Models and methods for analyzing phenotypic evolution in lineages and clades

—In this chapter we discuss methods for analyzing continuous traits, with an emphasis on those approaches that rely on explicit statistical models of evolution and incorporate genealogical information (ancestor–descendant or phylogenetic relationships). After discussing the roles of models and genealogy in evolutionary inference, we summarize the properties of commonly used models including random walks (Brownian motion), directional evolution, and stasis. These models can be used to devise null-hypothesis tests about evolutionary patterns, but it is often better to fit and compare models equally using information criteria and related approaches. We apply these methods to a published data set of dental measurements in a sequence of ancestor–descendant populations in the early primate Cantius, with the particular goal of determining the best-supported mode of evolutionary change in this lineage. We also assess a series of questions about the evolution of femoral dimensions in several clades of dinosaurs, including testing for a trend of increasing body size (Cope’s Rule), testing for correlations among characters, and reconstructing ancestral states. Finally, we list briefly some additional models, approaches, and issues that arise in genealogically informed analyses of phenotypic evolution. PrelIMInarIes: scoPe and strategy THE FOSSIL record is a vast archive of lineages and their phenotypes, arrayed through geological time. Paleontologists seek to document the patterns of phenotypic evolution revealed by this record, and, when possible, to link these patterns to drivers and processes. In this chapter, we review some of the analytical methods available for understanding phenotypic evolution. As this topic is potentially enormous, we have chosen to narrow it to a more manageable size. First, we limit the discussion to phenotypic traits that vary continuously, an entirely pragmatic restriction of scope. In addition, we focus almost entirely on methods that (i) specify explicit statistical models of trait evolution and (ii) incorporate genealogy in the form of hypothesized ancestor–descendant or phylogenetic relationships. These restrictions reflect our view that these methods are often the most powerful and flexible means for testing evolutionary hypotheses. Moreover, whereas non-genealogical methods are already well described and known to paleontologists (e.g., McKinney, 1990; Foote, 1991; McShea, 1994; Roy and Foote, 1997), the analytical tools appropriate for analyses that are model-based and genealogically-informed are less widely appreciated. After an overview of the importance of genealogy and models, we will devote the bulk of this chapter to demonstrating the methods as applied to ancestor–descendant and phylogenetic data. In doing so, we will rely heavily on two published data sets: dental measurements in an evolutionary sequence of the early primate Cantius (Clyde and Gingerich, 1994), and femoral dimensions in several dinosaur clades (Carrano, 2006). All analyses in this chapter were performed using the R statistical software package (R Development Core Team, 2009), which is freely available for all popular computer operating systems. In addition to its availability, R has many powerful statistical methods built-in, and is a fully functional programming language for analysis and graphics (all figures in this chapter are nearly unmodified R output). Perhaps most importantly for the present work, R is extendible in that users can create modules, called packages, to perform functions not already implemented. We make heavy use of the 246 the PaleontologIcal socIety PaPers, vol.16 packages paleoTS (Hunt, 2008c) for analyzing ancestor–descendant series, and ape (Paradis et al., 2004) and geiger (Harmon et al., 2009) for various phylogenetic analyses. These packages need to be installed and then loaded into the R session prior to running the analyses in this chapter (e.g., library(ape) loads the ape package once it has been installed). Other packages are relevant to this chapter; readers are referred to the list of packages related to phylogenetic and comparative methods maintained on the R website (http://cran.rproject.org/web/views/Phylogenetics.html). In the text of this chapter, we include the main commands for performing R analyses in a fixed width font. The online supplement, in addition to covering a few topics too technical to warrant inclusion in the main text, provides an R workspace file with the data analyzed in this chapter. the IMPortance oF genealogy Whether focused on individual species or on the broad sweep of life, evolutionary inference requires some information about the genealogical relationships among the morphological units being studied. At a coarse level, taxonomy delimits groups of species that (we hope) are more closely related to each other than they are to all outgroup taxa. For paleontologists, more detailed genealogy comes in two forms: sequences of populations construed to form a chain of ancestor–descendant relationships (Fig. 1.1), or hypotheses that link populations through sister-group relationships into larger clades (Fig. 1.2). Both of the panels in Figure 1 represent a richer source of genealogical information relative to traditional taxonomy, and this richness demands its own set of analytical methods. In Figure 1, the lines represent the pathways of accumulated evolutionary change, and the points are snapshots of evolving populations or species. We assume that some aspect of phenotype has been recorded for these populations, and the goal is to learn something about how one or more traits evolve. The detailed goals will depend on the specific research agenda, but can include questions such as: What is the general pattern, or mode, of evolution? What are the best estimates for the phenotypes of unobserved ancestors? How fast does a character evolve? Are changes in one character correlated with changes in another, or with changes in the environment? Under most notions of how phenotypes evolve, changes accrue—the phenotypic state at one point in time is equal to the ancestral condition plus all subsequent changes leading to the focal population. When evolution builds from pre-existing states in this manner, observations across genealogical units will not be FIGURE 1. —Two kinds of genealogical information in paleontological research. 1, populations forming an ancestor–descendant sequence. 2, populations related through phylogeny. Values of a phenotypic trait are represented by the vertical axis in 1 and by the size of the symbol in 2. Horizontal axes in both represent time, measured forward from the oldest population in 1, and measured backwards from the youngest taxon in 2. hunt and carrano—analyZIng PhenotyPIc evolutIon In lIneages and clades 247 independent. Nearby points in ancestor–descendant sequences share more of their history compared to more distant pairs, and the same is true of closely related species such as Taxa E and F in Figure 1.2. This creates an analytical difficulty because most statistical approaches assume observations are independent, and they can mislead when applied naively to data such as those shown in Figure 1. Faced with dependence among observations, two basic strategies can be used. First, one can construct a new set of observations from the data that are independent. Alternatively, one can accept that the observations are not independent, and account for this statistically. All of the methods that we describe in this chapter rely on one of these two strategies. In order to work correctly, both approaches require assumptions about how evolution proceeds; that is, they assume a particular evolutionary model. Thus it is necessary to first understand common models of phenotypic change. Models oF PhenotyPIc evolutIon Paleontologists commonly measure features that vary continuously, including sizes of organisms and their parts, and shape metrics such as those derived from geometric morphometrics (Webster and Sheets, this volume). Measurements that reflect size, such as lengths and areas, should usually be log-transformed so they are considered on a proportional scale (see, for example, Foote, 1991; Gingerich, 2000). This is especially true when values span orders of magnitude because proportional differences will be more comparable across scales (e.g., a length increase of 1 cm matters much more to a mouse than to an elephant, but a 10% increase is similar for both). Meristic (count) variables are restricted to integer values and thus are not truly continuous, but they can be reasonably approximated as such as long as the range of realized values is not too small. Discrete characters with few states, such as the presence or absence of structures, arise frequently in studies of phylogenetic relationships and morphological disparity. We will not cover such traits here; see instead Wagner and Marcot (this volume) for a treatment of these traits in the context of phylogenetic analysis. Several other works review some of the important model-based comparative methods for discrete traits (Pagel, 1994; Felsenstein, 2004). In this chapter, we focus on approaches that model evolutionary outcomes using just a few parameters. Although the models we discuss can be related to microevolutionary scenarios, we do not pursue this avenue extensively here. Except for truly exceptional circumstances (e.g., Hunt et al., 2008), it is usually very difficult to infer specific microevolutionary processes from fossil data. Any paleontological pattern is consistent with a myriad of combinations of selection, drift, mutation and gene flow, and we generally lack the information required to discriminate among possibilities. As a result, it is almost always more profitable to use simple models of evolution to extract meaningful aspects of evolutionary divergence, such as directionality and rates of change, without committing to any specific microevolutionary scenario. We discus