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This chapter suggests a general working framework for experimental study of large-scale dynamics of EEG, including interpretation of data recorded at different spatial and temporal scales. It views source dynamics as a stochastic (random) process having statistical properties that change with changes in behavior and cognition. It avoids any attempts to choose the “best” methods of EEG or SSVEP data analysis because any such optimization requires prior knowledge of the underlying source dynamics. Fourier-based methods are emphasized to estimate power, phase, coherence, and closely related dynamic measures in distinct frequency bands. Additional methods include estimates of phase velocity across the scalp and frequency-wavenumber spectral analysis. The latter is expressed in terms of spherical harmonics, the natural spatial functions for dynamics on a spherical surface. This approach is used to pick out individual Schumann resonances as an example, in preparation for a similar application to EEG and SSVEP presented in Chapter 10.

This chapter is an analysis of the frequency-power spectrum. It first discusses the probabilistic methods for detecting signatures of individual modes in the spectrum, including schemes that incorporate a Bayesian framework for the analysis. The chapter then turns to the automated detection of the ensemble signatures of the oscillations. Next, this chapter considers the detailed peak-bagging analysis, where a multiparameter model is fitted to the spectrum to provide robust estimates of parameters of the individual modes. It introduces the fundamentals, discusses the practical implementation and challenges, and finally considers the additional challenges posed by subgiants and red giants showing mixed modes.

This chapter details the frequency-domain properties of observational data on stars. It is from the analysis of the frequency spectrum of the observations that the asteroseismic parameters are usually extracted. The chapter looks at each of the intrinsic stellar contributions in turn, always with an eye to how each must be handled in the asteroseismic analysis. It also considers the impact on the analysis of gaps in the data. In performing the analyses, this chapter begins by covering practical fundamentals associated with estimation of the frequency spectra, which underpin everything that follows. In addition, this chapter will be making use of Fourier transforms in studying the data.

Different types and phases of a selective sweep (hard, soft, partial, polygenic) generate different patterns of departures from neutrality, and hence require different tests. It is thus not surprising that a large number of tests have been proposed that use sequence information to detect ongoing, or very-recently completed, episodes of selection. This chapter critically reviews over 50 such tests, which use information on allele-frequency change, linkage disequilibrium patterns, spatial allele-frequency patterns, site-frequency spectrum data, allele-frequency spectrum data, and haplotype structure. This chapter discusses the domain of applicability for each test, and their strengths and weaknesses. Finally, this chapter examines application of these methods in the search for recent, or ongoing, selection in humans and for genes involved in the domestication process in plants and animals.

This chapter focuses on the International Telecommunication Union’s (ITU) complex governance of international radio frequency spectrum and orbital slots for geostationary satellites. It shows that the ITU’s global governance framework generally favors first movers over latecomers. It considers current pressures on the framework and offers suggestions for enhancing the interests of non-dominant players. The chapter first examines spectrum uses that cross borders and how they raise equity and national sovereignty concerns. It then discusses conflict avoidance and conflict resolution through multilateral coordination, pooling investment in international satellites to promote access, the push for market resource allocation alternatives, and the strengths and weaknesses in the ITU spectrum management process. It also looks at issues concerning the registration of unviable “paper satellites,” the use of a block allocation method for allocating spectrum, property ownership, and problems in competitive bidding and spectrum congestion remedies. Finally, the chapter analyzes empowerment opportunities for developing countries with respect to addressing spectrum congestion and interference.

This chapter discusses a sum of many waves with different frequencies, resulting in wave forms with particular time dependence. The propagation of the time-dependent wave solution through free space, or media with a particular dispersion relation, are analysed. Interesting cases such as the effect of group velocity dispersion, slow light, and fast light are highlighted.

