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Diego Pol, Mark A. The ages of first appearance of fossil taxa in the stratigraphic record are inherently associated to an interval of error or uncertainty, rather than being precise point estimates. Contrasting this temporal information with topologies of phylogenetic relationships is relevant to many aspects of evolutionary studies. Several indices have been proposed to compare the ages of first appearance of fossil taxa and phylogenies. For computing most of these indices, the ages of first appearance of fossil taxa are currently used as point estimates, ignoring their associated errors or uncertainties.
A solution based on randomization of the ages of terminal taxa is implemented, resulting in a range of possible values for measures of stratigraphic fit to phylogenies, rather than in a precise but arbitrary stratigraphic fit value. Sample cases show that ignoring the age uncertainty of fossil taxa can produce misleading when comparing the stratigraphic fit of competing phylogenetic hypotheses. Empirical test cases of alternative phylogenies of two dinosaur groups are analyzed through the randomization procedure proposed here.
Comparing the age of origination of taxa with a phylogenetic tree provides insight into the tempo and mode of the evolutionary history of a group, such as divergence age of its clades, evolutionary rates, and gaps in the fossil record as implied by that particular tree. Several empirical measures have been proposed for assessing the fit between these ages and phylogenetic trees that include fossil taxa.
These measures compare the temporal order of successive branching events with the age of appearance of terminal taxa in the stratigraphic record and are usually referred to as the stratigraphic fit to a phylogeny Norell and Novacek, ; Benton and Stors, ; Huelsenbeck, ; Siddall, ; Wills, ; Pol and Norell, ; Pol et al.
Such comparisons are frequently used to describe the stratigraphic fit of competing phylogenetic trees. Alternatively, similar comparisons have been proposed as auxiliary optimality criteria e. Some of these procedures not only provide a measure of how well the stratigraphic appearance of terminal taxa fits their relative ordering in a phylogeny, but also provide minimal ages of divergences for every node in the tree based on temporal information in the fossil record. The order of branching events on a phylogenetic tree is derived from hypotheses of evolutionary relationships, usually obtained from biological data alone, independent from temporal information Norell, ; but see Fox et al.
As noted ly, uncertainty in estimates of phylogenetic relationships could certainly affect the outcome of these metrics Huelsenbeck, ; Benton et al. Consequently, some researchers have attempted to predict how these measures behave in response to erroneous phylogenetic trees through simulations Wagner, a ; Wagner and Sidor, The other kind of information used in analysis of stratigraphic fit to phylogenies is the age of fossil terminal taxa. The discussion presented here is restricted to ghost lineage metrics that have been formulated Siddall, ; Wills, and used in empirical studies assuming the absence of ancestors among the terminal taxa of the phylogenetic tree Benton and Storrs, ; Benton and Simms, ; Benton and Hitchin,; Weishampel, ; Hitchin and Benton, ; Benton et al.
Under such an assumption, the only relevant temporal information for measuring the stratigraphic fit of a phylogeny is the age of the first appearance datum FAD of each terminal taxon in the fossil record. Analysis of stratigraphic fit to phylogenies that allow the recognition of ancestors among the terminal taxa also considers the last appearance datum LAD as potentially relevant information as in stratocladistic or stratolikelihood methods, which also use stratigraphic fit as auxiliary optimality criterion to evaluate phylogenetic trees; see Fisher [ ] and Wagner .
Irrespective of this distinction, the age of both F and L is generally determined through some form of chronostratigraphy. Although the ages of F are commonly taken as if they were raw observations without observational errorsthey are, in fact, inferences made upon observations of spatial location using a variety of assumption sets. Therefore, their ontological status is also hypothetical and, within a given temporal interval, inherently uncertain.
The impact of age uncertainty in measures of stratigraphic fit to phylogenies is explored here and a possible solution to its problems is proposed for measures of stratigraphic fit that are based on the extent of ghost lineages sensu Norell, This procedure incorporates uncertainties in age asment for F of fossil taxa.
In most cases the age of the FAD of a fossil taxon is inferred by determining the age of the associated sediments. Several direct and indirect methods are used for this purpose. Direct dating methods, such as radioisotopic dating, provide observations that can be used to estimate the absolute age of the rock directly. These ages typically consist of a temporal range usually a point estimate with an associated error.
Unfortunately, when such direct methods are used, suitable materials for dating are rarely associated to the exact horizon where a fossil is found. Even in the best cases they usually represent a temporal interval corresponding to dated sediments above and below the stratigraphic point of FAD of a fossil taxon or a linear interpolation between these two dates.
Indirect dating methods are much more commonly used but certainly less precise than radioisotopic dating. These methods are based on the identification of certain changes in the sediments e. This information is then used to correlate these sediments with other, better-studied rocks referred to a temporal unit of a given temporal scale by more precise methods e.
Examples of these temporal scales to which sediments are usually referred are the discrete chrons of the paleomagnetic time scale i. Some of these time scales provide geological dates with narrow uncertainty intervals, and a great deal of chronostratigraphic research is being conducted on these subjects, ificantly increasing the temporal resolution of the fossil record e.
Unfortunately, some of these high-resolution time scales are not widely applicable, whereas others have a great potential but are not yet available for most terrestrial sedimentary basins e. Although future research on chronostratigraphy will likely provide more precisely constrained ages of first appearances, it is still relatively common in particular for pre-Cenozoic continental sediments to have stratigraphic correlations only at the level of a given chronostratigraphic stage e.
