ESM-3
Computing evolutionary and diversification rates on simulated trees with simulated character
evolution.
We performed a simulation study to explore the behavior of our methods, in terms of their sensitivity
to sampling inequality, of their ability to reproduce real diversification and evolutionary rates, and power to
detect rate change through time. Since we found declining diversification and evolutionary rates, and
evidence for significant statistical association between the two (over the Cenozoic as a whole and during the
Palaeogene in particular) our simulation experiments were specifically tailored to test if these findings could
be statistical artifacts of the way we computed rates and their association.
In most studies dealing with rates of phenotypic evolution the rate itself is computed from the
phylogeny and tip data, in terms of variance of the Brownian process. Specific methods for studying
temporal patterns in both the evolutionary rate and the diversification rate are available in literature as well.
For instance, by applying Pagel’s transform one could detect either slowdown or acceleration of phenotypic
evolution (i.e. the evolutionary rate). The same applies to the calculation of diversification rates (e.g. by
computing Pybus and Harvey’s gamma statistic, Pybus and Harvey 2000 and its numerous later
implementations). Yet, these methods do not provide a mean to inspect the temporal coupling of
diversification and phenotypic evolution rates, were not meant to deal with fossil phylogenies, and are
subjected to problems of interpretation of the underlying phenomena (Quental and Marshall 2010, Rabosky
2010, Rabosky and Alfaro 2010, Losos 2011, Tarver and Donoghue 2011, Rabosky 2012).
In this study we decided to cut the full tree into discrete, consecutive time bins, each including
(chronologically) a subset of the tree limited to the species which were extant during each bin. This
procedure, known as time slicing of the tree, was specifically meant to deal with fossil lineages (Ruta et al.
2007, Lloyd et al. 2008, Ezard and Purvis 2009). In practice, the full tree is reduced to the species present in
a given time bin. This time bin phylogeny has the root at the same age as the full tree, whereas the tips
terminate at the time bin upper boundary. For example, time-slicing our full tree (whose root is at 110
million years ago) to a bin of length 2 million years ending at 50 million years ago produces a time-bin
phylogeny rooted at 110 million years ago, with an height of 60 (110-50) million years, but limited to the
species that were extant during the 52 – 50 million years ago temporal interval.
After the application of time slicing we computed both the diversification and evolutionary rates on
each time bin phylogeny and regressed the rates to each other. This procedure is likely influenced by
sampling issues, so much as when dealing with molecular phylogenies (Tarver and Donoghue 2011). For
instance, better sampled time bins are more likely to include extreme (if rare) phenotypes, with the potential
to increase the apparent evolutionary rate. This implies that by time slicing a fossil phylogeny the
evolutionary rate could increase from the oldest (typically poorly sampled) time bins to the youngest even if
the rate is in fact constant. On the opposite, given a couple of sister species sp1 and sp2 both present in two
consecutive bins, their expected phenotypic divergence (under the Brownian motion [BM] model) is larger in
the second (younger) time bin than in the former. This is because under BM the amount of (expected)
phenotype divergence between sp1 and sp2 depends on the age of parental node (which is the same over the
two consecutive bins) but also on the time they evolved independently, which increases from the older bin to
the younger, by an amount of time equal to the bin length. This implies, that the rate parameter in the
Brownian process would be lower in the younger bin although the phenotypes are the same, all else being
equal. An interesting consequence of this is that declining extinction rates (= longer species duration)
towards the present may artificially decrease the computed evolutionary rate, giving the impression that the
two rates (extinction and evolutionary) are coupled and both declining even if the evolutionary rate is not.
Finally, since species present in a bin i may survive to the next bin i+1 the evolutionary rate computed over i
is not statistically independent from the rate computed for i+1 (i.e. there is temporal autocorrelation in the
evolutionary rate).
