Here, we calculate upper bounds for our calibrations using the outgroup sequence method of Hedman (2010), specifically its implementation in an R script provided in the supplement of Friedman et al. (2013) (Dryad link: http://doi.org/10.5061/dryad.48f62). Following Friedman et al. (2013), stratigraphically inconsistent outgroups are excluded from the sequences.

To source the original script (= taken from Friedman et al. 2013 and modified by me to plot the resulting densities):

source("/Users/David/Grive/Alfaro_Lab/Calibrations/hedman_plotting.R")

Further modifications: I broke up the original function containing nested function declarations into three separate ones, one of which specifically handles visualization:

nodeage <- function(tsteps, tnodes, t0) {
  nn <- length(tnodes)                                   # number of outgroups
  nt <- length(tsteps)                                   # number of time steps
  pnodes <- matrix(0, nrow = nn, ncol = nt)
  ii <- which(tsteps > t0 & tsteps < tnodes[1])          # first get pdf for node 1, at discrete values
  pnodes[1, ii] <- 1.0 / length(ii)                      # assume uniform distribution for oldest node
  for (i in 2:nn) {
    for (j in 1:nt) {
      p21 <- rep(0, nt) 
      
      # get pdf for i-th node, at discrete values:
      ii <- which(tsteps >= tsteps[j] & tsteps < tnodes[i])
      # conditional probability of this age given previous node age, times probability
      # of previous node age
      p21[ii] <- 1.0 / length(ii) * pnodes[(i - 1), j]
      # add to cumulative sum:
      pnodes[i, ii] <- pnodes[i, ii] + p21[ii]
    }
  }
  list(pp = as.vector(pnodes[nn, ]))                     # get the pdf vector for the youngest node
}

Hedman.2010 <- function(tnodes, t0, resolution = 1000) {
  tsteps <- seq(-t0, -min(tnodes), length = resolution)  # uniformly spaced time steps
  vector <- nodeage(tsteps, -tnodes, -t0)                # get the pdf
  vector <- vector$pp
  
  # convert from p-value scale to age scale:
  integral.vector <- vector*((abs(t0 - min(tnodes)))/resolution) 
  # get sum of probabilities in order to re-scale as pdf:
  probability.sum <- sum(integral.vector)
  
  CIs <- c(0.025, 0.5, 0.975)                            # percentiles of interest
  percentiles <- rep(NA, length(CIs))
  for(j in 1:length(CIs)) {
    value <- 0
    i <- resolution
  
    while(value < probability.sum*CIs[j]) {
      value <- value + integral.vector[i]
      i <- i - 1
    }
    percentiles[j] <- tsteps[i]
  }
  
  Best.guess.lower <- percentiles[which(CIs == 0.025)]
  Best.guess.upper <- percentiles[which(CIs == 0.975)]
  
  mean <- sum((vector*tsteps))/(sum(vector))
  
  dd <- density(integral.vector, cut = 3)
  dd$y <- integral.vector
  dd$x <- seq(from = t0, to = min(tnodes), by = (min(tnodes) - t0)/(length(integral.vector) - 1))
  
  return(list(CI95 = Best.guess.upper, density.info = dd))
}
  
Hedman.visualization <- function(density, CI95upper) {
  plot(density, xlim = rev(range(density$x)), yaxs = "i", ylim = c(0, 1.2*max(density$y)),
       zero.line = F, main = "Hedman calibration density", xlab = "Age (Ma)")
  abline(v = -CI95upper, col = "white")
  segments(x0 = -CI95upper, y0 = 0, x1 = -CI95upper, y1 = density$y[density$x == -CI95upper],
           col = "red", lwd = 2)
  polygon(density, col = adjustcolor("lightblue", alpha.f = 0.3), border = "blue")
}

Non-neornithine outgroup sequences

We will set \(t_0\), the arbitrary oldest age to consider, to 160 Ma (very approximately, the age of anchiornithids and other near-avian dinosaurs from Tiaojishan); Hedman (2010) showed that the resulting estimates are relatively insensitive to the choice of this value. We will use the default resolution of 1,000 time steps. Below, we visualize the Hedman-style densities for the root calibration:

# Field et al. 2018, S15
f18s15 <- Hedman.2010(c(117.0, 117.0, 117.0, 100.5, 81.13, 69, 62.22, 55.88), 160)
f18s15$CI95
## [1] -81.72761
Hedman.visualization(f18s15$density.info, f18s15$CI95)

