Identifying the critical parameters of a cyanobacterial growth and movement model by using generalised sensitivity analysis

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling of cyanobacteria in freshwaters is an important tool for understanding their population dynamics and predicting the location and timing of the bloom events in lakes and rivers. A new deterministic-mathematical model was developed, which simulates the growth and movement of cyanobacterial blooms in river systems. The model focuses on the mathematical description of the bloom formation, vertical migration and lateral transport of colonies within river environments by taking into account the major factors that affect the cyanobacterial bloom formation in rivers including, light, nutrients and temperature. A technique called generalised sensitivity analysis was applied to the model to identify the critical parameter uncertainties in the model and investigates the interaction between the chosen parameters of the model. The result of the analysis suggested that 8 out of 12 parameters were significant in obtaining the observed cyanobacterial behaviour in a simulation. It was found that there was a high degree of correlation between the half-saturation rate constants used in the model.

Land use for England and Wales: evaluation of management options to support 'good ecological status' in surface freshwaters

This paper analyses historic records of agricultural land use and management for England and Wales from 1931 and 1991 and uses export coefficient modelling to hindcast the impact of these practices on the rates of diffuse nitrogen (N) and phosphorus (P) export to water bodies for each of the major geo-climatic regions of England and Wales. Key trends indicate the importance of animal agriculture as a contributor to the total diffuse agricultural nutrient loading on waters, and the need to bring these sources under control if conditions suitable for sustaining 'Good Ecological Status' under the Water Framework Directive are to be generated. The analysis highlights the importance of measuring changes in nutrient loading in relation to the catchment-specific baseline state for different water bodies. The approach is also used to forecast the likely impact of broad regional scale scenarios on nutrient export to waters and highlights the need to take sensitive land out of production, introduce ceilings on fertilizer use and stocking densities, and controls on agricultural practice in higher risk areas where intensive agriculture is combined with a low intrinsic nutrient retention capacity, although the uncertainties associated with the modelling applied at this scale should be taken into account in the interpretation of model output. The paper advocates the need for a two-tiered approach to nutrient management, combining broad regional policies with targeted management in high risk areas at the catchment and farm scale.

Spatial analysis of the error in a model of soil nitrogen

Models of the dynamics of nitrogen in soil (soil-N) can be used to aid the fertilizer management of a crop. The predictions of soil-N models can be validated by comparison with observed data. Validation generally involves calculating non-spatial statistics of the observations and predictions, such as their means, their mean squared-difference, and their correlation. However, when the model predictions are spatially distributed across a landscape the model requires validation with spatial statistics. There are three reasons for this: (i) the model may be more or less successful at reproducing the variance of the observations at different spatial scales; (ii) the correlation of the predictions with the observations may be different at different spatial scales; (iii) the spatial pattern of model error may be informative. In this study we used a model, parameterized with spatially variable input information about the soil, to predict the mineral-N content of soil in an arable field, and compared the results with observed data. We validated the performance of the N model spatially with a linear mixed model of the observations and model predictions, estimated by residual maximum likelihood. This novel approach allowed us to describe the joint variation of the observations and predictions as: (i) independent random variation that occurred at a fine spatial scale; (ii) correlated random variation that occurred at a coarse spatial scale; (iii) systematic variation associated with a spatial trend. The linear mixed model revealed that, in general, the performance of the N model changed depending on the spatial scale of interest. At the scales associated with random variation, the N model underestimated the variance of the observations, and the predictions were correlated poorly with the observations. At the scale of the trend, the predictions and observations shared a common surface. The spatial pattern of the error of the N model suggested that the observations were affected by the local soil condition, but this was not accounted for by the N model. In summary, the N model would be well-suited to field-scale management of soil nitrogen, but suited poorly to management at finer spatial scales. This information was not apparent with a non-spatial validation. (c),2007 Elsevier B.V. All rights reserved.

The role of satellite image-processing for national-scale estimates of gene flow from genetically modified crops: rapeseed in the UK as a model.

