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This chapter discusses adaptive diversification due to predator–prey interactions. It has long been recognized that consumption, that is, predation, can not only exert strong selection pressure on the consumer, but also on the consumed species. However, predation has traditionally received much less attention than competition as a cause for the origin and maintenance of diversity. By using adaptive dynamics theory as well as individual-based models, the chapter then illustrates that adaptive diversification in prey species due to frequency-dependent predator–prey interactions is a theoretically plausible scenario. It also describes conditions for diversification due to predator–prey interactions in classical Lotka–Volterra models, which requires analysis of coevolutionary dynamics between two interacting species, and hence of adaptive dynamics in two-dimensional phenotype spaces.

This chapter introduces mathematical and statistical modelling approaches in population ecology. It starts with a conceptual section, continues with mathematical and statistical sections, and ends with a perspectives section. The conceptual section motivates the modelling approaches by providing the necessary background to population ecology. The mathematical sections start by constructing an individual-based model in homogeneous space, and then simplifies the model to derive the classical model of logistic population growth. The models are then expanded to heterogeneous space in two contrasting ways, resulting in models called the plant population model and the butterfly metapopulation model. Both types of models are used to analyse the consequences of habitat loss and fragmentation at the population level. To illustrate the interplay between models and data, the statistical section analyses data generated by the mathematical models, with emphasis on the analyses of time-series data, species distribution modelling, and metapopulation modelling.

This chapter summarizes the key characteristics of the approach for modeling, studying, and understanding populations and communities of adaptive individuals described here, and outlines the lessons learned from all the models examined in this book. Many of these characteristics are shared with individual-based population modeling in general. First, state- and prediction-based theory (SPT) explicitly includes multiple levels of organization: models of individual adaptive behavior explain population and higher-level dynamics. Second, doing theory is more productive when one models real systems and applied problems. Third, the approach relies on simulation, approximation, and updating instead of traditional mathematical frameworks. Fourth, SPT and the theory testing cycle facilitate beneficial linkage of modeling and empirical work. Finally, the pattern-oriented theory development cycle gives ecologists the power of strong inference.

This chapter provides an overview of adaptive trade-off behaviors, which are common in natural systems and probably often important, as illustrated by the large body of research that has used giving-up food densities to quantify predation risk across a broad range of taxa. Adaptive trade-off behaviors can range from short-term decisions such as habitat and activity selection, to midterm responses such as energy allocation, to seasonal decisions such as when and where to migrate, to irreversible life-history decisions such as whether to enter a reproductive state. Understanding and quantifying the importance of adaptive trade-off behavior has been a major theme of ecology in recent decades. The chapter then reviews the different models and publications that have addressed the problem of modeling populations and communities of adaptive individuals, one example of which are individual-based models. It also considers the importance of physiology and neurobiology to adaptive behavior, and introduces the state- and prediction-based theory.

This chapter provides an introduction to a set of theoretical and numerical models that have been developed for this purpose. Spatial dynamic models are presented in three integral parts: modelling core, context, and method. Modelling cores are dynamic models for describing population demography and spread. Lagrangian models of random walks and step-selection functions that aim to portray and explain individual movement, and Eulerian models of reaction-diffusion and integrodifference equations that aim to capture the spatial dynamics of populations are introduced. Modelling context defines the arena for implementing the core. The basics of species distribution models to provide the context of suitable habitat are presented, leaving aspects of hybrid models, biotic interactions, and non-equilibrium dynamics to other chapters. Modelling methods are techniques for implementing cores in context. Different agent-based models, including individual-based models, cellular automata, and gravity (network) models, are explained.

Mathematical models are essential components of the toolbox of any disease ecologist. They should be used as an integral part of any investigation into the impact and management of infectious disease in wildlife populations. Simple models are important to conceptualize the processes occurring during host–pathogen interactions and to identify key components of these interactions. More detailed models, specific to the system in question, can be developed later in an investigation and are essential for evaluating the consequences of alternative management actions. Various models of infectious disease dynamics are available to assist in managing disease in wildlife, including single-host and multihost models, and are discussed here. The basic reproductive number R₀, the number of secondary cases per primary case when disease is rare, can be derived from these models. This is a key concept in practical epidemiology, because eliminating a pathogen from a population entails reducing R₀ to below one and disease emergence can only occur if R₀ becomes greater than one.

When theorists are confronted with highly idealized models of phenomena, they require a method for determining which aspects of their models make trustworthy predictions or can reliably be used in explanations. In some cases, such as when one is modeling physical systems, fundamental theories can guide the theorist. Such theories have the resources to estimate the effect of various idealizations, providing guidance about which idealizations are acceptable when particular degrees of accuracy and precision are required. In the study of many complex systems, however, such theories are unavailable. In these cases, robustness analysis provides an alternative method for determining when models make trustworthy predictions about their targets.