The calculation of diversification rates per time bin might be biased as well. In our procedure we
assumed that the diversification rates computed over the lineages sampled in a given bin are an unbiased
representation of diversification rates computed over the full tree (i.e. a tree where all lineages are actually
sampled). This may not be true. Since oldest lineages are less thoroughly known in terms of both phylogeny
and remains, older time bins might include a restricted (phylogenetically) subset of the total tree, limited to
those successful lineages whose remains are more abundant in the fossil record, and are better studied since.
If these sampled lineages were also rapidly diversifying, old time bins would artificially show high
diversification rates even if mammals as a whole would not.
To verify the potential impact of both methodological and sampling issues on our procedure we
conducted a number of simulations, under specified diversification rate, evolutionary rate, and sampling
inequality among bins. In particular, we asked whether significant temporal coupling between diversification
and phenotypic evolution rates could be a by-product of sampling inequality, of computing rates on discrete,
time bin phylogenies, or any combination of these factors. To do that, we first simulated random trees
assuming either constant, or declining diversification rates (to reproduce what we found with our original
tree and data) by using the functions sim.bd.taxa and sim.rateshift.taxa, respectively, in the R
package TreeSim (Stadler 2011).
Our goal was to produce random trees similar in size to the real tree (which has 1031 tips) after
removing one third of the species to account for sampling issues. We also wanted the random trees to have a
ratio between the number of species surviving to the last few bins to the total number of species similar to
the original tree (where the ratio is some 1/6). With sim.bd.taxa we empirically found that goal was
accomplished, under constant diversification, by imposing arbitrary speciation rate  = 0.7, and extinction
rate  = 0.6, and imposing that 300 species to survive to the recent. The diversification rate is thus constant
and equal to - =0.1. We produced 100 random trees under these specifications. The average tree size was
2198 ±127 species. After the tree was produced, it was scaled to a height of 110 Ma, as with the original tree.
We then produced 100 additional trees with declining diversification rate using the function
sim.rateshift.taxa in TreeSim. With sim.rateshift.taxa it is possible to change the speciation
and extinction rates at user-specified “times” (computed from the Recent towards the past), whereas it is not
possible to specify the tree height. These trees were designed as to branch very slowly close to the root, to
mimic the early emergence and slow diversification of eutherians during the Mesozoic. Then, diversification
rate becomes very high over one period, followed by another period of the same length with lower
diversification rate, and then by a period twice as long as the former when diversification rate is slightly
negative. The first period was arbitrarily considered to be “mesozoic”. The two successive periods were
assigned to the Palaeogene, and the last to the Neogene (bins younger than 5 Ma were not considered. The
Quternary is therefore excluded from analyses) . This means that diversification is high early in the
Palaeogene and then declines to become slightly negative during the Neogene, consistently with the
adaptive-radiation like mode of diversification in mammals after the demise of dinosaurs at the beginning of
the Cenozoic (Smith et al., 2010), and with our findings as with the original tree.
In sim.rateshift.taxa we imposed the following parameters:
"neogene"
0.1

0.4

r = ()
-0.3
"time" from the recent
0-4
"palaeogene"
"mesozoic"
1
2
0.1
0.3
0.2
0.1
0.7
1.8
0
4-6
6-8
which produce trees of 1674 ±27 species on average. In these simulations, the Palaeogene corresponds to the
interval between 8 and 4 time units before the present, whereas the “neogene” covers the 0-4 time interval.
Since the average tree height was 14.52 time units, the Mesozoic extends between 8 and 12.52 time units on
average. After each tree was produced, it was rescaled to a height of 110 Ma. This means that, on average,
what we consider to be neogene extends over the last (4/14.52 = 30.3 Million years). The Palaeogene extends
from 30.3 to 60.6 Ma, and the Mesozoic from the beginning of the Palaeogene to the tree root. One-hundred
random trees were produced this way.
