Ecological Modelling

Levins' Loop Analysis was developed for investigating the behavior of distributed, interconnected systems in which the interactions are not known well enough to completely model quantitatively, such as in many ecological communities. The presence or absence and the signs of the interactions between the subsystems may be all that is assumed in the model structure. The analysis focuses on the question of the qualitative stability, in the small, of the equilibrium points of the system as well as the possible first order shifts in these equilibrium points due to the influence of constantly acting disturbances. The Loop method is extended in this discussion to the qualitative analysis of the transient and long term tracking behavior of stable systems experiencing time-dependent and periodic disturbances.

The use of regression, ordination and dynamic ecosystem modelling in limnology is discussed by evaluating some of the vices and virtues of these techniques. Both general characteristics of the approaches and a few examples are used to stress the importance of analysis of the residuals for evaluation of the models. Not completely unexpected, a simple ordination model did not perform worse than a complicated ecosystem model, both applied to the same lake system. Both models are shown to fail for prediction purposes, mainly because the error variance in the data used for parameter estimation is large compared to the variance that can be explained.Integration of regression, multivariate analysis and dynamic ecosystem modelling, all followed by analysis of the residuals, is advised. Nested models are proposed as a solution for the problem of changing parameters and for the problem of parameters being different among lakes.

The problem of uncertainty in ecological modelling, in particular uncertainty of ecological data and uncertainty of expert knowledge, appears to be crucial. This paper presents some initial results obtained by investigation of this problem based on the fuzzy logic approach.

The aim of this paper is to analyze the behavior of models which describe the population dynamics taking into account the subjectivity in the state variables or in the parameters. The models in this work have demographic and environmental fuzziness. The environmental fuzziness is presented using a life expectancy model where the fuzziness of parameters is considered. The demographic fuzziness is presented using the continuous Malthus and logistic discrete models. An outstanding result in this case is the emergence of new fixed points and bifurcation values to the discrete logistic model with subjective state variables in form of fuzzy sets. An interpretation is offered for this fact which differs from the deterministic one.

Using a three-dimensional stochastic model of radionuclides in forests developed in Part I, this work simulates the long-term behavior of Cs-137 in forest soil. It is assumed that the behavior of Cs-137 in soils is driven by its advection and dispersion due to the infiltration of the soil solution, and its sorption to the soil matrix. As Cs-137 transport through soils is affected by its uptake and release by forest vegetation, a model of radiocesium behavior in forest vegetation is presented in Part III of this paper. To estimate the rate of infiltration of water through the soil, models are presented to estimate the hydrological cycle of the forest including infiltration, evapotranspiration, and the root uptake of water. The state transition probabilities for the random walk model of Cs-137 transport are then estimated using the models developed to predict the distribution of water in the forest. The random walk model is then tested using a base line scenario in which Cs-137 is deposited into a coniferous forest ecosystem.

Sensitivity and uncertainty analysis were conducted on a stretch of the Rhone River (France) with CASTEAUR, a model computing radionuclides transfers to abiotic and biotic components of fluvial ecosystems. The sensitivity of accumulation in omnivorous fish was analysed by constructing linear models between this output variable and some input parameters sets constructed using the Latin Hypercube sampling technique. When sedimentation occurred, the fish feeding ratio and the river suspended matter load explained the major part of the uncertainty associated to accumulation in fish. Results of an uncertainty analysis were also confronted to the accumulation measured in chubs (Leuciscus cephalus L.) of the Rhone River, downstream from a nuclear reprocessing plant. The model predictions and their associated uncertainties enclosed the observed radioactivity in fish, but only when suspended solids deposition was included in the model. We conclude from these observations that the sedimentary dynamics and the fish feeding habits should be properly characterized when assessing the impact of effluents in rivers using mathematical simulation models such as CASTEAUR.

A dynamic simulation model of salt accumulation on irrigated lands is presented. The original version of the model is part of a large-scale socio-economic model of irrigation-based regional development. The model introduced in this paper is a systemic one in the sense that it integrates four major sub-processes of rootzone salinization: irrigation, drainage, groundwater discharge and groundwater intrusion. It provides a comprehensive and general description of the long-term process of salt accumulation in lowlands under continuous irrigation practice, where irrigated lands are annually increased. Analysis of the model and simulation results reveal, under what conditions the salinity reaches alarming levels and with what strategies it can be controlled. For instance, in situations where the mixing of drainage water into irrigation water supplies is high, rootzone salinity quickly reaches alarming levels. More importantly, in this setting, the typical strategy of increasing the drainage in order to control the salinity level yields unprecedented exponentially growing salinity levels, a catastrophic result for the agriculture. The model structure can represent the basin wide salinization process on different geographical settings in agricultural development. In general, the model provides an experimental simulation platform, which can be used by the policy makers in the long term strategic management of large scale irrigation development projects. The model can also be of interest to the students and learners in teaching and research, in the related fields of environmental sciences.

Ecopath is mass-balance modeling approach that is widely used for incorporating ecosystem considerations into fisheries science. Up to now, users of Ecopath software who are constructing a model of a given area must carefully adjust input biomass, diets, and other parameters until the Ecopath parameterization is mass-balanced, a slow process leading to non-unique solutions. We present a new computer-automated iterative technique for mass-balancing Ecopath models which has the advantages of (1) reducing the lengthy process of and opportunity for encoding errors of the manual approach; (2) standardizing results for the same set of starting conditions; and (3) allowing exploration of alternative solutions, with consideration of the estimated confidence of each input parameter. Users can select random and/or gradient descent model perturbation of biomass and/or diet parameters, specify an objective (cost) function for optimization of the search, and modify decision logic, including simulated annealing. An objective function is defined to help target mass-balance solutions with minimum change to original input parameters. A Monte Carlo mode allows exploration of sensitivity to different starting conditions and random perturbations. The new procedure is implemented in the current version of the freely available Ecopath with Ecosim software (http://www.ecopath.org).

The high number of cases where pesticide residues have been found in groundwater during the last decade has enhanced the need for more knowledge about the fate of pesticides in soil. The purpose of the present study was to extend the knowledge of pesticide mineralisation in soil. Many publications have described the difficulties of finding a useful mathematical model for the description of pesticide mineralisation. In the present study a mathematical model is presented, which was useful for describing cometabolic mineralisation as well as metabolic mineralisation. On the basis of mineralisation studies of mecoprop in Danish soils, a predictive model, which described the mineralisation as a function of biological activity, soil texture, humus content and soil depth, was developed. The model was validated against mecoprop mineralisation studies in German soils and was shown to be very useful for the prediction of time for total mineralisation of mecoprop.

