wiegand, T., S. J. Milton, C. Wissel. 1995. Ecology 6:2205-2211

Plant community dynamics in semi-arid 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 semi-arid Karoo on a large temporal scale and to identify the significant events which 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 behaviour 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 less than 30% of all years for the four other species. We identify two types of abrupt and discontinuous changes in species composition: (1) big recruitment events which can only occur if plant density is low and if rainfall conditions are extraordinarilly favourable and (2) big mortality events which can only occur if cohorts, originating from big recruitment events, die within a short period of time and if little further recruitment has taken place. However, this behavior is not a property of the biota but is generated by rainfall input to the model. By using a different rainfall input, the model can also display regular cyclic succession. Therefore there appeared to be no contradiction between sudden, discontinuous changes and gradual, continuous and reversible changes in vegetation composition.

Key-words: individual-based; simulation model; automata; non-equilibrium; semi-arid ecosystem; spatial and temporal dynamics; event-driven system.

Vegetation change in semiarid communities: simulating probabilities and time scales
Wiegand, T., and S. J. Milton. 1996. Vegetatio 125:169-183.

In arid regions, the effects of grazing or sparing management on natural communities of long-lived plants generally take decades to become evident. Event-driven dynamic behavior, unpredictable and low rainfall and complicated interactions between species make it difficult to assess probabilities and time scales of vegetation change. To gain a better understanding of the main processes and mechanisms involved in vegetation change, we have developed a spatially explicit individual based model that simulates changes in plant communities over long time spans. The model, based on life-history attributes of the five dominant component plant species of a typical Karoo shrub community, follows the fate of each individual plant within the community, the sum of which is community dynamics. The model explores the differential effects of a realistic range of rainfall pattern on the abilities of these species to compete, survive, grow and reproduce. The specific aim of the model is to identify key processes of vegetation change and to calculate probabilities and timespans for transitions between different vegetation states. Such knowledge is needed for species conservation and sustained animal production.

We show that the time-scale for changes of the dynamic state of the system are long compared with human lifespans. Employing the full range of possible rainfall scenarios showed that short-term community dynamics (years to decades) and species composition depend strongly on the short-term (years) sequence of rainfall events. In all simulation experiments the final vegetation state varied by more than 37% after a 60 year simulation period. Simulating resting of an overgrazed part of the shrub community indicated that little improvement in rangland condition was likely during a period of 60 years. Even such active management, as (simulated) clearing of unpalatable shrubs, resulted in only a 66% probability that degraded shrubland would be in good condition after 60 years resting. Simulated overgrazing of a rangeland in good initial condition only became obvious 40 or 50 years after the initiation of heavy grazing, and after 70 years the mean vegetation state eventually reached that of an overgrazed rangeland.

Keywords: event-driven dynamics, grid based model, grazing, individual-based simulation model, Karoo.

Simulated plant population responses to small scale disturbance in semi-arid shrublands
Wiegand, T., M. R. J. Dean, and S. J. Milton. 1997. Journal of Vegetation Science 8:163-176.

We used a spatially explicit simulation model to examine the impact of small scale disturbance on the temporal and spatial dynamics of a typical Karoo shrub plant community, and to gather insight into the interplay between disturbance architecture and population dynamics. Establishment, growth, mortality, seed dispersal and competitive interactions were modelled over long time scales in annual time-steps under the influence of stochastic and unpredictable rainfall. Disturbances were created by the digging of aardvarks (Orycteropus afer) and bat-eared foxes (Otocyon megalotis) or by humans as management action. 

We examined the impact of three different disturbance regimes on long-term population dynamics by varying the type, rate and size of the small scale disturbances. The impact that a disturbance regime has on long-term community dynamics depends on complex interactions between disturbance characteristics and life-history attributes of component species. Plant density decreased with overall disturbance rates; this effect was independent of the type of disturbance. A given type and rate of disturbance did not influence all species within a guild (e.g. coloniser species) in the same way. The reason for these differences was that species were responding not only to the disturbance but to changes in competition intensity from other species and changes in their reproductive potential relative to other species. Such interactions resulted in a sequential change in dominant species within guilds as disturbance rates increased. An increase in the overall disturbance rate did not always produce the trend in evenness expected from the intermediate disturbance hypothesis, but was influenced by the relative abundance of different types of disturbances.

Keywords: individual-based simulation model; Karoo; South Africa; spatial and temporal dynamics; spatial modelling.

Population dynamics, disturbance, and pattern evolution: identifying the fundamental scales of organization in a model ecosystem. 
Wiegand, T., K. Moloney, S. J. Milton. 1998.  American Naturalist 152:321-337. 

We used auto- and crosscorrelation analysis and L function analysis to analyze spatio-temporal pattern evolution in a spatially explicit simulation model of a semiarid shrubland (Karoo, South Africa), and to determine the impact of small-scale disturbances on system dynamics. Without disturbance, local dynamics were driven by a pattern of cyclic succession, where “colonizer” and “successor” species alternately replaced each other. This results in a strong pattern of negative correlation in the temporal distribution of colonizer and successor species. As disturbance rates were increased, the relationship shifted from being negatively correlated in time to being positively correlated — the dynamics became decoupled from the ecologically-driven cyclic succession and were increasingly influenced by abiotic factors (e.g., rainfall events). Further analysis of the spatial relationships among colonizer and successor species showed that without disturbance periods of attraction and repulsion between colonizer and successor species alternate cyclically at intermediate spatial scales. This was due to the spatial “memory” embedded in the system through the process of cyclic succession. With the addition of disturbance, this pattern breaks down, although there is some indication of increasing ecological organization at broader spatial scales. We suggest that many of the insights that can be gained through spatially explicit models will only be obtained through a direct analysis of the spatial patterns produced.

Key words: individual-based simulation model, disturbance, Karoo shrubland, Ripley’s L-Analysis, spatio-temporal dynamics, time-series correlation analysis.

Assessing the risk of extinction for the brown bear (Ursus arctos) in the Cordillera Cantabrica, Spain. 
Wiegand, T, J. Naves, T. Stephan, A. Fernandez. 1998. Ecological Monographs 68:539-571.

The status of the brown bear (Ursus arctos) in Spain has suffered a dramatic decline during the last centuries, both in area and numbers. Current relict populations are suspected to be under immediate risk of extinction. The aim of our model is to attain an understanding of the main processes and mechanisms determining population dynamics in the Cordillera Cantabrica. We compile the knowledge available about brown bears in the Cordillera Cantabrica, Northern Spain, and perform a population viability analysis (PVA) to diagnose the current state of the population and to support current management. The specially constructed simulation model, based on long-term field investigations on the western brown bear population in the Cordillera Cantabrica, includes detailed life history data and information on environmental variations in food abundance. The method of individual-based modeling is employed to simulate the fate of individual bears. Reproduction, family breakup, and mortalities are modeled in annual time steps under the influence of environmental variations in food abundance, mortality rates and reproductive parameters. In parallel, we develop an analytical model that describes the mean behavior of the population and that enables us to perform a detailed sensitivity analysis.