After modeling diversification, on each random tree (n = 200) we first simulated body size evolution
according to a constant rate process, then we re-simulated evolution designing the evolutionary rate to
decline towards the present. To produce constant rate body size data, we modified the function fastBM in
the package phytools (Revell 2012) in order to deal with a fossil phylogeny, setting 2 (the evolutionary rate)
= 1. To produce declining rate body size data, we repeated the simulation of body size evolution on each
tree imposing exponentially declining evolutionary rate 2 (in keeping with our empirical findings) by
modifying the function exponentialchangeTree in the package Geiger (Harmon et al. 2009) to deal with
non-ultrametric trees (exponentialchangeTree computes branching times as the tree was ultrametric). In
simulating declining evolutionary rate, we imposed 2 at the present to be 1/1000 than its value at the tree
root.
At this stage, we had 200 random trees (100 produced imposing constant- and 100 imposing
declining diversification rate), and two body size data sets for each tree (one by imposing constant and the
other assuming declining evolutionary rate). We used these trees and body size data to test the effect of
sampling inequality. To do that, we assumed that sampling probability is an inverse function of species ages
(which means that older remains and their embedding sediments are naively assumed to have lower chances
of being preserved to the present). We removed 1/3 of the species from each random tree as a function of
their age by using Brewer’s method, applying the function UPbrewer in the package sampling (Tillé and
Matei 2012). This function removes without replacement species from the sample of tree tips by assuming
that sampling probability is an inverse function of species ages.
In sum, we have 8 types simulations, 4 under constant and 4 under declining diversification
rates. Four under constant, and 4 under declining and4 with- plus 4 without sampling inequality taken
into account.
After each simulation, we computed the evolutionary rate and diversification rate for time bin (bins are 2 My
long), regressed rates to each other over the whole “Cenozoic”, and for the Palaeogene and the Neogene
separately.
The diversification rate in our procedure is computed differently than with the simulations. For this reason, it
is possible to compare rates between time bins, but not to compare estimated absolute values to the input
values. Conversely, for the evolutionary rate it is also possible to calculate how much rates should differ
between Palaeogene and Neogene bins when the rate is set to decline over time. The rate decline is described
by the equation (see the Geiger package instructions):
Where r is evolutionary rate at the present, r0 is the rate at the root, t is the distance from the tree root, and a
is:
From the above the expected ratio between average evolutionary rate during the Paleogene/to the average
evolutionary rate in the Neogene is computed as:
Where f(x) is the function for rate decline described above, 110 is the tree height (in millions of years), n1
and n2 are the time elapsed from the tree root to the beginning of the Neogene, and the time elapsed from the
tree root and the end of the Neogene, respectively. The same applies to Palaeogene boundaries p1 and p2.
Results of the simulations
A table (S1) with the results of the simulations is reported below. Simulating body size evolution under
constant rates and without sampling effect (Table S1A) rejects statistically significant association between
diversification and evolutionary rates (the expected outcome) 87 times out of 100 simulations. Of the 13
false hits, 8 refer to positive relationships (indicated as S+ in table S1) and 5 to negative relationships (S-).
By imposing sampling inequality, constant rates simulation (table S1B) produces 8 erroneous significant
relationships (5 S+ and 3 S-). Significant regression between the rates over the Palaeogene is correctly
rejected 92 times without accounting for sampling inequality (table S1A), and 95 when sampling inequality
is accounted for (table S1B). For the Neogene, the corresponding figures are 93 and 96.
When the evolutionary rate was designed to decline, diversification rate kept constant, and sampling
inequality ignored (table S1A), the significant relationship between the rates was correctly rejected 82 times
over the whole Cenozoic (10 S+, 8S-), 91 over the Palaeogene (7S+, 2 S-), and 95 over the Neogene (3S+,
2S-). When sampling inequality is introduced (table S1B), the corresponding figures are: 94 rejections over
the Cenozoic (4S+, 2S-), 98 over the Palaeogene(1S+, 1S-), and 96 over the Neogene (1S+, 3S-).
Evolutionary rates under the constant diversification model are statistically equal to1 (Brownian motion), on
average. Yet, significant differences occurred in 18 simulations (9S+, 9S-) without accounting for sampling
inequality (table S1A), and 16 times (6S+, 10S-) when sampling inequality is accounted for (table S1B).
