A revised calculation of the econometric factors α- and β for the Extended Exergy Accounting method

Extended Exergy Accounting (“EEA”) is a method to compute the space- and time integral of the primary exergy required to produce a good or a service: the extended exergy of a commodity measures its “embodied exergy”, including externalities (Labour, Capital and Environmental Costa). A crucial point of the method is the calculation of two econometric coefficients, commonly referred to as “α” and “β”,used to calculate the extended exergy equivalents of Labour and Capital respectively. In previous applications of the EEA method, these coefficients have been assigned approximate values estimated on the basis of global system considerations. In this paper, a novel procedure is described that leads to the calculation of “exact” values of both econometric coefficients, based on detailed exergy- and monetary balances of the Society to which the EEA is applied. It is shown that both α and β depend in a non-trivial way from the consumption patterns, the technological level and the life- and socio-economic standards of each Country. It is also shown that the values are substantially different for developed (OECD) and underdeveloped Countries, and representative samples of values are calculated and critically analysed. On the basis of these new model coefficients, the specific exergy equivalents of Labour (ee_L) and of Capital (ee_K) are calculated, and shown to differ from the values used in previous EEA calculations.     

Identification of important factors for water vapor flux and CO2 exchange in a cropland

Water vapor flux and carbon dioxide (CO₂) exchange in croplands are crucial to water and carbon cycle research as well as to global warming evaluation. In this study, a standard three-layer feed-forward back propagation neural network technique associated with the Bayesian technique of automatic relevance determination (ARD) was employed to investigate water vapor and CO₂ exchange between the canopy of summer maize and atmosphere in responses to variations of environmental and physiological factors. These factors, namely the photosynthetically active radiation (PAR), air temperature (T), vapor pressure deficient (VPD), leaf-area index (LAI), soil water content in root zone (W), and friction velocity (U*), were used as inputs in neural network analysis. Results showed that PAR, VPD, T and LAI were the primary factors regulating both water vapor and CO₂ fluxes with VPD and W more critical to water vapor flux and PAR and T more crucial to CO₂ exchange. Furthermore, two time variables “day of the year (DOY)” and “time of the day (TOD)” could also improve the simulation results of neural network analysis. The important factors identified by the neural network technique used in this study were in the order of PAR > T > VPD > LAI > U* > TOD for water vapor flux and in the order of VPD > W > LAI > T > PAR > DOY for CO₂ exchange. This study suggests that neural network technique associated with ARD could be a useful tool for identifying important factors regulating water vapor and CO₂ fluxes in terrestrial ecosystem.     

Dissolved organic carbon concentrations and fluxes in forest catchments and streams: DOC-3 model

Dissolved organic carbon (DOC) concentrations in south-western Nova Scotia streams, sampled at weekly to biweekly intervals, varied across streams from about 3 to 40 mg L⁻¹, being highest mid-summer to fall, and lowest during winter to spring. A 3-parameter model (DOC-3) was proposed to project daily stream DOC concentrations and fluxes from modelled estimates for daily soil temperature and moisture, year-round, and in relation to basin size and wetness. The parameters of this model refer to (i) a basin-specific DOC release parameter “k_DOC^”, related to the wet- and open-water area percentages per basin, (ii) the lag time “τ” between DOC production and subsequent stream DOC emergence, related to the catchment area above the stream sampling location; and (iii) the activation energy “Ea”, to deal with the temperature effect on DOC production. This model was calibrated with the 1988-2006 DOC concentration data from three streams (Pine Marten, Moosepit Brook, and the Mersey River sampled at or near Kejimkujik National Park, or KNP), and was used to interpret the biweekly 1999-2003 DOC concentrations data (stream, ground and lake water, soil lysimeters) of the Pockwock-Bowater Watershed Project near Halifax, Nova Scotia. The data and the model revealed that the DOC concentrations within the streams were not correlated to the DOC concentrations within the soil- and groundwater, but were predictable based on (i) the hydrologically inferred weather-induced changes in soil moisture and temperature next to each stream, and (ii) the topographically inferred basin area and wet- and open-water area percentages associated with each stream (R² = 0.53; RMSE = 3.5 mg L⁻¹). Model-predicted fluxes accounted 74% of the hydrometrically determined DOC exports at KNP.     