The Cantabrian Sea shelf ecosystem is described using a mass-balance model of trophic interactions, in order to understand the effects of the different fisheries that operate in this area. The study was based on a database of bottom trawl surveys, ICES stock assessment working groups, stomach analyses, fisheries research and was supplemented by published information. The model had 28 trophic groups corresponding to pelagic, demersal and benthic domains, also including detritus and fishery discards. The results indicated that the biomass and production of some groups would be unrealistic if they were independently estimated by single-species assessment approaches. Summaries are given to illustrate the flow distributions between groups. Strong relationships existed between the pelagic, demersal and benthic domains due to key groups, like zooplankton suprabenthic and horse mackerel, that transferred the flow from primary production to the upper trophic levels. Feeding pressure on phytoplankton was low and detritivorous species were an important component of the ecosystem.

Keystones are defined as relatively low biomass species with a structuring role in their food webs. Thus, identifying keystone species in a given ecosystem may be formulated as: (1) estimating the impact on the different elements of an ecosystem resulting from a small change to the biomass of the species to be evaluated for its ‘keystoneness’; and (2) deciding on the keystoneness of a given species as a function of both the impact estimated in (1) and its own biomass. Experimental quantification of interaction strength necessarily focus on few species, and require a priori assumptions on the importance of the interactions, which can bias the identification of keystone species. Moreover, empirical measurements, although very important, are expensive and time consuming and, owing to the spatio-temporal heterogeneity of habitats, physical conditions, and densities of organisms, published results tend to be case-specific and context-dependent.Although models can only represent but a caricature of the complexity of the real world, the modelling approach can be helpful since it allows overcoming some of the difficulties mentioned. Here we present an approach for estimating the keystoneness of the functional groups (species or group of species) of food web models. Network mixed trophic impact analysis, based on Leontief's economic input–output analysis, allows to express the relative change of biomasses in the food web that would result from an infinitesimal increase of the biomass of the observed group, thus identifying its total impact. The analysis of the mixed trophic impacts presented here was applied to a suite of mass-balance models, and the results allow us to rank functional groups by their keystoneness. Overall, we concluded that the straightforward methodology proposed here and the broad use of Ecopath with Ecosim (where mixed trophic impact analysis is implemented) together give a solid empirical basis for identification of keystone functional groups.

Geographic information about historical and possible future land-use changes is necessary for various kinds of ecological models. Introduced here is a global scenario which is regionalized on a 2.5° grid. The scenario consists of two parts. One part is historical pertaining to the period 1860–1980. It is based on available data concerning site and area of land-use changes. In contrast, the second part of the scenario includes a probability estimate for land-use development and distribution for the assumed period, 1981–2500. Here, on grid-element level, clearings occur due to logistic functions. The turning point for each logistic function is calculated by the global clearing function. The sequence in which the grid elements are cleared is determined by clearing probability. This is the product of four individual probability factors: the intensity of land use in neighbouring grid elements, natural productivity, soil fertility, and historical land-use changes.

Regime shifts, consisting of decadal-scale oscillations in atmosphere–ocean systems, have recently been the focus of many marine ecosystem studies. These ‘regime shifts’ effect the sea surface temperature and mixed layer depth (MLD), changing the environment for marine ecosystems. We simulated changes in the marine ecosystem caused by interdecadal climate variability, using data from 1948 to 2002 to drive an ecosystem model, NEMURO, embedded in a global three-dimensional physical–biological coupled model, ‘3D-NEMURO’.The results were consistent with observations. Comparing before and after the late 1970s regime shift, primary production and biomass of phytoplankton increased in the north central Pacific but decreased in the sub-tropical northwestern and eastern Pacific. This corresponds to the Pacific decadal oscillation (PDO) index that indicates interdecadal climate variability in the sub-tropical and tropical Pacific. In the north central Pacific, biomass correlated positively with PDO while that in the north eastern and western Pacific correlated negatively with PDO.

Using a nitrogen balance model based on statistical data, nitrogen loads due to food production and consumption and energy production were estimated for each 0.5° × 0.5° grid cell in the 13 countries of eastern Asia from 1961 to 2002. Groundwater quality was estimated with a simple first-order reaction model. Total nitrogen load, including natural nitrogen fixation, increased by a factor of 3.8 between 1961 and 2002 (with an increase by a factor of 15.6 due to crop production, 14.1 due to livestock waste, 2.4 due to human waste, and 4.5 due to energy production). The present estimate of average nitrogen load is 3.9 t km−2 yr−1. Our model indicated high nitrogen concentrations in groundwater in eastern and northeastern China and some areas of Republic of Korea and Japan. In many countries, per capita food consumption and the common logarithm of per capita NOx emission show significant linear relationships with the common logarithm of per capita GDP. Based on these relationships, we predicted food demands, fertilizer demand, NOx emission, and the resulting nitrogen loads for the next 18 years. Our model predicts that in 2020, the total nitrogen load will be 1.3–1.6 times the present load across the entire region according to several scenarios on economic growth and population increase, with various patterns of change in the different countries.

The northern Benguela ecosystem has been overfished and physically challenged over the past three decades. Ecopath with Ecosim was used to construct three ecosystem models (1971–1977, 1980–1989, and 1990–1995) and to compare differences in ecosystem structure. In the 1970s, the system sustained high catches, and had large populations of a few planktivorous fish. In the 1980s, the planktivorous fish species were expanded (horse mackerel, mesopelagic fish, and other small pelagics), although anchovy and sardine biomass was reduced. Catches remained high in the 1980s and the system was well connected. In the 1990s, the system was severely stressed, catches were much lower and omnivory was reduced. Most of the energy flowed through few pathways in the 1990s, and the energy was not transferred as efficiently up the trophic chain as in the 1980s. The fishery operated at the highest trophic level during the 1980s and there are some indications of “fishing down the foodweb” in this ecosystem between the 1980s and the 1990s. The high catches of sardine and hake in the 1970s are reflected in the high primary production required (PPR) by those compartments; the high catches of horse mackerel in the 1980s are shown by the high PPR for horse mackerel. The overall PPR for the fishery was highest in the 1980s, when the system was fished at nearly the same intensity as the 1970s, but the species taken were from higher trophic levels, requiring larger concentrations of primary production for their own existence. The importance of ecosystem–environmental interactions are highlighted by the abundance of horse mackerel, mesopelagics, small pelagics, and hake in the 1980s and the reduced biomass of most species in the 1990s, not only due to overfishing, but also due to the Benguela Niño that occurred in 1995. The system changed from an efficient ecosystem dominated by only two planktivores (anchovy and sardine) in the 1970s, to a system of large resilience and a varied planktivore population during the 1980s. However, the system’s resilience was lower, but its connectance was higher in the 1990s, where sardine was making a comeback and the marine mammals were doing well until the Benguela Niño reduced the system to a state of lower maturity.

