Moving forward in circles: challenges and opportunities in modelling population cycles

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non‐intuitive ways, the high‐dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco‐evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem‐level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research.     

The use of regression methods to study genotype-environment interactions: extending Griffing's model for diallel cross experiments and testing an empirical grouping method.

A model combining features of Griffing's diallel cross analysis with regression analysis for genotype-environment interactions is introduced using carp data of Moav et al. (1975) as an example. An analysis of variance based on this model provides information on the combining abilities of genetic effects and the interactions of these effects with environments from which inferences can readily be made on heterosis and heterosis-environment interactions. Applying the empirical grouping method of Lin and Thompson (1975) to these data (ignoring their diallel cross structure) established groups which were remarkably consistent with their members' crossing backgrounds.     

Modelling nutritional mutualisms: challenges and opportunities for data integration

Nutritional mutualisms are ancient, widespread, and profoundly influential in biological communities and ecosystems. Although much is known about these interactions, comprehensive answers to fundamental questions, such as how resource availability and structured interactions influence mutualism persistence, are still lacking. Mathematical modelling of nutritional mutualisms has great potential to facilitate the search for comprehensive answers to these and other fundamental questions by connecting the physiological and genomic underpinnings of mutualisms with ecological and evolutionary processes. In particular, when integrated with empirical data, models enable understanding of underlying mechanisms and generalisation of principles beyond the particulars of a given system. Here, we demonstrate how mathematical models can be integrated with data to address questions of mutualism persistence at four biological scales: cell, individual, population, and community. We highlight select studies where data has been or could be integrated with models to either inform model structure or test model predictions. We also point out opportunities to increase model rigour through tighter integration with data, and describe areas in which data is urgently needed. We focus on plant‐microbe systems, for which a wealth of empirical data is available, but the principles and approaches can be generally applied to any nutritional mutualism.     

英国多克隐花植物保护区森林土壤和凋落叶特性及其与真菌的关系

报道了英国独特的真菌保护区里真菌的生态学和生物多样性,而该保护区内有关物种构成的数据自1994年就开始进行收集了。关于真菌的生态学相互关系以及它们在总的生态系统功能中的作用可以作为生物多样性数据的补充。5~8月期间,在8块覆盖着不同植被（山毛榉,桦树,桦栎山毛榉,禾本科植物）实验区里,研究了森林凋落叶和叶本层土壤的特性和构成,测量了细菌种群数量和真菌的生物量（针对麦角固醇而言）。用相关分析和分段回归建模方法,结合可通过并行研究采集到的原生动物和线虫数据,得到了一系列结果。这些结果强调了某些因素的复杂性,这些因素影响着森林土壤和森林凋落叶中真菌生物量空间可变性的时间动态。大多数的相互作用看起来是瞬时的,在解释环境观测记录时应该对这一点给予充分考虑。最后,解释了若干具体关系,给出了进一步研究的方向,讨论了对整个生态系统功能研究的必要性。     

Some aspects of forest soil and litter ecology in the Dawyck Cryptogamic Sanctuary with a particular reference to fungi

Here we report on ecology and biodiversity of fungi in a unique mycological sanctuary in Britain, where data on species composition have been collected since 1994. To complement the biodiversity data by the information on the fungal ecological interactions and their role in the overall ecosystem functioning, soil properties and the composition of forest litter and field layer, bacterial population numbers and fungal biomass (in terms of ergosterol) were measured in 8 plots covered with different vegetations (beech, birch, birch-oak-beech, grass) over a May–Aug. period, and the results were analysed by correlation analysis and stepwise regression modelling together with data on protozoa and nematodes available from parallel research. The results highlighted the complexity of factors influencing temporal dynamics and spatial variability of fungal biomass in soil and forest litter. Most of the registered interactions appeared to be transient, and this should be taken into account while interpreting environmental observations. Interpretation of the specific relationships is given and implications for further research and overall ecosystem functioning are discussed.     