Different proxies for the reactivity of aquatic sediments towards oxygen: A model assessment

Information on benthic carbon mineralization rates is often derived from the analysis of oxygen microprofiles in sediments. To enable a direct comparison of different sediment environments, it is often desirable to characterize sediments by a single proxy that expresses their “reactivity” towards oxygen. For this, there are three commonly used proxies: the oxygen penetration depth (OPD), the oxygen flux at the sediment-water interface (DOU), and the maximum volumetric oxygen consumption rate (R_max). The OPD can be directly determined from the oxygen depth profile, while the DOU is usually obtained by a linear fit to the oxygen gradient either in diffusive boundary layer. The oxygen consumption rate R_max requires the fitting of a reactive-transport model to the data profile. This article shows that the OPD alone is a suboptimal proxy, because it shows a strong dependence on the half-saturation constant K_s, and secondly, because it is sensitive to the particular re-oxidation conditions right above the oxic-anoxic interface. Similarly, the volumetric oxygen consumption rate R_max is rather strongly dependent on the kinetic model formulation employed. To show this we fitted three different (Bouldin, Blackman and Monod) kinetics to the same oxygen data profiles. When fitting these models, the R_max values obtained differed by 20% for exactly the same oxygen profile. Accordingly, if one reports R_max values, it is crucial to specify the kinetic model alongside. Overall, DOU emerges as sediment reactivity proxy which is the least model dependent.     

Establishment patterns in a secondary tree line ecotone

On semi-open pre-alpine fen pastures Alder encroachment creates a dynamic mosaic of grassland and woodland, which is rich in ecotones from fen to Carr. The structural diversity in colonisation patterns of Alder on fens suggests a dependency on multiple environmental drivers. Unidirectional progressive ecotone development provides an opportunity to address a current deficit in understanding successional patterns, i.e. process-pattern relationships in a multiple factor regime.We developed an individual-based model of Alder establishment on fen grassland to investigate the dependency of encroachment patterns upon seed production, dispersal distances and safe site availability. The purpose of the model is to provide a causal understanding of establishment patterns of Alder. In the model, all life processes of Alder individuals were parameterised with field data. This allowed us to strictly perform bottom-up simulations and successfully check plausibility by comparing simulated establishment patterns of cohorts with observed ecotone structures.Simulation results show that establishment patterns strongly depend on environmental drivers. Spatial progression of Alder encroachment and width of ecotones, respectively, mainly depend on wind speed during seed dispersal. Dense establishment of Alder leading to community change from fen grassland to Carr, requires windows of opportunity, which are defined by the rare coincidence of widespread dispersal, high seed production and favorable establishment conditions. Life-history traits of Alder (mast year cycle, high seed weight, weak establishment in fen) spatially and temporarily constrain the encroachment process. The structural diversity of long-term encroachment patterns is explained by the event-driven character of encroachment.Modelling individual establishment pathways of seedlings starting from germination revealed an endogenous stochasticity in establishment patterns emerging from low seed densities in the tail of the dispersal function. We conclude an inherent stochastic structure of dispersal-limited tree line ecotones, which limits reconstruction of processes from patterns.In order to describe long-term successional patterns of Alder encroachment at landscape scale, we propose the combination of two concepts: deterministic “patch-movement” of Alder woodland driven by continuous ecotone migration together with rare and stochastic “infiltration” of single Alder trees into open fen grasslands. Conservation management can control predictable “patch-movement” by cutting off maturing saplings around existing Alder woods. But the preservation of the actual large proportion of open grassland in fen pastures from infiltrating Alder seedlings and from the subsequent shift of the pasture to a densely wooded state would require mowing additionally to extensive grazing.     

Allometric scaling of resource acquisition by ruminants in dynamic and heterogeneous environments

We present a mechanistic formulation of the intake response of ruminants to vegetation biomass based solely on physiological and morphological parameters that scale allometrically with the animal's body mass. The model is applied to describe herbivore-vegetation interactions in dynamic and heterogeneous landscapes with low quality but abundant “tall grass” and high quality but sparsely available “short grass”, under two conditions: “uncoupled” (such that the effect of food intake on vegetation biomass can be neglected), or “coupled” (such that the vegetation biomass is determined by herbivore feeding). The results show that under uncoupled conditions, the minimum acceptance (proportion of vegetation consumed by the herbivore) at which the herbivore can leave its current patch without reducing its intake rate is when it has depleted the current patch by the energetic cost required to travel to another patch. The maximum acceptance at which the herbivore should leave its patch is when it has depleted the current patch by the cumulative energetic cost of traveling, handling, cropping, and digesting. Under coupled conditions, the optimal acceptance equals half the relative growth rate of the vegetation. Analytical solutions are obtained for equilibrium values for utilization of the vegetation, and for the densities of vegetation and ruminants, expressed in physiological and morphological herbivore parameters.     

