Large scale parameter study of an individual-based model of clonal plant with volunteer computing

Understanding clonal strategies (i.e. the ability of plants to reproduce vegetatively) is particularly important to explain species persistence. A clonal individual may be considered as a network of interconnected ramets that colonizes space. Resources in this network can be shared and/or stored. We developed an individual-based model (IBM) to simulate the growth of an individual clonal plant. Typically a realistic IBM requires a large set of parameters to adequately represent the complexity of the clonal plant growth. Simulations in the literature are often limited to small subsets of the parameter space and are guided by the a priori knowledge and with heuristic aims of the researcher. The aim of this paper was to demonstrate the benefit of volunteer computing in computational ecology to systematically browse the parameter space and analyze the simulation results in order to draw rigorous conclusions. To be specific, we simulated clonal plant growth using nine growth rules related to the metabolic process, plant architecture, resource sharing and storage and nineteen input parameters. We chose 2-4 values per input parameter which corresponded to 20 millions of combinations tested through volunteer computing. We used three criteria to evaluate plant performance: plant total resource, ramet production and maximum length of one branch. The 1% top-performing plants were sorted according to these criteria. Plant total resource and ramet production were correlated while considering the top-performing plants. The maximum length of one branch was independent from the other two performance traits. We detected two processes promoting at least one of the plant performance traits: (i) a relatively high metabolic gain (high photosynthetic activity and low production cost for new growth units), a low resource storage and long integration distance for resource sharing; (ii) short spacer lengths and the predominance of elongation of existing branches over branching. Interactive effects between parameter values were demonstrated for more than half of the input parameters. Best performance was reached for plants with slightly different combinations of values for these parameters (i.e. different strategies) rather than a single one (i.e. unique strategy). This modeling approach with volunteer computing enabled us to proceed to large-scale virtual experiments which provided a new quality of insight into ecological processes linked with clonal plant growth.     

Environmental variability and allocation trade-offs maintain species diversity in a process-based model of succulent plant communities

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

Development and test of a crop growth model for application within a Global Change decision support system

When examining potential impacts of Global Change on water resources on the regional scale, spatial and temporal changes in crop water and nitrogen demand are of fundamental significance. State-of-the-art crop growth models are powerful tools to assess the response of crops to altered environmental conditions and cultivation practices. In this paper, the process-based, object-oriented and generic DANUBIA crop growth model is presented. To evaluate the performance of the model, a validation analysis is carried out by comparing modelled data with various field measurements of sugar beet, spring barley, maize, winter wheat and potato crops. Model performance statistics show that crop growth is efficiently simulated. The closest agreement between measured and modelled biomass and leaf area index is achieved for sugar beet and winter wheat. Additionally, the response of the model to changed nitrogen availability caused by cultivation practices is analysed and reveals good results. The results suggest that the model is a suitable tool for numerically assessing the consequences of Global Change on biomass production, water and nitrogen demand, taking into account the complex interplay of water, carbon and nitrogen fluxes in agro-ecosystems.     

Validation of a multispecies forest dynamics model using 50-year growth from Eucalyptus forests in eastern Australia

One of the key problems confronting ecological forecasting is the validation of computer models. Here we report successful validation of a forest dynamics model Ecosystem Dynamics Simulator (EDS), adapted from the JABOWA-II forest succession model. This model and many variants derived from it have successfully simulated growth dynamics of uneven-aged mixed forests under changing environment with a moderate amount of input data. But rarely are adequate time-series data available for quantitative model validation. This study tested the performance of EDS in projecting the tree density, tree diameter at breast height (dbh), tree height, basal area and aboveground biomass of uneven-aged, mixed species sclerophyll forests in St. Mary state forests of eastern Australia. The test data were collected between 1951 and 2005. Every tree was uniquely numbered, tagged and measured in consecutive re-measurements. Projected growth attributes were compared with those observed in an independent validation dataset. The model produced satisfactory projections of tree density (91.7%), dbh (92.3%), total tree height (82.8%), basal area (89.3%) and aboveground biomass (87.6%) compared to the observed attributes. These results suggest that the EDS model can provide reasonable capability in projecting growth dynamics of uneven-aged, mixed species sclerophyll forests.     

