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Paleontology and the Comparative Method: Ancestral Node Reconstructions Versus Observed Node Values

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Paleontology and the Comparative Method: Ancestral Node Reconstructions Versus Observed Node Values vol. 157, no. 6 the american naturalist june 2001 Paleontology and the Comparative Method: Ancestral Node Reconstructions versus Observed Node Values P. David Polly* Molecular and Cellular Biology Section, Division of Biomedical years. The problem is not the same as testing for differences Sciences, Queen Mary and Westfield College, London E1 4NS, in population means with t-tests because random fluctua- United Kingdom; and Department of Palaeontology, Natural tion in trait values over time can lead to apparently signif- History Museum, London, United Kingdom icant differences in successive population means (Bookstein Submitted May 31, 2000; Accepted February 1, 2001 1987) and can mimic patterns of evolutionary interest such as directional change or stasis (Gingerich 1993). The sta- tistical significance of evolutionary differences—between species, clades, or between ancestor-descendant populations within a single lineage—must be evaluated as a time series. abstract: Comparative methods are used to reconstruct ancestral node values for continuously varying traits. The confidence intervals These issues are pertinent to phylogenetically based (CIs) around such estimates may be wider than the range of tip data comparative methods. These methods are sometimes used from which they are calculated. Without historical data with which to estimate ancestral or node values on phylogenetic trees to compare estimates, it is not clear whether such broad CIs reflect using observed data from the tree tips and an explicit evolutionary lability or methodological imprecision. In this study, a evolutionary model (see reviews by Harvey and Pagel 1991; fully resolved phylogeny of fossil carnivorans, in which observed Martins and Hansen 1996). Usually an optimal estimate samples are found not only at the tree tips but also along branches and at nodes, is used to compare observed ancestral node values of the ancestral trait value is calculated, often with an error with node estimates based on a Brownian motion model of evolution. factor indicating a range of other possible values. Recent As in previous studies, the CIs surrounding node estimates were studies have revealed that the range of 95% confidence wider than the range of tree tip values, but observed values fell well intervals (CIs) around node reconstructions is quite large, within them, reasonably close to the values predicted by comparative sometimes exceeding the range of tip data themselves. This methods. Confidence intervals calculated using paleontological rate implies either that the methods used to estimate node estimates were comparable to those calculated using only terminal taxa. This implies that evolution of at least some traits is conservative values are not precise enough or that evolution is so vol- enough for node reconstruction techniques to be useful, despite their atile that node reconstruction is futile (Schluter et al. 1997; large standard errors. The Brownian motion model of evolutionary Harvey and Rambaut 1998; Garland et al. 1999). change was a good predictor of node values. But is evolution as unpredictable as node CIs suggest? In this article, I explore the power of phylogenetic com- Keywords: phylogenetically based statistical methods, independent contrasts, squared-change parsimony, Brownian motion, Carnivora. parative methods to predict ancestral node values by ap- plying them to a fully resolved phylogeny of extinct car- nivores. In this phylogeny, trait values are known not only Judging the significance of evolutionary change in quanti- for tip taxa but also for those at nodes and along branches. tative characters can be difficult. The diversity of structure This allows node reconstructions (and their CIs) to be among organisms tells us that considerable change has oc- compared directly with observed samples. Such data could curred, but when confronted with a quantified exam- be used either to test an evolutionary model against real ple—average body mass increased by 1.36 g over a period data (e.g., to determine whether a Brownian motion or of 600,000 yr, for instance—we are at an intuitive loss to Ornstein-Uhlenbeck model of evolution better describes evaluate significance because there is no clear expectation observed patterns) or to test data for departure from a of how much body mass can change over a set number of particular model (e.g., to determine whether long-term directional selection has affected the evolution of a par- * E-mail: [email protected]. ticular clade). Here the observed data will be tested against