When the evolutionary rate is designed to decline, Palaeogene rates are higher 100 times (the expected
outcome) without (table S1A), and 90 times with sampling inequality taken into account (table S1B).
Neogene rates were never statistically larger than Palaeogene rates under all conditions. The expected ratio
between average Palaeogene to Neogene rates is 5.31. When sampling inequality is accounted for our
procedure produces a mean ratio of 4.76 (± 0.63). Ignoring sampling, the corresponding figure is 5.79 (±
0.44).
Simulating body size evolution under declining rates and without considering sampling effects (Table S1C)
correctly produce statistically significant and positive associations between diversification and evolutionary
rates (the expected outcome) 94 times out of 100 simulations. By imposing sampling inequality (table S1D),
the frequency of positive and significant relationships reaches 99/100. Significant regression between the
rates for the two periods of the Cenozoic is rarely found. Without accounting for sampling inequality (table
S1C), there are 4 S+ and 1S- for the “paleogene”, 7S+ and 6S- for the “neogene”. When sampling inequality
is introduced (table 1SD), the corresponding figures becomes: “palaeogene”: 26S+, 0S-, “neogene” 7S+, 1S-.
When the evolutionary rate is kept constant, diversification rate is designed to decline, and sampling
inequality ignored (table S1C) , the significant relationship between the rates was correctly rejected 85 times
over the whole Cenozoic (7 S+, 8S-), 93 over the “palaeogene” (3S+, 4 S-), and 93 over the “neogene” (3S+,
4S-). When sampling inequality is introduced (table S1D), the corresponding figures are: 85 correct
rejections over the Cenozoic (6S+, 9S-), 95 over the “palaeogene” (2S+, 3S-), and 92 over the “neogene”
(6S+,2S-).
When the evolutionary rate is fixed to 1 (Brownian motion) and kept constant, our procedure correctly
recognizes both the rate value and constancy under declining diversification rate simulations (Table S1C,D).
Spurious differences between the Palaeogene and “neogene” evolutionary rates appear erratically 18 times
when sampling inequality is ignored (8S+,10S-, table S1C), and 14 times when accounting temporal
differences in sampling (6 S+, 8S-, table S1D).
When the evolutionary rate is designed to decline, “palaeogene” rates are higher than neogene’s 89 times
(the expected outcome) without (table S1C), and 95 times with sampling inequality taken into account (table
S1D). “neogene” rates were never statistically larger than “palaeogene” rates under all conditions. In
simulations assuming declining diversification rate the expected ratio between average “palaeogene” to
“neogene” rates is not fixed. The ratio changes from one simulation to the next because whereas the tree
height is fixed, the boundaries of “palaeogene” and “neogene” periods change arbitrarily. This means that the
expected ratio must be calculated at each run. Computed this way, the expected ratio is 8.26 (± 0.57).
Ignoring sampling inequality, the corresponding figure retrieved by our procedure is 1.69 ± 0.06. When
sampling inequality is considered, the average ratio is 1.37 ± 0.05.
Discussion of the results
The frequency of false positive (statistically significant temporal associations between evolutionary and
diversification rates when the association is in fact false) is comfortably low (Table S1 A,B). When both
rates were designed to be constant such frequency is 2-8% (depending on the inclusion of sampling effects,
and if either the whole Cenozoic or the two periods it includes are tested). When the diversification rate is
kept constant but the evolutionary rate is designed to decline the frequency of false positive stays in the 115% range, and even in this case the frequency of positive relationships is some 8% on average.
The frequency of false negative (the rejection rate of [simulated] significant temporal associations between
evolutionary and diversification rates) is 1% accounting for, and 6% without taking sampling issues in
consideration. These values refer to the two regressions computed over the entire Cenozoic. Since our
subdivision of the Cenozoic into “palaeogene” and “neogene” periods is arbitrary, and the decline in the rates
was not linear but exponential, no significant relationship is expected to occur for the “neogene” to begin
with, and only limitedly so for the “palaeogene”.
