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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.

There is now overwhelming empirical evidence for age-related declines in fitness-related traits, i.e. senescence, during adulthood in wild vertebrate populations, presumably underpinned by physiological deterioration. Longitudinal field studies are also demonstrating that the rates of these observed declines vary among individuals and among traits. From an evolutionary perspective, the challenge remains to determine the contribution of genetic sources to this variation and the genetic correlations among traits underpinning fitness at different ages in natural systems. Although laboratory studies are revealing an ever-increasing amount about potential genetic and physiological pathways regulating lifespan and ageing in model systems, quantitative genetic studies in the wild can provide unique insights into how selection has shaped and maintained variation in ageing trajectories and senescence under complex, natural conditions. This chapter briefly discusses the classical evolutionary theories of ageing, emphasising the importance of estimating age-dependent patterns of genetic (co)variance (genotype-by-age interactions; G × A), rather than attempting to disentangle non-mutually exclusive putative mechanisms such as mutation accumulation and antagonistic pleiotropy. It provides an overview of approaches for quantifying G × A, emphasising the importance of function-valued trait models, such as the random regression animal model, and presents a critical review of the limited number of studies that have implemented these approaches in the context of wild populations. Finally, this chapter identifies a number of statistical issues/challenges that are likely to hold back much needed developments in this field and provides recommendations of ways to overcome these challenges as well as for avenues for future work.