Estimating the spatio-temporal risk of disease epidemics using a bioclimatic niche model

There are presently few tools available for estimating epidemic risks from forest pathogens, and hence informing pro-active disease management. In this study we demonstrated that a bioclimatic niche model can be used to examine questions of epidemic risk in temperate eucalypt plantations. The bioclimatic niche model, CLIMEX, was used to identify regional variation in climate suitability for Mycosphaerella leaf disease (MLD), a major cause of foliage damage in temperate eucalypt plantations around the world. Using historical observations of MLD damage, we were able to convert the relative score of climatic suitability generated by CLIMEX into a severity ranking ranging from low to high, providing for the first time a direct link between risk and impact, and allowing us to explore disease severity in a way meaningful to forest managers. We determined that the ‘Compare Years’ function in CLIMEX could be used for site-specific risk assessment to identify severity, frequency and seasonality of MLD epidemics. We explored appropriate scales of risk assessment for forest managers. Applying the CLIMEX model of MLD using a 0.25° or coarser grid size to areas of sharp topographic relief frequently misrepresented the risk posed by MLD, because considerable variation occurred between individual forest sites encompassed within a single grid cell. This highlighted the need for site-specific risk assessment to address many questions pertinent to managing risk in plantations.     

A comparison of four process-based models and a statistical regression model to predict growth of Eucalyptus globulus plantations

In forest management and ecological research, consideration of the impacts and risks of climate change or management optimisation is complex. Computer models have long been applied as tools for these tasks. Process-based forest growth models claim to overcome the limitations of empirical statistical models, but the capacity of different process-based models and modelling approaches have rarely been compared directly. This study evaluates stepwise multiple regression models in comparison to four process-based modelling approaches (3-PG, 3-PG+, CABALA and Forest-DNDC) for greenfield predictions of Eucalyptus globulus plantation growth from 2 to 8 years after planting throughout southern Australia.     

A two-dimensional simulation model of phosphorus uptake including crop growth and P-response

Modelling nutrient uptake by crops implies considering and integrating the processes controlling the soil nutrient supply, the uptake by the root system and relationships between the crop growth response and the amount of nutrient absorbed. We developed a model that integrates both dynamics of maize growth and phosphorus (P) uptake. The crop part of the model was derived from Monteith's model. A complete regulation of P-uptake by the roots according to crop P-demand and soil P-supply was assumed. The soil P-supply to the roots was calculated using a diffusion equation and assuming that roots behave as zero-sinks. The actual P-uptake and crop growth were calculated at each time step by comparing phosphate and carbohydrate supply–demand ratios. Model calculations for P-uptake and crop growth were compared to field measurements on a long term P-fertilization trial. Three P-fertilization regimes (no P-fertilization, 42.8 kg P ha⁻¹ year⁻¹ and 94.3 kg P ha⁻¹ year⁻¹) have led to a range of P-supply. Our model correctly simulated both the crop development and growth for all P-treatments. P-uptake was correctly predicted for the two non-limiting P-treatments. Nevertheless, for the limiting P-treatment, P-uptake was correctly predicted during the early period of growth but it was underestimated at the last sampling date (61 day after sowing). Several arguments for under-prediction were considered. However, most of them cannot explain the observed magnitude in discrepancy. The most likely reason might be the fact that biomass allocation between shoot and root must be modelled more precisely. Despite this mismatch, the model appears to provide realistic simulations of the soil–plant dynamic of P in field conditions.     

Application of a temperature-dependent von Bertalanffy growth model to bullhead (Cottus gobio)

The most studied and commonly applied model of fish growth is the von Bertalanffy model. However, this model does not take water temperature into account, which is one of the most important environmental factors affecting the life cycle of fish, as many physiological processes that determine growth, e.g. metabolic rate and oxygen supply, are directly influenced by temperature. In the present study we propose a version of the von Bertalanffy growth model that includes mean annual water temperatures by correlating the growth coefficient, k, explicitly and the asymptotic length, L_∞, implicitly to water temperature. All relationships include parameters with an obvious biological relevance that makes them easier to identify. The model is used to fit growth data of bullhead (Cottus gobio) at different locations in the Bez River network (Drme, France). We show that temperature explains much of the growth variability at the different sampling sites of the network.     