Forest fragmentation threatens biodiversity in one of the last remaining temperate rainforests that occur in South America. We study the current and future impacts of fragmentation on spatial configuration of forest habitats at the landscape level time in southern Chile. For this purpose, we identify the geophysical variables (“pattern drivers”) that explain the spatial patterns of forest loss and fragmentation between 1976 and 1999 using both a GIS-based land-use change model (GEOMOD) and spatially explicit logistic regression. Then, we project where and how much forest fragmentation will occur in the future by extrapolation of the current rate of deforestation to 2010 and 2020. Both modeling approaches showed consistent and complementary results in terms of the pattern drivers that were most related to deforestation. Between 1976 and 1999, forest fragmentation has occurred mainly from the edges of small fragments situated on gentle slopes (less than 10°) and far away from rivers. We predict that patch density will decline from 2010 to 2020, and that total forest interior area and patch proximity will further decline as a result of forest fragmentation. Drivers identified by these approaches suggest that deforestation is associated with observed local socio-economic activities such as clearance of forest for pasture and crops and forest logging for fuelwood.

The spatial pattern of forest fire locations is of interest for fire occurrence prediction and for understanding the role of fire in landscape processes. A spatial statistical analysis of lightning-caused fires in the province of Ontario, between 1976 and 1998, was carried out to investigate the spatial pattern of fires, the way they depart from randomness, and the scales at which spatial correlation occurs. Fire locations were found to be spatially clustered. Kernel estimation of the spatial pattern of lightning strikes on days when the dryness of the forest floor exceeded a designated threshold yielded clusters in the same areas as the lightning fire clusters.

The coastal ecosystem of the Pearl River Estuary (PRE) has been overfished and received a high level of combined pollution since the 1980s. Ecopath with Ecosim was used to construct two ecosystem models (for 1981 and 1998) to characterize the food web structure and functioning of the ecosystem. Pedigree work and simple sensitivity analysis were carried out to evaluate the quality of data and the uncertainty of the models. The two models seem reliable with regards to input data of good quality. Comparing the variations of outputs of these two models aimed to facilitate assessment of changes of the ecosystem during the past two decades.

Replicate mass-balanced solutions to Ecopath models describing carbon-based trophic structures and flows were developed for the Lake Ontario offshore food web before and after invasion-induced disruption. The food webs link two pathways of energy and matter flow: the grazing chain (phytoplankton–zooplankton-fish) and the microbial loop (bacteria–protozoans) and include 19 species-groups and three detrital groups. Mass-balance was achieved by using constrained optimization techniques to randomly vary initial estimates of biomass and diet composition. After the invasion, production declined for all trophic levels and species-groups except Chinook salmon. The trophic level (TL) increased for smelt, adult sculpin, adult alewife and Chinook salmon. Changes to ecotrophic efficiencies indicate a reduction in phytoplankton grazing, increased predation pressure on Mysis, adult smelt and alewife and decreased predation pressure on protozoans. Specific resource to consumer TTE changed; increasing for protozoans (8.0–11.5%), Mysis (0.6–1.0%), and Chinook salmon (1.0–2.3%) and other salmonines (0.4–0.5%) and decreasing for zooplankton (20.2–15.1%), prey-fish (9.7–8.8%), and benthos (1.7–0.6%). Direct trophic influences of recent invasive species were low. The synchrony of the decline in PP and species-group production indicates strong bottom-up influence. Mass balance required an increase of two to threefold in lower trophic level biomass and production, confirming a previously observed paradoxical deficit in lower trophic level production. Analysis of food web changes suggest hypotheses that may apply to other similar large pelagic systems including, (1) as pelagic primary productivity declines, overgrazing of zooplankton results in an increase in protozoan production and a loss of trophic transfer efficiency, (2) habitat and food web changes increased Mysis predation on Diporeia and contributed to their recent decline, and (3) production of Chinook salmon, the primary piscivore, was uncoupled from pelagic production processes. This study demonstrates the value of food web models to better understand the impact of invasive species and to develop novel hypotheses concerning trophic influences.

Trophic interactions and community structure of commercial fishery species off Central Chile (33°–39°S) were analyzed and compared for 1992 and 1998 by ecotrophic modelling, using the Ecopath modelling software. The model encompasses the fishery, pinnipeds (sea lions), small pelagic fish (anchovy, pilchard), medium-sized pelagic fish (horse mackerel), demersal fish (e.g. Chilean hake, black conger), benthic invertebrates (carrot prawn, yellow prawn), and other groups such as zooplankton, phytoplankton, and detritus. Input information for the model was gathered from published and unpublished reports and our own estimates. Also, the effects of fishing and predation on fishery resources and on the most important components of the system were investigated, within an ecotrophic framework.Predators consumed the greater part of the production of the most important fishery resources, particularly juvenile stages, and the fishery removed a large fraction of adult production. Mortality by predation is an important component of natural mortality, especially in recruit and prerecruit groups. Analysis of direct and indirect trophic impact shows that adult Chilean hake have a negative impact on juvenile Chilean hake through cannibalism, and on pilchard, anchovy, and carrot prawn through predation. Also, fishing has a strong impact on fishery resources, such as Chilean hake, pilchard, and anchovy. Total biomass in 1998 was 1.5 times higher than in 1992. However, total catches in 1998 were about 80% of those in 1992. Changes in biomass and total yields of the system between 1992 and 1998 can be observed in such properties as total flows, consumption, respiration, and production. It is concluded that ecotrophic modelling is an useful tool for fishery management, since it can improve our understanding of the predator–prey interactions among the exploited (fishery resources) and unexploited but potential fishery resources of the system.