# Field et al. 2018, S17
f18s17 <- Hedman.2010(c(129.3, 129.3, 117.0, 114.1, 100.5, 69, 62.22, 55.88), 160)
f18s17$CI95
## [1] -88.71063
Hedman.visualization(f18s17$density.info, f18s17$CI95)

# Wang et al. 2020
wea20 <- Hedman.2010(c(129.3, 125.0, 120.49, 114.1, 100.5, 69, 62.22, 55.88), 160)
wea20$CI95
## [1] -88.71063
Hedman.visualization(wea20$density.info, wea20$CI95)

# Kundrát et al. 2018, Appendix 14
kea18 <- Hedman.2010(c(117.0, 100.5, 90.24, 81.13, 71.9, 69, 62.22, 55.88), 160)
kea18$CI95
## [1] -74.32769
Hedman.visualization(kea18$density.info, kea18$CI95)

# Wang et al. 2019
wea19 <- Hedman.2010(c(117.0, 117.0, 117.0, 114.1, 100.5, 69, 62.22, 55.88), 160)
wea19$CI95
## [1] -87.98106
Hedman.visualization(wea19$density.info, wea19$CI95)

# Zheng et al. 2018
zea18 <- Hedman.2010(c(151.2, 129.3, 129.3, 129.3, 100.5, 69, 62.22, 55.88), 160)
zea18$CI95
## [1] -92.15003
Hedman.visualization(zea18$density.info, zea18$CI95)

# Hartman et al. 2019
hea19 <- Hedman.2010(c(125.0, 124.07, 81.13, 71.9, 71.9, 69, 62.22, 55.88), 160)
hea19$CI95
## [1] -73.70234
Hedman.visualization(hea19$density.info, hea19$CI95)

# McLachlan et al. 2017
mea17 <- Hedman.2010(c(117.0, 100.5, 90.24, 81.13, 71.94, 69, 62.22, 55.88), 160)
mea17$CI95
## [1] -74.32769
Hedman.visualization(mea17$density.info, mea17$CI95)

# Cordes-Person et al. 2020, Supp. Mat. 6
cpea19 <- Hedman.2010(c(117.0, 114.1, 100.5, 90.24, 70.8, 69, 62.22, 55.88), 160)
cpea19$CI95
## [1] -76.93329
Hedman.visualization(cpea19$density.info, cpea19$CI95)

mean(sapply(list(f18s15, f18s17, wea20, kea18, wea19, zea18, hea19, mea17, cpea19),
            function(x) x$CI95))
## [1] -82.06344

We see that the difference between the youngest (Hartman et al. 2019; 73.70 Ma) and oldest (Zheng et al. 2018; 92.15 Ma) estimates is almost 20 Ma; the mean is approximately intermediate between the two extreme values.

Based on these results, we define the following function:

# Write a function that concatenates the within-Charadriiformes outgroup sequence with the
# non-charadriiform ones and outputs the upper bounds of the 95% credibility interval for all
# individual sequences (labeled), as well as their mean:

inner.calib.ci95 <- function(outgroup_vect) {
  outseq <- list(c(117.0, 117.0, 117.0, 100.5, 81.13, 69, 62.22, outgroup_vect),
                 c(129.3, 129.3, 117.0, 114.1, 100.5, 69, 62.22, outgroup_vect),
                 c(129.3, 125.0, 120.49, 114.1, 100.5, 69, 62.22, outgroup_vect),
                 c(117.0, 100.5, 90.24, 81.13, 71.9, 69, 62.22, outgroup_vect),
                 c(117.0, 117.0, 117.0, 114.1, 100.5, 69, 62.22, outgroup_vect),
                 c(151.2, 129.3, 129.3, 129.3, 100.5, 69, 62.22, outgroup_vect),
                 c(125.0, 124.07, 81.13, 71.9, 71.9, 69, 62.22, outgroup_vect),
                 c(117.0, 100.5, 90.24, 81.13, 71.94, 69, 62.22, outgroup_vect),
                 c(117.0, 114.1, 100.5, 90.24, 70.8, 69, 62.22, outgroup_vect))
             
  labels <- c("Field et al. 2018, S15", "Field et al. 2018, S17", "Wang et al. 2020",
           "Kundrát et al. 2018, Appendix 14", "Wang et al. 2019", "Zheng et al. 2018",
           "Hartman et al. 2019", "McLachlan et al. 2017",
           "Cordes-Person et al. 2020, Supp. Mat. 6")     
  
  ci95s <- Map(function(x) Hedman.2010(x, 160)$CI95, outseq)
  ret <- unlist(Map(function(x, y) paste(x, ": ", round(y, 3), " Ma", sep = ""), labels, ci95s))
  names(ret) <- NULL
  print(ret)
  print(paste("Mean:", round(mean(unlist(ci95s)), 3), "Ma"))
}

