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For almost 30 years, Lande and Arnold's approximation of individual fitness surfaces through multiple regression has provided a common framework for comparing the strength and form of phenotypic selection across traits, fitness components and sexes. This chapter provides an overview of the statistical and geometric approaches available for the multivariate analysis of phenotypic selection that build upon the Lande and Arnold approach. First, it details least squares based approaches for the estimation of multivariate selection in a single population. Second, it shows how these approaches can be extended for the statistical comparison of individual fitness surfaces among groups such as populations or experimental treatments, addressing the inferential differences between analyses of randomly chosen groups versus situations in which groups are experimentally fixed. In each case, it points out known issues and caveats associated with the approaches. Finally, using case studies, the chapter shows how these estimates of multivariate selection can be integrated with quantitative genetic analyses to better understand issues such as the maintenance of genetic variance under selection and how genetic constraints can bias evolutionary responses to selection.

The concept of adaptive accuracy allows more refined measurement of maladaptation by considering not only the relation of a population or individual mean phenotype to a fixed optimum, but also the effects of variation across individuals and environments or in the developmental realization of a genotype. Previous models of adaptive inaccuracy have been based on a simple quadratic fitness function for a single trait. It should be kept in mind, however, that the validity of interpreting fitness surfaces and population distribution in terms of adaptive inaccuracy, bias and imprecision strongly depends on the quality of the estimated fitness function and trait(s) distribution. Building a full fitness surface is challenging, regarding both the necessary knowledge to include the proper fitness components and the amount of data required for building accurate fitness surfaces. Furthermore, the natural distribution of quantitative traits generally limits the range over which precise fitness function can be estimated. Our understanding of adaptation therefore depends on long term data on natural selection and proper estimation of adaptive landscapes. Nevertheless our conceptual approach of testing adaptation supports the idea that the adaptive landscape, as defined by Simpson and further developed by Lande and Arnold and others, is not only a heuristic device to illustrate the effects of natural selection, but also a powerful tool to quantify the levels of adaptation and maladaptation of phenotypic traits.

This chapter examines various estimates of the fitness of an individual, focusing on statistical issues and potential sources of bias. With estimates of individual fitness in hand, one can then search for fitness-trait association, and this topic comprises the second half of the chapter. A number of metrics for describing how the phenotypic distribution of a trait is perturbed by selection are examined, again along with a discussion of statistical issues and sources of bias.

The adaptive landscape metaphor is one of the most persistent in evolutionary biology, and has generated much theoretical debate (if far less empirical investigation). This chapter briefly traces the history of the concept since its introduction by Sewall Wright in the 1930s. It then distinguishes four types of landscapes pertinent to evolutionary theory: fitness landscapes, adaptive landscapes, fitness surfaces, and morphospaces. These are more or less loosely related to each other, and sometimes the relationship is complex and difficult to explore empirically. The chapter argues that some versions of the landscape metaphor have lost their utility and should be replaced by more sophisticated metaphors, or abandoned altogether. It suggests that — somewhat surprisingly — the most useful type of landscape may turn out to be the morphospace, a concept that allows for a productive bridge between theoretical analyses and empirical results, especially in fields such as palaeontology and evolutionary developmental biology. In particular, the chapter discusses examples from the paleontological literature that constitute instances of truly (and stunningly) predictive theoretical analysis in what is often considered an entirely descriptive historical science.