Our procedure reproduces real evolutionary rate values and ratios (averaged over Paleogene and neogene
samples) when the evolutionary rate is kept constant. The ratio between Paleogene and neogene rates is very
close to the expected when the diversification rate is kept constant, but quite lower than expected (down to
some 1/5) when both diversification rate and the evolutionary rate are designed to decline. Although
“palaeogene” ratios comfortably remain higher than “neogene’s” even in the latter condition (89-95% of the
times, see table S1C,D) and “neogene” rates are never statistically higher than “palaeogene’s” (table S1C,D),
this result indicates that our procedure underestimate real temporal differences in the evolutionary rate when
it is designed to decline, as a consequence of changing (= declining) diversification rates. Above we pointed
out that a decrease in extinction rate is likely to make the computed evolutionary rate lower as an artifact. It
is worth repeating the rationale here. Imagine to have a tree of n species in time bin i. Now let’s assume that
all of the n species survive to the next time bin i+1. Finally, let’s also assume there is no speciation. Under
these assumptions, in the time bin i+1 the tree topology and tip data are the same as they are in bin i. The
off-diagonal entries of the phylogenetic variance/covariance matrix (the distance from the tree root to the
most recent common ancestor of any pair of species) is also the same. Yet, the expected phylogenetic
variance (the root to tip distance of each species) is increased by an amount equal to the bin length. In fact,
higher phylogenetic variances (the sum [trace] of diagonal elements in the phylogenetic variance-covariance
matrix) imply higher expected variance in the n phenotypes, all else being equal (O’Meara et al. 2006). This
means that lower extinction rate (= higher chance to survive from one bin to the next) translate into lower
(estimated) evolutionary rates. In our simulations, extinction rate increases towards the present. This means
that early Cenozoic rates are probably underestimated, which would account for the low Palaeogene to
“neogene” evolutionary rates ratio we found when we designed both diversification and evolutionary rates to
decline over time, and makes our original finding (evolutionary rates 3 times higher in the Paleogene as
compared to neogene’s) really conservative.
We are aware that our simulations do not cover the full spectrum of possible paths in both
diversification and evolutionary rates. In fact, in our simulations rates were never designed to increase over
time. Whereas we regard interesting repeating our tests on rates designed to increase over time, we maintain
our simulations are those relevant to our findings (with the original tree and data). Although in some cases
the error percentage as inferred by the simulation results lays above the 5% significance level, we believe we
got convincing evidence from the simulation experiments that our procedure to compute rates on time sliced
trees is correct (and even conservative as for the finding that evolutionary rates are higher in the Paleogene).
False inference is reasonably improbable. It’s worth noticing that in our simulations diversification and
evolutionary rates change over time (where applicable) independently. This means that a causal association
between the rates would make regression results stronger.
Table S3 – Results of simulation experiments. A = the trees were generated under constant diversification
rate and ignoring sampling differences. B = the trees were generated under constant diversification rate and
including sampling differences. C = the trees were generated under declining diversification rate and
ignoring sampling differences. D = the trees were generated under declining diversification rate and
including sampling differences. div neo = diversification rate during the neoquat. div paleo = diversification
rate during the Paleogene. ph neo = evolutionary rate during the neoquat. The evolutionary rate was
designed to be constant and = 1. ph paleo = diversification rate during the Paleogene. The evolutionary rate
was designed to be constant and =1. ph neo D = evolutionary rate during the neoquat. The evolutionary rate
was designed decline towards the present. ph paleo D = diversification rate during the Paleogene. The
evolutionary rate was designed to decline towards the present. ceno.regr, paleo.regr, neo.regr = regression
of the diversification vs the evolutionrary rate computed over the Cenozoic, and over the Paleogene and
neoquat separately. ceno.regrD, paleo.regrD, neo.regrD = the same as before, computed by taking the
evolutionary rate designed to decline over time. S+ = number of significant and positive or significant and
negative (S-) relationships. The symbols S+ and S- apply to both the comparison of Paleogene to neoquat
rates, and to the regression between diversification and evolutionary rates.