Estimating upper bounds for non-root calibrations

The general idea is to place an upper bound on a given calibration using other calibrations located around it in the tree (see Alfaro et al. 2018: Supplementary Information for a previous example). In doing so, we are making several assumptions:

  1. All fossils that are informative with regard to outgroup sequences are already included in the tree as calibrations. The only exception is represented by potential calibrations that were considered but ultimately discarded as redundant (see Figure A.1 in the Appendix).

  2. If a calibration is incertae sedis within the clade it calibrates, and this is due to the fact that there are several equally supported alternative positions for it (e.g., several most parsimonious trees, or several independent analyses), that calibration is assumed to occupy the earliest-diverging position within the least inclusive clade to which it can be assigned.

  3. If a calibration is incertae sedis within the clade it calibrates, and this is due to the fact that its exact position within this clade is poorly supported, that weakly supported position is nevertheless used to place it within the outgroup sequence.

Assumptions 2 and 3 are potentially problematic: the former is arbitrary and mainly employed to maximize the number of informative outgroups, while the latter effectively means that the same fossil will be assigned to different nodes as a calibration and as a member of another calibration’s outgroup sequence. However, potential alternative treatments would be even less justified. For example, extending assumption 2 to calibrations covered by assumption 3 would, at best, amount to preferring a position supported by no evidence to a position supported by weak evidence. Similarly, if calibrations of uncertain phylogenetic position were supplanted by younger fossils whose phylogenetic position is better supported, a calibration’s outgroup sequence would end up being stratigraphically inconsistent with the nested structure of the calibrations themselves. Finally, removing calibrations of uncertain phylogenetic position without replacement may result in sequences including excessively distant outgroups, and thus in overly diffuse calibration priors.

In the preliminary sequences below, we first mark the cases described in (2) for inclusion “if applicable”. If an outgroup includes multiple calibrations, we include all of them in the preliminary sequence, choosing the oldest one for the final sequence.

Locations of the calibrations in the total-evidence RAxML tree

Calibration 1: Uria lomvia vs. Uria aalge

Preliminary sequence

  • Primary calibrations: 1, 2, 3 (if applicable), 6 (if applicable), oldest of (9, 10, 11), 14 (if applicable)
  • Ages (in Ma): 2.58, 6.91, 18.1 (if applicable), 34.44 (if applicable), oldest of (20.0, 30.5, 24.47), 55.88 (if applicable)
  • Additional calibrations: Pseudocepphus teres, 13.9 Ma (to be inserted between calibrations 2 and 3)

Notes

Calibration 3. Most phylogenetic analyses place calibration 3 (Miocepphus bohaskai) within the total group of Alcini, either in the stem group of Alle (Smith & Clarke 2011; the parsimony analysis of Smith & Clarke 2014) or of the (Alca + Pinguinus) clade (the Bayesian analysis of Smith & Clarke 2014; the time-free Bayesian analysis of DiGiacomo 2018). However, it was recovered was as a stem-group member of Alcinae (Alca + Brachyramphus) in the tip-dating analysis of DiGiacomo (2018), which makes the total group of Alcinae the least inclusive clade in which it can be safely placed. By assumption 2, we treat it as a stem-group alcine in this calibration sequence.

Calibration 6. Smith (2011) found calibration 6 (specimen GCVP 5690) in a polytomy at the base of Alcinae, but noted that its inclusion in this clade depended on a single character that could be plesiomorphic for Alcidae as a whole. Smith (2015) therefore preferred to treat the fossil as Pan-Alcidae incertae sedis. By assumption 2, we prefer the basalmost plausible position for the fossil.

