The use of spatially explicit models (SEMs) in ecology has grown enormously in the past two decades. One major advancement has been that fine-scale details of landscapes, and of spatially dependent ...biological processes, such as dispersal and invasion, can now be simulated with great precision, due to improvements in computer technology. Many areas of modeling have shifted toward a focus on capturing these fine-scale details, to improve mechanistic understanding of ecosystems. However, spatially implicit models (SIMs) have played a dominant role in ecology, and arguments have been made that SIMs, which account for the effects of space without specifying spatial positions, have an advantage of being simpler and more broadly applicable, perhaps contributing more to understanding. We address this debate by comparing SEMs and SIMs in examples from the past few decades of modeling research. We argue that, although SIMs have been the dominant approach in the incorporation of space in theoretical ecology, SEMs have unique advantages for addressing pragmatic questions concerning species populations or communities in specific places, because local conditions, such as spatial heterogeneities, organism behaviors, and other contingencies, produce dynamics and patterns that usually cannot be incorporated into simpler SIMs. SEMs are also able to describe mechanisms at the local scale that can create amplifying positive feedbacks at that scale, creating emergent patterns at larger scales, and therefore are important to basic ecological theory. We review the use of SEMs at the level of populations, interacting populations, food webs, and ecosystems and argue that SEMs are not only essential in pragmatic issues, but must play a role in the understanding of causal relationships on landscapes.
The ‘ODD’ (Overview, Design concepts, and Details) protocol was published in 2006 to standardize the published descriptions of individual-based and agent-based models (ABMs). The primary objectives ...of ODD are to make model descriptions more understandable and complete, thereby making ABMs less subject to criticism for being irreproducible. We have systematically evaluated existing uses of the ODD protocol and identified, as expected, parts of ODD needing improvement and clarification. Accordingly, we revise the definition of ODD to clarify aspects of the original version and thereby facilitate future standardization of ABM descriptions. We discuss frequently raised critiques in ODD but also two emerging, and unanticipated, benefits: ODD improves the rigorous formulation of models and helps make the theoretical foundations of large models more visible. Although the protocol was designed for ABMs, it can help with documenting any large, complex model, alleviating some general objections against such models.
Agent-based modelling (ABM) has become an established methodology in many areas of biology, ranging from the cellular to the ecological population and community levels. In plant science, two ...different scales have predominated in their use of ABM. One is the scale of populations and communities, through the modelling of collections of agents representing individual plants, interacting with each other and with the environment. The other is the scale of the individual plant, through the modelling, by functional-structural plant models (FSPMs), of agents representing plant building blocks, or metamers, to describe the development of plant architecture and functions within individual plants. The purpose of this review is to show key results and parallels in ABM for growth, mortality, carbon allocation, competition and reproduction across the scales from the plant organ to populations and communities on a range of spatial scales to the whole landscape. Several areas of application of ABMs are reviewed, showing that some issues are addressed by both population-level ABMs and FSPMs. Continued increase in the relevance of ABM to environmental science and management will be helped by greater integration of ABMs across these two scales.
Individual-based models simulate populations and communities by following individuals and their properties. They have been used in ecology for more than four decades, with their use and ubiquity in ...ecology growing rapidly in the last two decades. Individual-based models have been used for many applied or "pragmatic" issues, such as informing the protection and management of particular populations in specific locations, but their use in addressing theoretical questions has also grown rapidly, recently helping us to understand how the sets of traits of individual organisms influence the assembly of communities and food webs. Individual-based models will play an increasingly important role in questions posed by complex ecological systems.
Like predation and competition, mutualism is now recognized as a consumer-resource (C-R) interaction, including, in particular, bi-directional (e.g., coral, plant-mycorrhizae) and uni-directional ...(e.g., ant-plant defense, plant-pollinator) C-R mutualisms. Here, we develop general theory for the density-dependent population dynamics of mutualism based on the C-R mechanism of interspecific interaction. To test the influence of C-R interactions on the dynamics and stability of bi- and uni-directional C-R mutualisms, we developed simple models that link consumer functional response of one mutualistic species with the resources supplied by another. Phase-plane analyses show that the ecological dynamics of C-R mutualisms are stable in general. Most transient behavior leads to an equilibrium of mutualistic coexistence, at which both species densities are greater than in the absence of interactions. However, due to the basic nature of C-R interactions, certain density-dependent conditions can lead to C-R dynamics characteristic of predator-prey interactions, in which one species overexploits and causes the other to go extinct. Consistent with empirical phenomena, these results suggest that the C-R interaction can provide a broad mechanism for understanding density-dependent population dynamics of mutualism. By unifying predation, competition, and mutualism under the common ecological framework of consumer-resource theory, we may also gain a better understanding of the universal features of interspecific interactions in general.