A hydrodynamic and water quality modeling study of spatial and temporal patterns of phytoplankton growth in a stratified lake with buoyant incoming flow

A three-dimensional hydrodynamic and water quality model was applied to Lake Paldang, a lake in South Korea that is stratified by incoming flows. The spatial and temporal patterns of phytoplankton growth in this lake were determined from the model. The model was calibrated and verified using data measured under different hydrological conditions. The model results were in reasonable agreement with the field measurements, in both the calibration and verification phases. The distributions of water quality and residence time in the lake and phytoplankton response to changes in nutrient loads were examined with the model, and the influence of the hydrodynamics on phytoplankton response was analyzed. The simulation results indicated that Lake Paldang is an essentially phosphorus-limited system, but that phytoplankton growth is limited by low water temperature and short residence time during the winter and the summer monsoon period, respectively. The results of sensitivity analyses also suggested that the hydrodynamics within the lake may have an indirect influence on phytoplankton responses to changes in the limiting nutrient loads, and that reducing phosphorus loading from Kyoungan Stream should be a high priority policy for controlling algal blooms during the pre- and post-monsoon periods. From this study, it was concluded that the three-dimensional water quality model incorporating hydrodynamic processes could successfully simulate phytoplankton response to changes in nutrient loads and that it could become a useful tool for identifying the essential factors determining phytoplankton growth and for developing the best management policy for algal blooms in Lake Paldang.     

On the risk of extinction of a wild plant species through spillover of a biological control agent: Analysis of an ecosystem compartment model

Invasive plant species can be controlled by introducing natural enemies (insect herbivores) from their native range. However, such introduction entails the risk that the introduced herbivores attack indigenous plant species in the area of introduction. Here, we study the effect of spillover of a herbivore from a managed ecosystem compartment (agriculture) to a natural compartment (non-managed) and vice versa. In the natural compartment, an indigenous plant species is attacked by the introduced herbivores, whereas another indigenous plant species, which competes with the first, is not attacked. The combination of competition and herbivory may result in extinction of the attacked wild plant species. Using a modelling approach, we determine model parameters that characterize the risk of extinction for a wild plant species. Risk factors include: (1) a high attack rate of the herbivores on the wild non-target species, (2) niche overlap expressed as strong competition between the attacked non-target species and its competitor(s), and (3) factors favouring large spillover from the managed ecosystem compartment to the natural compartment; these include (3a) a high dispersal ability, and (3b) a moderate attack rate of the introduced herbivore on the target species, enabling large resident populations of the insect herbivore in the managed compartment. The analysis thus indicates that a high attack rate on the target species, which is a selection criterion for biocontrol agents with respect to their effectiveness, also mitigates risks resulting from spillover and non-target effects. While total eradication of an invasive plant species is not possible in the one-compartment-one-plant-one-herbivore system, natural enemy spillover from a natural to a managed compartment can make the invasive weed go extinct.     

Application of a spatial meta-population model with stochastic parameters to the management of the invasive grass Nassella trichotoma in North Canterbury, New Zealand

Optimising the management of invasive plants requires the identification of the population size outcomes for alternative management strategies. Mathematical models can be useful tools for making such management strategy comparisons. In this paper we develop a generic landscape meta-population model and apply it to the weedy grass, Nassella trichotoma, an invasive species occupying approximately 800 land parcels, predominantly pastoral farms, in the Hurunui district, North Canterbury, New Zealand. Empirical evidence reveals that this meta-population is currently stable (at a median density of 6 plants ha⁻¹) under a community strategy requiring manual removal (termed ‘grubbing’) of plants annually from all land parcels. Reduction in population size requires an alternative management strategy. Field data, collected over a 12 year period, were used to provide stochastic parameter values for land parcel size, carrying capacity, rates of local population growth and grubbing.The model reveals that at steady state, the most significant contribution to population growth on a land parcel comes from within the land parcel itself; the expected annual per capita growth on an individual land parcel is 4 orders of magnitude greater than the expected annual contribution from plants arising from other land parcels. This result implies that many of the farms currently supporting N. trichotoma may pose little or no threat to, nor are threatened themselves by, other farms infested by the weed. However, the steady state distribution (of the weed's population density) was sensitive to the spread rate, revealing a need for data on this process. It was also sensitive to how any increase in the grubbing rate is distributed; increasing it via a uniform distribution U(0, 1) where all rates between 0 and 100% year⁻¹ are equally probable did not affect the steady state, whereas increasing the rates via the uniform distribution U(0.25, 0.75) resulted in fewer farms with high population densities. In general the model provides a basis for exploring the effects of a wide range of alternative grubbing strategies on population growth in N. trichotoma.     

The Time Invariance Principle,the absence of ecological chaos,and a fundamental pitfall of discrete modeling

This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology.