50 John R. Paul and Stephen J. Tonsor
from 101Piper(andMacropiper) species and five
outgroup species using ClustalW (Thompsonet al.
1994), followed by manual corrections. We used
Modeltest (Posada and Crandall 1998) to eval-
uate the most appropriate model of molecular
evolution for our analysis, which was deter-
mined by Akaike’s information criterion (AIC)
model selection to be the general time reversible
model with gamma distributed rates and pro-
portion of invariable sites (GTR+I+G). We ran
our analysis in MrBayes 3.1.1 (Ronquist and
Huelsenbeck 2003), using model specifications
for the GTR+I+G model, with a Dirichlet prior
on substitution rates and state frequencies, and
an unconstrained, exponential prior distribution
on branch lengths. All analyses with MrBayes
used two concurrent runs, each with four Markov
Chain Monte Carlo (MCMC) chains (one “cold”
and three “heated” chains). We examined an
initial run of 2 million generations of MCMC
simulations to assess if the chain had reached
a stable distribution. Although the log-likelihood
values stabilized by approximately 200,000 gen-
erations, clade probabilities failed to stabilize until
nearly 1.5 million generations (assessed using
the program “Are We There Yet?,” Wilgenbusch
et al. 2004, Nylanderet al. 2008). As a result,
we ran a second analysis for 5 million genera-
tions, discarding the initial 2 million generations
as burnin.This analysis effectively sampled from a
stable distribution (with samples taken every 100
generations), resulting in a total of 60,000 trees
after combining the two runs, from which a major-
ity rule consensus tree was derived (Figure 4.2).
This tree recovered the major clades described for
Piperin previous work on ITS sequences (Jaramillo
and Callejas 2004b).
We then used the topology of this phylo-
genetic tree as our input tree for the relative
age analysis in BEAST. We held the topology
of the tree constant for the analysis and fixed
the mean substitution rate to one. BEAST uses
MCMC sampling to assess branch lengths and
divergence times by varying substitution param-
eters and the rate distribution based on a model
of molecular evolution (we used the GTR+I+G).
A preliminary analysis running for 2 million
generations did not stabilize and the effective
sample sizes of many parameters were low. The
analysis presented here ran for 10 million gen-
erations, with the first 4 million discarded as
burnin. The resulting samples (taken every 100
generations) showed a stable log-likelihood dis-
tribution and good effective sample sizes for all
parameters. We assessed the posterior probability
densities of ages (divergence times of two species
subtending these nodes) for 47 nodes on the phy-
logenetic tree (Figure 4.2). The mean divergence
time values of these nodes were used to deter-
mine the relative ages of the neotropicalPiper
species for the age and area analysis (Table 4.1).
Since BEAST analyses have a stochastic element,
we also ran the same analysis two additional
times. The results were nearly identical (e.g., cor-
relation coefficients of node ages between runs
were>0.99) so only the first run results are
presented here.
To estimate range sizes, we counted the num-
ber of 1◦× 1 ◦latitude–longitude squares occu-
pied by geo-referenced herbarium records in
W^3 Tropicos. This is effectively an area of occur-
rence measure (Gaston 1994). A few species for
which we determined the age did not have records
in W^3 Tropicos; most of these were species listed
as endemic to Colombia in Trelease and Yuncker
(1950).Therefore, we present our analysis exclud-
ing these species; however, we also provided gen-
erous range-size estimates for these species and
ran the analyses including them – the results were
nearly identical and thus are not included here.
The distribution of range sizes we calculated for
the species with W^3 Tropicos records is presented
in Figure 4.3. The distribution is characterized by
a few species with large range sizes and a long
tail of species with small ranges (<10 of 1◦× 1 ◦
latitude–longitude squares).
To assess the relationshi pbetween relative
species age and range size, we used linear least-
squares regression using SAS 8.2 (SAS Insti-
tute 2001). We log-transformed both the mean
species’ ages and range sizes of the 58 neotropi-
calPiperspecies for which we had data. We found
a highly significant positive relationship (y =
0.9399x+2.6143,P<0.001) that explains 25%
(r^2 = 0.252) of the variation in range size
for thesePiperspecies (Figure 4.4). Thus, our
analysis supports the simple, positive relationship
between species age and range size predicted by