In socially structured animal populations, vital rates such as survival and reproduction, are affected by complex interactions among individuals of different social ranks and among social groups. Due to this complexity, mechanistic approaches to model vital rates may be preferred over commonly used structured population models. However, mechanistic approaches come at a cost of increased modelling complexity, computational requirements, and reliance on simulated metrics, while structured population models are analytically tractable. This chapter compares different approaches to modelling population dynamics of socially structured populations. It first simulates individual-based data based on the life cycle of a hypothetical cooperative breeder and then projects population dynamics using a matrix population model (MPM), an integral projection model (IPM), and an individual-based model (IBM). The authors demonstrate that, when projecting population size or structure, the relatively simpler MPM can outperform both the IPM and IBM. However, mechanistic details parametrised in the more complex IBM are required to accurately project interactions within social groups. The R scripts in this chapter provide a roadmap to both simulate data that best describe a socially structured system and assess the level of model complexity needed to capture the dynamics of the system.

This chapter assesses how state- and prediction-based theory (SPT), as a nontraditional approach to modeling adaptive behavior embedded in a nontraditional population modeling approach, faces a significant credibility challenge. This challenge is complicated by the many ways that models can gain or lose credibility, and widespread confusion surrounding the term model validation. The chapter then addresses the task of testing, improving, and establishing the credibility of individual-based models (IBMs) that contain adaptive individual behavior. The experience with the trout and salmon models provides the primary basis for this discussion, but other long-term modeling projects have produced similar experiences. The chapter summarizes some of the issues and challenges that typically arise and how they have been dealt with, before presenting lessons learned from two decades of empirical and simulation studies addressing credibility of the salmonid models.

This chapter outlines the guidance on using state- and prediction-based theory (SPT) to build models of populations and communities of adaptive individuals, detailing five steps unique to SPT. The most important aspect of SPT to remember is that one is not trying to build optimal, or even necessarily accurate, models of how an organism's behavior affects its future fitness. Instead, one is trying to find simplistic models that produce realistic behavior in contexts where optimization is impossible. While SPT can be used like dynamic state variable modeling (DSVM), as a framework for thinking about and modeling how an individual makes a particular decision, its main purpose is to model adaptive trade-off decisions in individual-based population models. Thus, using SPT is part of the larger process of developing, analyzing, and applying an IBM to address population-level questions, and the five steps therefore include that process.

To acquire a more thorough understanding of the complexity of natural systems, researchers have sought the assistance of advanced computer-based technologies in the development of integrated modeling and simulation systems. Computer simulations have been utilized in a variety of natural resource management applications from modeling animal populations, to forest fires, to hydrologic systems. Computer models may be developed to understand more about how a real system works, as when scientists develop models of ecological processes. Such models may facilitate predictions of a real system’s behavior under a variety of conditions, or a greater understanding of the structure of a real system. There are numerous advantages to developing and experimenting with models of real-system phenomena. Experimenting with the real system itself may be too costly and time consuming, or even impossible. Simulations are completely repeatable and nondestructive. The data produced by simulations is often easier to interpret than data from a real system. Geographic information systems (GIS) technology has led these developments providing powerful databases for storing and retrieving spatially referenced data. Spatial information is stored in many different themes representing quantitative, qualitative, or logical information. These data can have different resolutions that range from detailed local information to small-scale satellite imagery. GIS operators provide the means for manipulating and analyzing layers of spatial information and for generating new layers. Since it allows distributed parametrization, a GIS is useful for ecological models that need to explicitly incorporate the spatial structure and the variability of system behavior. A raster-based GIS represents spatial information as a grid of cells, and each cell corresponds to a uniform parcel of the landscape. Cells are spatially located by row and column and the cell size depends on the resolution required. GIS provides an excellent means of capturing real-world data in multiple layers (three dimensional) and resolutions (spatial scales) over time. Due to the complexity of ecosystem dynamics, interest has increased in using GIS for simulation of spatial dynamic processes.

This chapter highlights the importance of testing and refining the behavior theory in individual-based models (IBMs). Establishing a model's credibility is not the only reason to test theory for behavior. Doing so also offers a new and productive approach to theoretical ecology: a way to develop a toolbox of across-level theory useful for modeling populations of adaptive individuals. One can refer to testing and refining behavior sub-models as theory development, and one can do it by following the classic inductive reasoning cycle of posing, testing, and falsifying alternative hypotheses. The chapter provides a brief introduction to the pattern-oriented theory development process and presents several examples.

This chapter introduces mathematical and statistical modelling approaches in community ecology. It starts with a conceptual section, continues with mathematical and statistical sections, and ends with a perspectives section. The conceptual section motivates the modelling approaches by providing the necessary background to community ecology. The mathematical sections start with models of two interacting species in homogeneous space, including a model with competitive interactions, a resource–consumer model, and a predator–prey model. The competition model is expanded to heterogeneous space and to the case of many competing species. This model is used to analyse the consequences of habitat loss and fragmentation at the community level. To illustrate the interplay between models and data, the statistical section analyses data generated by the mathematical models, with emphasis on time-series data of two interacting species, point pattern analyses, and joint species distribution models.