Am. Nat. 2001. Vol. 157, pp. 596–609. ᭧ 2001 by The University of Chicago. the values expected under a Brownian motion random 0003-0147/2001/15706-0002$03.00. All rights reserved. walk. Brownian motion is a good null model for detecting Paleontology and the Comparative Method 597 Figure 1: Phylogeny of late Paleocene and early Eocene viverravid carnivorans from the Bighorn Basin, Wyoming. The tree is a stratocladogram from Polly (1997). It is drawn here as a graph with time as the ordinate and molar area as the abscissa. Time is indicated using three scales: millions of years ago (MYA), geological divisions (the smallest of which are North American Land Mammal Subages), and meter level in the Bighorn Basin. Paleomagnetic normal and reversed intervals are also indicated. Within the tree, molar areas of individual specimens are indicated by squares. Mean molar area, body mass, and generation length are reported for each species. Note that the molar areas of Viverravus politus and Didymictis leptomylus overlap at Wa-2. nonrandom behavior because it is stochastic, with no in- positively with the per-step rate of character change and herent directionality (Berg 1993; Schluter et al. 1997). tree branch lengths. The greater the per-step rate, the Brownian motion is a time series process whose outcome greater the possible net change along a branch; the longer depends on the starting value, the number of steps in the the branch, the greater the possible net change. Change series, and the amount of change at each step; furthermore, in either of these parameters changes the range of the node the direction of change at any step is random and is not CIs. It is, therefore, important that they be estimated as biased by change at other steps. precisely as possible. In most comparative studies, the rate Confidence intervals around node reconstructions scale of character change is estimated from the squared differ- 598 The American Naturalist Figure 2: A simplified version of the phylogeny shown in figure 1 showing only terminal and node taxa (filled rectangles) and squared-change parsimony estimates of node values (open rectangles). The ordinate and abscissa are the same as in figure 1 except that the age (MYA; shown on right) is estimated from the meter level of each sample. Dashed lines connecting the terminals with the estimated node values indicate the tree topology. Branch lengths in both years and generations are indicated. ence (or variance) among terminal taxa, scaled by their Material and Methods divergence time. In this paleontological study, node and branch taxa are also available, allowing the rate variance The Trait: First Lower Molar Area to be estimated from more data and allowing branch The character trait considered in this study is the area of lengths to be measured (with error) directly from the tree. the first lower molar. It is a continuously variable trait of These data emphasize, however, that there are many layers the sort normally considered in comparative methods and of inference underlying node reconstruction, particularly is of evolutionary and ecological interest because it is cor- with the estimation of divergence times. Phylogenetic and related with body mass and, thus, many other physiological stratigraphic error will be shown to be factors in this study, and life-history variables (Calder 1984; Damuth and but they are more rigorously controlled here than in pre- MacFadden 1990). It is also commonly preserved in fossil vious comparative studies. This permits an unusually ro- mammal material, thus maximizing sample size. Molar bust test of a predictive model against empirical data. areas were calculated as the product of mesio-distal length Paleontology and the Comparative Method 599 Table 1: Age and estimated parameters for paleontological samples Age Mass Generation Species NALMS Meters (MYA) N Mean SD (g) (yr) Didymictis proteus Ti-4 550 57.5 2 3.85 .071 3,323 1.3 D. proteus Ti-5 700 57.2 1 3.60 … 2,055 1.2 D. proteus Cf-1 1,050 56.2 3 3.69 .057 2,455 1.2 D. proteus Cf-2 1,300 55.6 20 3.95 .092 4,001 1.4 D. proteus Cf-3 1,430 55.3 9 3.97 .064 4,222 1.4 D. proteusa Wa-0 1,550 54.9 3 3.61 .103 2,097 1.2 Didymictis leptomylus Wa-1 1,600 54.8 7 3.89 .128 3,612 1.4 D. leptomylusb Wa-2 1,700 54.6 6 3.66 .142 2,306 1.2 D. leptomylus Wa-3 1,900 54.0 1 3.38 … 1,347 1.1 Didymictis protenus Wa-1 1,600 54.8 3 4.44 .158 10,336 1.8 D. protenusb Wa-2 1,700 54.6 2 4.14 .007 5,824 1.5 D. protenus Wa-3 1,900 54.0 6 4.12 .197 5,573 1.5 D. protenus Wa-4 2,100 53.5 14 4.23 .105 6,943 1.6 D. protenus Wa-5 2,250 53.1 12 4.34 .145 8,474 1.7 D. protenus Wa-6 2,400 52.7 8 4.57 .261 13,158 1.9 Viverravus laytoni Ti-5 700 57.2 2 2.05 .057 104 .6 V. laytonia Cf-2 1,300 55.6 2 2.11 .129 117 .6 Viverravus acutus Cf-3 1,430 55.3 1 1.92 … 82 .5 V.
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