A - constant diversification rate ~ no sampling differences
Rates
div neo
div paleo
ph neo
ph paleo
ph neo D
ph paleo D
Mean rate
Regressions
ceno.regr
ceno.regrD
paleo.regr
neo.regr
paleo.regrD
neo.regrD
Mean Slope
0.038
0.037
0.970
0.971
0.037
0.211
Confidence interval (95%)
S+
S(0.021 - 0.065)
(0.020 - 0.071)
1
1
(0.900 - 1.084)
(0.847 - 1.159)
9
9
(0.018 - 0.090)
(0.130 – 0.286)
100
0
0.001
-0.014
-0.002
0.001
-0.021
-0.175
Confidence interval (95%) S+
(-0.016 - 0.019)
(-0.046 – 0.018)
(-0.023 – 0.018)
(-0.018 – 0.035)
(-0.064 – 0.021)
(-0.432 – 0.082)
S8
10
5
2
7
2
5
8
3
5
2
3
B – constant diversification rate ~ with sampling differences
Rates
div neo
div paleo
ph neo
ph paleo
Mean rate
0.035
0.034
0.977
0.939
Confidence interval (95%)
S+
(0.004 - 0.07)
(0.005 - 0.062)
(0.842 - 1.103)
(0.725 - 1.11)
S1
3
6
10
ph neo D
ph paleo D
Regressions
ceno.regr
ceno.regrD
paleo.regr
neo.regr
paleo.regrD
neo.regrD
0.043
0.207
(0.018 - 0.111)
(0.085 - 0.463)
Mean Slope
0.005
0.009
-0.006
0.019
0.012
0.115
Confidence interval (95%) S+
(-0.021 - 0.032)
(-0.06 - 0.028)
(-0.039 - 0.026)
(-0.035 - 0.074)
(-0.096 - 0.121)
(-0.653 - 0.882)
90
0
S5
4
3
2
1
1
3
2
2
2
1
3
C - declining diversification rate ~ no sampling inequality
Rates
div neo
div paleo
ph neo
ph paleo
ph neo D
ph paleo D
Mean rate
-0.036
0.079
0.978
0.973
0.254
0.420
Regressions
ceno.regr
ceno.regrD
paleo.regr
neo.regr
paleo.regrD
neo.regrD
Mean Slope
-0.008
0.326
0.002
-4.00E-06
0.04
0.016
Confidence interval (95%)
S+
(-0.046 - -0.029)
(0.069 - 0.095)
(0.867 - 1.094)
(0.837 - 1.144
(0.073 - 0.408)
(0.142 – 0.660)
Confidence interval (95%)
S+
(-0.029 - 0.013)
(0.169 - 0.484)
(-0.007 - 0.011)
(-0.003 - 0.003)
(0.014 - 0.067)
(-0.015 - 0.044)
S100
0
8
10
89
0
S-
7
94
3
3
4
7
8
0
4
4
1
6
D - declining diversification rate ~ with sampling inequality
Rates
div neo
div paleo
ph neo
ph paleo
ph neo D
ph paleo D
Mean rate
-0.04
0.075
0.961
0.979
0.301
0.510
Confidence interval (95%)
S+
S(-0.055 - -0.032)
(0.059 - 0.107)
100
0
(0.822 - 1.12)
(0.805 - 1.172)
6
8
(0.069 - 0.641)
(0.126 – 1.186)
95
0
Regressions
ceno.regr
Mean Slope
-0.0129
Confidence interval (95%)
S+
(-0.028 - 0.002)
S6
9
ceno.regrD
paleo.regr
neo.regr
paleo.regrD
neo.regrD
0.247
-0.009
-0.0004
0.061
-0.009
(0.183 - 0.311)
(-0.0001 - -0.018)
(-0.003 - 0.003)
(0.047 - 0.074)
(-0.035 - 0.018)
99
2
6
26
7
0
3
2
0
1
References
-
Pagel M. 1999 Inferring the historical patterns of biological evolution. Nature vol 401 : 877884 doi:10.1038/44766
-
Oliver G. Pybus* and Paul H. Harvey Testing macro–evolutionary models using incomplete
molecular phylogenies. Proc. R. Soc. Lond. B 22 November 2000 vol. 267no. 1459 22672272 doi:10.1098/rspb.2000.1278
-
Daniel L. Rabosky 2012 Positive correlation between diversification rates and phenotypic
evolvability can mimic punctuated equilibrium on molecular phylogenies Evolution
DOI: 10.1111/j.1558-5646.2012.01631.x
-
James E. Tarver and Philip C. J. Donoghue 2011 The Trouble with Topology: Phylogenies
without Fossils Provide a Revisionist Perspective of Evolutionary History in Topological
Analyses of Diversity Systematic Biology 60 (5): 700-712. doi: 10.1093/sysbio/syr018
-
Losos, J. B. (2011). Seeing the forest for the trees: the limitations of phylogenies in
comparative biology. The American Naturalist, 177: 709–727.