The uncertain blitzkrieg of Pleistocene megafauna

We investigated, using meta‐analysis of empirical data and population modelling, plausible scenarios for the cause of late Pleistocene global mammal extinctions. We also considered the rate at which these extinctions may have occurred, providing a test of the so‐called ‘blitzkrieg’ hypothesis, which postulates a rapid, anthropogenically driven, extinction event. The empirical foundation for this work was a comprehensive data base of estimated body masses of mammals, comprising 198 extinct and 433 surviving species > 5 kg, which we compiled through an extensive literature search. We used mechanistic population modelling to simulate the role of human hunting efficiency, meat off‐take, relative naivety of prey to invading humans, variation in reproductive fitness of prey and deterioration of habitat quality (due to either anthropogenic landscape burning or climate change), and explored the capacity of different modelling scenarios to recover the observed empirical relationship between body mass and extinction proneness. For the best‐fitting scenarios, we calculated the rate at which the extinction event would have occurred. All of the modelling was based on sampling randomly from a plausible range of parameters (and their interactions), which affect human and animal population demographics. Our analyses of the empirical data base revealed that the relationship between body mass and extinction risk relationship increases continuously from small‐ to large‐sized animals, with no clear ‘megafaunal’ threshold. A logistic ancova model incorporating body mass and geography (continent) explains 92% of the variation in the observed extinctions. Population modelling demonstrates that there were many plausible mechanistic scenarios capable of reproducing the empirical body mass–extinction risk relationship, such as specific targeting of large animals by humans, or various combinations of habitat change and opportunistic hunting. Yet, given the current imperfect knowledge base, it is equally impossible to use modelling to isolate definitively any single scenario to explain the observed extinctions. However, one universal prediction, which applied in all scenarios in which the empirical distribution was correctly predicted, was for the extinctions to be rapid following human arrival and for surviving fauna to be suppressed below their pre‐‘blitzkrieg’ densities. In sum, human colonization in the late Pleistocene almost certainly triggered a ‘blitzkrieg’ of the ‘megafauna’, but the operational details remain elusive.     

Global change alters the stability of food webs

Recent research has generally shown that a small change in the number of species in a food web can have consequences both for community structure and ecosystem processes. However ‘change’ is not limited to just the number of species in a community, but might include an alteration to such properties as precipitation, nutrient cycling and temperature. How such changes might affect species interactions is important, not just through the presence or absence of interactions, but also because the patterning of interaction strengths among species is intimately associated with community stability. Interaction strengths encompass such properties as feeding rates and assimilation efficiencies, and encapsulate functionally important information with regard to ecosystem processes. Interaction strengths represent the pathways and transfer of energy through an ecosystem. We review the best empirical data available detailing the frequency distribution of interaction strengths in communities. We present the underlying (but consistent) pattern of species interactions and discuss the implications of this patterning. We then examine how such a basic pattern might be affected given various scenarios of ‘change’ and discuss the consequences for community stability and ecosystem functioning.     

Modelling of soil salinity and halophyte crop production

In crop modelling the soil, plant and atmosphere system is regarded as a continuum with regard to root water uptake and transpiration. Crop production, often assumed to be linearly related with transpiration, depends on several factors, including water and nutrient availability and salinity. The effect of crop production factors on crop production is frequently incorporated in crop models using empirical reduction functions, which summarize very complex processes. Crop modelling has mainly focused on conventional crops and specific plant types such as halophytes have received limited attention. Crop modelling of halophytes can be approached as a hierarchy of production situations, starting at the situation with most optimal conditions and progressively introducing limiting factors. We analyse crop production situations in terms of water- and salt limited production and in terms of combined stresses. We show that experimental data as such may not be the bottleneck, but that data need to be adequately processed, to provide the basis for a first analysis. Halophytic crops offer a production perspective in saline areas, but in other areas long-term use of low quality irrigation water for halophyte production can result in serious soil quality problems. An overview is given of potential problems concerning the use of (saline) irrigation water, leading to the conclusion that soil quality changes due to poor quality water should be considered in determining the areas selected for halophyte growing.     