A methodological approach to develop “contaminant migration–population effects” models

The main aim of the present work is to discuss the methodological approaches that underpin the “contaminant migration–population effects” models for the evaluation of the detriment to populations of moving organisms in environmental systems with spatial and time dependent pollution levels. A technique to couple the equations controlling the population dynamics and the pollutant dispersion is described and discussed. The domain of application and the limitations of the methodology are analysed and illustrated by some examples. Possible alternative approaches are briefly presented.     

Dynamic compartment approach for modelling regimes of carbon cycle functioning in bog ecosystems

Svirezhev's method of dynamic model design by a given “storage-flow” diagram [Svirezhev Y.M., 1997. On some general properties of trophic networks. Ecol. Model. 99, 7–17] is developed and used for investigating dynamic regimes of carbon cycle functioning in a typical boreal transitional bog ecosystem. Ecosystems are often represented by static “storage-flow” diagrams reflecting their structure and matter or energy transfer between components at fixed time moments. Using the data of such diagrams aggregated in ecological field studies one can construct a dynamic model of the ecosystem to predict its future behaviour and to estimate a response to external perturbations—natural and human. Stability of both current equilibrium and possible alternative steady states and more complicated attractors are studied under two types of parameter perturbation: CO₂ atmospheric concentration increase initiated by greenhouse effect, and change in the rate of carbon output from dead organic matter and litter which depends on the water table level and possible peat excavation. Calculation of bifurcation curves gives areas in the parameter space where stable functioning of carbon cycle is provided. Steady states can be interpreted as raised bog, meadow, forest and fen. CO₂ concentration increase leads the current state of transitional bog to loose stability with appearance of oscillatory dynamics and further evolution to the chaotic attractor. The model is rich by chaotic solutions serving as transition regimes between regular steady and periodic attractors. Another chaotic regime is formed from forest equilibrium and exists in the same area of phase space where current equilibrium is stable.     

Evaluation of biological water purification functions of inland lakes using an aquatic ecosystem model

An effective measure to cope with eutrophication of lakes is to remove nutrients that can cause algal blooming by taking advantage of natural water purification processes. Here the term “purification” is defined, in a wide sense, as the potential role of a water body to contribute to the reduction of pollutants and thus controlling eutrophication. Also regarded as a kind of ecological regulating services, biological purification involves various processes concerning seasonal nutrient fixation, such as uptake by aquatic macrophytes, biofouling onto foliage substrates, feeding by organisms in higher trophic level, and eternal loss or removal of substance from the water. In order to evaluate the water purification ability, a numerical lake ecosystem model highlighting the role of macrophyte colonies in the shore zone was developed and applied to Lakes Suwa, Kasumi and Biwa, as well as five small lakes attached to Lake Biwa.     

Analysis of annual fluctuations of C. nodosa in the Venice lagoon: Modeling approach

A simple simulation model was developed to describe the growth trends of Cymodocea nodosa (Ucria) Ascherson based on data sets from the Venice lagoon. The model reproduces the seasonal fluctuations in the above and belowground biomass and in shoot density. The modeling results are in good agreement with data on net production, growth rates and chemical–physical parameters of water. It was assumed that light and temperature are the most important factors controlling C. nodosa development, and that the growth was not limited by nutrient availability. The aim was to simulate biomass production as a function of external forcing variables (light, water temperature) and internal control (plant density). A series of simulation experiments were performed with the basic model showing that among the most important phenomena affecting C. nodosa growth are: (1) inhibition of production and recruitment of new shoots by high temperature and (2) light attenuation due to seasonal fluctuation.     

Application of an evolutionary algorithm to the inverse parameter estimation of an individual-based model

Inverse parameter estimation of individual-based models (IBMs) is a research area which is still in its infancy, in a context where conventional statistical methods are not well suited to confront this type of models with data. In this paper, we propose an original evolutionary algorithm which is designed for the calibration of complex IBMs, i.e. characterized by high stochasticity, parameter uncertainty and numerous non-linear interactions between parameters and model output. Our algorithm corresponds to a variant of the population-based incremental learning (PBIL) genetic algorithm, with a specific “optimal individual” operator. The method is presented in detail and applied to the individual-based model OSMOSE. The performance of the algorithm is evaluated and estimated parameters are compared with an independent manual calibration. The results show that automated and convergent methods for inverse parameter estimation are a significant improvement to existing ad hoc methods for the calibration of IBMs.     