We determine current population parameters by iterating the model with plausible values and compare simulation results with the 1982-1995 time pattern of observed number of females with cubs of the years. Our results indicate that the population suffered a mean annual decrease of ~4-5% during the study period 1982-1995. We found that this decrease could be explained by a coincidence of high poaching pressure with a series of climatically unfavorable years during the period 1982-1988. Thereafter, population size probably stabilized. We estimated that the population currently consist of 25 or 26 independent females and a total of 50-60 individuals. However, our viability analysis showed that the population does not satisfy the criterion of a minimum viable population if mortalities remain at the level of the last few years of 1988-1995. The "salvation" of at least one independent female every three years is required. The population retains relatively high reproductive parameters, indicating good nutritive conditions of the habitat, but mortality rates are higher than those known in other brown bear populations. The most sensitive parameters, adult and subadult mortality of females, form the principal management target. Our model shows that the series of females with cubs contains valuable information on the state of the population. We recommend monitoring of females with cubs as the most important management action, both for collecting data and for safeguarding the most sensitive part of the population.

Key words: brown bear; endangered species; extinction; individual-based stochastic simulation model; population dynamics; Ursus arctos; viability analysis.

Simulation models for semi-arid rangelands of Southern Africa.
Wiegand, T., F. Jeltsch, S. Bauer, K. Kellner. 1999.  African Journal of Range and Forage Science 15:48-60. 

In semi-arid regions, the effects of grazing or sparing management on natural communities of long-lived plants generally take decades to become evident. Event driven dynamic behaviour, unpredictable and low rainfall and complicated interactions between species make it difficult to gather sufficient understanding of vegetation dynamics to be able to develop guidelines for sustainable management. Simulation models that consider the essential processes that determine vegetation dynamics offer scope for quantitatively exploring long-term vegetation dynamics of arid and semi-arid rangelands. In this paper we review three models that were aimed to provide an understanding of the vegetation dynamics and management of different typical vegetation types in South Africa; including the Karoo shrubland, the shrub-grassland of the southern Kalahari, and pure semi-arid grasslands. 

Key words: Kalahari, Karoo, semi-arid grasslands, shrubland, vegetation dynamics.

Finding the missing link between landscape structure and population dynamics: a spatially explicit perspective.
Wiegand, T., K. Moloney, J. Naves, F. Knauer. 1999.  American Naturalist 154:605-627. 

We compile and exemplify a general modeling framework that allows for a systematic investigation of the impact of changes in landscape structure on population dynamics. The essential parts of the framework are a landscape generator with independent control over landscape composition and physiognomy, an individual-based spatially explicit population model that simulates population dynamics within heterogeneous landscapes, and scale-dependent landscape indices that depict the essential aspects of landscape which interact with dispersal and demographic processes. Landscape maps are represented by a grid of 50 x 50 cells and consist of good-quality, poor-quality or (inhabitable) matrix habitat cells. The population model was shaped in accordance to the biology of European brown bears (Ursus arctos), and demographic parameters were adjusted to yield a source-sink configuration. Results obtained with the spatially explicit model do not confirm results of earlier non-spatial source-sink models where addition of sink habitat resulted in a decrease of total population size because of dilution of high-quality habitat. Our landscape indices, that describe scale-dependent correlation between and within habitat types, were able to explain variations in variables of population dynamics (mean no. of females with sink home-ranges, the mean no. of females with source home-ranges, and mean dispersal distance) due to different landscape structure. When landscape structure changed, changes in these variables generally followed the corresponding change of an appropriate landscape index in a linear way. Our general approach incorporates source-sink dynamics as well as metapopulation dynamics, and the population model can easily be modified for other species groups. 

Key words: habitat connectivity, heterogeneous landscapes, scale-dependent landscape indices, population dynamics, spatially explicit population models, source-sink dynamics.

Live fast, die young: estimating size-age relations and mortality pattern of shrubs species in the semi-arid Karoo, South Africa.
Wiegand, T., S. J. Milton, K. J. Esler, and G. Midgley. 2000. Plant Ecology, 150: 115-131. 

We present a technique for estimating size-age relations and size-dependent mortality patterns of long-lived plants. The technique requires two sets of size data of individual (non-marked) plants that should be collected with a time-lag of several years in the same area of a study site. The basic idea of our technique is to assume general (three parameter) families of size-dependent functions which describe growth and mortality that occurred between the two data gathering events. We apply these growth and mortality functions to the size data of the early data set and construct predicted size-class distributions to compare it, in a systematic way, to the size-class distribution of the later data set. In a next step we calculate the size-age relations from the resulting growth functions, which yield the smallest difference between observed and predicted size-class distribution. Applying this technique to size data of five dominant shrub species at the Tierberg study site in the semiarid Karoo, South Africa produced new insight into the biology of these species which otherwise cannot be obtained without frequent measurements of marked plants. We could relate characteristics of growth behavior and mortality, for certain subgroups of the five species, to the life-history attributes evergreen vs. deciduous, succulent vs. woody, and early reproductive vs. late reproductive. The results of our pilot-study suggest a broad applicability of our technique to other shrublands of the world. This requires at least one older record of (individual) shrub-size data and performance of resampling. 

Key words: growth models, Karoo, mortality, size-age relation, shrub community.

Rule-based assessment of suitable habitat and patch connectivity for the Eurasian lynx in Germany
Schadt, S., F. Knauer,  P. Kaczensky, E. Revilla E., T. Wiegand, and L. Trepl. 2002. Ecological Applications 12:1469-1483

Conservation biologists often have to take decisions for which little information derived from detailed field studies is available. The urgency of most conservation issues and scarcity of financial resources make it impossible to obtain empirical data, but rather require that conservationists make the best out of the existing information to improve current management. In Germany lynx recovery and reintroduction initiatives are controversially discussed, one concern being that there is not enough suitable habitat left to support a viable population. The extent and the spatial arrangement of potentially suitable habitat is unknown and almost no data are available to address this question. The aim of this study was to predict the location of potentially suitable habitat for lynx in Germany, to obtain rough estimates of the potential maximum number of resident lynx, and to estimate connectivity between patches of suitable habitat. In a rule-based model habitat preferences of lynx were described as availability of forest cover, defined by patch size, degree of fragmentation and spatial structure. The model rules were implemented on a Geographic Information System (GIS) to produce a map showing the resulting patches of suitable habitat. Optimal corridors between patches were modeled with a cost-path analysis, based upon habitat type specific probabilities for lynx to cross. Our results show that patches of suitable habitat vary greatly in size, with 10 areas large enough to sustain more than 20 resident lynx. Overall, the 10 areas could sustain about 380 resident lynx. Uncertainty analyses of various critical model assumptions and parameters show that the predictions of our model are more or less stable, mainly due to the strong constraining impact of forest distribution. Our analyses suggest that reintroduction programs should focus less on small and isolated areas, but should include large scale connectivity into the decision making process. Our model is an example of a cross-boundary analysis of landscape structure based upon the needs of a species with large spatial requirements, an approach suitable as a basis for co-ordinating reintroduction initiatives and focus conservation efforts on the most promising areas.

Key words: Eurasian lynx, Lynx lynx, rule-based model, predictive habitat model, patch connectivity, GIS, costpath-analysis, limited resources, large-scale approach, decision making process, conservation, species reintroduction.