Use of models for integrated assessment of ecosystem health

An argument is presented for a greater use of numerical models in integrated assessment of ecosystem health. Ecosystem health has many facets which are interconnected and interact, and which can only be measured in integrated assessments. Modelling is an essential feature of integrated assessment being one of the few ways human groups can form a consensus understanding of the complex dynamics which occur. Functional assumptions are made explicit. The argument is expanded in response to a series of key questions: What is ecosystem health? How do we do integrated assessments? What is modelling? What are some successful examples? What should one conclude? The answers are illustrated with references to the International Joint Commission's program to develop and implement Remedial Action Plans for the Great Lakes' Areas of Concern, particularly in the Bay of Quinte, Lake Ontario. Three recommendations are offered: (i) Increase the use of models, (ii) Build models with existing data and hypotheses before initiating new programs, and (iii) Allow for iterative model development but be prepared to build a new model when a new problem arises.     

Predicting the outcome of trophic manipulation in lakes—a comment on Harris (1994)

1. Harris ( Freshwater Biology , 32 , 143–160, 1994) asserts that while empirical modelling of lake ecosystem properties has yielded general predictions and useful explanations, research into the effects of food-web interactions has not. I provide an explicit example of a useful, quantitative prediction gleaned from experiments on food-web effects—the relationship between total phosphorus and the magnitude of response of algal biomass.
2. I further argue that Harris errs in asserting that food-web effects will be ineffective in eutrophic lakes. This error stems from a misconception about the relevance of ecosystem behaviour in unmanipulated systems for predictions of how an ecosystem will respond to manipulation. I cite empirical evidence demonstrating that, contrary to Harris's contention, the response of algal biomass to a change in food-web structure increases as lakes are enriched.     

Conundrums in mixed woody–herbaceous plant systems

Aims To identify approaches to improve our understanding of, and predictive capability for, mixed tree–grass systems. Elucidation of the interactions, dynamics and determinants, and identification of robust generalizations that can be broadly applied to tree–grass systems would benefit ecological theory, modelling and land management. Methods A series of workshops brought together scientific expertise to review theory, data availability, modelling approaches and key questions. Location Ecosystems characterized by mixtures of herbaceous and woody plant life‐forms, often termed ‘savannas’, range from open grasslands with few woody plants, to woodlands or forests with a grass layer. These ecosystems represent a substantial portion of the terrestrial biosphere, an important wildlife habitat, and a major resource for provision of livestock, fuel wood and other products. Results Although many concepts and principles developed for grassland and forest systems are relevant to these dual life‐form communities, the novel, complex, nonlinear behaviour of mixed tree–grass systems cannot be accounted for by simply studying or modelling woody and herbaceous components independently. A more robust understanding requires addressing three fundamental conundrums: (1) The ‘treeness’ conundrum. What controls the relative abundance of woody and herbaceous plants for a given set of conditions at given site? (2) The coexistence conundrum. How do the life‐forms interact with each other? Is a given woody–herbaceous ratio dynamically stable and persistent under a particular set of conditions? (3) The net primary productivity (NPP) conundrum. How does NPP of the woody vegetation, the herbaceous vegetation, and the total ecosystem (woody + herbaceous) change with changes in the tree–grass ratio? Tests of the theory and conceptual models of determinants of mixed woody–herbaceous systems have been largely site‐ or region‐specific and have seldom been broadly or quantitatively evaluated. Cross‐site syntheses based on data and modelling are required to address the conundrums and identify emerging patterns, yet, there are very few data sets for which either biomass or NPP have been quantified for both the woody and the herbaceous components of tree–grass systems. Furthermore, there are few cross‐site comparisons spanning the diverse array of woody–herbaceous mixtures. Hence, initial synthesis studies should focus on compiling and standardizing a global data base which could be (1) explored to ascertain if robust generalizations and consistent patterns exist; and (2) used to evaluate the performance of savanna simulation models over a range of woody–herbaceous mixtures. Savanna structure and productivity are the result of complex and dynamic interactions between climate, soils and disturbances, notably fire and herbivory. Such factors are difficult to isolate or experimentally manipulate in order to evaluate their impacts at spatial and temporal scales appropriate for assessing ecosystem dynamics. These factors can, however, be evaluated with simulation models. Existing savanna models vary markedly with respect to their conceptual approach, their data requirements and the extent to which they incorporate mechanistic processes. Model intercomparisons can elucidate those approaches most suitable for various research questions and management applications. Conclusion Theoretical and conceptual advances could be achieved by considering a broad continuum of grass–shrub–tree combinations using data meta‐analysis techniques and modelling.     