Ecological models are important for environmental decision support because they allow the consequences of alternative policies and management scenarios to be explored. However, current modeling ...practice is unsatisfactory. A literature review shows that the elements of good modeling practice have long been identified but are widely ignored. The reasons for this might include lack of involvement of decision makers, lack of incentives for modelers to follow good practice, and the use of inconsistent terminologies. As a strategy for the future, we propose a standard format for documenting models and their analyses: transparent and comprehensive ecological modeling (TRACE) documentation. This standard format will disclose all parts of the modeling process to scrutiny and make modeling itself more efficient and coherent.
The Overview, Design concepts and Details (ODD) protocol for describing Individual- and Agent-Based Models (ABMs) is now widely accepted and used to document such models in journal articles. As a ...standardized document for providing a consistent, logical and readable account of the structure and dynamics of ABMs, some research groups also find it useful as a workflow for model design. Even so, there are still limitations to ODD that obstruct its more widespread adoption. Such limitations are discussed and addressed in this paper: the limited availability of guidance on how to use ODD; the length of ODD documents; limitations of ODD for highly complex models; lack of sufficient details of many ODDs to enable reimplementation without access to the model code; and the lack of provision for sections in the document structure covering model design rationale, the model's underlying narrative, and the means by which the model's fitness for purpose is evaluated. We document the steps we have taken to provide better guidance on: structuring complex ODDs and an ODD summary for inclusion in a journal article (with full details in supplementary material; Table 1); using ODD to point readers to relevant sections of the model code; update the document structure to include sections on model rationale and evaluation. We also further advocate the need for standard descriptions of simulation experiments and argue that ODD can in principle be used for any type of simulation model. Thereby ODD would provide a lingua franca for simulation modelling.
Individual-based models (IBMs) allow the explicit inclusion of individual variation in greater detail than do classical differential-equation and difference-equation models. Inclusion of such ...variation is important for continued progress in ecological and evolutionary theory. We provide a conceptual basis for IBMs by describing five major types of individual variation in IBMs: spatial, ontogenetic, phenotypic, cognitive, and genetic. IBMs are now used in almost all subfields of ecology and evolutionary biology. We map those subfields and look more closely at selected key papers on fish recruitment, forest dynamics, sympatric speciation, metapopulation dynamics, maintenance of diversity, and species conservation. Theorists are currently divided on whether IBMs represent only a practical tool for extending classical theory to more complex situations, or whether individual-based theory represents a radically new research program. We feel that the tension between these two poles of thinking can be a source of creativity in ecology and evolutionary theory.
Carrying capacity is a key concept in ecology. A body of theory, based on the logistic equation, has extended predictions of carrying capacity to spatially distributed, dispersing populations. ...However, this theory has only recently been tested empirically. The experimental results disagree with some theoretical predictions of when they are extended to a population dispersing randomly in a two-patch system. However, they are consistent with a mechanistic model of consumption on an exploitable resource (consumer–resource model). We argue that carrying capacity, defined as the total equilibrium population, is not a fundamental property of ecological systems, at least in the context of spatial heterogeneity. Instead, it is an emergent property that depends on the population’s intrinsic growth and dispersal rates.
The logistic equation, with carrying capacity, K, and growth rate, r, has traditionally been used to describe dynamics of ecological populations.Experiments confirmed the prediction that dispersal could increase metapopulation abundance in heterogeneous environments, whereas they rejected the prediction that heterogeneous environments support a larger metapopulation abundance than homogeneous environments with the same sum over K values.Consumer-resource models, which explicitly consider the resource inputs and time scales of feedbacks between organisms and their resource, agree consistently with experimental results, suggesting they are more appropriate for describing populations in space.The theoretical results have important management implications on wildlife, such as the important role of dispersal, or habitat connectivity, in influencing population abundance in patchy environments.
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