Electronic Supplementary Material
Historical species losses in bumblebee evolution
Fabien L. Condamine and Heather M. Hines
Contents
Text S1 Extended Methods.
Table S1 Time-dependent diversification analyses.
Figure S1 Convergence of the BAMM analysis.
Figure S2 Frequency distribution of distinct macroevolutionary rate regimes
estimated using BAMM.
Figure S3 Credible set of configuration shifts of bumblebees inferred with BAMM.
Figure S4 Estimates of speciation rates along the bumblebee phylogeny obtained
from BAMM analyses.
Figure S5 Estimates of extinction rates along the bumblebee phylogeny obtained
from BAMM analyses.
Text S1. Extended Methods
Diversification analyses
While time-constant models are useful, there are many reasons why diversification
rates can vary over the evolutionary history of a clade, including changes in the biotic
and abiotic environments, diversity-dependent effects, or the combination of both. A
straightforward and widespread approach to account for time variation in
diversification rates is to assume a functional dependence of speciation and extinction
rates with time [1-5]. Likelihood expressions of phylogenetic branching times for
such models are available, for both continuous (e.g. linear, exponential; [2,4,5]) and
discrete (referred to as the ‘discrete shift’ model; [3,5]) forms of time variation. These
time-dependent models allow a quantitative estimation of how diversification rates
have varied through time.
Discrete time-variation of diversification
The TreePar package [3] was used to assess speciation and extinction rates through
time. This method relaxes the assumption of constant rates by allowing rates to
change at specific points in time. Such a model allows for the detection of rapid
changes in speciation and extinction rates due to environmental factors like the
geological changes in the region. We employed the ‘bd.shifts.optim’ function that
allows for estimating discrete changes in speciation and extinction rates and mass
extinction events in under-sampled phylogenies. Going backward in time, it estimates
the maximum likelihood speciation and extinction rates together with the rate shift
times t=(t1,t2,...,tn) in a phylogeny. At each time t, the rates are allowed to change and
the species may undergo a shift in diversification. TreePar analyses were run with the
following settings: start = 0, end = crown age estimated by dating analyses, grid = 0.1
Myr, four possible shift times were tested, and posdiv = FALSE to allow the
diversification rate to be negative (i.e. allows for periods of declining diversity).
TreePar analyses were run as follows: start=0 (present), end=Bombus crown
age (34 million years, Myr, see Hines [2008]), grid=0.1 Myr (examining potential rate
shifts every 0.1 Myr), with no more than six shift times. Speciation and extinction
rates are inferred given the diversification rate (=speciation–extinction) and turnover
(=extinction/speciation).
Continuous time-variation diversification
We used the Morlon et al. [4]’s approach. This method has the advantage to take into
account the heterogeneity of diversification rates across the tree such that clades may
have their own speciation and extinction rates (and their own diversity dynamics), and
to estimate continuous variations of rates over time (whereas extinction is constant in
BAMM). The Morlon et al.’s approach is suitable to potentially infer a declining
diversity pattern in which extinction can exceed speciation meaning that
diversification rates can be negative [4]. We designed four models to be tested: (i)
BCSTDCST, speciation and extinction rates are constant; (ii) BVARDCST,
speciation rate is exponentially varying and extinction rate is constant; (iii)
BCSTDVAR, speciation rate is constant and extinction rate is exponentially varying;
and (iv) BVARDVAR, speciation and extinction rates are exponentially varying. We
also repeated these four models with a linear dependence through time. Models with
exponential variation are: 𝜆(𝑡) = 𝜆0 × 𝑒 𝛼𝑡 and 𝜇(𝑡) = 𝜇0 × 𝑒 𝛽𝑡 , and models with
linear variation are: 𝜆(𝑡) = 𝜆0 + 𝛼𝑡) and 𝜇(𝑡) = 𝜇0 + 𝛽𝑡), in which 𝜆0 and 𝜇0 are
the speciation and extinction rates at present, and α and β are the rates of change
according to time.
Across-clade and time-variation diversification
We used the Bayesian Analysis of Macroevolutionary Mixture (BAMM, www.bammproject.org) to estimate speciation and extinction rates through time and among/within
clades [6]. BAMM is an analytical tool for studying complex evolutionary processes
on phylogenetic trees, potentially shaped by a heterogeneous mixture of distinct
evolutionary dynamics of speciation and extinction across clades. The method uses
reversible jump MCMC (rjMCMC) to detect automatically rate shifts and sample
distinct evolutionary dynamics that best explain the whole diversification dynamics of
the clade. Within a given regime, evolutionary dynamics can involve time-variable
diversification rates; in BAMM, the speciation rate is allowed to vary exponentially
through time while extinction is maintained constant [7]. Subclades in the tree might
diversify faster (or slower) than others, and BAMM allows detecting these
diversification rate shifts without a priori hypotheses on how many and where these
shifts might occur. BAMM provides estimates of marginal probability of speciation
and extinction rates at any point in time along any branch of the tree. Marginal
probabilities of the number of evolutionary regimes can also be computed, allowing
comparisons of models with a given number of shifts with Bayes factors.