Pseudocepphus teres is usually recovered within the total group of the genus Cepphus (Smith 2011; Smith & Clarke 2014; the parsimony, maximum-likelihood, and time-free Bayesian analyses of DiGiacomo 2018), but DiGiacomo (2018) found it to be a stem-group alcine in her tip-dating analysis, more closely related to the crown than Miocepphus bohaskai (calibration 3). By assumption 2, this is the position that its placement in the outgroup sequence is based on.

Final sequence

  • Calibrations: 1, 2, Pseudocepphus teres, 3, 6, 16
  • Ages (in Ma): 2.58, 6.91, 13.9, 18.1, 34.44, 55.88
inner.calib.ci95(c(55.88, 34.44, 18.1, 13.9, 6.91, 2.58))
## [1] "Field et al. 2018, S15: -23.538 Ma"                
## [2] "Field et al. 2018, S17: -23.853 Ma"                
## [3] "Wang et al. 2020: -23.853 Ma"                      
## [4] "Kundrát et al. 2018, Appendix 14: -23.223 Ma"      
## [5] "Wang et al. 2019: -23.853 Ma"                      
## [6] "Zheng et al. 2018: -24.011 Ma"                     
## [7] "Hartman et al. 2019: -23.223 Ma"                   
## [8] "McLachlan et al. 2017: -23.223 Ma"                 
## [9] "Cordes-Person et al. 2020, Supp. Mat. 6: -23.38 Ma"
## [1] "Mean: -23.573 Ma"

Calibration 2: Alca vs. Pinguinus

Preliminary sequence

  • Primary calibrations: 2, 1, 3 (if applicable), 6 (if applicable), oldest of (9, 10, 11), 14 (if applicable)
  • Ages (in Ma): 6.91, 2.58, 18.1 (if applicable), 34.44 (if applicable), oldest of (20.0, 30.5, 24.47), 55.88 (if applicable)
  • Additional calibrations: Pseudocepphus teres, 13.9 Ma (to be inserted between calibrations 1 and 3)

Notes

For notes on calibrations 3 and 6, see calibration 1.

Final sequence

  • Calibrations: 2, Pseudocepphus teres, 3, 6, 14
  • Ages (in Ma): 6.91, 13.9, 18.1, 34.44, 55.88
inner.calib.ci95(c(55.88, 34.44, 18.1, 13.9, 6.91))
## [1] "Field et al. 2018, S15: -33.574 Ma"                 
## [2] "Field et al. 2018, S17: -34.187 Ma"                 
## [3] "Wang et al. 2020: -34.187 Ma"                       
## [4] "Kundrát et al. 2018, Appendix 14: -33.115 Ma"       
## [5] "Wang et al. 2019: -34.187 Ma"                       
## [6] "Zheng et al. 2018: -34.494 Ma"                      
## [7] "Hartman et al. 2019: -32.961 Ma"                    
## [8] "McLachlan et al. 2017: -33.115 Ma"                  
## [9] "Cordes-Person et al. 2020, Supp. Mat. 6: -33.268 Ma"
## [1] "Mean: -33.676 Ma"

Calibration 3: Alcinae vs. Fraterculinae

Preliminary sequence

  • Primary calibrations: 3, 6 (if applicable), oldest of (9, 10, 11), 14 (if applicable)
  • Ages (in Ma): 18.1, 34.44 (if applicable), oldest of (20.0, 30.5, 24.47), 55.88 (if applicable)

Notes

For notes on calibration 6, see calibration 1.

Final sequence

  • Calibrations: 3, 6, 14
  • Ages (in Ma): 18.1, 34.44, 55.88
inner.calib.ci95(c(55.88, 34.44, 18.1))
## [1] "Field et al. 2018, S15: -57.304 Ma"                 
## [2] "Field et al. 2018, S17: -59.292 Ma"                 
## [3] "Wang et al. 2020: -59.292 Ma"                       
## [4] "Kundrát et al. 2018, Appendix 14: -55.599 Ma"       
## [5] "Wang et al. 2019: -59.15 Ma"                        
## [6] "Zheng et al. 2018: -60.286 Ma"                      
## [7] "Hartman et al. 2019: -55.315 Ma"                    
## [8] "McLachlan et al. 2017: -55.599 Ma"                  
## [9] "Cordes-Person et al. 2020, Supp. Mat. 6: -56.025 Ma"
## [1] "Mean: -57.54 Ma"

Calibration 4: Aethiini vs. Fraterculini

Preliminary sequence

  • Calibrations: 4, 3 (if applicable), 6 (if applicable), oldest of (9, 10, 11), 14 (if applicable)
  • Ages (in Ma): 9.3, 18.1 (if applicable), 34.44 (if applicable), oldest of (20.0, 30.5, 24.47), 55.88 (if applicable)

Notes

Since both Pseudocepphus teres and calibration 3 (Miocepphus bohaskai) belong to the total group of Alcinae, they represent the same outgroup lineage vis-à-vis the Fraterculini incertae sedis that calibration 4 is based on. Therefore, only the older of the two can be used in the latter’s outgroup sequence.

Final sequence

  • Calibrations: 4, 3, 6, 14
  • Ages (in Ma): 9.3, 18.1, 34.44, 55.88
inner.calib.ci95(c(55.88, 34.44, 18.1, 9.3))
## [1] "Field et al. 2018, S15: -44.75 Ma"                  
## [2] "Field et al. 2018, S17: -45.806 Ma"                 
## [3] "Wang et al. 2020: -45.806 Ma"                       
## [4] "Kundrát et al. 2018, Appendix 14: -43.694 Ma"       
## [5] "Wang et al. 2019: -45.655 Ma"                       
## [6] "Zheng et al. 2018: -46.258 Ma"                      
## [7] "Hartman et al. 2019: -43.543 Ma"                    
## [8] "McLachlan et al. 2017: -43.694 Ma"                  
## [9] "Cordes-Person et al. 2020, Supp. Mat. 6: -43.996 Ma"
## [1] "Mean: -44.8 Ma"

Calibration 5: Fratercula arctica vs. Fratercula corniculata

Preliminary sequence

  • Calibrations: 5, 4 (if applicable), 3 (if applicable), 6 (if applicable), oldest of (9, 10, 11), 14 (if applicable)
  • Ages (in Ma): 3.92, 6.6 (if applicable), oldest of (18.1, 1.73, 6.6, 1.73), 34.44 (if applicable), oldest of (20.0, 30.5, 24.47), oldest of (20.0, 24.76), 55.88 (if applicable)
  • Additional calibrations: Cerorhinca sp., 3.92 Ma (to be inserted between calibrations 5 and 4)

Notes

Calibration 4. Smith (2011: Figure 4.13) found calibration 4 (specimen LACM 18275) in a single unresolved polytomy comprising the three extant species of Fratercula and the single extant species of Cerorhinca. No other members of Fraterculini were included in the analysis. Given the close affinity of specimens USNM 192994 and USNM 215783 (jointly comprising calibration 5) to the extant F. arctica, we consider it unlikely that LACM 18275 (originally considered to represent a species of Cerorhinca; Howard 1968) is more closely related to that taxon than they are. By assumption 2, we consider calibration 4 to be able to constitute an outgroup vis-à-vis calibration 5.

Calibration 6. In this case, it matters whether GCVP 5690 (calibration 6) is treated as an Alcinae incertae sedis following the unshown analysis reported by Smith (2011), or as a Pan-Alcidae incertae sedis, a position preferred by Smith (2011, 2015) because of the unclear polarization of the single character supporting the alcine affinity. Here, we conservatively choose the latter option and, by assumption 2, treat calibration 6 as a stem-alcid.

Cerorhinca sp. has been recovered within the total group of the genus Cerorhinca (Smith 2011: Figures 4.16, 4.17; Smith & Clarke 2014), and as such lies outside of the (F. arctica + F. cirrhata) clade calibrated by calibration 5. By assumption 2, we consider calibration 4 to be more basal still. This effectively amounts to assuming that LACM 18275 (calibration 4) is a member of the Fraterculini stem group, falling outside of (Cerorhinca + Fratercula); such a position is neither supported nor rejected by the only phylogenetic analysis in which it was included (Smith 2011: Figure 4.13).

For notes on calibrations 3 and 14, see calibration 1.