1. There is concern over the possibility of unwanted environmental change following transgene movement from genetically modified (GM) rapeseed Brassica napus to its wild and weedy relatives. 2. The aim of this research was to develop a remote sensing-assisted methodology to help quantify gene flow from crops to their wild relatives over wide areas. Emphasis was placed on locating sites of sympatry, where the frequency of gene flow is likely to be highest, and on measuring the size of rapeseed fields to allow spatially explicit modelling of wind-mediated pollen-dispersal patterns. 3. Remote sensing was used as a tool to locate rapeseed fields, and a variety of image-processing techniques was adopted to facilitate the compilation of a spatially explicit profile of sympatry between the crop and Brassica rapa. 4. Classified satellite images containing rapeseed fields were first used to infer the spatial relationship between donor rapeseed fields and recipient riverside B. rapa populations. Such images also have utility for improving the efficiency of ground surveys by identifying probable sites of sympatry. The same data were then also used for the calculation of mean field size. 5. This paper forms a companion paper to Wilkinson et al. (2003), in which these elements were combined to produce a spatially explicit profile of hybrid formation over the UK. The current paper demonstrates the value of remote sensing and image processing for large-scale studies of gene flow, and describes a generic method that could be applied to a variety of crops in many countries. 6. Synthesis and applications. The decision to approve or prevent the release of a GM cultivar is made at a national rather than regional level. It is highly desirable that data relating to the decision-making process are collected at the same scale, rather than relying on extrapolation from smaller experiments designed at the plot, field or even regional scale. It would be extremely difficult and labour intensive to attempt to carry out such large-scale investigations without the use of remote-sensing technology. This study used rapeseed in the UK as a model to demonstrate the value of remote sensing in assembling empirical information at a national level.

Ecological and life-history traits predict bee species responses to environmental disturbances

The ability to predict the responses of ecological communities and individual species to human-induced environmental change remains a key issue for ecologists and conservation managers alike. Responses are often variable among species within groups making general predictions difficult. One option is to include ecological trait information that might help to disentangle patterns of response and also provide greater understanding of how particular traits link whole clades to their environment. Although this ‘‘trait-guild” approach has been used for single disturbances, the importance of particular traits on general responses to multiple disturbances has not been explored. We used a mixed model analysis of 19 data sets from throughout the world to test the effect of ecological and life-history traits on the responses of bee species to different types of anthropogenic environmental change. These changes included habitat loss, fragmentation, agricultural intensification, pesticides and fire. Individual traits significantly affected bee species responses to different disturbances and several traits were broadly predictive among multiple disturbances. The location of nests – above vs. below ground – significantly affected response to habitat loss, agricultural intensification, tillage regime (within agriculture) and fire. Species that nested above ground were on average more negatively affected by isolation from natural habitat and intensive agricultural land use than were species nesting below ground. In contrast below-ground-nesting species were more negatively affected by tilling than were above-ground nesters. The response of different nesting guilds to fire depended on the time since the burn. Social bee species were more strongly affected by isolation from natural habitat and pesticides than were solitary bee species. Surprisingly, body size did not consistently affect species responses, despite its importance in determining many aspects of individuals’ interaction with their environment. Although synergistic interactions among traits remain to be explored, individual traits can be useful in predicting and understanding responses of related species to global change.

Managing invasive alien species with professional and hobby farmers: insights from ecological-economic modelling

Biosecurity is a great challenge to policy-makers globally. Biosecurity policies aim to either prevent invasions before they occur or to eradicate and/or effectively manage the invasive species and diseases once an invasion has occurred. Such policies have traditionally been directed towards professional producers in natural resource based sectors, including agriculture. Given the wide scope of issues threatened by invasive species and diseases, it is important to account for several types of stakeholders that are involved. We investigate the problem of an invasive insect pest feeding on an agricultural crop with heterogeneous producers: profit-oriented professional farmers and utility-oriented hobby farmers. We start from an ecological-economic model conceptually similar to the one developed by Eiswerth and Johnson [Eiswerth, M.E. and Johnson, W.S., 2002. Managing nonindigenous invasive species: insights from dynamic analysis. Environmental and Resource Economics 23, 319-342.] and extend it in three ways. First, we make explicit the relationship between the invaded state carrying capacity and farmers' planting decisions. Second, we add another producer type into the framework and hence account for the existence of both professional and hobby fanners. Third, we provide a theoretical contribution by discussing two alternative types of equilibria. We also apply the model to an empirical case to extract a number of stylised facts and in particular to assess: a) under which circumstances the invasion is likely to be not controllable; and b) how extending control policies to hobby farmers could affect both types of producers. (C) 2008 Elsevier B.V. All rights reserved.