Spatial memory, habitat auto-facilitation and the emergence of fractal home range patterns

Animals interact with their habitat in a manner which involves both negative and positive feedback mechanisms. We apply a specific modeling approach, “multi-scaled random walk”, for the scenario where a spatially explicit positive feedback process emerges from a combination of a spatial memory-dependent tendency to return to familiar patches and a consequently objective or subjective improvement of the quality of these patches (habitat auto-facilitation). In addition to the potential for local resource improvement from physically altering a patch, primarily known from the ecology of grazing ungulates, auto-facilitation from site fidelity may also embed more subtle subjective, individual-specific advantages from patch familiarity. Under the condition of resource superabundance, fitness gain from intra-home range patch fidelity creates a self-reinforcing use of the preferred patches on expense of a broader foraging in a priori equally favorable patches. Through this process, our simulations show that a spatially fractal dispersion of accumulated locations of the individual will emerge under the given model assumptions. Based on a conjecture that intra-home range patch fidelity depends on spatial memory we apply the multi-scaled random walk model to construct a spatially explicit habitat suitability parameter H_ij, which quantifies the dispersion of the generally most constraining resource from the individual's perspective. An intra-home range set of observed H-scores, H_obs, can then be estimated from a simple 2-scale calculation that is derived from the local dispersion of fixes. We show how the spatially explicit habitat utilization index H_obs not necessarily correlates positively with the local density fluctuations of fixes. The H-index solves some well-known problems from using the pattern of local densities of telemetry fixes - the classic utilization distribution - as a proxy variable for relative intra-home range habitat quality and resource selection. A pilot study on a set of telemetry fixes collected from a herd of free-ranging domestic sheep with overlapping summer home ranges illustrates how the H-index may be estimated and interpreted as a first-level approach towards a more extensive analysis of intra-home range habitat resource availability and patch preferences. Spatial memory in combination with site fidelity requires a modeling framework that explicitly describes the property of positive feedback mechanism under auto-facilitation in a spatio-temporally explicit manner.     

Foliage profiles of individual trees determine competition,self-thinning,biomass and NPP of a Cryptomeria japonica forest stand: A simulation study based on a stand-scale process-based forest model

A simulation study was carried out to investigate simultaneously the effects of eco-physiological parameters on competitive asymmetry, self-thinning, stand biomass and NPP in a temperate forest using an atmosphere–vegetation dynamics interactive model (MINoSGI). In this study, we selected three eco-physiological relevant parameters as foliage profiles (i.e. vertical distribution of leaf area density) of individual trees (distribution pattern is described by the parameter η), biomass allocation pattern in individual tree growth (χ) and the maximum carboxylation velocity (V_max). The position of the maximal leaf area density shifts upward in the canopy with increasing η. For scenarios with η < 4 (foliage concentrated in the lowest canopy layer) or η > 12 (foliage concentrated in the uppermost canopy layer), a low degree of competitive asymmetry was produced. These scenarios resulted in the survival of subordinate trees due to a brighter lower canopy environment when η < 4 or the generation of spatially separated foliage profiles between dominant and subordinate trees when η > 12. In contrast, competition between trees was most asymmetric when 4 ≤ η ≤ 12 (vertically widespread foliage profile in the canopy), especially when η = 8. In such cases, vertically widespread foliage of dominant trees lowered the opportunity of light acquisition for subordinate trees and reduced their carbon gain. The resulting reduction in carbon gain of subordinate trees yielded a higher degree of competitive asymmetry and ultimately higher mortality of subordinate trees. It was also shown that 4 ≤ η ≤ 12 generated higher self-thinning speed, smaller accumulated NPP, litter-fall and potential stand biomass as compared with the scenarios with η < 4 or η > 12. In contrast, our simulation revealed small effects of χ or V_max on the above-mentioned variables as compared with those of η. In particular, it is notable that greater V_max would not produce greater potential stand biomass and accumulated NPP although it has been thought that physiological parameters relevant to photosynthesis such as V_max influence dynamic changes in forest stand biomass and NPP (e.g. the greater the V_max, the greater the NPP). Overall, it is suggested that foliage profiles rather than biomass allocation or maximum carboxylation velocity greatly govern forest dynamics, stand biomass, NPP and litter-fall.     

Ecological and biological features of a mesopelagic ostracod,Conchoecia pseudodiscophora,in the Japan Sea

The abundance and vertical distribution pattern of a halocyprid ostracod,Conchoecia pseudodiscophora, were investigated in the Japan Sea in 1985, 1987 and 1989. Vertical sampling from 500 m depth to the surface in the water around Yamato Rise revealed that this ostracod was second in dominance by number and third to fourth by biomass of the total zooplankton collected with a 0.35 mm mesh Norpac net. Horizontal net tows in Toyama Bay indicated that the major population ofC. pseudodiscophora was distributed below 250 to 300 m depth. No diel migration pattern was evident. Its contribution to total zooplankton there was 5 to 10% or more in terms of biomass. A total of five subadult instars (II to VI) and adult males and females were identified from instar analysis based on sizes and morphological characteristics of specimens collected with 0.10 mm mesh Norpac nets. Data on body length, wet weight and dry weight of each instar are presented. Carbon content of 35 to 48% of dry weight, and nitrogen content of 5.3 to 7.3% of dry weight, were recorded on fresh, freeze-dried specimens of selected instars (subadult Instars IV to VI, adult females). Water and ash contents of mixed specimens of these four instars were 76% of wet weight and 25% of dry weight, respectively. Feasibility of laboratory maintenance ofC. pseudodiscophora was tested, and it produced characteristic J shaped faecal pellets. Oxygen consumption rates of subadult instars V and VI, and adult female ranged 0.011 to 0.021µl O₂ ind.^–1 h^–1 at 1 °C, or 2.9 to 6.1µl O₂ (mg body N)^–0.85 h^–1 in terms of Adjusted Metabolic Rate (AMR_{o 2}). There was no appreciable metabolic reduction inC. pseudodiscophora compared to other ostracods, despite their mesopelagic life mode. Subdominance in total zooplankton and nonreduced metabolic activity ofC. pseudodiscophora suggest that this species may be an important link in mesopelagic energy-flow and matter cycling in the Japan Sea.     

Development and validation of an individual based Daphnia magna population model: The influence of crowding on population dynamics

An individual-based model was developed to predict the population dynamics of Daphnia magna at laboratory conditions from individual life-history traits observed in experiments with different feeding conditions. Within the model, each daphnid passes its individual life cycle including feeding on algae, aging, growing, developing and – when maturity is reached – reproducing. The modelled life cycle is driven by the amount of ingested algae and the density of the Daphnia population. At low algae densities the population dynamics is mainly driven by food supply, when the densities of algae are high, the limiting factor is “crowding” (a density-dependent mechanism due to chemical substances released by the organisms or physical contact, but independent of food competition).     

Effects of feeding and light intensity on the response of the coral Porites rus to ocean acidification

Recently, it has been suggested that there are conditions under which some coral species appear to be resistant to the effects of ocean acidification. To test if such resistance can be explained by environmental factors such as light and food availability, the present study investigated the effect of 3 feeding regimes crossed with 2 light levels on the response of the coral Porites rus to 2 levels of pCO₂ at 28 °C. After 1, 2, and 3 weeks of incubation under experimental conditions, none of the factors—including pCO₂—significantly affected area-normalized calcification and biomass-normalized calcification. Biomass also was unaffected during the first 2 weeks, but after 3 weeks, corals that were fed had more biomass per unit area than starved corals. These results suggest that P. rus is resistant to short-term exposure to high pCO₂, regardless of food availability and light intensity. P. rus might therefore represent a model system for exploring the genetic basis of tolerance to OA.     

Principle of the worst scenario in the modelling past and future of biosphere dynamics

The “biosphere–climate” system is subjected to different influences (influx of anthropogenic CO₂ and pollutants, deforestation, harmful land management, biological species depopulation, etc.). Therefore, the vital question arises: “Can these influences lead to irreversible negative changes in the climate–biosphere system or a global ecological catastrophe?” The possibility of irreversible changes may be not very high, but one cannot ignore it. So the main aim of our investigation is to evaluate possible consequences of human impact on the biosphere focusing on irreversible changes of it.     