Final sequence

  • Calibrations: 5, Cerorhinca sp., 4, 3, 6, 14
  • Ages (in Ma): 3.92, 3.92, 9.3, 18.1, 34.44, 55.88
inner.calib.ci95(c(55.88, 34.44, 18.1, 9.3, 3.92, 3.92))
## [1] "Field et al. 2018, S15: -22.512 Ma"                 
## [2] "Field et al. 2018, S17: -22.825 Ma"                 
## [3] "Wang et al. 2020: -22.825 Ma"                       
## [4] "Kundrát et al. 2018, Appendix 14: -22.2 Ma"         
## [5] "Wang et al. 2019: -22.825 Ma"                       
## [6] "Zheng et al. 2018: -22.981 Ma"                      
## [7] "Hartman et al. 2019: -22.2 Ma"                      
## [8] "McLachlan et al. 2017: -22.2 Ma"                    
## [9] "Cordes-Person et al. 2020, Supp. Mat. 6: -22.356 Ma"
## [1] "Mean: -22.547 Ma"

Calibration 6: Alcidae vs. Stercorariidae

Preliminary sequence

  • Calibrations: 6, oldest of (9, 10, 11), 14 (if applicable)
  • Ages (in Ma): 34.44, oldest of (20.0, 30.5, 24.47), 55.88 (if applicable)

Notes

For notes on calibration 14, see calibration 1.

Final sequence

  • Calibrations: 6, 14
  • Ages (in Ma): 34.44, 55.88
inner.calib.ci95(c(55.88, 34.44))
## [1] "Field et al. 2018, S15: -69.506 Ma"                 
## [2] "Field et al. 2018, S17: -73.78 Ma"                  
## [3] "Wang et al. 2020: -73.78 Ma"                        
## [4] "Kundrát et al. 2018, Appendix 14: -65.484 Ma"       
## [5] "Wang et al. 2019: -73.403 Ma"                       
## [6] "Zheng et al. 2018: -75.791 Ma"                      
## [7] "Hartman et al. 2019: -65.107 Ma"                    
## [8] "McLachlan et al. 2017: -65.484 Ma"                  
## [9] "Cordes-Person et al. 2020, Supp. Mat. 6: -66.616 Ma"
## [1] "Mean: -69.883 Ma"

Calibration 7: Calidris vs. Arenaria

  • Calibrations: 7, 8, 9 (if applicable), oldest of (10, 11), 6, 14 (if applicable)
  • Ages (in Ma): 12.6, 6.1, 20.0 (if applicable), oldest of (30.5, 24.47), 34.44, 55.88 (if applicable)

Notes

Calibration 9. The genera Elorius and Parvelorius, which jointly comprise calibration 9, have never been included in a formal phylogenetic analysis. However, detailed anatomical comparisons suggest that both genera are early-diverging scolopacids outside of the clade formed by Arenariinae, Tringinae, and Scolopacinae, possibly related to Limosa (de Pietri & Mayr 2013). As such, they are suitable for inclusion in the outgroup sequence of calibration 7 (Mirolia brevirostrata), a member of Arenariinae.

For notes on calibration 14, see calibration 1.

Final sequence

  • Calibrations: 7, 9, 10, 6, 14
  • Ages (in Ma): 12.6, 20.0, 30.5, 34.44, 55.88
inner.calib.ci95(c(55.88, 34.44, 30.5, 20.0, 12.6))
## [1] "Field et al. 2018, S15: -37.683 Ma"                 
## [2] "Field et al. 2018, S17: -38.273 Ma"                 
## [3] "Wang et al. 2020: -38.421 Ma"                       
## [4] "Kundrát et al. 2018, Appendix 14: -37.24 Ma"        
## [5] "Wang et al. 2019: -38.273 Ma"                       
## [6] "Zheng et al. 2018: -38.568 Ma"                      
## [7] "Hartman et al. 2019: -37.093 Ma"                    
## [8] "McLachlan et al. 2017: -37.24 Ma"                   
## [9] "Cordes-Person et al. 2020, Supp. Mat. 6: -37.388 Ma"
## [1] "Mean: -37.798 Ma"

Calibration 8: Gallinago vs. (Coenocorypha + “Gallinago” undulata + Chubbia)

  • Calibrations: 8, 7, 9 (if applicable), oldest of (10, 11), 6, 14 (if applicable)
  • Ages (in Ma): 6.1, 12.6, 20.0 (if applicable), oldest of (30.5, 24.47), 34.44, 55.88 (if applicable)

Notes

For notes on calibration 9, see calibration 7. For notes on calibration 14, see calibration 1.