BAMM is implemented in a C++ command line program and the BAMMtools
R-package [8]. We ran BAMM analyses on the chronogram calibrated with four
fossils, and reconstructed with either the Yule or the birth-death prior. We set four
rjMCMC running for 507 generations and sampled every 50,000 generations. We
accounted for incomplete taxon sampling using the implemented analytical
correction, with a sampling fraction taking into account the missing species. We
performed four independent runs (with a burn-in of 10%) using different seeds, and
we used ESS to assess the convergence of the runs, considering values above 200 as
indicating good convergence. The posterior distribution was used to estimate the
configuration of the diversification rate shifts; alternative diversification models were
compared using Bayes factors.
Model selection
For TreePar and the Morlon et al.’s approach, we computed the corrected Akaike
information criterion (AICc) based on the log-likelihood and the number of
parameters of each diversification model [9]. A difference of two in the AICc
(ΔAICc) between two models suggests significant support for the model with the
lowest AICc. We also checked support for the selected model against all models
nested within it using the likelihood ratio test (LRT), which shows significant support
at P < 0.05. The scenario supported by LRT and with the lowest AICc was considered
the best. If the model with the lowest AICc was not supported by LRT, the model
with less parameter was considered the best.
For the BAMM analyses, we used posterior probabilities and Bayes factors to
compare the fit of different evolutionary scenarios (i.e. with no shift, one shift…). We
considered Bayes factors values above 5 to significantly favour one model over
another [10].
References
1. Nee S, May RM, Harvey PH. 1994b The reconstructed evolutionary process.
Philos. Trans. R. Soc. Lond. B Biol. Sci. 344: 305 – 311.
(doi.org/10.1098/rstb.1994.0068)
2. Rabosky DL, Lovette IJ. 2008 Explosive evolutionary radiations: decreasing
speciation or increasing extinction through time? Evolution 62: 1866–1875.
(doi.org/10.1111/j.1558-5646.2008.00409.x)
3. Stadler T. 2011 Mammalian phylogeny reveals recent diversification rate shifts.
Proc.
Natl.
Acad.
Sci.
USA
108,
6187–6192.
(doi.org/10.1073/pnas.1016876108)
4. Morlon H, Parsons TL, Plotkin J. 2011 Reconciling molecular phylogenies with the
fossil record. Proc. Natl Acad. Sci. USA 108, 16327–16332.
(doi.org/10.1073/pnas.1102543108)
5. Hallinan N. 2012 The generalized time variable reconstructed birth–death process.
J. Theor. Biol. 300: 265–276. (doi.org/10.1016/j.jtbi.2012.01.041)
6. Rabosky DL, Santini F, Eastman JM, Smith SA, Sidlauskas B, Chang J, Alfaro
ME. 2013 Rates of speciation and morphological evolution are correlated
across the largest vertebrate radiation. Nature Commun. 4, 1958.
(doi.org/10.1038/ncomms2958)
7. Rabosky DL, Donnellan SC, Grundler M, Lovette IJ. 2014 Analysis and
visualization of complex macroevolutionary dynamics: An example from
Australian
scincid
lizards.
Syst.
Biol.
63:
610-627.
(doi.org/10.1093/sysbio/syu025)
8. Rabosky DL, Grundler M, Anderson C, Shi JJ, Brown JW, Huang H, Larson JG.
2014b BAMMtools: an R package for the analysis of evolutionary dynamics
on
phylogenetic
trees.
Methods
Ecol.
Evol.
5:
701–707.
(doi.org/10.1111/2041-210X.12199)
9. Cavanaugh JE. 1997 Unifying the derivations of the Akaike and corrected Akaike
information criteria. Stat. Prob. Lett. 31: 201–208. (doi.org/10.1016/S01677152(96)00128-9)
10. Kass RE, Raftery AE. 1995 Bayes factors. J. Am. Stat. Assoc. 90: 773-795.
(doi.org/10.1080/01621459.1995.10476572)
Table S1. Time-dependent diversification analyses. The TreePar model with four shifts, and the model with speciation and extinction varying linearly though
time (BTimeVarDTimeVar_LIN) are supported. (a) TreePar models, in which ‘r1’ denotes the diversification rate and ‘τ1’ is the turnover, both inferred
between Present and the shift time 1 (‘st1’). (b) Models of Morlon et al., in which λ0 and μ0 are the speciation and extinction rates at present, with α and β the
rates of their respective variation through time.