Assessing the suitability of central European landscapes for the reintroduction of Eurasian lynx.
Schadt, S., E. Revilla, T. Wiegand, F. Knauer, P. Kaczensky, U. Breitenmoser, L. Bufka, J. Cerveny, P. Koubek, T. Huber, C. Stanisa, and L. Trepl. 2002. Journal of Applied Ecology 39:189-203

1. After an absence of almost 100 years the Eurasian lynx Lynx lynx is slowly recovering in Germany along the German-Czech border. Additionally, many reintroduction schemes have been discussed controversially in various locations. We present a habitat suitability model for lynx in this region as a basis for further management and conservation efforts aimed at recolonisation and population development.

2. We developed a statistical habitat model using logistic regression to quantify the factors that describe lynx home ranges in a fragmented landscape. As no data were available for lynx distribution in Germany, we used data from the Swiss Jura Mountains for model development and validated the habitat model with telemetry data from the Czech Republic and Slovenia. We derived several variables describing land use and fragmentation, introducing also variables that described the connectivity of forested and non-forested semi-natural areas on a larger scale than the map resolution.

3. We obtained a model with only one significant variable that described the connectivity of forested and non-forested semi-natural areas on a scale of about 80 km². This result is biologically meaningful, reflecting the absence of intensive human land use on the scale of an average female home range. Model testing at a cut level P > 0.5 correctly classified more than 80% of the Czech and Slovenian telemetry location data of resident lynx. Application of the model to Germany showed that the most suitable habitats for lynx were large forested low mountain ranges and the large forests in east Germany.

4. Our approach illustrates how information on habitat fragmentation on a large-scale can be linked with local data to the potential benefit of lynx conservation in central Europe. Spatially-explicit models like ours can form a basis for further assessing population viability of species of conservation concern in suitable patches.

Key-words: GIS, large-scale approach, logistic regression, Lynx lynx, spatially explicit connectivity index, species reintroduction, statistical habitat model.Key-words: GIS, large-scale approach, logistic regression, Lynx lynx, spatially explicit connectivity index, species reintroduction, statistical habitat model.

Using pattern-oriented modeling for revealing hidden information: a key for reconciling ecological theory and application
Wiegand, T., F. Jeltsch, I. Hanski, and V. Grimm. 2003. Oikos 100: 209-222.

We suggest that the conscious use of information that is “hidden” in distinct structures in nature itself and in data extracted from nature (= pattern) during the process of modeling (= pattern-oriented modeling) can substantially improve models in ecological application and conservation. Observed patterns, such as time-series patterns and spatial patterns of presence/absence in habitat patches, contain a great deal of data on scales, site-history, parameters and processes. Use of these data provides criteria for aggregating the biological information in the model, relates the model explicitly to the relevant scales of the system, facilitates the use of helpful techniques of indirect parameter estimation with independent data, and helps detect underlying ecological processes. Additionally, pattern-oriented models produce comparative predictions that can be tested in the field.

We developed a step-by-step protocol for pattern-oriented modeling and illustrate the potential of this protocol by discussing three pattern-oriented population models: (1) a population viability analysis for brown bears (Ursus arctos) in northern Spain using time-series data on females with cubs of the year to adjust unknown model parameters; (2) a savanna model for detecting underlying ecological processes from spatial patterns of tree distribution; and (3) the incidence function model of metapopulation dynamics as an example of process integration and model generalization.

We conclude that using the pattern-oriented approach to its full potential will require a major paradigm shift in the strategies of modeling and data collection, and we argue that more emphasis must be placed on observing and documenting relevant patterns in addition to attempts to obtain direct estimates of model parameters.

Keywords: Brown bear; conservation biology; ecological application; error propagation; incidence function model; indirect parameter adjustment; Kalahari; pattern-oriented modeling; population models; savanna, uncertainty, virtual ecologist

Endangered species balancing between natural and human constrains: the case of brown bears (Ursus arctos) in northern Spain
Naves, J., T. Wiegand, E. Revilla, and M. Delibes. 2003, Conservation Biology 17:1276-1289.

We developed a conceptual framework for classifying habitat quality that requires the construction of separate habitat models for each demographic key-feature, to be applied when the factors that determine different demographic processes differ substantially. For example, survival of large carnivores is mainly determined by human-induced mortality, while nutritional condition determines the reproductive rate. Hence, a two-dimensional habitat model built for reproduction and survival yields five hypothetical habitat categories: matrix (no reproduction and/or very high mortality), sink (low reproduction, high mortality), refuge (low reproduction, low mortality), attractive sink (high reproduction, high mortality) and source (high reproduction, low mortality). We applied this framework to two endangered brown bear sub-populations in the Cantabrian Mountains, Spain. Our aim was to generate working hypotheses on the quality and the spatial arrangement of bear habitat for analyzing the present conditions of the different population nuclei, for identifying core areas of high conservation value, conflictive areas, or areas with unoccupied potential habitat. We used a geographic information system (GIS) and two spatial long-term data sets on presence and reproduction, and performed logistic regressions for building a two-dimensional habitat model. The analysis reveals that both populations seem to exist under sub-optimal habitat conditions: the eastern population occupies mainly areas of sub-optimal natural habitat and relatively low human impact, while the western population is mainly located in areas with high human impact, but otherwise good natural quality. To test hypotheses on demographic features of the obtained habitat categories we classified data on historic extinction in the north of Spain (14th to 19th centuries) within the two-dimensional model. Extinction probabilities within each habitat category confirmed the hypotheses: most extinctions occurred in matrix habitat, and the least in source habitat.

Keywords: attractive sink; endangered species; extinction; habitat model; human impact; logistic regression; matrix; refuge; source-sink theory; Ursus arctos

Expansion of brown bears (Ursus arctos) into the eastern Alps: a spatially explicit population model.
Wiegand, T., F. Knauer, P. Kaczensky, and J. Naves. 2004. Biodiversity and Conservation 13:79-114. 2004.

We present a spatially-explicit population model for analysing the expansion of brown bears (Ursus arctos) after the reintroduction program in central Austria. The model is based on field investigations into brown bears in Austria and Slovenia and on current knowledge of brown bears. The landscape of the eastern Alps is represented by a GIS-derived raster map defining local habitat suitability and five major spatial barriers to dispersal. The population model follows the fate of individual bears and simulates reproduction, dispersal, home range establishment, and mortality in annual time steps. We indirectly adjust unknown or uncertain model parameters with 10-year data on the number of females with cubs in central Austria and determine key variables of population dynamics, such as population sizes and growth rates within different population nuclei, dispersal distances, or mortality rates, for model parameterisations that reproduces the data on females with cubs.

We estimated a current (1996-2000) growth rate of the population in Austria and adjacent parts of Italy of some 14%; a high proportion of this growth was due to immigration from Slovenia. Consequently, the growth rate of the subpopulation in central Austria, which probably is isolated functionally (i.e., no exchange of females) from the nuclei along the Austrian-Slovenian border, yielded some 7%. This subpopulation may comprise seven residents, and we estimated for females a 33% risk of extinction during the 1992-2000 period. Validation and confirmation of our model results with data on bear densities that were not used for model construction and parameterization supported our findings. The high female mortality rates together with the vulnerability of the small population to chance events (i.e., demographic stochasticity) are the most pressing threat for the population in the eastern Alps. Our approach could be widely applied for analysing dynamics of rare and endangered species in which the paucity of data precludes an appraisal of the state of the population using standard methods

Keywords: extinction, individual-based model, landscape, management, population dynamics, spatially explicit population model

Reducing uncertainty in spatially explicit population models
Wiegand, T., E. Revilla, and F. Knauer. 2004. Biodiversity and Conservation 13:53-78.