Final sequence

  • Calibrations: 8, 7, 9, 10, 6, 14
  • Ages (in Ma): 6.1, 12.6, 20.0, 30.5, 34.44, 55.88
inner.calib.ci95(c(55.88, 34.44, 30.5, 20.0, 12.6, 6.1))
## [1] "Field et al. 2018, S15: -28.438 Ma"                
## [2] "Field et al. 2018, S17: -28.592 Ma"                
## [3] "Wang et al. 2020: -28.592 Ma"                      
## [4] "Kundrát et al. 2018, Appendix 14: -28.13 Ma"       
## [5] "Wang et al. 2019: -28.592 Ma"                      
## [6] "Zheng et al. 2018: -28.746 Ma"                     
## [7] "Hartman et al. 2019: -27.976 Ma"                   
## [8] "McLachlan et al. 2017: -28.13 Ma"                  
## [9] "Cordes-Person et al. 2020, Supp. Mat. 6: -28.13 Ma"
## [1] "Mean: -28.369 Ma"

Calibration 9: Crown-group Scolopacidae

  • Calibrations: 9, oldest of (10, 11), 6, 14 (if applicable)
  • Ages (in Ma): 20.0, oldest of (30.5, 24.47), 34.44, 55.88 (if applicable)

Notes

For notes on calibration 14, see calibration 1.

Final sequence

  • Calibrations: 9, 10, 6, 14
  • Ages (in Ma): 20.0, 30.5, 34.44, 55.88
inner.calib.ci95(c(55.88, 34.44, 30.5, 20.0))
## [1] "Field et al. 2018, S15: -48.168 Ma"                 
## [2] "Field et al. 2018, S17: -49.289 Ma"                 
## [3] "Wang et al. 2020: -49.289 Ma"                       
## [4] "Kundrát et al. 2018, Appendix 14: -47.187 Ma"       
## [5] "Wang et al. 2019: -49.289 Ma"                       
## [6] "Zheng et al. 2018: -49.85 Ma"                       
## [7] "Hartman et al. 2019: -47.047 Ma"                    
## [8] "McLachlan et al. 2017: -47.187 Ma"                  
## [9] "Cordes-Person et al. 2020, Supp. Mat. 6: -47.467 Ma"
## [1] "Mean: -48.308 Ma"

Calibration 10: Jacanidae vs. Rostratulidae

  • Calibrations: 10, 11, 9, 6, 14 (if applicable)
  • Ages (in Ma): 30.5, 24.47, 20.0, 34.44, 55.88 (if applicable)

Notes

For notes on calibration 14, see calibration 1.

Final sequence

  • Calibrations: 10, 6, 14
  • Ages (in Ma): 30.5, 34.44, 55.88
inner.calib.ci95(c(55.88, 34.44, 30.5))
## [1] "Field et al. 2018, S15: -58.889 Ma"                 
## [2] "Field et al. 2018, S17: -60.963 Ma"                 
## [3] "Wang et al. 2020: -60.963 Ma"                       
## [4] "Kundrát et al. 2018, Appendix 14: -56.944 Ma"       
## [5] "Wang et al. 2019: -60.833 Ma"                       
## [6] "Zheng et al. 2018: -62 Ma"                          
## [7] "Hartman et al. 2019: -56.685 Ma"                    
## [8] "McLachlan et al. 2017: -56.944 Ma"                  
## [9] "Cordes-Person et al. 2020, Supp. Mat. 6: -57.463 Ma"
## [1] "Mean: -59.076 Ma"

Calibration 11: Pedionomidae vs. Thinocoridae

  • Calibrations: 11, 10, 9, 6, 14 (if applicable)
  • Ages (in Ma): 24.47, 30.5, 20.0, 34.44, 55.88 (if applicable)

Notes

For notes on calibration 14, see calibration 1.