This chapter discusses the state- and prediction-based theory (SPT) and its use in individual-based models (IBMs). The fundamental concept of modern theory in behavioral ecology is that behavior acts to maximize a specific measure of fitness at a specific future time, and that this fitness measure incorporates multiple elements, such as the need to avoid predators, the need to avoid starvation, and the benefits of energy accumulation for reproduction. This concept has been applied widely and successfully in dynamic state variable modeling (DSVM), and SPT was developed as a way of using the same principle in IBMs when feedback from the behavior of other individuals, combined with unpredictable environmental conditions, make the assumption of optimality used by DSVM impossible. The chapter then looks at the differences between SPT and DSVM. To model populations of adaptive individuals, SPT is implemented using five steps. These steps include embedding SPT in an IBM that simulates the processes that drive behavior, both internal to the individual and external.

This chapter starts with a discussion of some common criticisms of the artificial chemistry approach to modeling systems. It turns out that “opaque thought experiments” are an answer to some of them. Next we delimit the borders of the field, since obviously not everything can be modeled as an AC. After a summary of the main features of artificial chemistries we conclude the book with appeal to curiosity and research initiative of the reader.

After 600 years of persecution, during which dramatic population fluctuations occurred, common buzzards are increasing in abundance and recolonizing most of lowland UK. But recovery is bringing them to the heart of a controversy. Once again, game-managers and poultry farmers blame buzzards for killing stock and thus harming livelihoods. To better understand buzzard biology and assess their impact on wildlife and domestic stock, field data and well-established and innovative modelling techniques were used. It was noted that phylopatry resulted in a naturally slow rate of buzzard population expansion, while habitat availability now limits population abundance. The impact of buzzard predations on released pheasants was found be variable but typically small, and it was also found that high predation can be reduced with simple pen management measures. Licensed translocation of ‘problem’ buzzards may also be an option, but only if accompanied by improvements in management to avert re-colonizing buzzards from also developing a livelihood-harming diet. The worry is, however, that concern about translocation of raptors risks diverting public opinion from the more serious issues of poor land use and climate change.

The social and behavioral sciences have a long-standing interest in the factors that foster selfish (or individualistic) versus altruistic (or cooperative) behavior. Since the 1960s, evolutionary biologists have also devoted considerable attention to this issue. In the last 25 years, mathematical models (reviewed in Wilson and Sober 1994) have shown that, under particular demographic conditions, natural selection can favor traits that benefit group members as a whole, even when the bearers of those traits experience reduced reproductive success relative to other members of their group. This process, often referred to as "trait group selection" (D. S. Wilson 1975) can occur when the population consists of numerous, relatively small "trait groups," defined as collections of individuals who influence one another's fitness as a result of the trait in question. For example, consider a cooperative trait such as alarm calling, which benefits only individuals near the alarm caller. A trait group would include all individuals whose fitness depends on whether or not a given individual gives an alarm call. If the cooperative trait confers sufficiently large reproductive benefits on the average group member, it can spread. This is because trait groups that happen to include a large proportion of cooperators will send out many more offspring into the population as a whole than will groups containing few, or no cooperators. Thus, even though noncooperators out reproduce cooperators within trait groups (because they experience the benefits of the presence of cooperators without incurring the costs), this advantage can be offset by differences in rates of reproduction between trait groups. Numerous models of group selection (Wilson and Sober 1994) show that whether cooperative traits can spread depends on the relative magnitude of fitness effects at these two levels of selection (within and between trait groups). In addition, there is a growing body of empirical evidence for the operation of group selection in nature (e.g., Colwell 1981; Breden and Wade 1989; Bourke and Pranks 1995; Stevens et al. 1995; Seeley 1996; Miralles et al. 1997; Brookfield 1998) and under experimental conditions (reviewed in Goodnight and Stevens 1997).

The number of reproductive units is expected to grow exponentially in the absence of regulating feedbacks. The lack of feedbacks is a definitive assumption of any model predicting exponential growth, be it individual- or population-based, discrete or continuous, deterministic or stochastic. The exponential growth of a population can be characterised by its long-term per capita rate of increase (population growth rate, pgr) in any actual representation. Exponential growth with a constant pgr will occur whenever the stochastic changes in the environmental conditions—including modifying and regulating ones—affecting births and deaths are stationary in the long run. Case studies indicate that temporary periods of exponential population increase or decline must be regular in nature, and pgrs may show remarkable temporal and spatial invariance.

This chapter introduces mathematical and statistical modelling approaches to study the ecology of movement. It starts with a conceptual section, continues with mathematical and statistical sections, and ends with a perspectives section. The conceptual section motivates the modelling approaches by providing the necessary background to movement ecology. The mathematical sections first introduce random walk and diffusion models in homogeneous space, and use these models to illustrate the relationship between the Lagrangian and the Eulerian viewpoints. The movement models are then expanded to heterogeneous space, and in particular to highly fragmented patch networks. To illustrate the interplay between models and data, the statistical section analyses data generated by the mathematical models, with emphasis on the analyses of tracking data and capture-mark-recapture data.