It has been argued that spatially explicit population models (SEPMs) cannot provide reliable guidance for conservation biology because of the difficulty of obtaining direct estimates for their demographic and dispersal parameters and because of error propagation. We argue that appropriate model calibration procedures can access additional sources of information, compensating the lack of direct parameter estimates. Our objective is to show how model calibration using population-level data can facilitate the construction of SEPMs that produce reliable predictions for conservation even when direct parameter estimates are inadequate. We constructed a spatially explicit and individual based population model for the dynamics of brown bears (Ursus arctos) after a reintroduction program in Austria. To calibrate the model we developed a procedure that compared the simulated population dynamics with distinct features of the known population dynamics (= patterns). This procedure detected model parameterizations that did not reproduce the known dynamics. Global sensitivity analysis of the uncalibrated model revealed high uncertainty in most model predictions due to large parameter uncertainties (coefficients of variation CV » 0.8). However, the calibrated model yielded predictions with considerably reduced uncertainty (CV » 0.2). A pattern or a combination of various patterns that embed information on the entire model dynamics can reduce the uncertainty in model predictions, and the application of different patterns with high information content yields the same model predictions. In contrast, a pattern that does not embed information on the entire population dynamics (e.g., bear observations taken from sub-areas of the study area), does not reduce uncertainty in model predictions. Because population-level data for defining (multiple) patterns are often available our approach could be applied widely.

Keywords: individual-based model; model calibration; pattern-oriented modeling; population dynamics; spatially explicit population model; Ursus arctos; uncertainty

Do Grasslands have a Memory: Modeling Phytomass Production of a semiarid African Grassland
Wiegand,T., H. A. Snyman, K. Kellner, and J. M. Paruelo. 2004. Ecosystems 7:243-258.  

We analyzed data sets on phytomass production, basal cover, and monthly precipitation of a semiarid grassland in South Africa for good, medium, and poor rangeland condition (1) to investigate whether phytomass production per unit of basal cover differed among rangeland conditions, (2) to quantify the time-scales of a carry-over effect from production in previous months, and (3) to construct predictive models for monthly phytomass. Finally, we applied the best models to a 73-year data set of monthly precipitation data to study the long-term variability of grassland production.

Mean phytomass production per unit of basal cover did not vary significantly between rangeland conditions, i.e., vegetated patches in degraded grassland have approximately the same production as vegetated patches in grassland in good condition. Consequently, the stark decline in production with increasing degradation is a first-order effect of reduced basal area. Current year precipitation accounted for 64%, 62%, and 36% of the inter-annual variation in phytomass production for good, medium, and poor condition, respectively, and we found that 61%, 68%, and 33%, respectively, of the unexplained variation is related to a memory index that combines mean monthly temperature and a memory of past precipitations. We found a carry-over effect in production from the previous 4 years for grassland in good condition, and from the previous 1 or 3 month for medium and poor. The memory-effect amplified the response of production to changes in precipitation due to alternation of prolonged periods of dry or wet years/months at the time scale of the memory. The interannual variability in phytomass production per unit basal cover (CV = 0.42 0.50 for our 73-year prediction, CV = 0.57 0.71 for the 19-year data) was greater than the corresponding temporal variability in seasonal rainfall (CV = 0.29).

Keywords: basal cover, climate, carry-over effect, desertification, drought, grassland condition, long-term data set.

Rings, Circles and Null-Models for Point Pattern Analysis in Ecology
Wiegand, T., and K. Moloney 2004 Oikos 104: 209-229

A large number of methods for the analysis of point pattern data have been developed in a wide range of scientific fields. First-order statistics describe large-scale variation in the intensity of points in a study region, whereas second-order characteristics are summary statistics of all point-to-point distances in a mapped area and offer the potential for detecting both different types and scales of patterns. Second-order analysis based on Ripley's K-function is increasingly used in ecology to characterize spatial patterns and to develop hypothesis on underlying processes; however, the full range of available methods has seldomly been applied by ecologists. The aim of this paper is to provide guidance to ecologists with limited experience in second-order analysis to help in the choice of appropriate methods and to point to practical difficulties and pitfalls. We review (1) methods for analytical and numerical implementation of two complementary second-order statistics, Ripley's K and the O-ring statistic, (2) methods for edge correction, (3) methods to account for first-order effects (i.e., heterogeneity) of univariate patterns, and (4) a variety of useful standard and non-standard null models for univariate and bivariate patterns. For illustrative purpose, we analyze examples that deal with non-homogeneous univariate point patterns. We demonstrate that large-scale heterogeneity of a point-pattern biases Ripley's K-function at smaller scales. This bias is difficult to detect without explicitly testing for homogeneity, but we show that it can be removed when applying methods that account for first-order effects. We synthesize our review in a number of step-by-step recommendations that guide the reader through the selection of appropriate methods and we provide a software program that implements most of the methods reviewed and developed here.

Key words: Bivariate second-order analysis; edge correction; irregularly-shaped plot; heterogeneous point patterns; Monte Carlo simulation; null models; O-ring statistic; pair-correlation function; Ripley's K-function; spatial association.
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Effects of Habitat Loss and Fragmentation on Population Dynamics
Wiegand, T., E. Revilla, and K. A. Moloney. 2005, Conservation Biology 19:108-121.
 

We used a spatially explicit population model that was generalized to produce nine ecological profiles of long-lived species with stable home ranges and natal dispersal to investigate the effects of habitat loss and fragmentation on population dynamics. We simulated population dynamics in landscapes composed of three habitat types (good-quality habitat ranging from 10-25%, poor-quality habitat ranging from 10-70%, and matrix). Landscape structures varied from highly fragmented to completely contiguous. The specific aims of our model were (1) to investigate under which biological circumstances the traditional approach of using two types only (habitat and matrix) failed and assess the potential impact of restoring matrix to poorquality habitat, (2) to investigate how much of the variation in population size was explained by landscape composition alone and which key attributes of landscape structure can serve as predictors of population response, and (3) to estimate the maximum fragmentation effects expressed in equivalent pure loss of goodquality habitat. Poor-quality habitat mattered most in situations when it was generally not considered (i.e., for metapopulations or spatially structured populations when it provides dispersal habitat). Population size increased up to 3 times after restoring matrix to poor-quality habitat. Overall, habitat amount accounted for 68% of the variation in population size, whereas ecological profile and fragmentation accounted for approximately 13% each. The maximal effect of (good-quality) habitat fragmentation was equivalent to a pure loss of up to 15% of good-quality habitat, and the maximal loss of individuals resulting from maximal fragmentation reached 80%. Abundant dispersal habitat and sufficiently large dispersal potential, however, resulted in functionally connected landscapes, and maximal fragmentation had no effect at all. Our findings suggest that predicting fragmentation effects requires a good understanding of the biology and habitat use of the species in question and that the uniqueness of species and the landscapes in which they live confound simple analysis.

Key Words: ecological profiles, individual-based spatially explicit population model, landscape metrics, landscape
structure, matrix heterogeneity, metapopulation, source-sink

Fragmented landscapes, road mortality and patch connectivity: modeling dispersal for the Eurasian lynx in Germany *
Kramer-Schadt, S., E. Revilla, T. Wiegand, U. Breitenmoser. 2004. Journal of Applied Ecology 41:711-723

1. Although many reintroduction schemes for the Eurasian lynx Lynx lynx in Germany have been discussed, the implications of connectivity between suitable patches have not been assessed.

2. We introduce an individual-based, spatially explicit dispersal model to assess the probability of a dispersing animal reaching another suitable patch in the complex heterogeneous German landscape, with its dense transport system. The dispersal model was calibrated using telemetric data from the Swiss Jura and based on a map of potential lynx dispersal habitat.

3. Most suitable patches could be interconnected by movements of dispersing lynx within 10 years of reintroduction. However, when realistic levels of mortality risks on roads were applied, most patches become isolated except along the German–Czech border. Consequently, patch connectivity is limited not so much by the distribution of dispersal habitat but by the high mortality of dispersing lynx. Accordingly, rather than solely investing in habitat restoration, management efforts should try to reduce road mortality.

4. Synthesis and applications. Our approach illustrates how spatially explicit dispersal models can guide conservation efforts and reintroduction programmes even where data are scarce. Clear limits imposed by substantial road mortality will affect dispersing lynx as well as other large carnivores, unless offset by careful road-crossing management or by the careful selection of release points in reintroduction programmes.

Key-words: conservation, large carnivores, large-scale approach, Lynx lynx, movement, spatially explicit individual-based model, species reintroduction

*'This is an electronic version of an article published in Journal of Applied Ecology: complete citation information for the final version of the paper, as published in the print edition of Journal of Applied Ecology, is available on the Blackwell Synergy online delivery service, accessible via the journal's website at http://www.blackwellpublishing.com/journals/jpe or http://www.blackwell-synergy.com.

Effects of matrix heterogeneity on animal dispersal: from individual behavior to metapopulation-level parameters.
Revilla, E., T. Wiegand, F. Palomares, P. Ferreras, and M. Delibes. 2004. The American Naturalist 164: E-130-E153 .

Mounting theoretical and empirical evidence shows that matrix heterogeneity may have contrasting effects on metapopulation dynamics by contributing to patch isolation in non-trivial ways. We analyze the movement properties during interpatch dispersal in a metapopulation of Iberian lynx (Lynx pardinus). On a daily temporal scale lynx habitat selection define two types of matrix habitats where individuals may move: open and dispersal habitats (avoided and used as available, respectively). There was a strong and complex impact of matrix heterogeneity on movement properties at several temporal scales (hourly and daily radiolocations, and the entire dispersal event). We use the movement properties on the hourly temporal scale to build a simulation model to reconstruct individual dispersal events. The two most important parameters affecting model predictions at both the individual (daily) and metapopulation scales were related to the movement capacity (number of movement steps per day and autocorrelation in dispersal habitat), followed by the parameters representing the habitat selection in the matrix. The model adequately reproduced field estimates of population-level parameters (e.g. interpatch connectivity, maximum and final dispersal distances), and its performance was clearly improved when including the effect of matrix heterogeneity on movement properties. Assuming a homogeneous matrix results in large errors in the estimate of interpatch connectivity, especially for close patches separated by open habitat or corridors of dispersal habitat, showing how important it is to consider matrix heterogeneity when it is present. Movement properties on the interaction of dispersing individuals with the landscape can be used as a mechanistic representation of dispersal at the metapopulation level. This is so when the effect of matrix heterogeneity on movement properties is evaluated under biologically meaningful spatial and temporal scales.

Key-words: autocorrelated random walk, Lynx pardinus, matrix fragmentation, individual-based spatially explicit simulations, interpatch connectivity, standard of plausibility.

Modeling Species Distributions to Improve Conservation in Semiurban Landscapes: Koala Case Study 

Rhodes, J. R., T. Wiegand, C. A. McAlpine, J. Callaghan, D. Lunney, M. Bowen, and H. P. Possingham. 2006. Conservation Biology 20:449-459

Species distribution models are commonly used to inform landscape and conservation planning. In urban and semiurban landscapes, the distributions of species are often determined by a combination of natural habitat and anthropogenic impacts. Understanding the spatial influence of these two processes is crucial for making spatially explicit decisions about conservation actions. We present a logistic regression model for the distribution of koalas (Phascolarctos cinereus), in a semiurban landscape in eastern Australia, that explicitly separates the effect of natural habitat quality and anthropogenic impacts on koala distributions. We achieved this by comparing the predicted distributions with the predicted distributions assuming anthropogenic variables are fixed at their mean values. Similar approaches have relied on making predictions assuming anthropogenic variables are zero, which will be unreliable if the training data set does not include anthropogenic variables close to zero. Our approach is novel because it can be applied to landscapes where anthropogenic variables are never close to zero. Our model showed that, averaged across the study area, natural habitat was the main determinant of koala presence. However, at a local scale, anthropogenic impacts could be more important, with consequent implications for conservation planning. We demonstrate that, by using this modeling approach and presenting predictions visually as a map, provides important information for making decisions on how different conservation actions should be spatially allocated. This approach is particularly useful for areas where wildlife and human populations exist in close proximity.

Key words: anthropogenic impacts, conservation planning, logistic regression, natural habitat quality, mixed effects model, spatial distribution model

Lynx reintroductions in fragmented landscapes of Germany: projects with a future or misunderstood wildlife conservation?

Kramer-Schadt, S.,.E. Revilla, and T. Wiegand. 2005.  Biological Conservation 125: 169-182

Eurasian lynx are slowly recovering in Germany after an absence of about 100 years, and additional reintroduction programs have been launched. However, suitable habitat is patchily distributed in Germany, and whether patches could host a viable population or contribute to the potential spread of lynx is uncertain. We combined demographic scenarios with a spatially explicit population simulation model to evaluate the viability and colonization success of lynx in the different patches, the aim being to conclude guidelines for reintroductions. The spatial basis of our model is a validated habitat model for the lynx in Germany. The dispersal module stems from a calibrated dispersal model, while the demographic module uses plausible published information on the lynx_ life history. The results indicate that (1) a viable population is possible, but that (2) source patches are not interconnected except along the German–Czech border, and that (3) from a demographic viewpoint at least 10 females and 5 males are required for a start that will develop into a viable population with an extinction probability of less than 5% in 50 years. The survival rate of resident adults was the most sensitive parameter, and the best management strategy for the success of reintroduction would be to reduce the mortality of residents in the source patches. Nevertheless, the extremely low probability of connectivity between suitable patches makes most of the reintroduction plans isolated efforts, and they are therefore questionable in the long run. With such a model, the suitability of the single habitat patches can be assessed and the most appropriate management scheme applied. This study shows that simulation models are useful tools for establishing the comparative effectiveness of reintroduction plans aimed at increasing the viability of the species.
 

Keywords: large carnivores, Lynx lynx L., mortality scenarios, population viability analysis, spatially explicit individual-based model, species reintroduction

Detailed assessment of microhabitat suitability for Aedes aegypti (Diptera: Culicidae) in Buenos Aires, Argentina.

D. Vezzani, D., A. Rubio, S. M. Velazquez, N. Schweigmann and T. Wiegand. 2005. Acta Tropica 95: 123-131

Little information is available on the ecology of Aedes aegypti Linnaeus at the southern extreme of its distribution (Buenos Aires, Argentina), particularly on microhabitat suitability. The aim of our study was to identify at a detailed scale, microhabitat factors that correlate with the presence of preimaginal stages of the mosquito. In March 2001 we performed a spatial census of all containers located in a 1-ha patch within a cemetery in Buenos Aires City. On a reference map (1:700) we plotted the position of graves and surrounding corridors, the location of containers, the shade projected by each plant between 10:00 and 16:00 hours and vegetation cover. We classified vegetation by height, substrate by composition and shadow by level of exposure to sunlight. We performed univariate and multivariate logistic regression analyses with 9 constructed independent variables, some of them at scales of 0.5, 1, 2, 3, and 10 m. Of 850 receptacles examined, 101 contained preimaginal stages of Ae. aegypti. Level of exposure to sunlight, type of substratum, vegetation height and distance of containers to vegetation were significantly associated with the presence of breeding sites at the studied scales. Final multivariate models were significant at scales of 2 (c2(3)=25.693, p<0.001) and 3 m (c2(3)=26.440, p<0.001), and 65.9% and 66.8% of our data were correctly classified respectively for each scale. Our results suggest that sites less exposed to sunlight, with taller and closer vegetation, and in shaded and vegetated neighbourhoods were the most favourable microhabitats for Ae. aegypti breeding.

Key words: mosquitoes - Aedes aegypti - microhabitat suitability - vegetation - shade - statistical habitat model - Argentina

Context-dependent negative and positive interactions between adult shrubs and seedlings in a semi-arid shrubland

Riginos, C., S. J. Milton, and T. Wiegand. 2005. Journal of Vegetation Science 16:331-340

Question: In semi-arid systems, rainfall gradients can cause plant-plant interactions to shift from negative to positive or vice versa. However, the importance of a second major abiotic factor, soil nutrients, has rarely been considered. We consider different combinations of both factors and ask: do net adult-seedling interactions become less competitive and more facilitative with increasing overall abiotic harshness?

Location: Succulent Karoo, Western Cape, South Africa.

Methods: We examined the interactions between seedlings and adult shrubs at two sites. Sites differ in rainfall, and each contain two habitats: nutrient-rich mounds associated with underground termitaria and a relatively nutrient-poor matrix. We carried out a spatial pattern analysis of community-wide seedling-adult associations. We then conducted field and greenhouse experiments to test the effects of soil and the presence of neighboring shrubs on the growth and survival of six seedling species.

Results: At the higher rainfall site, both competitive and facilitative effects of adults on seedlings were found but did not differ by habitat, despite the more benign conditions in the mound habitat. At the lower rainfall site, adult shrubs generally had neutral effects on seedlings in the matrix habitat. In the nutrient-rich mound habitat, however, adult shrubs had strong and consistently competitive effects on seedlings.

Conclusion: Seedling-adult interactions could not be predicted by a simple overall gradient of abiotic harshness, demonstrating the need for more complex, mechanistic models to predict plant-plant interactions. We suggest that rainfall and soil nutrients affect seedling-adult relations through their interactive effects on the life-history attributes of the species involved.

Key words: Competition; facilitation; nurse-plant effect; point pattern analysis; Succulent Karoo

Pattern-oriented Modeling of Agent-based Complex Systems: Lessons from Ecology

Volker Grimm, Eloy Revilla, Uta Berger, Florian Jeltsch, Wolf M. Mooij, Steven F. Railsback, Hans-Hermann Thulke, Jacob Weiner, Thorsten Wiegand, Donald L. DeAngelis,  Science 310:987-991

Agent-based complex systems are dynamic networks of many interacting agents; examples include ecosystems, the immune system, financial markets, and cities. In the search for general principles underlying the internal organization of such systems, bottom-up simulation models such as cellular automata and agent-based models are widely used. So far, however, no general framework for designing, testing, and analyzing bottom-up models has been established. However, recent advances in bottom-up ecological modeling have come together in a general strategy we call Pattern-oriented Modeling. This strategy provides a unifying framework for decoding the internal organization of agent-based complex systems and may lead toward unifying algorithmic theories of the relationship between adaptive behavior and system complexity.

Extending Point Pattern Analysis for Objects of Finite Size and Irregular Shape* Appendix (100K)
Thorsten Wiegand, W. Daniel Kissling, Pablo A. Cipriotti, and Martin R. Aguiar,  Journal of Ecology 94: 825-837
 
1 We use a grid- and simulation-based approach to extend point pattern analysis to deal with plants of finite size and irregular shape, and compare the results of our approach with that of the conventional point approximation. The plants are approximated by using an underlying grid and may occupy several adjacent grid cells depending on their size and shape. Null models correspond to that of point pattern analysis but need to be modified to account for the finite size and irregular shape of plants.
 

2 We use a mapped area of a grass-shrub steppe in semiarid Patagonia, Argentina, to show that the shrub community is essentially randomly structured, but that shrubs facilitate grasses in their immediate neighbourhood.
 

3 The occurrence of this random spatial structure provides important new information on the biology of shrub populations. In general, previous data from semiarid and arid ecosystems have showed that adult shrubs tend to show over-dispersed patterns, whereas juveniles are clumped.
 

4 We find that the point approximation may produce misleading results (1) if plant size varies greatly, (2) if the scale of interest is of the same order of magnitude as the size of the plants and (3) if the plants of a given pattern are constrained through competition for space by the presence of other plants. The point approximation worked well in all other cases, but usually depicted weaker significant effects than when the size and shape of plants were taken into account.
 

5 Our approach to quantifying small-scale spatial patterns in plant communities has broad applications including the study of facilitation and competition. Ecologists will be able to use the software available to take advantage of these methods.
 
Key-words: Community structure, facilitation, grid-based implementation, neighbourhood effects, null models, pair-correlation function, point pattern-analysis, Ripley’s K-function, spatial pattern, second-order spatial statistics.

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*This is an electronic version of an article published in Journal of Ecology: complete citation information for the final version of the paper, as published in the print edition of Journal of Ecology, is available on the Blackwell Synergy online delivery service, accessible via the journal's website at http://www.blackwellpublishing.com/journals/jec or http://www.blackwell-synergy.com.

Abrupt population changes in treeline ecotones along smooth gradients* Appendices (246K)
Thorsten Wiegand,  J. Julio Camarero, Nadja Rüger, and Emilia Gutiérrez,  Journal of Ecology 94: 880-892
 

1 We developed a spatially explicit and individual-based simulation model describing the dynamics of tree populations across treeline ecotones. Our aims were to identify minimal factors and processes able to generate treeline types with abrupt vs. smooth transitions in different variables (tree height, age, density), to investigate the role of positive feedback in pattern generation, and to find out why krummholz appears at some treelines, but not at all. We hypothesised that a different balance between smooth growth and mortality gradients across the treeline ecotone could account for differences between commonly observed treeline types.