Final sequence

  • Calibrations: 11, 10, 6, 14
  • Ages (in Ma): 24.47, 30.5, 34.44, 55.88
inner.calib.ci95(c(55.88, 34.44, 30.5, 24.47))
## [1] "Field et al. 2018, S15: -48.89 Ma"                  
## [2] "Field et al. 2018, S17: -49.975 Ma"                 
## [3] "Wang et al. 2020: -49.975 Ma"                       
## [4] "Kundrát et al. 2018, Appendix 14: -47.804 Ma"       
## [5] "Wang et al. 2019: -49.839 Ma"                       
## [6] "Zheng et al. 2018: -50.518 Ma"                      
## [7] "Hartman et al. 2019: -47.669 Ma"                    
## [8] "McLachlan et al. 2017: -47.804 Ma"                  
## [9] "Cordes-Person et al. 2020, Supp. Mat. 6: -48.076 Ma"
## [1] "Mean: -48.95 Ma"

Calibration 12: (Haematopodidae + Ibidorhyncha) vs. Recurvirostridae

  • Calibrations: 12, 13, oldest of (6, 9, 10, 11), 14 (if applicable)
  • Ages (in Ma): 20.0, 24.76, oldest of (34.44, 20.0, 30.5, 24.47), 55.88 (if applicable)

Notes

Calibration 14. Our re-analysis of the dataset of Heingård et al. (2021) found moderate support for a sister-group relationship between IGM 100/1435 and the genus Chionis (posterior probability of 0.899–0.921 depending on the backbone constraint used). However, none of the deeper nodes, including Chionida (Chionoidea + Burhinidae) and Charadrii (Chionida + Charadriida), received comparable support, and the only clade within which IGM 100/1435 was nested with a posterior probability of at least 0.95 was the charadriiform crown as a whole. For the purposes of primary calibration choice, we therefore regarded its exact position within the charadriiform crown as unresolved. However, by assumption 3, we use its moderately supported position within Chionida to place it within the outgroup sequence as a member of Charadrii. In this position, it supersedes calibration 15, and makes all subsequent outgroups from the preliminary sequence unsuitable for the inclusion in the final sequence.

Final sequence

  • Calibrations: 12, 14
  • Ages (in Ma): 20.0, 55.88
inner.calib.ci95(c(55.88, 20.0))
## [1] "Field et al. 2018, S15: -67.928 Ma"                 
## [2] "Field et al. 2018, S17: -71.992 Ma"                 
## [3] "Wang et al. 2020: -72.132 Ma"                       
## [4] "Kundrát et al. 2018, Appendix 14: -64.424 Ma"       
## [5] "Wang et al. 2019: -71.712 Ma"                       
## [6] "Zheng et al. 2018: -73.814 Ma"                      
## [7] "Hartman et al. 2019: -64.004 Ma"                    
## [8] "McLachlan et al. 2017: -64.424 Ma"                  
## [9] "Cordes-Person et al. 2020, Supp. Mat. 6: -65.405 Ma"
## [1] "Mean: -68.426 Ma"

Calibration 13: Chionoidea vs. Burhinidae

  • Calibrations: 13, 12, oldest of (6, 9, 10, 11), 14 (if applicable)
  • Ages (in Ma): 24.76, 20.0, oldest of (34.44, 20.0, 30.5, 24.47), 55.88 (if applicable)

Notes

Calibration 14. The sparse taxon sampling does not allow to determine the exact relationship of IGM 100/1435 (calibration 14) with respect to the Chionoidae and to Pluvianellus; therefore, by assumption 2, we treat it as a stem chionoid. This is the same position that was also suggested for Chionoides australiensis (calibration 13) by de Pietri et al. (2016) based on the fact that the fossil displays a mosaic of chionid and pluvianellid traits, and that it predates the split the Pluvianellus/Chionidae split as estimated by molecular dating analyses. Regardless of the exact relationship between the two (as sister groups or as successive outgroups to Chionoidea), calibration 14 is suitable for the inclusion in the outgroup sequence of calibration 13. It supersedes all other outgroups from the preliminary sequence.

Final sequence

  • Calibrations: 13, 14
  • Ages (in Ma): 24.76, 55.88
inner.calib.ci95(c(55.88, 24.76))
## [1] "Field et al. 2018, S15: -68.351 Ma"                 
## [2] "Field et al. 2018, S17: -72.548 Ma"                 
## [3] "Wang et al. 2020: -72.548 Ma"                       
## [4] "Kundrát et al. 2018, Appendix 14: -64.696 Ma"       
## [5] "Wang et al. 2019: -72.141 Ma"                       
## [6] "Zheng et al. 2018: -74.443 Ma"                      
## [7] "Hartman et al. 2019: -64.29 Ma"                     
## [8] "McLachlan et al. 2017: -64.696 Ma"                  
## [9] "Cordes-Person et al. 2020, Supp. Mat. 6: -65.779 Ma"
## [1] "Mean: -68.832 Ma"

References