(a)
Models
Constant birth-death
BD with 1 shift
BD with 2 shifts
BD with 3 shifts
BD with 4 shifts
N
logL
-460.44
±2.366
-449.46
5
±2.478
-445.57
8
±2.500
-438.55
11
±2.506
-434.44
14
±2.501
2
AICc
924.87
±4.733
908.92
±4.956
907.15
±5.000
899.10
±5.012
896.88
±5.002
ΔAICc
AIC
weight
P (LRT)
27.99
0
-
12.03
0.0013
<0.0001
10.26
0.00
0.051
2.214
0.17
0.001
0
0.515
0.042
ΔAICc
AIC
weight
P (LRT)
r1
τ1
st1
r2
τ2
st2
r3
τ3
st3
r4
τ4
st4
r5
τ5
0.175
±0.001
0.032
±0.003
-0.217
±0.004
-1.538
±0.006
-2.036
±0.005
0.000
±0.008
0.409
±0.016
5.017
±0.030
28.719
±0.054
28.330
±0.054
-
-
-
-
-
-
-
-
-
-
-
-
0.8
±0.039
0.8
±0.046
0.8
±0.044
0.8
±0.040
0.155
±0.001
0.100
±0.020
0.561
±0.032
0.679
±0.037
-
-
-
-
-
-
-
-
-
-
-
-
-
λ0
α
μ0
β
-
-
-
-
0
±0.0051
-
-
-
0 ±0
-
(b)
Models
N
Yule model
1
Constant birth-death
2
BTimeVar_EXPO
2
BTimeVarDCST_EXPO
3
BCSTDTimeVar_EXPO
3
BTimeVarDTimeVar_EXPO
4
BTimeVar_LIN
2
BTimeVarDCST_LIN
3
BCSTDTimeVar_LIN
3
BTimeVarDTimeVar_LIN
4
logL
AICc
-610.86
±2.512
-610.86
±2.631
-610.63
±2.708
-610.63
±2.708
-610.86
±2.706
-610.63
±2.731
-610.58
±2.679
-610.58
±2.695
-609.97
±2.702
-600.79
±2.633
1223.741
±5.025
1225.778
±5.261
1225.316
±5.415
1227.373
±5.415
1227.835
±5.413
1229.448
±5.463
1225.213
±5.357
1227.269
±5.391
1226.048
±5.405
1209.778
±5.267
0.1742
±0.0025
0.1742
16.000 0.0003
0.99
±0.0051
0.1823
15.538 0.0004
0.497
±0.0041
0.1822
17.595 0.0001
0.794
±0.0041
0.1743
18.057 0.0001
0.99
±0.0044
0.1821
19.670 0.00005 0.927
±0.0041
0.1837
15.435 0.0004
0.453
±0.0032
0.1838
17.491 0.0002
0.754
±0.0040
0.1833
16.270 0.0003
0.409
±0.0041
0.0272
0
0.997 <0.0001
±0.0056
13.963
0.0009
-
-0.0077
±0.0011
-0.0077
±0.0011
0
±0.0029
-0.0076
0
±0.0016 ±0.0005
-0.0016
±0.0002
-0.0016
0
±0.0002 ±0.0010
0.0079
±0.0018
0.1353 0.0814
±0.0029 ±0.0021
-
0.0187
±0.0104
0.0256
±0.0088
0.0040
±0.0005
-0.1291
±0.0040
0.345
±0.010
0.664
5.6
±0.094 ±0.761
0.000
3.3
±0.114 ±0.535
0.000
3.3
±0.121 ±0.486
0.102
±0.011
-0.188
±0.027
-0.237
±0.148
0.826
±0.036
1.746
5.6
±0.040 ±0.748
1.731
5.6
±0.042 ±0.589
0.106
±0.038
-0.002
±0.031
0.892
±0.034
1.002
14.6
0.050 0.991
±0.115 ±0.697 ±0.153 ±0.030
Figure S1. Convergence of the BAMM analysis with the chronogram. (a) The
stationary of the MCMC before applying a burn-in. (b) The posterior distribution of
number of shifts estimated before applying a burn-in. (c) The stationary of the
MCMC after removing the burn-in phase. (d) The posterior distribution of number of
shifts estimated after removing the burn-in phase.
Figure S2. Frequency distribution of distinct macroevolutionary rate regimes
estimated using BAMM. (a) Prior distribution of the number of distinct processes. (b)
Posterior distribution of the number of distinct processes (including the root process).
A one-process model outperforms a two-process model.
Figure S3. Credible set of configuration shifts of bumblebees inferred with BAMM.
For each shift configuration, the locations of rate shifts are shown as red (rate
increases) and blue (rate decreases) circles, with circle size proportional to the
marginal probability of the shift. Text labels (e.g. f =0.86) denote the posterior
probability of each shift configuration.
Figure S4. Estimates of speciation rates along the bumblebee phylogeny obtained
from BAMM analyses. Colours at each point in time along branches denote
instantaneous rates of speciation inferred as the mean scenario, with colours
indicating mean rates across all the shift configurations sampled in the Bayesian
posterior.
Figure S5. Estimates of extinction rates along the bumblebee phylogeny obtained
from BAMM analyses. Colours at each point in time along branches denote
instantaneous rates of extinction inferred as the mean scenario, with colours
indicating mean rates across all the shift configurations sampled in the Bayesian
posterior.