NPRS analysesThe non-parametric rate smoothing analyses were done using the r8s program (Sanderson
1997). To prevent the optimization algorithm from converging on a local optimum, the
searches were started at five different initial time estimates (num_time_guesses=5) and
were restarted three times for each guess (num_restarts=3). Three consecutive analyses
were done using the different branch length estimates from ACCTRAN, DELTRAN, and
maximum likelihood optimizations. No minimum age constraints were enforced during
the analyses.
A bootstrap resampling procedure was employed to estimate errors arising from the
stochastic nature of the substitution process (Efron and Tibshirani 1993; Sanderson 1997).
One hundred bootstrap replicates of the dataset were constructed using the seqboot
program (Felsenstein 1993), and branch lengths were estimated on our single tree using
ACCTRAN optimization for each replicate and input to the r8s program. Bootstrap
estimates of standard errors for each node were calculated for the age distribution
estimates obtained (Efron and Tibshirani 1993).
Calibrating relative agesThe output from NPRS analyses is a set of relative ages, and a calibration point has to be
selected to convert these ages into absolute times. In most cases, this is done with
reference to the fossil record. Important considerations for choosing the calibration point
include: (1) terminal nodes should be avoided to minimize any effects of poor taxon
sampling; (2) the fossil taxon should indisputably be part of the group defined by the
selected node; (3) the age of the fossil taxon should as closely as possible represent the
actual divergence time for the selected node; and (4) relationships of the selected group to
other taxa should be well supported by the bootstrap/ jackknife.
Based on the occurrence of Protofagacea (Herendeen et al. 1995) and Antiquacupula
(Sims et al. 1998) in the Campanian and Late Santonian of Georgia, we chose to fix the
split between the Fagales and Cucurbitales (node CALL; Figure 8.5) in the late Santonian
(84 Ma). Several floral features indicate that they are both part of the Fagales lineage, and
both have flowers and fruits born in a typical Fagales cupule (Herendeen et al. 1995; Sims
et al. 1998). Evaluating their precise relationships is, however, complicated by
uncertainties surrounding the origin of the cupule. Analyses based on both morphological
and molecular data indicate that the Fagaceae sensu lato are paraphyletic and that the
Fagaceae sensu stricto and Notofagaceae form two separate lineages (Nixon 1989; Chase et
al. 1993; Manos et al. 1993; Manos 1997; Manos and Steele 1997). The cupule must
therefore either have originated twice or originated once in the Fagales lineage and
subsequently been lost in the lineage leading to the Betulaceae, Casuarinaceae,
Juglandaceae, and Myricaceae. Although our choice of calibration point (Fagales-
Cucurbitales split) could be seen as too conservative, it allows us to control the direction
of any errors incorporated through the calibration, and we can be confident that we are
underestimating the true age of our calibration point.
150 ANGIOSPERM DIVERGENCE