Empirical and mechanistic mathematical models of temporal evolution of milk production in ruminants.

In the various sectors of animal science there has been little exploration of the theoretical mathematical aspects of data analysis and modelling. The dominant statistical methods used for the analysis of experimental data are rarely valuable for developing a deeper understanding of the problem. In addition they do not take account of the evolution over time of those variables of major interest to be studied. Only recently have more sophisticated methods of mathematical modelling begun to be used. Nonetheless attention tends to be focused exclusively on empirical models. Mathematical models with greater explanatory power, in particular those which use differential equations, are as yet little used. This work develops a mathematical approach to a problem that is of great interest in animal science: the development over time of milk production in economically important ruminant species.     

Human exploitation shapes productivity–biomass relationships on coral reefs

Coral reef fisheries support the livelihoods of millions of people in tropical countries, despite large‐scale depletion of fish biomass. While human adaptability can help to explain the resistance of fisheries to biomass depletion, compensatory ecological mechanisms may also be involved. If this is the case, high productivity should coexist with low biomass under relatively high exploitation. Here we integrate large spatial scale empirical data analysis and a theory‐driven modelling approach to unveil the effects of human exploitation on reef fish productivity–biomass relationships. We show that differences in how productivity and biomass respond to overexploitation can decouple their relationship. As size‐selective exploitation depletes fish biomass, it triggers increased production per unit biomass, averting immediate productivity collapse in both the modelling and the empirical systems. This ‘buffering productivity’ exposes the danger of assuming resource production–biomass equivalence, but may help to explain why some biomass‐depleted fish assemblages still provide ecosystem goods under continued global fishing exploitation.     

Predicting the outcome of trophic manipulation in lakes—a comment on Harris (1994)

1. Harris ( Freshwater Biology , 32 , 143–160, 1994) asserts that while empirical modelling of lake ecosystem properties has yielded general predictions and useful explanations, research into the effects of food-web interactions has not. I provide an explicit example of a useful, quantitative prediction gleaned from experiments on food-web effects—the relationship between total phosphorus and the magnitude of response of algal biomass.
2. I further argue that Harris errs in asserting that food-web effects will be ineffective in eutrophic lakes. This error stems from a misconception about the relevance of ecosystem behaviour in unmanipulated systems for predictions of how an ecosystem will respond to manipulation. I cite empirical evidence demonstrating that, contrary to Harris's contention, the response of algal biomass to a change in food-web structure increases as lakes are enriched.     

Studying Individual Patterns of Development Using I-States as Objects Analysis (ISOA)

An approach is presented for studying individual pattern development in person-oriented terms focusing on the concept of i-state, i.e. an individual's configuration of information at a specific point in time. The procedure is called I-States as Objects Analysis (ISOA). First common i-states (typical states) are identified using cluster analysis of subindividuals and then this information is used for describing typical developmental patterns. Both a general procedure and a specific procedure used on a demonstration data set were developed. Using ISOA, change and stability can be studied both with regard to structure and with regard to individual variation. An empirical example was given which concerned longitudinal data about school grades at four different ages for 333 boys and girls. The data were split into a test sample and a replication sample of equal sizes. It was contended from the empirical study that ISOA functioned reasonably well on the sample studied. In the discussion, it was pointed out that ISOA can be a powerful method to use for small samples with many measurement occasions and that the method is optimal for studying short-term change.     

Tracking and forecasting ecosystem interactions in real time

Evidence shows that species interactions are not constant but change as the ecosystem shifts to new states. Although controlled experiments and model investigations demonstrate how nonlinear interactions can arise in principle, empirical tools to track and predict them in nature are lacking. Here we present a practical method, using available time-series data, to measure and forecast changing interactions in real systems, and identify the underlying mechanisms. The method is illustrated with model data from a marine mesocosm experiment and limnologic field data from Sparkling Lake, WI, USA. From simple to complex, these examples demonstrate the feasibility of quantifying, predicting and understanding state-dependent, nonlinear interactions as they occur in situ and in real time—a requirement for managing resources in a nonlinear, non-equilibrium world.     

