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This chapter examines the dynamics of basic population models, with a particular focus on the general biological conditions under which population dynamics are stabilized, or destabilized, by increased population growth rates. Three classes of population models are discussed in relation to excitable and nonexcitable interactions: continuous logistic growth models, discrete equations, and continuous models with stage-structured lags. The chapter shows how increasing per capita growth rates tend to stabilize population models as a result of excitable interactions; that is, when dynamic trajectories monotonically approach an equilibrium after a localized perturbation. However, lags in population models tend to give rise to dynamics with oscillatory decays to equilibrium or sustained oscillations around the carrying capacity. Such oscillatory decays or sustained oscillations are only further destabilized by increased growth or production rates. The chapter concludes with a review of empirical evidence for excitable dynamics.

Shows how the dominant design shapes the nature of the competition in the new mass market. Using the mobile market as an example, it describes the typical pattern of market growth as a logistic one, with an initial slow rate, followed by a sudden take‐off into a period of rapid growth, which, eventually, slows. It devotes the rest of the chapter to look into the factors that might explain this S‐shaped growth. Genetically modified food and shipbuilding are some of the product‐case studies used to illustrate the analysis.

This chapter reviews the basic mathematics of population growth as described by the exponential growth model and the logistic growth model. These simple models of population growth provide a foundation for the development of more complex models of species interactions covered in later chapters on predation, competition, and mutualism. The second half of the chapter examines the important topic of density-dependence and its role in population regulation. The preponderance of evidence for negative density-dependence in nature is reviewed, along with examples of positive density dependence (Allee effects). The study of density dependence in single-species populations leads naturally to the concept of community-level regulation, the idea that species richness or the total abundance of individuals in a community may be regulated just like abundance in a single-species population. The chapter concludes with a look at the evidence for community regulation in nature and a discussion of its importance.

This chapter introduces basic concepts in population modeling that will be applied throughout the book. It begins with the oldest example of a population model, the rabbit problem, which was described by Leonardo of Pisa (“Fibonacci”) and whose solution is the Fibonacci series. The chapter then explores what is known about simple models of populations (i.e. those with a single variable such as abundance or biomass). The two major classes are: (1) linear models of exponential (or geometric) growth and (2) models of logistic, density-dependent growth. It covers both discrete time and continuous time versions of each of these. These simple models are then used to illustrate several different population dynamic concepts: dynamic stability, linearizing nonlinear models, calculation of probabilities of extinction, and management of sustainable fisheries. Each of these concepts is discussed further in later chapters, with more complete models.

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 assesses how social feedbacks, and particularly runaway dispersal resulting from social copying, influence population extinction. Several forms of the logistic model are built to assess the role of density-dependent and cooperation mechanisms in the generation of nonlinearities in the path to extinction. Interestingly, transience to an extinction stable state may be delayed and may result in quasi-extinction population queues. Some empirical examples of quasi-extinction stable states are shown, including human populations. It is also explained how social sunk-cost effects—when individuals are trapped in a patch due to its momentum of suitability, social copying, or emotional drivers—can influence these quasi-extinction dynamics. The chapter also reviews several statistical tools for anticipating critical transitions and other nonlinear behaviours in populations. These tools include the early warning signals, which quantify when a critical threshold is approaching.

This chapter starts with proving the inevitability of population growth regulation, and concludes with an explanation of the exclusive resource limitation principle that, through determining community structure, shapes the landscape surrounding us. Population regulation may be mediated by resource-limitation (Tilman model) or site-limitation (Levins model), or natural enemies like predators, parasites, or parasitoids. Food chain length sometimes determines the main quantitative features of complete communities through top-down regulation. All regulatory mechanisms share one feature: they feed back population abundance on population growth, ultimately setting strict limits on population growth and fluctuations, even if facilitation-induced positive ecological feedbacks (e.g. Allee effects) may act at low population sizes. The way of modelling interactions between individuals (e.g., functional responses) is explained and illustrated by examples. The relations of explicit (logistic) and implicit (process-based) models of population dynamics and some model-based interpretations of case studies and experimental results are shown.

Across a wide range of different organisms, abundance data form one of the backbones for understanding the dynamics of populations. This type of data consists of measures of population size over time or space in the form of numbers of individuals, biomass, areal cover, or other measures. Abundance data contain no direct information about demographic processes but are available at larger scales or higher resolution in space and time than direct demographic data. This chapter introduces some of the basic statistical modeling strategies that can be used to learn about populations from abundance data in the absence of information about demographic details. These strategies include standard but flexible regression techniques, including mixed and additive models, time-series methods such as auto-regressive and state-space models, as well as simple population growth models derived from ecological theory.

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).

As academic disciplines ecology and wildlife ecology both recognize the importance of habitat to the daily survival of individuals and long-term persistence of populations. Although the explicit and direct study of habitat originally emerged in ecology, wildlife ecologists historically have been more involved in its study and in the analysis of species–habitat relationships. This is partly due to wildlife ecologists being interested in habitat management for particular species and applying a resource-based concept of habitat to better understand population growth rates, particularly for harvested or hunted species. In the 1930s onward for several decades, Aldo Leopold played a prominent role in establishing wildlife ecology (and management) as its own academic field and practice. Leopold was keenly aware of population dynamics although he seemed to not directly link his empirical observations of population fluctuations to any of the emerging mathematical population growth models of the day. This may have also indirectly allowed the early growth of wildlife ecology to proceed without any of its own emergent theory. Despite historical, paradigmatic, practical, and subject matter differences between the two disciplines, both are becoming more similar to one another as interdisciplinary collaboration and communication continue to increase.

There are several reasons for conducting a habitat analysis and identifying the environmental (habitat) characteristics that a species associates with. (1) Knowledge of a species’ habitat requirements is crucial in restoring and managing habitat for the species. (2) Carrying capacity informs us about the potential (or lack thereof) for future population growth based on resource availability. Knowledge of a species’ habitat requirements allows us to interpret the importance of carrying capacity in a habitat-specific way. (3) The study of species interactions and the potential for species coexistence is supported by having knowledge of the habitat of each species under investigation. (4) Habitat preference and selection as eco-evolutionary processes continue to be widely studied by ecologists—interpretation of the results of such studies is best done with knowledge of the species–habitat associations. Such knowledge can also be useful in the design of preference and selection studies. (5) Knowledge of species–habitat associations can also be of great use in selecting the environmental variables to use in species distribution models. All five of these goals point to the great utility of conducting a habitat analysis as a supporting investigation or as a way to obtain knowledge to put to a practical purpose.