Ontic openness: An absolute necessity for all developmental processes

The physicist Walter M. Elsasser is mostly known for his work on the Earth's magnetism. Less attention has been paid to his efforts toward identifying what are the real differences between physical and biological systems. One essential distinction he recognized was that physical systems are largely homogenous while biological systems always revealed what he called ordered heterogeneity. Calculation of the possible configurations of such heterogeneous systems almost always leads to combinatorial explosions and to what Elsasser referred to as immense numbers. Such calculations have the consequence that any such systems are necessarily unique - mathematically speaking they represent one-sets.Another consequence is that immense numbers automatically introduce enormous uncertainty and indeterminacy into the system. Such systems are said to be ontically open. Applying this perspective to the genome and employing the notion of informational entropy reveals a common drive behind all development. This means that both conventional Darwinian evolution as well as the genomic mistakes that are believed to lie behind processes like aging and diseases can be interpreted against the background of one and the same process.At the same time the approach demonstrates how Darwinian evolution encompasses other notions such as Kauffman's “adjacent possible” ( [Kauffman, 1995] and [Kauffman, 2000]) and Eldrege's and Gould's “evolution via punctuated equilibria” (e.g., [Eldredge and Gould, 1972] and [Gould and Eldredge, 1977]).     

Relationships between simulated water stress and mortality and growth rates in underplanted Toona ciliata Roem. in subtropical Argentinean plantations

Toona ciliata Roem. (Australian red cedar) requires a nurse-tree overstory to prevent damage from drought and irradiation in some regions of north-eastern Argentina. T. ciliata was planted in the understory of Pinus taeda L. (625 stems/ha), Pinus elliottii Engelm. × Pinus caribaea Morelet (625 stems/ha), and Grevillea robusta A. Cunn. (833 stems/ha) nurse trees, which were thinned to 0, 25, 50, 75 and 100% of the initial densities. We measured initial T. ciliata mortality and growth as well as Leaf Area Index (LAI) based on light transmission. T. ciliata soil water availability and its effect on early growth and mortality were examined by modelling drought stress using the two-dimensional forest hydrology model ForWaDy. Simulated patterns in T. ciliata water stress for the different overstory treatments were consistent with observed patterns of mortality. Early mortality was lowest with a G. robusta overstory, with corresponding lowest drought stress values and high modelled soil water contents in the top soil layer in intermediate and high overstory densities. Mortality was highest with a P. elliottii × P. caribaea overstory in treatments with the highest modelled drought stress values in the most open treatments. The model supported our field observations by indicating that water stress was an important limitation to T. ciliata survival and growth on our study sites. The linkage between T. ciliata establishment success, early growth and soil water availability as indicated by ForWaDy, leads us to conclude that the model is a suitable stand management tool for guiding establishment of T. ciliata plantations.     

Losers in the ‘Rock-Paper-Scissors’ game: The role of non-hierarchical competition and chaos as biodiversity sustaining agents in aquatic systems

Processes occurring within small areas (patch-scale) that influence species richness and spatial heterogeneity of larger areas (landscape-scale) have long been an interest of ecologists. This research focused on the role of patch-scale deterministic chaos arising in phytoplankton assemblages characteristic of “Rock-Paper-Scissors” population dynamics (i.e., competitively non-hierarchical). We employed a simple 2-patch model configuration with lateral mixing and through-flow, and tested the robustness of species richness at the scale of the landscape and spatial heterogeneity. Three different assemblages were used that in a dimensionless box model configuration exhibited chaotic behavior. Our results showed that when a spatial dimension was added to the model configuration, and when all species were shared between patches (i.e., no invading populations), chaos-induced species richness and spatial heterogeneity were quickly reduced with the onset of mixing. While assemblages in each patch were comprised of exactly the same species, they differed in their proportional population densities due to differing stages of succession and the incidence of alternative assemblage structures. Even at very low mixing rates (0.001 d⁻¹), which produced low passive migration rates (0.1% of the total biomass per day), the incidence of high richness and heterogeneity decreased by ∼80%. Interestingly, this sensitivity was not the same for the three assemblages tested. Declines in species richness and spatial heterogeneity associated with mixing were greater in assemblages comprised of competitively dissimilar species (based on the area occupied in the resource-tradeoff space defined by the R* model). The underlying mechanisms may involve the degree to which nutrient dynamics are altered with the arrival of immigrants. Our findings suggest that in partially to well-mixed aquatic systems, the roles of patch-scale non-hierarchical competition and chaos as factors maintaining species richness and spatial heterogeneity may be limited. However, in aquatic systems that experience periods of very low mixing, or even disconnection, non-hierarchical competition and chaos might indeed contribute significantly to biodiversity.