We used the one-dimensional DYRESM–CAEDYM model to elucidate and quantify the influence of the external phosphorus loading on ecosystem dynamics in moderately deep Lake Ravn, which is situated in an agricultural landscape in Denmark. Model simulations were used to quantify the extent to which the external phosphorus loading must be reduced to meet upcoming lake ecological quality requirements according to the European Union Water Framework Directive (WFD). The model generally showed good agreement with observed data for temperature and oxygen from the epilimnion and hypolimnion during the calibration period (7 years) as well as the validation period (5 years); although peaks of oxygen concentrations in epilimnion during late spring often were underestimated. Phosphate and total phosphorus (TP) concentrations were generally well reproduced in both the epilimnion and hypolimnion, though hypolimnetic phosphorus was occasionally underestimated in late summer. There was also good agreement between monitored data and modelled biomass of diatoms and dinoflagellates as well as the zooplankton biomass of cladocerans and calanoid copepods, although the timing of biomass peaks occasionally deviated from observations. Root-mean-square-errors (RMSE), used to quantify the model error, were overall similar for the calibration and the validation period. Simulations of scenarios with a reduced external TP loading suggest that a substantial reduction (40–50%) of the TP loading is required if phytoplankton biomass is to drop to a level sufficiently low to meet the proposed WFD requirements (summer average <6.5 μg chlorophyll a l−1). The predicted outcomes of considerable loading reductions should, however, be treated with some caution, as the conceptual model in this study could not fully account for the changes in trophic structure occurring at radically reduced TP loading. This particularly applies to changes in the fish stock, which may have extensive cascading effects via increased zooplankton grazing on the phytoplankton when external TP loading is reduced. This would most likely lead to higher transparency than that predicted by the model. To further improve the reliability of the predicted outcomes of various model scenarios, future work should include a series of test simulations also including fish predation. Today, fish predation is available in the DYRESM–CAEDYM model as well as other dynamic lake models; however, only sparse data is available on fish stock dynamics in Lake Ravn (as for most other lakes). An applicable test of the fish algorithms in today’s dynamic models will require reliable estimates of fish stock biomass in the study lakes during both the model calibration and validation period.

Sensitivity analysis consists of an integral and important validatory check of a computer simulation model before the code is used in performing any kind of analysis operation. The present paper demonstrates the use of a relatively new method and tool for conducting global sensitivity analysis (GSA) for environmental models, providing simultaneously the first GSA study of the widely used 1d soil–vegetation–atmospheric transfer (SVAT) model named SimSphere. A software platform called the Gaussian emulation machine for sensitivity analysis (GEM SA), which has been developed for performing a GSA via Bayesian theory, is applied to SimSphere model in order to identify the most responsive model inputs to the simulation of key model outputs, detect their interactions and derive absolute sensitivity measures concerning the model structure. This study is also very timely in that, use of this particular SVAT model is currently being considered to be used in a scheme being developed for the operational retrieval of the soil surface moisture content by National Polar-orbiting Operational Environmental Satellite System (NPOESS), in a series of satellite platforms that are due to be launched in the next 12 years starting from 2016.The employed GSA method was found capable of identifying the most responsive SimSphere inputs and also of capturing their key interactions for each of the simulated target quantities on which the GSA was conducted. The most sensitive model inputs were the topography parameters (slope, aspect) as well as the fractional vegetation cover and soil surface moisture availability. The implications of these findings for the future use of SimSphere are discussed.

Soil carbon (C) models are important tools for examining complex interactions between climate, crop and soil management practices, and to evaluate the long-term effects of management practices on C-storage potential in soils. CQESTR is a process-based carbon balance model that relates crop residue additions and crop and soil management to soil organic matter (SOM) accretion or loss. This model was developed for national use in U.S and calibrated initially in the Pacific Northwest. Our objectives were: (i) to revise the model, making it more applicable for wider geographic areas including potential international application, by modifying the thermal effect and incorporating soil texture and drainage effects, and (ii) to recalibrate and validate it for an extended range of soil properties and climate conditions. The current version of CQESTR (v. 2.0) is presented with the algorithms necessary to simulate SOM at field scale. Input data for SOM calculation include crop rotation, aboveground and belowground biomass additions, tillage, weather, and the nitrogen content of crop residues and any organic amendments. The model was validated with long-term data from across North America. Regression analysis of 306 pairs of predicted and measured SOM data under diverse climate, soil texture and drainage classes, and agronomic practices at 13 agricultural sites having a range of SOM (7.3–57.9 g SOM kg−1), resulted in a linear relationship with an r2 of 0.95 (P < 0.0001) and a 95% confidence interval of 4.3 g SOM kg−1. Using the same data the version 1.0 of CQESTR had an r2 of 0.71 with a 95% confidence interval of 5.5 g SOM kg−1. The model can be used as a tool to predict and evaluate SOM changes from various management practices and offers the potential to estimate C accretion required for C credits.

Rectangular grids are frequently used in spatial simulations, often with nearest neighbour interactions, but each cell has diagonal as well as orthogonal nearest neighbours. Here, a simple, abstract model of weed spread demonstrates that the relative strength of diagonal and orthogonal interactions affects simulation outcomes, by determining the threshold conditions required for spread from isolated and aggregated colonized cells. The relative strength of diagonal and orthogonal interactions implicitly represents the range of interaction processes. The von Neumann neighbourhood, which has no diagonal interactions, represents processes with zero or negligible range, such as contact processes; increasing the relative strength of diagonal interactions represents processes with increasing range, such as seed dispersal. Diagonal interactions are only likely to equal orthogonal interactions for processes with ranges that allow significant interactions beyond the nearest neighbours of a cell. Thus, the Moore neighbourhood of diagonal and orthogonal nearest neighbours with equal weight may be considered an inaccurate approximation to a larger neighbourhood. Accurate diagonal and orthogonal nearest neighbour interactions can be calculated by a method proposed by Buffon in the 18th century. This method is also useful for calculating the impacts of rescaling a grid on intercellular interactions. If the area represented by each cell in the grid is increased, diagonal interactions should be reduced more than orthogonal interactions. In a rectangular grid, setting diagonal interactions to half the strength of orthogonal interactions can achieve a good match to an equivalent simulation in a hexagonal grid in some cases, but not always.

Ecological Modelling publishes from time to time editorials, that review the development of the journal: after 50 volumes, after 100 volumes and at our 25 years anniversary. This time we celebrate 30 years anniversary and focus on the time 2000–2005, corresponding to the volumes 126–185. Sixty volumes – almost one third of all volumes of Ecological Modelling! We will review the development by means of statistics as we have done previously but this time we will also try to look behind the statistics and try to assess the development in the scientific fields of ecosystem theory (systems ecology) and of ecological modelling. What are the recent research focus in these two subfield of ecology?

The individual-based (aka agent-based) approach is now well established in ecological modeling. Traditionally, most applications have been to organisms at higher trophic levels, where the importance of population heterogeneity (intra-population variability), complete life cycles and behavior adapted to internal and external conditions has been recognized for some time. However, advances in molecular biology and biochemistry have brought about an increase in the application of individual-based modeling (IBM) to microbes as well. This literature review summarizes 46 IBM papers for bacteria in wastewater treatment plants, phytoplankton in ocean and inland waters, bacteria in biofilms, bacteria in food and other environs, and “digital organisms” and “domesticated computer viruses” in silico. The use of IBM in these applications was motivated by population heterogeneity (45%), emergence (24%), absence of a continuum (5%), and other unknown reasons (26%). In general, the challenges and concepts of IBM modeling for microbes and higher trophic levels are similar. However, there are differences in the microbe population dynamics and their environment that create somewhat different challenges, which have led to somewhat different modeling concepts. Several topics are discussed, including producing, maintaining and changing population heterogeneity (different life histories, internal variability, positive feedback, inter-generation memory), dealing with very large numbers of individuals (different up-scaling methods, including representative space vs. super-individual, number vs. biomass based, discrete vs. continuous kinetics, various agent accounting methods), handling space, simulating interactions with the extracellular environment (hybrid Eulerian–Lagrangian approach), modeling agent–agent interaction (self-shading, predation, shoving) and passive transport (random walk with spatially variable diffusivity, well-mixed reactors). Overall, the literature indicates that the application of IBM to microbes is developing into a mature field. However, several challenges remain, including simulating various types of agent–agent interactions (formation and function of colonies or filaments, sexual reproduction) and even smaller individuals (viruses, genes). Further increases in intracellular detail and complexity in microbe IBMs may be considered the combination of systems biology and systems ecology, or the new field of systems bioecology.