Predicting the unexpected: using a qualitative model of a New Zealand dryland ecosystem to anticipate pest management outcomes

Pest management is expensive and there is often uncertainty about the benefits for the resources being protected. There can also be unintended consequences for other parts of the ecosystem, especially in complex food webs. In making decisions managers generally have to rely on qualitative information collected in a piecemeal fashion. A method to assist decision making is a qualitative modelling approach using fuzzy cognitive maps, a directed graphical model related to neural networks that can take account of interactions between pests and conservation assets in complex food webs. Using all available information on relationships between native and exotic resources and consumers, we generated hypotheses about potential consequences of single‐species and multi‐species pest control on the long‐term equilibrium abundances of other biotic components of an ecosystem. We applied the model to a dryland ecosystem in New Zealand because we had good information on its trophic structure, but the information on the strength of species interactions was imprecise. Our model suggested that pest control is unlikely to significantly boost native invertebrates and lizards in this ecosystem, suggesting that other forms of management may be required for these groups. Most of the pest control regimes tested resulted in greater abundances of at least one other pest species, which could potentially lead to other management problems. Some of the predictions were unexpected, such as more birds resulting from possum and mouse control. We also modelled the effects of an increase in invasive rabbits, which led to unexpected declines of stoats, weasels, mice and possums. These unexpected outcomes resulted from complex indirect pathways in the food web. Fuzzy cognitive maps allow rapid construction of prototype models of complex food webs using a wide range of data and expert opinion. Their utility lies in providing direction for future monitoring efforts and generating hypotheses that can be tested with field experiments.     

Non‐invasive techniques for investigating and modelling root‐feeding insects in managed and natural systems

1 Root‐feeding insects are now considered to play a greater role in ecosystem processes than previously thought, yet little is known about their specific interactions with host plants compared with above‐ground insect herbivores. Methodological difficulties associated with studying these insects in the soil, together with the lack of empirical and theoretical frameworks, have conventionally hindered progress in this area. 2 This paper reviews recent empirical and theoretical developments that have been adopted for studying root‐feeding insects, focusing on the non‐invasive techniques of X‐ray tomography and acoustic field detection and how these can be integrated with new mathematical modelling approaches. 3 X‐ray tomography has been used for studying the movements of several insects within the soil and has helped to characterize the host plant location behaviour of the clover root weevil, Sitona lepidus. Acoustic detection of soil insects has been used in various managed systems, ranging from nursery containers to citrus groves. 4 Mathematical modelling plays a complementary role for investigating root‐feeding insects, illustrated by a number of published models. A model is presented for the movement of S. lepidus in the soil, which suggests that these insects undergo Lévy movements, similar to those recently demonstrated for above‐ground organisms. 5 The future directions and challenges for investigating root‐feeding insects are discussed in the context of the wider ecosystem, incorporating both above and below‐ground organisms.     

Evaluation method for coalmining-based cities ecosystem based on attribute mathematical model with Huainan City as an example

Attributive recognition model of coalmining-based cities ecosystem classification is developed in terms of attributive mathematical theory. Based on the analysis of main causes of coalmining-based cities ecosystem, the city vitality, city structure strength, city resilience ability, service functions and health status are chosen as the criterion indicators of coalmining-based cities ecosystem classification; the attributive measurement functions are constructed to compute the attributive measurement of single indicator and multi-indicator; and the synthetic attributive measurement is calculated by the AHP; the health classification of cities ecosystem are recognized by the confidence criterion. An empirical analysis is made by the proposed model and method, the synthetic evaluation results are better than fuzzy comprehensive evaluation method which validates the proposed model feasible, effective and reliable in coalmining-based cities ecosystem classification. As attributive recognition theory can success fully resolve certain issues with a number of fuzzy attribution in comprehensive evaluation, its confidence criterion is established on the basis of the ordered evaluation sets, consequently it will make the evaluation results more reliable.