When a favorable allele increases in frequency, it alters the coalescent structure (the pattern of times back to a common ancestor) at linked sites relative to that under drift. This creates patterns of sequence polymorphism than can be used to potentially detect ongoing, or very recent, selection. This idea of a neutral allele hitchhiking up to high frequency when coupled to a favorable allele is the notion of a selective sweep, and this chapter reviews the considerable body of associated population-genetics theory on sweeps. Different types of sweeps leave different signatures, resulting in the very diverse collection of tests of selection discussed in Chapter 9. Either a history of recurrent sweeps, or of background selection, results in linked genomic regions of reduced effective population size. This implies that more mutations in sich regions are efficiently neutral, which can result in increased substitution rates and lower codon bias. Finally, the chapter examines the theory for when response is expected to start from existing variation, as opposed to waiting for the appearance of new mutations.

Chapter 7 is an introduction to molecular population genetics that includes the principal concepts of nucleotide polymorphism and divergence, the site frequency spectrum, and tests of selection and their limitations. Highlighted are rates of nucleotide substitution in coding and noncoding DNA, nucleotide and amino acid divergence between species, corrections for multiple substitutions, and the molecular clock. Discussion of the folded and unfolded site frequency spectrum includes the strengths and limitations of Tajima’s D, Fay and Wu’s H, and other measures. The chapter also discusses an emerging consensus to resolve the celebrated selection–neutrality controversy. It also includes examination of demographic history through the use of ancient DNA with special emphasis on the surprising findings in regard to the ancestral makeup of contemporary human populations. Also discussed are the population dynamics of transposable elements in prokaryotes and eukaryotes.

This chapter reviews the population-genetic theory of neutral alleles in finite populations, examining the probabilities and times to loss or fixation, summary statistics for molecular variation, coalescent theory (the distribution of times back to common ancestry for a sample of alleles), and both mutation-drift and mutation-drift-migration equilibrium models.

Linear age-structured models eventually grow geometrically, and reach a stable age distribution (as in Chapter 3). This chapter describes what happens before “eventually.” That is, it describes the short-term, “transient” dynamics that occur when a population is perturbed, then begins to return to its stable distribution. Transients involve eigenvalues other than the largest (real) one, so the chapter begins by showing how complex eigenvalues can produce population cycles. It then addresses factors that make transients shorter or longer. In some cases, frequent environmental disturbances may prevent populations from ever reaching equilibrium. That scenario can be described by switching from linear models to linearized models varying about an equilibrium. The chapter describes temporal characteristics of that variability (such as time scales and frequencies), which require new tools: Fourier transforms and wavelets. These reveal how age-structured populations are more sensitive to certain environmental frequencies than to others, a phenomenon termed cohort resonance.

Chapter 3, “Quantifying genetic variation at the molecular level,” introduces quantitative methods for measuring variation directly in DNA sequences to help decipher fundamental properties of populations and what they can tell us about evolution. It provides an overview of the evolutionary factors that contribute to genetic variation, like mutational input, effective population size, genetic drift, migration rate, and models of migration. This chapter surveys the principal ways to measure and summarize polymorphisms within a single population and across multiple populations of a species, including heterozygosity, nucleotide polymorphism estimators of θ‎, the site frequency spectrum, and F_ST, and by providing illustrative natural examples. Populations are where evolution starts, after mutations arise as the spark of population genetic variation, and Chapter 3 describes how to quantify the variation to connect observations to predictions about how much polymorphism there ought to be under different circumstances.

Chapter 8, “Molecular deviants: sequence signatures of selection and demography,” dives into the logic and mechanics of some of the most common tests of neutrality to show how and why data can reveal differences from the predictions of the standard neutral model. It introduces approaches based on skewed patterns of polymorphism alone, including Tajima’s D test, and on differentiation or divergence alone, like the Lewontin-Krakauer, Population Branch Statistic (PBS), and K_A / K_S relative-rates tests. Chapter 8 also covers tests of neutrality that integrate information from both within and between species, including the HKA-test and McDonald-Kreitman (MK) test. The logic for other tests of neutrality also is introduced, including ABBA-BABA, Composite Likelihood Ratio (CLR), Extended Haplotype Homozygosity (EHH), and other approaches. Practical implications of ancestral polymorphism and slightly deleterious polymorphisms are discussed, for example, in calculating and interpreting the neutrality index and fraction of positively selected sites (α‎). The goal of this chapter is to explain the logic of methods applied to molecular population genetic data to read the story of evolutionary history from the genome.