Trophic interactions and the relevance of the “classical” (CFW) versus the “microbial” (MFW) food webs were studied in the upwelling system of Antofagasta (23°S), northern Humboldt Current System (HCS) off Chile. Biological and ecological data gathered from the study area during 1996 and 1999–2002 and complementary data from the literature were analysed using the Ecopath with Ecosim software version 5.0 (EwE). The model includes the following functional groups: Detritus, dissolved organic matter (DOM), bacteria, phytoplankton, appendicularians, salps, calanoid copepods, cyclopoid copepods, chaetognaths, ctenophores, clupeiform fishes.

A method of sensitivity analysis for stochastic population models is proposed in which logistic regression is used to relate the probability of population decline to the parameters of the model. The regression equation serves to summarise the effects of different model parameters and interactions. The method was applied to a model of the helmeted honeyeater. The results may be used to place bounds on the predictions of the model. The predicted risk of population decline within the next 50 years is subject to substantial error.

Like many ecosystems that of Port Phillip Bay (Australia) shows spatial and temporal variability. As such, we have constructed a spatially structured dynamic model (the full model) to describe it. However, such complex models are very difficult to design and analyse. We have derived earlier a simple model of a semi-enclosed marine ecosystem, whose analytical solution has allowed the determination of the dependence of major variables and fluxes on model formulation and parameter values. Here we apply this simplified model to the analysis of responses to changes in nutrient loads and zooplankton mortality formulation (trophic closure). Output of the simple model compares well with output from the full model (averaged in space and time) at current and moderately elevated nutrient loads; but at highly elevated loads, there is a breakdown in the linkage between the predictions of the two models due to the role of spatial variation in moderating ecosystem responses. Observations obtained from Port Phillip Bay are then used to select the most realistic zooplankton mortality formulation of this bay. Observed chlorophyll concentration supports a quadratic over a linear zooplankton mortality model. Observation of phytoplankton size fractions indicate that in productive waters of the bay picophytoplankton are grazer controlled, while microphytoplankton escape grazer control; analytical solutions show how rather subtle differences in parameter values allow this to occur. This analysis tool allows the prediction of the effects of changes to model formulation, parameter values and external forcing on the full model. However, the simple model is not intended to be, or used as, a realistic model in itself; rather it is a design tool that has been used for the development of more detailed models.

A two-step methodology is presented for long-term eco-hydrodynamic simulation of a dendritic reservoir that can be subdivided into many interacting subsystems. This approach provides a balance between spatial resolution and simulation time extent. The first step aims at defining the exchange mass and water fluxes among basins. The second step is the eco-hydrodynamic modelling of the subsystems. This methodology is applied to Rapel reservoir, located in central Chile, which can be subdivided into three distinct basins. For this application, a 2D depth-averaged model is used to define exchange fluxes at the basin confluence, while a 1D, horizontally-averaged, vertically resolving model is used to simulate the hydrodynamics and biochemical behaviour of each basin. Dimensional analysis is introduced to analyse the water quality simulations and to determine whether internal processes or external loading are dominant and better explain the measured differences in phytoplankton biomass among the basins. The product of biomass growth rate and basin retention time is identified as an important dimensionless parameter describing the associated dynamics.

A two-dimensional model (2DLEAF) of leaf photosynthesis and transpiration has been developed that explicitly accounts for gas diffusion through the boundary layer and the intercellular space as well as for stomatal regulation. The model has been validated for tomato. It was used to study the effect of stomatal density on photosynthesis and transpiration rate. It has been demonstrated by varying stomatal density in the model that the stomatal density measured on tomato leaves provides the maximal photosynthesis rate for both 300 and 600 μl 1−1 [CO2]. The transpiration rate varied in direct proportion to stomatal density at all values of stomatal aperture, but transpiration efficiency (photosynthesis rate/transpiration rate) was higher at 600 μl 1−1 [CO2] with a normal stomatal density than at 300 μl 1−1 [CO2] with a stomatal density reduced 25%. Such calculations with 2DLEAF can be useful for analysis of contradicting data presented in publications on possible changes in stomatal density in a future high [CO2] atmosphere.

We developed a 3D ecosystem-biogeochemical model based on NEMURO (North Pacific Ecosystem Model Used for Regional Oceanography) and applied it to the western North Pacific in order to predict the effects of global warming on ecosystem dynamics and biogeochemical cycles. Using datasets of observed climatology and simulated fields according to a global warming scenario, IS92a (CO-AGCM developed by CCSR/NIES) as boundary conditions for our ecosystem model, we conducted present-day and global warming experiments and compared their results. Model results in the global warming experiment show increases in vertical stratification due to rising temperatures. As a result, the predicted nutrient and chlorophyll-a concentrations in the surface water decrease at the end of the 21st century, and the dominant phytoplankton group shifts from diatoms to other small phytoplankton. The P/B ratio slightly increases from that in the present as a result of favorable temperature conditions, although nutrient conditions become worse. The increase in the P/B ratio causes increases in the NPP and GPP, although new and export productions decrease. Increases in the regeneration rates (i.e., decrease in the e-ratio) also contribute to increases in NPP and GPP through nutrient supplies within the surface water. Changes in seasonal variations of biomass and the dominant phytoplankton group in the subarctic–subtropical transition region associated with the global warming are large in all regions. In the global warming scenario, the onset of the diatom spring bloom is predicted to take place 1.5 month earlier than in the present-day simulation due to strengthened stratification. The maximum biomass in the spring bloom is predicted to decrease drastically compared to the present due to the decreases in nutrient concentration. In contrast, the biomass maximum of the other small phytoplankton at the end of the diatom spring bloom is the same as the present, because they can adapt to the low nutrient conditions due to their small half-saturation constant. Therefore, a change in the dominant phytoplankton group appears notably at the end of spring bloom. Since the present nutrient concentrations and phytoplankton biomass from summer to winter are low compared with those in spring, these changes associated with the global warming are small. That is, it is interesting that the changes do not occur uniformly in all seasons, but occur dramatically at the end of the spring and in the fall bloom.