2 The model contained only processes and factors we regarded as essential for producing a treeline ecotone and was parameterized with an extensive individual-based data set from Pinus uncinata treelines in the Spanish Pyrenees. However, parameters expected to influence treeline type were systematically varied.

3 The simple model was able to generate major treeline types differing in abruptness and krummholz abundance. The most important factors determining treeline types were the relative strength of the growth and mortality gradients, followed by facilitation strength, whereas demographic parameters accounted for more subtle differences.

4 We developed a tentative classification scheme to locate treelines types within a two-dimensional state space spanned by two parameters defining the growth and mortality gradients. Only certain combinations of growth inhibition, mortality, and facilitation allowed emergence of certain treeline types characterised by contrasting abruptness values and the presence or absence of krummholz.

5 High krummholz densities emerged only under positive feedback and strongly increasing growth inhibition across the ecotone. Abruptness in adult tree density was positively correlated with facilitation strength and growth inhibition. In contrast, treelines with abrupt height transitions occurred only, where both low growth inhibition and a strongly increasing mortality occurred across the ecotone.

6 Our analysis suggests that treeline features are not arbitrary but there is a clear signal in the pattern which allows for inference of the underlying processes. Our approach of a systematic comparison of model predictions and various observed patterns can be widely applied for testing hypotheses on the functioning of ecological systems and for deriving specific explanations to be verified in the field.

Key-words: demographic model, individual-based model, pattern-oriented modelling, Pinus uncinata, Pyrenees, spatially explicit population model, positive feedback.

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*This is an electronic version of an article published in Journal of Ecology: complete citation information for the final version of the paper, as published in the print edition of Journal of Ecology, is available on the Blackwell Synergy online delivery service, accessible via the journal's website at http://www.blackwellpublishing.com/journals/jec or http://www.blackwell-synergy.com.
 

Spatial patterns and competition of tree species in a Douglas-fir chronosequence on Vancouver Island.

Getzin, S., C. Dean, F. He, T. Trofymow, K. Wiegand, and T. Wiegand. Ecography 29: 671-682.

Douglas-fir forest is a major forest in the Pacific Northwest region. While the successional dynamics and large scale structure of the forest is well studied, the fine-scale spatial characteristics at the stand level are still poorly understood. Here we investigated four hypotheses on the fine-scale spatial structure of the forest on Vancouver Island. Our primary purpose is to understand how the three dominant species, Douglas-fir, western hemlock and western redcedar, coexist and partition space along a chronosequence comprising of three stands of immature, mature and old-growth. We used the O-ring statistic and Ripley’s L-function to quantify the change in spatial distribution and association of the species along the chronosequence. Evidence on intra- and inter-specific competition was also inferred from correlations between nearest-neighbor distances and tree size. Our results show that (1) variation in local site characteristics was highly important for the unexpected aggregated pattern of Douglas-fir in old-growth, (2) surviving trees of the species were less aggregated than their pre-mortality patterns, thus rejecting the random mortality hypothesis and being strong evidence for intra-specific competition, (3) tree death was a random process among larger overstorey trees in the plots, and (4) inter-specific competition declined with increasing plot age as a result of spatial resource partitioning. Here we highlight the importance of spatial heterogeneity for the long-term coexistence of shade-intolerant pioneer Douglas-fir and shade-tolerant colonizer species during forest succession.

Spatial ecology of a root-parasite—from pattern to process

Watson, D.M., Roshier, D.A., and T. Wiegand. Austral Ecology 32: 359-369.

Occurrence patterns of parasitic plants are constrained by the distribution of suitable hosts and movement patterns of seed vectors and, accordingly, represent a simplified system to study many aspects of spatial ecology and determinants of distribution. Previous work has focused on the aerially hemiparasitic mistletoes, and it is unclear whether root parasites are affected by similar factors. Here, we evaluate spatial patterns in the root-parasitic Santalum lanceolatum in an arid shrubland in northwestern New South Wales, central Australia. In this region, the principal host is a long lived nitrogen fixing shrub Acacia tetragonophylla closely associated with ephemeral creek-lines. The location of 765 individuals of both species was mapped along a 250 m section of creek-line using a total survey station, and occurrence patterns of the root parasite related to host distribution and landscape context. We used Ripley’s K-function and the O-ring statistic to determine whether the distribution of S. lanceolatum was random, aggregated or regular; the spatial scales at which these patterns occurred; and to quantify any spatial associations between the parasite and its host, A. tetragonophylla.  While acacias were closely associated with the creek-line, S. lanceolatum plants were more tightly clustered, displaying significant clustering at two spatial scales (1.2 m and 8.8 m). We suggest that host quality may act as an important constraint, with only those acacias growing in or near the creek-line being physiologically capable of supporting a parasite to maturity. Insights gained from spatial analysis are used to guide ongoing research in this system, and highlight the utility of the O-ring statistic for understanding patterns of distribution affected by multiple processes operating at critical scales.

Keywords:  Dispersal, Distribution, Host quality, O-ring statistic, Santalum.

Revealing driving forces of mid-cities urban growth patterns using spatial modeling: a case study of Los Angeles (Chile). 

Aguayo, M., T. Wiegand, G. Azócar, K. Wiegand, and C. Vega. Ecology and Society: 12 (1): 13.

[online] URL: http://www.ecologyandsociety.org/vol12/iss1/art13/  

City growth and changes in land use patterns cause several important social and environmental impacts. In order to understand the spatial and temporal dynamics of these processes, we must identify and analyze the factors that drive urban development, especially those that can be used to predict future changes and their potential environmental effects. The objectives of this research were to quantify the relationship between the urban growth and its driving forces, exemplified for Los Angeles, a city in central Chile, and to predict the spatial growth pattern based on historical land use changes. This involved (i) analysis of a set of multi-temporal images (1978, 1992, 1998) and characterization of the land use change spatial pattern; (ii) the construction of digital coverage in GIS; (iii) the selection of predictive variables through univariate analysis; (iv) construction of logistic regression models using 1978 - 1992 growth vs. non growth as dependent variable; and (v) the prediction of the probability of land use change through application of the regression model for the 1992-1998 period. To investigate the influence of spatial scale we constructed several blocks of models i) comprising only distance variables (e.g., distance to highway), ii) comprising only scale-dependent density variables (e.g., density of urban area within a 600m radius), iii) combining distance and density variables and iv) combining distance and density variables at several spatial scales. All blocks included the environmental variables. We found that combining distance and density variables at several scales are required to appropriately capture the multi-scale urban growth process. The best models correctly predict about 90% of the observed 1992-1998 land use changes. Distance to access roads, the densities of the urban road system and urbanized areas at different scales, and soil type were the strongest driving forces of the growth pattern. In turn, other environmental variables were less important or not significant for explaining the urban growth process. Our approach which combines spatial modeling tools and GIS significantly advances our understanding of urban growth patterns, it provides an important contribution to urban planning and management, and can be widely applied.