The effects of environmental perturbation and measurement error on estimates of the shape parameter in the theta-logistic model of population regulation

The theta-logistic is a widely used generalisation of the logistic model of regulated biological processes which is used in particular to model population regulation. Then the parameter theta gives the shape of the relationship between per-capita population growth rate and population size. Estimation of theta from population counts is however subject to bias, particularly when there are measurement errors. Here we identify factors disposing towards accurate estimation of theta by simulation of populations regulated according to the theta-logistic model. Factors investigated were measurement error, environmental perturbation and length of time series. Large measurement errors bias estimates of theta towards zero. Where estimated theta is close to zero, the estimated annual return rate may help resolve whether this is due to bias. Environmental perturbations help yield unbiased estimates of theta. Where environmental perturbations are large, estimates of theta are likely to be reliable even when measurement errors are also large. By contrast where the environment is relatively constant, unbiased estimates of theta can only be obtained if populations are counted precisely Our results have practical conclusions for the design of long-term population surveys. Estimation of the precision of population counts would be valuable, and could be achieved in practice by repeating counts in at least some years. Increasing the length of time series beyond ten or 20 years yields only small benefits. if populations are measured with appropriate accuracy, given the level of environmental perturbation, unbiased estimates can be obtained from relatively short censuses. These conclusions are optimistic for estimation of theta. (C) 2008 Elsevier B.V All rights reserved.

Phytohormones and plant-herbivore-pathogen interactions: integrating the molecular with the ecological

Current research into indirect phytopathogen–herbivore interactions (i.e., interactions mediated by the host plant) is carried out in two largely independent directions: ecological/mechanistic and molecular. We investigate the origin of these approaches and their strengths and weaknesses. Ecological studies have determined the effect of herbivores and phytopathogens on their host plants and are often correlative: the need for long-term manipulative experiments is pressing. Molecular/cellular studies have concentrated on the role of signaling pathways for systemic induced resistance, mainly involving salicylic acid and jasmonic acid, and more recently the cross-talk between these pathways. This cross-talk demonstrates how interactions between signaling mechanisms and phytohormones could mediate plant–herbivore–pathogen interactions. A bridge between these approaches may be provided by field studies using chemical induction of defense, or investigating whole-organism mechanisms of interactions among the three species. To determine the role of phytohormones in induced resistance in the field, researchers must combine ecological and molecular methods. We discuss how these methods can be integrated and present the concept of “kaleidoscopic defense.” Our recent molecular-level investigations of interactions between the herbivore Gastrophysa viridula and the rust fungus Uromyces rumicis on Rumex obtusifolius, which were well studied at the mechanistic and ecological levels, illustrate the difficulty in combining these different approaches. We suggest that the choice of the right study system (possibly wild relatives of model species) is important, and that molecular studies must consider the environmental conditions under which experiments are performed. The generalization of molecular predictions to ecologically realistic settings will be facilitated by “middle-ground studies” concentrating on the outcomes of the interactions.

The DigiBog model of peatland development 1: rationale, conceptual model, and hydrological basis

Using a literature review, we argue that new models of peatland development are needed. Many existing models do not account for potentially important ecohydrological feedbacks, and/or ignore spatial structure and heterogeneity. Existing models, including those that simulate a near total loss of the northern peatland carbon store under a warming climate, may produce misleading results because they rely upon oversimplified representations of ecological and hydrological processes. In this, the first of a pair of papers, we present the conceptual framework for a model of peatland development, DigiBog, which considers peatlands as complex adaptive systems. DigiBog accounts for the interactions between the processes which govern litter production and peat decay, peat soil hydraulic properties, and peatland water-table behaviour, in a novel and genuinely ecohydrological manner. DigiBog consists of a number of interacting submodels, each representing a different aspect of peatland ecohydrology. Here we present in detail the mathematical and computational basis, as well as the implementation and testing, of the hydrological submodel. Remaining submodels are described and analysed in the accompanying paper. Tests of the hydrological submodel against analytical solutions for simple aquifers were highly successful: the greatest deviation between DigiBog and the analytical solutions was 2·83%. We also applied the hydrological submodel to irregularly shaped aquifers with heterogeneous hydraulic properties—situations for which no analytical solutions exist—and found the model's outputs to be plausible.

Sizing reserves within a landscape: the roles of villagers' reactions and the ecological-socioeconomic setting

Traditionally, siting and sizing decisions for parks and reserves reflected ecological characteristics but typically failed to consider ecological costs created from displaced resource collection, welfare costs on nearby rural people, and enforcement costs. Using a spatial game-theoretic model that incorporates the interaction of socioeconomic and ecological settings, we show how incorporating more recent mandates that include rural welfare and surrounding landscapes can result in very different optimal sizing decisions. The model informs our discussion of recent forest management in Tanzania, reserve sizing and siting decisions, estimating reserve effectiveness, and determining patterns of avoided forest degradation in Reduced Emissions from Deforestation and Forest Degradation programs.

Linking pesticide exposure and spatial dynamics: An individual-based model of wood mouse (Apodemus sylvaticus) populations in agricultural landscapes

The wood mouse is a common and abundant species in agricultural landscape and is a focal species in pesticide risk assessment. Empirical studies on the ecology of the wood mouse have provided sufficient information for the species to be modelled mechanistically. An individual-based model was constructed to explicitly represent the locations and movement patterns of individual mice. This together with the schedule of pesticide application allows prediction of the risk to the population from pesticide exposure. The model included life-history traits of wood mice as well as typical landscape dynamics in agricultural farmland in the UK. The model obtains a good fit to the available population data and is fit for risk assessment purposes. It can help identify spatio-temporal situations with the largest potential risk of exposure and enables extrapolation from individual-level endpoints to population-level effects. Largest risk of exposure to pesticides was found when good crop growth in the “sink” fields coincided with high “source” population densities in the hedgerows. Keywords: Population dynamics, Pesticides, Ecological risk assessment, Habitat choice, Agent-based model, NetLogo

Sequential variations of phytoplankton growth and mortality in an NPZ model: a remote-sensing-based assessment

Radiometric data in the visible domain acquired by satellite remote sensing have proven to be powerful for monitoring the states of the ocean, both physical and biological. With the help of these data it is possible to understand certain variations in biological responses of marine phytoplankton on ecological time scales. Here, we implement a sequential data-assimilation technique to estimate from a conventional nutrient–phytoplankton–zooplankton (NPZ) model the time variations of observed and unobserved variables. In addition, we estimate the time evolution of two biological parameters, namely, the specific growth rate and specific mortality of phytoplankton. Our study demonstrates that: (i) the series of time-varying estimates of specific growth rate obtained by sequential data assimilation improves the fitting of the NPZ model to the satellite-derived time series: the model trajectories are closer to the observations than those obtained by implementing static values of the parameter; (ii) the estimates of unobserved variables, i.e., nutrient and zooplankton, obtained from an NPZ model by implementation of a pre-defined parameter evolution can be different from those obtained on applying the sequences of parameters estimated by assimilation; and (iii) the maximum estimated specific growth rate of phytoplankton in the study area is more sensitive to the sea-surface temperature than would be predicted by temperature-dependent functions reported previously. The overall results of the study are potentially useful for enhancing our understanding of the biological response of phytoplankton in a changing environment.

Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: a mathematical model

In this paper we have proposed and analyzed a simple mathematical model consisting of four variables, viz., nutrient concentration, toxin producing phytoplankton (TPP), non-toxic phytoplankton (NTP), and toxin concentration. Limitation in the concentration of the extracellular nutrient has been incorporated as an environmental stress condition for the plankton population, and the liberation of toxic chemicals has been described by a monotonic function of extracellular nutrient. The model is analyzed and simulated to reproduce the experimental findings of Graneli and Johansson [Graneli, E., Johansson, N., 2003. Increase in the production of allelopathic Prymnesium parvum cells grown under N- or P-deficient conditions. Harmful Algae 2, 135–145]. The robustness of the numerical experiments are tested by a formal parameter sensitivity analysis. As the first theoretical model consistent with the experiment of Graneli and Johansson (2003), our results demonstrate that, when nutrient-deficient conditions are favorable for the TPP population to release toxic chemicals, the TPP species control the bloom of other phytoplankton species which are non-toxic. Consistent with the observations made by Graneli and Johansson (2003), our model overcomes the limitation of not incorporating the effect of nutrient-limited toxic production in several other models developed on plankton dynamics.

Models of human behaviour in social-ecological systems

Environmental change research often relies on simplistic, static models of human behaviour in social-ecological systems. This limits understanding of how social-ecological change occurs. Integrative, process-based behavioural models, which include feedbacks between action, and social and ecological system structures and dynamics, can inform dynamic policy assessment in which decision making is internalised in the model. These models focus on dynamics rather than states. They stimulate new questions and foster interdisciplinarity between and within the natural and social sciences.