The function and dynamics of savanna ecosystems result from complex interactions and feedbacks between grasses and trees, involving numerous processes (i.e. competition for light, water and nutrients, fire, and herbivory). These interactions are characterised by strong relationships between vegetation structure and function. Given the heterogeneous structure of savannas, modelling appears as a convenient approach to study tree–grass interactions. Most current models that describe carbon and water fluxes are not spatially explicit, which restricts their ability to simulate plant interactions at small scales in heterogeneous ecosystems. We present here a new 3D process-based model called TREEGRASS. The model aims at predicting, in heterogeneous tree–grass systems, plant individual radiation, carbon and water fluxes at a local spatial scale. It is run at a daily time-step over periods ranging from one to a few years. The model includes (i) a 3D mechanistic submodel simulating radiation and energy (i.e. transpiration) budgets; (ii) a soil water balance submodel, and (iii) a physiologically based submodel of primary production and leaf area development. The ability of TREEGRASS to predict the seasonal courses of grass dead and leaf mass, soil water content and light regime as observed in the field has been tested for grassy and shrubby areas of Lamto savannas (Ivory Coast). Simulations showed that the spatial distribution of primary production can be strongly affected by the spatial vegetation structure. Potential applications involve predicting net primary production and water balance from the individual to the ecosystem and from the day to the annual vegetation cycle (e.g. effects of tree spatial patterns on carbon and water fluxes at the ecosystem level).

A 3D model of tree architecture is developed to simulate the photosynthesis of peach trees. The model uses a simple graphical procedure to compute the light interception and the corresponding photosynthesis. It allows to consider complex canopy arrangements, and is used to simulate the photosynthesis of laterals, trees and orchards. Results showed that the photosynthesis varied from 5 to 15 μmol m−2 s−1 between laterals of different architectures. The photosynthesis per unit leaf area was sensitive to the orientation of the lateral, its size (number of leaves, length, number of shoots), to the angle between the stem and the shoots, the distance between the leaves, and the angle between the leaf and the shoot. When the isolated lateral is placed in the context of a single tree, its photosynthesis per unit leaf area decreases by a factor of two due to the shadowing. For orchards, the photosynthesis per unit leaf area decreases as a function of the tree density. The photosynthesis per unit area of sunlit leaves at the lateral, tree or orchard levels, was found to be almost constant, because the leaf angle distribution of the illuminated leaves do not vary much. Therefore, one important result of this study is that the variation of photosynthesis per unit leaf area, is mainly determined by the fraction of sunlit leaf area.

It is an ongoing challenge to develop and demonstrate management practices that increase the sustainability of agricultural systems. Soil carbon and nitrogen dynamics directly affect soil quality, crop productivity and environmental impacts. Root systems are central to the acquisition of water and nutrients by plants, but are also a major pathway for the inputs of carbon and nutrients to soil. The complexity of both biotic and abiotic interactions, combined with stochastic changes in root architecture, makes it difficult to understand below-ground dynamics on the basis of experimentation alone. The integration of dynamic models of above-ground growth, three-dimensional root system demography, and interactions between plants and the environment, into one single model is a major challenge because of the complexity of the systems.

Combining process-based and three-dimensional (3D) structural models for specific crops to functional–structural plant models (FSPMs) enable ecophysiologists to investigate the interaction of single plants or plant stands with their biotic and abiotic environment in a unique way. The present study was part of a collaborative research program on the development of a FSPM for the sample plant (Hordeum vulgare L.). The emphasis of this paper is put on two main aspects. First, improved generic and flexible functions are formulated for modeling the shape of leaves and stems of graminaceous plants as organ-related triangulated surfaces, where the parameters may be directly interpreted in terms of morphological traits. The proposed functions constitute the structural model, which is amplified by topological information to a so-called architectural model. Second, we suggest a new approach to parameterize these functions based on 3D point cloud data obtained by digitization of entire plants. Since no automated technique is available to process 3D point clouds in a way appropriate for parameterization of the architectural model, the required algorithms are developed and implemented in Matlab®. Our approach comprises the following steps. First, the measured set of points is partitioned into subsets representing each organ. Each subset is then divided further to represent organ segments. Next, the centroid of each partial point cloud representing an organ segment is computed. The sequence of these centroid points describes the organ axis. By means of the architectural model for leaves and stems, triangulated surfaces are assembled from the computed organ axis points and from user-defined initial values for the various parameters in the model (e.g. maximum leaf width). Finally, the parameters in the functions describing leaf and stem surfaces are estimated by fitting computed triangulated surfaces into the related point cloud using least squares optimization. Hence, the proposed method allows the use of 3D point clouds obtained with modern 3D digitizing techniques for the parameterization of an organ-based architectural model.

During the past 10 years, soil scientists have started to use 3D Computed Tomography in order to gain a clearer understanding of the geometry of soil structure and its relationships with soil properties. We propose a geometric model for the 3D representation of pore space and a practical method for its computation. Our basic idea consists in representing pore space using a minimal set of maximal balls (Delaunay spheres) recovering the shape skeleton. In this representation, each ball could be considered as a maximal local cavity corresponding to the “intuitive” notion of a pore as described in the literature. The space segmentation induced by the network of balls (pores) was then used to spatialize biological dynamics. Organic matter and microbial decomposers were distributed within the balls (pores). A valuated graph representing the pore network, organic matter and distribution of micro-organisms was then defined. Microbial soil organic matter decomposition was simulated by updating this valuated graph. The method was implemented and tested using real CT images. The model produced realistic simulated results when compared with data in the literature in terms of the water retention curve and carbon mineralization. A decrease in water pressure decreased carbon mineralization, which is also in accordance with findings in the literature. From our results we showed that the influence of water pressure on decomposition is a function of organic matter distribution in the pore space. As far as we know, this is the approach to have linked pore space geometry and biological dynamics in a formal way. Our next goal will be to compare the model with experimental data of decomposition using different soil structures, and to define geometric typologies of pore space shape that can be attached to specific biological and dynamic properties.

This paper describes an application of MOHID modelling system to a shallow temperate coastal lagoon in Portugal's western coast (Ria de Aveiro), simulating more than one primary producer, for a better understanding of the existing ecological dynamics and creating a useful tool to delineate land activities management practices. MOHID water quality model is driven by a physical transport model and simulates the dynamics and productivity of the two main primary producers (phytoplankton and macroalgae) as well as the cycling of nitrogen, carbon and oxygen in interaction with sediment and hydrodynamics. The integrated model is forced by exchanges with the Atlantic Ocean (tide), atmosphere, and by sediment and nutrient inputs from the upstream rivers and other discharges. Focus is given to the light parameterization of primary production, influence of hydro and sediment dynamics and to the prediction of seaweed beds distribution. The results obtained show that the model is better adjusted to field data with macroalgae's simulation and that macroalgae can have an important role in primary production. Hydrodynamic conditions can be significant in the competition between the two primary producers, determining the predominant groups as well as their limiting factors.

A simulation model of perennial graminoid growth was developed that united morphometric traits with physiological processes: a shoot number submodel simulated vegetative production; a carbon submodel simulated assimilation and allocation; a nitrogen submodel simulated uptake and allocation. Growth of the coexisting shoot populations on a single plant were simulated simultaneously and growth was partitioned into four tissue types, based on morphometric measurements: blade, sheath, stem, and flower. Tissue was classified by age and canopy height, resulting in similar classifications of carbon and nitrogen. The processes of shoot growth, tillering, root growth, photosynthesis, nitrogen uptake, and translocation were interrelated through nitrogen/carbon ratios and plant reserve carbohydrate status.Simulation results indicated how morphology may influence ecological properties and interact with physiology to influence plant fitness. Simulated plant growth based upon the properties of Serengeti, East African graminoids suggested that an increased understanding of both primary production and plant adaptation could result from increased attention to the interactions among: (a) physiological processes; (b) demographic processes associated with populations of shoots on a single plant; and (c) morphometric traits that determine plant form.

Croatia is among those European countries without an Atlas of Flora produced till today as a result of constant lack of greater number of active botanists and inconsistency in gathering data in the field. Recently, a standard for collection of data, based on the Central European MTB (abbreviation of German term “Meßtischblätter” that stands for a sheet of topographic map) grid was proposed and tested in the field on the “Medvednica Nature Park” on Medvednica mountain near the city of Zagreb. Using the data collected in 97 MTB/64 quadrants (presence/absence of plant species), we tested the potential of estimating species occurrence at the proposed grid by models in a function of the Digital Elevation Model (DEM)-based variables, namely altitude, terrain slope, terrain aspect, and flow accumulation potential. Because of significant spatial variability of environmental factors within MTB/64 quadrants, each one was represented by descriptive statistics (median, 5-, 25-, 75- and 95-percentiles) of DEM-based variables. Thirty-seven plant species were selected arbitrarily, on the basis of their frequency in the studied area (40–60% of all quadrants). Three methods for development of predictive model were used and compared: discriminant analyses, logistic regression, and classification trees. Yielded results suggest that spatial modelling could be probably applied in flora mapping, which would optimise fieldwork. However, decreasing of mapping unit area is recommended, especially for rare species. For larger areas, inclusion of other environmental predictors (macroclimatic, lithological, landuse) in models is probably needed.

Based upon the contributions of the 8th ISEM conference on the state-of-the-art in ecological modelling in Kiel (Germany) recent general trends are discussed. The tendencies mentioned refer to theoretical and technical research as well as to environmental applications. Present changes in modelling philosophy have led to an estrangement from the mechanistic paradigm towards a holistic and dynamic approach combining different levels of integrations stressing the self-organization capacity of ecosystems. Due to these properties we have to accept an irreducible extent of uncertainties which characterize ecological developments. This limits model prognoses and requires particular management techniques to deal with unexpected situations. The potential of new modelling techniques to cope with these limitations are discussed. An intensified cooperation is demanded especially in the context of environmental application of models, which should be enforced by initiatives of scientists adressing decision makers as well as societies and human population.

SPUR (Simulation of Production and Utilization of Rangelands) is a physically-based model designed to simulate the complexity of rangeland ecosystems (Wight and Skiles, 1987). Results of extensive validation testing in Texas indicated a need to modify the model to improve submodel integration and procedural guidelines. A description of the modified model (SPUR-91) is provided. A sensitivity analysis was conducted, examining the influence of changes in model output corresponding to perturbations made to individual input parameters. The model was then extensively validated using a Texas data set composed of simultaneous measurements of hydrology, plant, livestock, and meteorological parameters.Results of validation testing of SPUR-91 confirmed that the model: (1) predicted initial soil water content within 3% of observed; (2) predicted evapotranspiration, even under very low cover conditions, within 1% of observed; (3) provided a good correlation of temporal fluctuation (R = 0.72) of observed herbaceous production, the observed 4-year mean live standing crop for the major individual species was predicted within 1–13%; (4) could produce a determinant-type growth curve to approximate the long-term response of shrubs and trees; and (5) responded to management (grazing, vegetation manipulation) in a manner consistent with observations. A discussion of why modifications to SPUR improved the performance of SPUR-91 is presented.

The catastrophic earthquake, 7.3 on the Richter scale, occurred on September 21, 1999. The 921 Earthquake was a terrifying disaster that caused numerous casualties in Central Taiwan. It is the severest earthquake in a recent hundred years. The land morphology and topography changed greatly with such features as land upheaval, river blockades and lakes dammed by debris in many locations. Severe disaster districts were found in the Jou-Jou Mountain landslide area in Nan-Tou County. A method was developed to assess the landslide characteristics and monitor the vegetation recovery at Jou-Jou Mountain. SPOT satellite imageries were used to analyze the Normalized Difference Vegetation Index (NDVI) derived from SPOT imagery before and after the earthquake for comparison. The vegetation recovery index (C) was proposed to calculate and evaluate the vegetation recovery rate. The results showed that the vegetation restoration rate has achieved 47.1% in natural plant succession one year after the earthquake. The poor and very poor locations were distributed mainly in mountain ridge, scoured slope base and acidic sulfate soil areas. Mountain ridges and acidic sulfate soil had lower recovery rates affected by the impacts of soil moisture and SO42−. Scoured slope bases next to the concave banks might need foundation engineering first to establish a stable habitat for plants.

Chamber method is commonly used to measure the CO2 exchange from plant communities. Due to low time resolution, actual measurements reflect only momentary CO2 exchange rates. Therefore, a common way to derive seasonal or annual estimates is to establish models describing the response of CO2 exchange to environmental variables, and then to reconstruct the CO2 exchange over the desired time period. There are several alternative ways to obtain the CO2 balance for the entire mire: models can be parameterized by individual sample plots, plant communities or the entire site. Similarly, the CO2 balance can be reconstructed by plots, plant communities or the entire site. We tested how the choice of the modelling and reconstruction approach influences the CO2 exchange estimates for the entire mire and for individual sample plots and plant communities. We measured the CO2 exchange in a spatially heterogeneous sedge-dominated northern aapa mire for two growing seasons. We observed high spatial variation in CO2 balance between the plant communities. We noticed that when the CO2 balances of individual sample plots or plant communities are of interest, using a model appropriate for the entire site may result in biased estimates. In worst case the different modelling approaches may turn the CO2 balance of an individual sample plot from positive to negative. Further, while using the whole ecosystem approach in modelling, the superior ability of chamber method in acknowledging spatial variation is lost. While the modelled growing season CO2 balance of the mire ranged from 232 to 625 g CO2 m−2 depending on the chosen modelling and reconstruction approach, the average estimates still remained within the uncertainty range of one another. Acknowledgement of the spatial variation in plant community level makes the areal estimate more robust to varying weather conditions. Further, the reliability of estimates is improved by explicit formulation of the choices behind the modelling and reconstruction units reflecting the study objectives.

