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This introductory chapter provides an overview of frequency-dependent selection—the phenomenon that the evolving population is part of the changing environment determining the evolutionary trajectory. Selection is frequency-dependent if the sign and magnitude of the correlations between heritable variation and reproductive variation change as a consequence of changes in the trait distribution that are themselves generated by such correlations. From the perspective of mathematical modeling, the realm of frequency dependence in evolution is larger than the realm of situations in which selection is not frequency dependent, because the absence of frequency dependence in a mathematical model of evolution essentially means that some parameters describing certain types of biological interactions are set to zero. Thus, in a suitable parameter space, frequency independence corresponds to the region around zero, while everything else corresponds to frequency dependence. In this way, frequency-dependent selection should therefore be considered the norm, not the exception, for evolutionary processes.

Although we must understand the mechanical nuts and bolts of inheritance, evolution occurs through changes in the population frequencies of traits, trait values, and genes in time and space, values that depend at least as much on the dynamics of populations as on the mechanics of inheritance. This chapter demonstrates the crucial roles of ecology in evolutionary change. There are two major types of dynamics that are essential to model evolution. The chapter develops the principles of strategy dynamics to examine the processes responsible for the success and failure of some traits, and trait values, over others. Different traits and their values represent competing strategies to be tested by adaptive evolution. The success of each strategy depends on the spatial and temporal dynamics of populations, and their respective influences on those dynamics. The chapter merges strategy and population dynamics to evaluate the evolutionary stability of competing strategies.

Müllerian mimicry arises when unpalatable or otherwise unprofitable species evolve a similar appearance. While Batesian mimicry is widely considered to have evolved in palatable prey as a consequence of selection to deceive predators into believing that they are unpalatable, Müllerian mimicry is believed to have arisen as a consequence of selection to spread the burden of predator education through the adoption of a shared warning signal. Müllerian mimics are therefore considered mutualists, collectively reinforcing the protective value of their shared warning signals. We begin by discussing some examples of Müllerian mimicry that cannot be explained simply on the basis of shared ancestry. We then discuss Müller’s explanation in more depth, before presenting evidence that the shared resemblance has arisen for the reason that Müller hypothesized. Finally, we consider some of the predicted and observed properties of Müllerian mimicry systems in detail, including ecological and co-evolutionary phenomena, and consider some common questions that have only been partly resolved. We end by considering the connection between Batesian and Müllerian mimicry, arguing that like many natural systems, the nature of relationships can readily fluctuate from being parasitic to mutualistic and vice versa.

Our responses to sound and light are crucial. We sense them over intensity ranges of at least one million to one. Our brain makes compromises to deal with so much information. The strategy is to just recognize relative signal levels (e.g. to if one signal is twice that of another). In terms of actual intensity, a doubling in sound (or brightness of light) means it has increased by a factor of ten. This logarithmic counting system means a detailed range of one to a million has compressed to just six intensity doublings (ditto for storm and earthquake intensity scales). The ear response creates many unexpected distortions. Our hearing changes with age, and quite dramatically falls when exposed to prolonged high-volume sounds, including exposure to excessively loud music. This is a negative side of electronic amplification and broadcasting, and for headphones or hearing aids there are many distortions.

The chapter starts with an introduction to game theory in biology, describing its overall aims. The basic concept of frequency dependence is then presented, together with a number of illustrative biological examples. Next, the modelling approach is outlined, emphasizing that the theory aims to predict phenomena by seeking stable evolutionary endpoints. The scope and challenges of the field are described in the setting of the history of ideas that have been important for the theory, summarizing past successes as well as long-standing questions that are likely to require further development of the theory. The chapter ends with an overview of the main issues dealt with in the book, including the challenges that are taken up. These include taking into account the co-evolution of traits, exploring the consequences of variation, and the modelling social interactions as games over time. In particular for the latter, models that include behavioural mechanisms are likely to be essential for the success of game theory in biology.

