APPENDIX 10. Lissamphibian biodiversity through time.
We computed three indices: 1, a simple count of observed species in each stage; 2, a
standardized count of observed species in each stage (obtained by dividing the first index by
the stage duration, in Ma); 3, a count of all observed species plus all inferred lineages (ghost
ranges) in each stage. The last index incorporates phylogenetic information and is based on
our supertree, incorporating the corresponding minimal branch length assumptions (each
species occupies at least a whole geological stage, minimal internal branch length is 3 Ma).
Thus, ghost ranges are longer here than in other studies because they have usually been
computed assuming zero-length internal branches (Wills, 1999). Ghost ranges are potentially
important in studies on biological crises performed on species (as opposed to larger taxa)
because the latter have a relative short duration (at least among vertebrates), on the order of a
single geological stage. Therefore, studies neglecting ghost ranges would be very sensitive to
taphonomic artefacts such as fluctuating quality of the fossil record; in a worst-case scenario,
a group with a good fossil record in one stage and no fossil record in the next would appear to
have undergone complete extinction. However, if many of the species present in the first
(oldest) stage had descendants and if the phylogeny were reasonably well known, methods
that take ghost lineages into consideration would infer much lower extinction rates.
Simulations are required to more precisely assess the merits of various approaches to study
mass extinctions, but they are beyond the scope of this paper. Most previous studies on
extinction patterns in early vertebrates did not incorporate ghost range estimates (Erwin,
1993; Hallam and Wignall, 1997). Our first two indices do not incorporate any phylogenetic
information, but it still differs from most previous studies in this field by being done at the
species (rather than genus, family or order) level.
Early studies on the evolution of biodiversity did not standardize for stage duration
“because of considerable uncertainty in the durations of stages” (Raup and Sepkoski,
2
1984:801). Over the last twenty years, this uncertainty has greatly diminished for the
Cenozoic, so we have calculated these durations from the ages given by Gradstein et al.
(2004). In the Mesozoic there are still stages whose beginning and end is associated with
uncertainty on the scale of the duration of the stage itself (e.g. the Kimmeridgian, whose
duration we consider to be 4.9 Ma, while both its beginning and its end have confidence
intervals of ± 4.0 Ma; Gradstein et al., 2004), but we do not try to test for mass extinctions
within the Mesozoic. Recent studies have generally standardized for time in various ways
(e.g. Alroy, 1999, 2000); therefore, our second biodiversity index is time-standardized.
We did not calculate extinction rates because the duration of most species is highly
uncertain; in most cases, they have been found in a single stage, but the actual duration of
their lineages (including ghost ranges) may be far greater. Thus, it is very difficult to measure
extinction rates; but minimal biodiversity at any given time can be measured more
objectively. Our analysis might indicate whether or not it is appropriate to include extinction
events in the model of lissamphibian biodiversity, although given the paucity of Triassic
lissamphibians, only the K/Pg boundary event and more minor crises that occurred in the
Cenozoic can be studied in this taxon.
Dating uncertainties in the Miocene complicated the analysis because many lissamphibian
fossils were dated only to Middle Miocene, whereas our scale divides this interval into
Langhian and Serravallian. Therefore, we computed all biodiversity indices using two
versions of our supertree, one in which all species of uncertain age were put in the Langhian
and another in which these species were placed in the Serravallian. There are also several
records of fossils whose taxonomic assignment is questionable and that could represent
distinct species or (often) the oldest records of their respective species. Again, we calculated
the three biodiversity indices either while considering these specimens of questionable
affinities to be distinct species, or excluding them. The latter approach would be justified if
3
these specimens were ancestors of at least some of the other species in our tree, or if they
belonged to other species, or if they were based on non-diagnostic material, as argued by
Bever (2005) for many fossils attributed to Bufo sensu lato. We then computed the maximal
and minimal biodiversity according to the three indices, and these are the values reported in
the Results section.
The raw (unstandardized) observed number of species varies widely and, to a large extent,
randomly (part a of the figure of this appendix). This index obviously reflects mostly
taphonomic artefact and is nearly useless to assess the fate of lissamphibians across the K/Pg
boundary. However, this graph shows the stratigraphic distribution of the lissamphibian
species that are included in the supertree, and, as such, nicely summarizes this aspect of our
data.
The standardized observed number of species also varies widely, but perhaps a little less
than the raw number of species (part b of the figure of this appendix). The differences
between both indices are enlightening. For instance, the raw number of species suggests a
50% diversity drop at the K/Pg boundary, but the standardized values suggest a more
moderate reduction. Similarly, the raw values suggest moderate drops in lissamphibian
diversity in three Cenozoic time intervals (Chattian/Aquitanian, Langhian/Serravallian, and
Tortonian/Messinian), but the standardized values show moderate increases in diversity,
which suggests that the raw values mostly represent taphonomic artefacts.
However, even the standardized observed number of species are probably affected by
taphonomic factors, as shown by comparisons with the observed number of lineages (see
below).
The count of lineages appears to be much less affected by taphonomic artefacts, judging
by the smooth shape of the diversity curve (part c of the figure of this appendix). However,
the signal in this index is probably overwhelmed to a large extent by the numerous ghost
4
ranges that lead to extant species. This is illustrated by the number of observed species (5 to
10) and high number of lineages (57) in the Maastrichtian; there are about 50 ghost lineages
in that stage, and most of them lead to extant species. Thus, this index should have a low
power to detect extinction events. Nevertheless, four drops in diversity are visible. The first
occurs between the Campanian (59 lineages) and the Danian (56 lineages). Thus,
lissamphibians may have been moderately affected by the K/Pg event, and a literal reading of
this index suggests a gradual decline rather than a catastrophic extinction event, although the
fact that the Campanian was longer than the Maastrichtian and the Danian together appears to
skew this, as shown by the low standardized number of species in the Campanian (Fig. 9b).
The second drop (from about 140 to about 135 lineages) is across the Chattian/Aquitanian
(Oligocene/Miocene) boundary that is not considered a time of major biological crisis
(Hallam and Wignall, 1997), although many species of corals became extinct at that time
(Edinger and Risk, 1995). Another slight reduction in number of lineages (from about 140 to
about 130) is across the Langhian/Serravallian boundary, in the middle Miocene. An
extinction event has been recognized at that time by Raup and Sepkoski (1984). The fourth,
very slight drop (from about 127 to about 123 lineages), between the Tortonian and the
Messinian (late Miocene), may result partly from the deliberate omission of the Pliocene and
Quaternary fossils, but it may also reflect a genuine reduction in lissamphibian biodiversity
because a decline in North American mammals has long been recognized at that time (Webb
and Barnoski, 1989). The three possible Tertiary crises identified on the basis of the number
of lineages also appear as times of elevated extinction level on the basis of the number of raw
observed species (Fig. 9a).
We found large differences in the lissamphibian biodiversity pattern shown by raw and
standardized observed number of species. Earlier studies of biodiversity through time (e.g.
Smith, 1994, and references therein) did not standardize for stage duration; the need for
5
standardization has been recognized by Alroy (1998, 1999, 2000) and Alroy et al. (2001),
who used absolute ages instead of stage assignments and also standardized for sampling
intensity (Alroy, 1999, 2000; Alroy et al., 2001). Unfortunately, we know too little about the
sampling of the lissamphibian fossil record in collections and in the literature to standardize
for it.
6
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FIGURE LEGEND. Lissamphibian biodiversity through time. Three indices are presented: (a) a
count of observed species in each geological stage; (b), (c) a count of lineages (observed
species and inferred ghost lineages in each geological stage). Major biological crises
identified in other taxa are shown as continuous gray lines. More minor crises that may have
affected lissamphibians are shown as dashed gray lines. Since most post-Miocene species are
excluded, this figure ends with the terminal Miocene. Minimal and maximal biodiversity for
all indices are given, under various assumptions about the age of several middle Miocene
species and the status of specimens of questionable affinities. Abbreviations: J, Jurassic; K,
Cretaceous; O, Oligocene; M, Miocene; P, Permian; Pg, Paleogene; Tr, Triassic.