Patterns for parameters in simulation models

Kramer-Schadt, S., E. Revilla, T. Wiegand, and V. Grimm. 2007. Ecological Modelling 204:553-556

Population simulation models are often used in conservation biology to assess human impact on species s urvival, but have been under heavy critique due to parameterization problems. The general notion is that only models for which parameters were directly assessed from field data can showthat a certain process isworking, in contrast to using field data to fit models. We would like to provide an update regarding the relationship between simulation model parameterization and the use of field data as ‘pattern’ for revealing ‘structurally realistic’ parameters and processes. ‘Pattern-oriented modelling’ is an inverse modelling technique in ecology that considers the use of multiple field data pattern simultaneously to filter the parameterizations whichwere successfully tested against all available data on system dynamics.We highlight this technique with an example of our own research and conclude that this approach is especially suitable for models in conservation of rare and elusive species, where data are gener ally scarce.

Analysis of spatial pattern in early stages of primary succession on former lignite mining sites.

Giesselmann, U.C., T. Wiegand, J. Meyer, R. Brandl, and M. Vogel. 2008.  Austral Ecology  32:359 - 369

The spatial organisation of individuals or groups of individuals within a population can provide valuable information about social organisation and population dynamics. We analysed the spatial distribution of communal nets of the colonial living sociable weaver (Philetairus socius) on two farms in the Kalahari. Sociable weavers build large communal nests on big savannah trees, forming a persisting point pattern of occupied and unoccupied trees. We used two spatial statistics, Ripley’s K and the pair-correlation function, to describe characteristics of the patterns over a range of distance scales. We found consistent results for the two farms. (1) At scales beyond 1000 m we found regular distribution of communal nests. (2) At scales between 200 and 300 m the communal nests were clustered. These two results were independent from the spatial distribution of trees. The regular distribution at larges scales may be due to competition of different colonies. The clustering of nests suggests that nearby communal nests (< 300 m) function as one colony.

Djossa, B.A., Fahr, J., Wiegand, T., Ayihouénou, B.E., Kalko, E.K.V., and B. A. Sinsin. 2008. Agroforestry Systems 72: 205-220
 

The shea tree, Vitellaria paradoxa, is a socio-economically important tree for the rural population in parts of West Africa. Our study assessed the current status of this native tree species with regard to increasing human pressure in northern Benin. We compared distribution of adult shea trees, seedlings and saplings in farmed lands with protected areas in the Biosphere Reserve of Pendjari (BRP). At our study site near BRP, agricultural activities foster recruitment of shea trees by regularly cropping of vegetation cover. Furthermore, traditional farming practices preserve adult individuals thus permitting regular fruit harvests. Consequently, most of the tallest and largest individuals of shea trees are found in framed lands. In contrast, the highest density of juvenile trees including seedlings (dbh <5 cm) and saplings (dbh 5-10 cm) occurred within BRP. Saplings were negatively affected by farming activities. Furthermore, spatial point pattern analysis revealed differences in the spatial structure of juveniles. Juveniles showed significant aggregations at small scale (< 20 m) in BRP as well as significant and positive small-scale associations with adult trees. This contrasts with farmed lands where we did not find such spatial patterns at similar small scale but only a weak aggregation between juveniles and absence of association (attraction) of adults to juveniles. Although our analyses indicate that shea trees are rather well preserved, we conclude that the observed severe reduction of saplings in farmed lands is likely to negatively impact the long-term viability of the tree population. Therefore agroforestry practices must consider the preservation of sapling populations in farming areas for long-term conservation.

Key words: Benin, conservation, Shea tree, spatial analysis.

Wiegand, T, C.V.S. Gunatilleke, I.A.U.N. Gunatilleke, and T. Okuda. Ecology 88: 3088–3102

Clustering at multiple critical scales may be common for plants since many different factors and processes may cause clustering. This is especially true for tropical rain forests where theories for explaining species coexistence and community structure rest heavily on spatial patterns. We used point-pattern analysis to analyze the spatial structure of Shorea congestiflora, a dominant species at a 25-ha forest dynamics plot in a rain forest at Sinharaja World Heritage Site (Sri Lanka), which apparently shows clustering at several scales. We developed cluster processes incorporating two critical scales of clustering for exploring the spatial structure of S. congestiflora and interpret it in relation to factors such as competition, dispersal limitation, recruitment limitation, and Janzen–Connell effects. All size classes showed consistent large-scale clustering with a cluster radius of approximately 25m. Inside the larger clusters, small-scale clusters with a radius of 8m were evident for recruits and saplings, weak for intermediates, but disappeared for adults. The pattern of all trees could be divided into two independent patterns, a random pattern (nearest neighbor distance > 8m) comprising about 12% of the trees and a nested double-cluster pattern. This finding suggests two independent recruitment and/or seed dispersal mechanisms. Saplings were several times as abundant as recruits and may accumulate several recruit generations. Recruits were only weakly associated to adults and occupied about half of the large-scale clusters, but saplings almost all. This is consistent with recruitment limitation. For about 70% (95%) of all juveniles the nearest adult was less than 26m (53m), suggesting a dispersal limitation which may also be related with the critical large-scale clustering. Our example illustrates how the use of specific and complex null hypothesis of spatial structure in point pattern analysis can help to better understand the biology of a species and to generate specific hypotheses to be further investigated in the field.

1 The spatial pattern of tree species retains signatures of factors and processes such as dispersal, available resource patches for establishment, competition, and demographics. Comparison of the spatial pattern of different size classes can thus help to reveal the importance and characteristics of the underlying processes. However, tree dynamics may be masked by large-scale heterogeneous site conditions, e.g., when the restricting size of regeneration sites superimposes emergent patterns.

2 Here we ask how environmental heterogeneity may influence the spatial dynamics of plant communities. We compared the spatial patterns and demographics of western hemlock in a homogeneous and a heterogeneous site of old-growth Douglas-fir forests on Vancouver Island using recent techniques of point pattern analysis. We used homogeneous and inhomogeneous K- and pair-correlation functions, and case-control studies to quantify the change in spatial distribution for different size classes of western hemlock.

3 Our comparative analyses show that biological processes interacted with spatial heterogeneity, leading to qualitatively different population dynamics at the two sites. Population structure, survival and size structure of western hemlock were different in the heterogeneous stand in such a way that compared to the homogeneous stand, seedlings were more clustered, seedling densities higher, seedling mortality lower, adult growth faster, and adult mortality higher. Under homogeneous site conditions, seedling survival was mainly abiotically determined by random arrival in small gaps with limiting light. At the heterogeneous site, seedling densities and initial survival were much higher leading to strong density-dependent mortality and selection for faster growing individuals in larger size classes. We hypothesise that the dynamics of the heterogeneous stand were faster due to asymmetric competition with disproportionate benefit to taller plants.

Synthesis Our study supports the hypothesis that successional dynamics are intensified in heterogeneous forest stands with strong spatial structures and outlines the importance of spatial heterogeneity as a determinant of plant population dynamics and pattern formation.

Key words: case-control, dispersal strategies, inhomogeneous pair-correlation function, large-scale heterogeneity, point pattern analysis, succession, western hemlock

Key words:  Cistus albidus, Ulex parviflorus, Helianthemum marifolium, Ononis fruticosa, Fabaceae, Cistaceae, Mediterranean gorse shrubland, Kaplan-Meier method, O-ring statistics, point-pattern analysis, segregation hypothesis