In the past 35 years, various kinds of dynamic models have been used to study vegetation development during primary or secondary succession. Typically, one specific model or models with the same conceptual background were employed. It remains largely unknown to what extent such model-based findings, e.g., on the speed of succession, depend on the specific model approach.To address this issue, we estimated the time elapsing during secondary succession in subalpine conifer forests of the Swiss National Park using three models of different conceptual background: (i) a forest gap model, (ii) a Markov chain model, and (iii) a minimum spanning tree model.Starting from a 95- to 125-year-old mountain pine (Pinus montana Miller) forest, all three models predicted a similar successional development. Even though the forest gap model and the Markov chain model are based on totally different approaches and were calibrated using different data sets, they both forecasted that it would take 500–550 years to reach a late-successional forest stage. The minimum spanning tree model, which only reveals a certain number of time steps yielding a minimum time estimate, showed a development of tree density (stems/ha) that was similar to the results of the forest gap model, but a strict quantitative comparison is not feasible.Our study shows that modeling forest development using three different approaches is quite powerful to obtain a robust estimate of the speed of forest succession. In our case, this estimate is higher than what has been suggested in previous studies that investigated secondary forest succession. The use of several approaches allows for a more comprehensive analysis in terms of variables covered (e.g., relative forest cover in the Markov approach vs. stand-scale species composition in the forest gap model). We recommend that in studies focusing on the speed of succession, several models should be employed simultaneously to identify inconsistencies in our knowledge and to increase confidence in the results.

In Italy quarrying causes relevant environmental damages and alterations to the land and the ecosystems. Despite the present Italian legislation requiring the restoration of the sites after exploitation, most of the quarries, both the abandoned and the still operational ones, are not restored.The objective of this work is to indicate a monitoring methodology in order to survey the present state of the quarry sites and their evolution in time, which are the basic data needed to implement an adequate land reclamation project.Such methodology has been applied to several abandoned limestone quarries in the Latina province (close to Rome), characterised by a typical Mediterranean vegetation, but it can be applied to any other kind of litology and vegetation.The land monitoring has been realised both by using remote sensing techniques, supported by a Geographic Information System of the studied area, and by in situ surveying. The in situ surveying was able to assess the capability of the remote sensing model to describe the state of each site.

The aim of the present work was to propose a model for the estimation of the endoparasitic load using morphological descriptors easily accessible without killing the animal i.e. non-destructive method. The study was conducted using plerocercoid forms of Ligula intestinalis in its second intermediate host, the roach (Rutilus rutilus). The Kohonen Self-Organizing Map (non-supervised neural network) made it possible to present the complex data matrix in a two-dimensional space, with individual clusters visualised by the U-matrix method. The six main descriptors were selected and used to build the predictive model, four lateral and two thickness measures. The generalisation ability of the backpropagation algorithm (supervised neural network) is confirmed by a determination coefficient higher than 0.90 between observed and predicted values. The study for the first partial derivatives of the parasitic load with respect to the six morphological variables is used to identify the factors influencing the parasitic load and the mode of action of each factor.

Although ungulate herbivory influences forest dynamics over a variety of spatial and temporal scales, relatively few models have been developed for investigating browsing effects on tree regeneration processes. We describe a new, mechanistic model (HUNGER) that modifies a well-established mathematical formulation for plant nutrient transport and conversion processes to simulate sapling response to ungulate browsing and light availability. The HUNGER model simulates primary production, height and diameter growth, dry matter allocation, and population dynamics of tree saplings at the scale of small (e.g. 0.001 ha) regeneration patches.The model was applied to Picea abies saplings in mountain forests of eastern Switzerland after calibration based on data for sapling height growth, radial growth, and biomass components under varying light conditions. Independent data were used to test the ability of the model to represent sapling responses to browsing. The model slightly over-predicted sapling height, while no significant differences were found between simulated and observed basal diameter, total biomass or leaf biomass. Model experiments were conducted to explore the interactive effects of winter browsing intensity and relative light availability upon sapling net growth. Simulated shading effects were gradual until approximately 40% relative light availability (if browsing pressure was low) or 60% relative light availability (if browsing pressure was high). Below these values, the model simulates sharp declines in net growth rate. Model results suggest nonlinear responses to browsing and light availability, and the existence of light intensity thresholds for forest regeneration that should be relevant for management activities affecting deer density and crown cover.

The spatial pattern and the patch structure of trees reflect small-scale disturbance regimes such as gap formation by single tree-falls; therefore, when gap parameters such as frequency and intensity are changing along an environmental gradient, spatial patterns should also be changing. This paper develops a point process model that can illustrate continuous changes in patch structure along a gradient and quantitatively estimate the gap parameters. The new model is a combination of the Neyman–Scott process and the inhomogeneous Poisson process. Its second-order moment can be approximately reduced to a function of two variables—i.e. the gradient and the spatial scale—and therefore can be visualized graphically for descriptive purposes as well as for constructing models, optimising parameters and checking model fit. The methodology is applied to an Abies sachalinensis population in a coniferous broad-leaved mixed forest on a slope in the boreal region of northern Japan. The results quantified the patch structure as being more frequent, denser and smaller with elevation, reflecting strong ocean winds that resulted in frequent disturbance in the more elevated areas.

Current threats of invasive species have significant implications for ecological systems. Given their potential impacts, invasive species have been the subject of extensive empirical and theoretical studies. However, these studies have tended to focus on species that produce highly visible ecological and economic impacts. In our study, we take a step back from focusing on these high-impact invasive species, and examine the general colonization (invasion) process of exotic species that have various “competitive abilities” against the native species. Using a two-species cellular automaton model, we demonstrate that: (1) a threshold level of competitive ability is required for the exotic species to successfully establish in a new landscape and (2) an exotic species with superior competitive ability does not necessarily become dominant in a landscape (alternatively, a species that has inferior competitive ability may successfully colonize a new system). Our findings have significant implications for the study of species invasions and also provide clues to how species assemble in ecological communities.