-
Rabosky, D. L., and M. E. Alfaro. 2010. Evolutionary bangs and whimpers: methodological
advances and conceptual frameworks for studying exceptional diversification. Systematic
Biology 59:615-618.
-
Rabosky, D. L. 2010. Extinction rates Should not be Estimated from molecular phylogenies.
Evolution 6:1816-1824.
-
Thomas H.G. Ezard, and Andy Purvis 2009 paleoPhylo: free software to draw
paleobiological phylogenies Paleobiology August 2009v. 35 no. 3 p. 460-464 doi: 10.1666/
0094-8373-35.3.460
-
Quental T., Marshall C.R. 2009. Diversity dynamics: molecular phylogenies need the fossil
record. Trends Ecol. Evol. 25:434–441. 10.1016/j.tree.2010.05.002
-
Ruta M., Pisani D., Lloyd G.T., Benton M.J. 2007. A supertree of Temnospondyli:
cladogenetic patterns in the most species-rich group of early tetrapods. Proc. R. Soc. B Biol.
Sci. 274:3087–3095
-
Lloyd G.T., Davis K.E., Pisani D., Tarver J.E., Ruta M., Sakamoto M., Hone D.W.E.,
Jennings R., Benton M.J. 2008. Dinosaurs and the cretaceous terrestrial revolution. Proc. R.
Soc. B Biol. Sci. 75:2483– 2490.
-
Tanja Stadler (2011). TreeSim: Simulating trees under the birth-death model. R package
version 1.5.
-
Felisa A. Smith1,*, Alison G. Boyer2, James H. Brown1, Daniel P. Costa3, Tamar Dayan4,
S. K. Morgan Ernest5, Alistair R. Evans6, Mikael Fortelius7, John L. Gittleman8, Marcus
J. Hamilto Larisa E. Harding9, Kari Lintulaakso7, S. Kathleen Lyons10, Christy McCain11,
Jordan G. Okie1, Juha J. Saarinen7, Richard M. Sibly12, Patrick R. Stephens8, Jessica
Theodor13 and Mark D. Uhen13 The Evolution of Maximum Body Size of Terrestrial
Mammals Science 26 November 2010: Vol. 330 no. 6008 pp. 1216-1219
DOI: 10.1126/science.1194830
-
Liam J. Revell phytools: an R package for phylogenetic comparative biology (and other
things). Volume 3, Issue 2, pages 217–223, April 2012 DOI: 10.1111/j.2041210X.2011.00169.x
-
Luke Harmon, Jason Weir, Chad Brock, Rich Glor, Wendell Challenger and Gene Hunt
(2009). geiger: Analysis of evolutionary diversification. R package version 1.3-1
-
Yves Tillé and Alina Matei (2012). sampling: Survey Sampling. R package version 2.5.
-
Brian C. O'Meara1, Cécile Ané2, Michael J. Sanderson3,†, Peter C. Wainwright testing for
different rates of continuous trait evolution using likelihood. Evolution Volume 60, Issue
5, pages 922–933, May 2006 DOI: 10.1111/j.0014-3820.2006.tb01171.x