1.2: The roots of comparative methods
The comparative approaches in this book stem from and bring together three main fields: population and quantitative genetics, paleontology, and phylogenetics. I will provide a very brief discussion of how these three fields motivate the models and hypotheses in this book (see Pennell and Harmon 2013 for a more comprehensive review) .
The fields of population and quantitative genetics include models of how gene frequencies and trait values change through time. These models lie at the core of evolutionary biology, and relate closely to a number of approaches in comparative methods. Population genetics tends to focus on allele frequencies, while quantitative genetics focuses on traits and their heritability; however, genomics has begun to blur this distinction a bit. Both population and quantitative genetics approaches have their roots in the modern synthesis, especially the work of Fisher (1930) and Wright (1984) , but both have been greatly elaborated since then (Falconer et al. 1996; see Lynch and Walsh 1998; Rice 2004) . Although population and quantitative genetic approaches most commonly focus on change over one or a few generations, they have been applied to macroevolution with great benefit. For example, Lande (1976) provided quantitative genetic predictions for trait evolution over many generations using Brownian motion and Ornstein-Uhlenbeck models (see Chapter 3). Lynch (1990) later showed that these models predict long-term rates of evolution that are actually too fast; that is, variation among species is too small compared to what we know about the potential of selection and drift (or, even, drift alone!) to change traits. This is, by the way, a great example of the importance of macroevolutionary research from a deep-time perspective. Given the regular observation of strong selection in natural populations, who would have guessed that long-term patterns of divergence are actually less than we would expect, even considering only genetic drift (see also Uyeda et al. 2011) ?
Paleontology has, for obvious reasons, focused on macroevolutionary models as an explanation for the distribution of species and traits in the fossil record. Almost all of the key questions that I tackle in this book are also of primary interest to paleontologists - and comparative methods has an especially close relationship to paleobiology, the quantitative mathematical side of paleontology (Valentine 1996; Benton and Harper 2013) . For example, a surprising number of the macroevolutionary models and concepts in use today stem from quantitative approaches to paleobiology by Raup and colleagues in the 1970s and 1980s (e.g. Raup et al. 1973; Raup 1985) . Many of the models that I will use in this book – for example, birth-death models for the formation and extinction of species – were first applied to macroevolution by paleobiologists.
Finally, comparative methods has deep roots in phylogenetics. In fact, many modern phylogenetic approaches to macroevolution can be traced to Felsenstein’s (1985) paper introducing independent contrasts. This paper was unique in three main ways. First, Felsenstein’s paper was written in a remarkably clear way, and convinced scientists from a range of disciplines of the necessity and value of placing their comparative work in a phylogenetic context. Second, the method of phylogenetic independent contrasts was computationally fast and straightforward to interpret. And finally, Felsenstein’s work suggested a way to connect the previous two topics, quantitative genetics and paleobiology, using math. I discuss independent contrasts, which continue to find new applications, in great detail later in the book. Felsenstein (1985) spawned a whole industry of quantitative approaches that apply models from population and quantitative genetics, paleobiology, and ecology to data that includes a phylogenetic tree.
More than twenty-five years ago, “The Comparative Method in Evolutionary Biology,” by Harvey and Pagel (1991) synthesized the new field of comparative methods into a single coherent framework. Even reading this book nearly 25 years later one can still feel the excitement and potential unlocked by a suite of new methods that use phylogenetic trees to understand macroevolution. But in the time since Harvey and Pagel (1991) , the field of comparative methods has exploded – especially in the past decade. Much of this progress was, I think, directly inspired by Harvey and Pagel’s book, which went beyond review and advocated a model-based approach for comparative biology. My wildest hope is that my book can serve a similar purpose.
My goals in writing this book, then, are three-fold. First, to provide a general introduction to the mathematical models and statistical approaches that form the core of comparative methods; second, to give just enough detail on statistical machinery to help biologists understand how to tailor comparative methods to their particular questions of interest, and to help biologists get started in developing their own new methods; and finally, to suggest some ideas for how comparative methods might progress over the next few years.