Macroevolutionary patterns concern phylogenies of hosts and their parasites. From those, co-speciation occurs; but host switching is a common evolutionary process and more likely when hosts are close phylogenetically and geographical ranges overlap. Microevolutionary processes refer to allele frequency changes within population. In arms races, traits of hosts and parasites evolve in one direction in response to selection by the other party. With selective sweeps, advantageous alleles rapidly spread in host or parasite population and can become fixed. With antagonistic negative frequency-dependent fluctuations (Red Queen dynamics) genetic polymorphism in populations can be maintained, even through speciation events. A Red Queen co-evolutionary process can favour sexual over asexual reproduction and maintain meiotic recombination despite its other disadvantages (two-fold cost of sex). Local adaptation of host and parasites exist in various combinations; the relative migration rates of the two parties, embedded in a geographical mosaic, are important for this process.

Following the rapid formation of the surface of a surfactant so′′lution, the dynamic interfacial tension falls with time as a result of the finite time needed for surfactant adsorption. Surfaces can either be sheared (involving shape change) or dilated (area is changed), and both these processes can give a viscous and/or elastic response. Usually, surfaces of surfactant solutions exhibit a combination of the two and are viscoelastic. If small sinusoidal area changes are imposed on the surface, changes in tension and area are out of phase because surfactant adsorption is relatively slow. The responses to area change are frequency dependent. The complex dilational viscoelastic modulus, ε‎*, has real (elastic) and imaginary (viscous) parts, ε‎′ and ε‎′′, respectively, whose variation with frequency provides insights into relaxation processes occurring at the surface. The way in which dynamic tensions can give insights into the kinetics of surfactant adsorption is explained.

Important information about the excitation spectra of semiconductors and insulators can be obtained by studying the frequency dependence of the absorption of light passing through the material. This chapter first introduces the matrix element for optical absorption spectra. At low temperatures, transitions take place only between the occupied valence band states and the unoccupied conduction band states. An expression is developed for the transition probability per unit time between two such states, wherein a matrix element — involving the perturbation Hamiltonian in Chapter 24 — connects the initial (valence band) state and the final (conduction band) state. The remainder of the chapter discusses the singular points in the optical absorption; the frequency-dependent susceptibility; some analytic properties of the susceptibility; the Kramers–Kronig relations; and some examples of optical spectra. Sample problems are also provided at the end of the chapter.

Understanding the allocation of energy is the goal of the evolutionary analysis of sex allocation. Whether one is concerned with the relative sizes of male and female flower parts in plants like those discussed by Campbell (1998), the ratio of males and females in insects like those discussed by Orzack et al. (1991), or the relative sizes of male and female reproductive organs in hermaphroditic fish like those discussed by Leonard (1993), one is concerned with how energy allocated toward reproduction is apportioned into one sex as opposed to the other (or more in the case of some kinds of organisms). Here, the sexes are entities that at regular or irregular intervals produce gametes, some of which come together to produce zygotes. The abstract nature of this description underscores the degree to which there are common evolutionary aspects to all of these problems, despite the fact that the biological details involved are so diverse. One of the most influential and important agendas for evolutionary studies of sex allocation was laid out by Charnov (1982). He described the underlying evolutionary similarities between phenomena as diverse as sex change in shrimp and sex ratio in vertebrates like us. Even more important, he promoted sex allocation as a central evolutionary problem by describing how seemingly unrelated allocation problems could all be analyzed with a kind of mathematical approach elaborated by Shaw and Mohler (1953). I consider in turn four important examples of this approach. Shaw and Mohler’s goal was to understand the evolution of the proportions of males and females. This problem of the sex ratio was most famously addressed by Darwin in his 1871 book, The Descent of Man, and Selection in Relation to Sex, as well as by others in the subsequent decades. The most influential analysis is that of Fisher (1930); however, Carl Düsing, who worked in the 1880s, can rightly be regarded as the progenitor of modern sex ratio theory (see Edwards 1998).

This chapter concerns Batesian mimicry, which is the resemblance of a palatable species to an unpalatable or otherwise unprofitable species. Often these unprofitable models have warning signals, which the mimic has evolved to copy. The chapter also considers another well-known form of deception, namely masquerade, which is the resemblance of a palatable species to the cues of an object of no inherent interest to a potential predator such as leaves, thorns, sticks, stones, or bird droppings. Batesian mimicry and masquerade share many properties, and both can be considered examples of ‘protective deceptive mimicry’. We begin by briefly reviewing some well-known examples of protective deceptive mimicry. We then compare and contrast the various theories that have been proposed to understand them. Next, we examine the evidence for the phenomenon and its predicted properties, and finally we address several important questions and controversies, many of which remain only partly resolved.