These units correspond to subdivisions of the geological time scale that vary in their time span, although most range between 2 and 12 million years. Referring the age of an FAD to this level of temporal resolution would have an associated error that extends for the duration of the corresponding geochronologic unit.
In empirical analyses of stratigraphic fit to phylogenies, the temporal uncertainty in the age of first appearance of fossil terminal taxa is not currently considered. Usually, when using indirect methods or when the age of a fossil's FAD is bracketed by direct methods, the age of first appearance of fossil taxa is taken as the midpoint of the geochronologic temporal unit to which the sediments are referred e. Such an approach can produce misleading because the temporal difference between the F of two fossil taxa is always disregarded if they are referred to the same chronostratigraphic unit, but counted if they are found in different units.
If the F of two fossil taxa are referred to the same geological subdivision or in the error interval associated with a precise [e. In contrast, if the F of two fossil taxa are referred to two contiguous chronostratigraphic units, in absence of further evidence, the real age difference between these F could be as large as the temporal length of both chronostratigraphic units or could approach zero Fig.
The F of taxa 1 and 2 would be ased the same age chronostratigraphic unit Bwhereas the FAD of taxon 3 is ased to chronostratigraphic unit A, irrespective that the underlying age difference between the F of taxa 2 and 3 is less than that between 1 and 2.
In addition to the uncertainty in determining the age of the FAD of a fossil taxon, there is also some uncertainty in that the observed first occurrence actually represents its age of origination. Several methods exist that estimate confidence intervals on the temporal range of a fossil taxon consequently extending its age of originationwhich are based upon the distribution of gaps and occurrences of that fossil taxon in the sedimentary section e.
In the following discussion and examples, we will refer to the uncertainty in the determination of the age of the observed FAD of fossil terminal taxa. However, this uncertainty interval could be modified to incorporate the confidence intervals mentioned above. In sum, several factors contribute to the uncertainty on estimates of the age of F. This uncertainty is translated into a temporal interval, the boundaries of which are usually well defined. It is therefore within these boundaries that the age uncertainty of the F should be considered.
Ignoring the inherent uncertainty of geological dates is not uncommon among phylogeneticists, and it is certainly not exclusive of studies dealing with stratigraphic fit of phylogenetic hypothesis. The use of geological dates of fossils for calibrating molecular clocks is usually conducted without much consideration of the uncertainty associated to the age of first appearance of a given taxon Smith and Peterson, ; Brochu et al.
The effect of age uncertainty on two measures is evaluated here. The age character is set by scoring each terminal taxon with a character state that represents the age of its FAD. The age character has an associated step matrix that determines the transformation costs between the character states as their pairwise temporal difference in Mya or any other unit.
The transformation costs from a younger age to an older age is set as infinite in order to as the minimum divergence age to each node of the tree see Pol and Norell, The age character is optimized using Sankoff parsimony Sankoff and Rousseau, on the phylogenetic tree being evaluated to obtain its length L o. These metrics are sensitive to the temporal duration of mismatches between phylogeny and stratigraphy and therefore are those most severely affected by age uncertainty. Two distinct effects are seen in these measures when there is age uncertainty in the F of terminal taxa.
The first occurs when the temporal uncertainties of the F of fossil taxa do not temporally overlap Fig. Here, the choice of a particular set of ages from the uncertainty intervals of F of terminal taxa can affect the absolute value of stratigraphic fit to a given tree. However, the relative fit value of a given tree, with respect to that of other trees of the same set of taxa, will not be overturned if a different set of ages is taken from the age uncertainty intervals of their F i.
Thus, this situation would be inconsequential for the comparison of trees and for ificance tests associated with these measures Siddall, ; Wills, The second case occurs when the uncertainty intervals associated to the age of F of some fossil taxa overlap. In this case, the relative stratigraphic fit of competing trees can change, depending on the set of ages taken from the uncertainty intervals of F of terminal taxa except for the trivial case in which the compared uncertainty intervals are identical. Hence, the stratigraphic fit of competing trees can be ordered differently if one takes the lower limit of all uncertainty intervals of the age of F rather than if one takes the midpoint of all uncertainty intervals of F Fig.
Given such a scenario, there is no rational basis for choosing between these two options or any other set of age asments. Two hypothetical phylogenetic trees mapped against geological time. The fossil terminal taxa have the uncertainty intervals of their F plotted with a dashed line, none of which overlap in time. Note that the different asments change the raw values of these metrics but the tree on the left always has a better fit than the tree on the right. The terminal taxa have the uncertainty intervals of their F plotted with a dashed line. The uncertainty intervals of the F of some terminal taxa overlap.
Note that the different age asments change both the raw values of these metrics and the relative fit of these two trees. These examples show that it is not possible to calculate precise measures of stratigraphic fit when the age of the F of terminal taxa are imprecise.
Because there is no rational justification for choosing any particular set of age asments, it is necessary to consider a range of possible values for measures of stratigraphic fit, instead of having a precise but arbitrary and in some cases biased metric value for each phylogenetic tree.
Fortunately, the temporal uncertainties of F of fossil taxa can be translated into a range of possible values for these two measures of stratigraphic fit. The possible range of stratigraphic fit values i. The randomization approach proposed here consists of performing multiple replicates, where in each replicate a precise age of first appearance is ased to each terminal taxon taken randomly from the uncertainty interval associated to the age of each taxon's FAD—which is the imprecision of age caused by error or the duration of the referred unit of geologic time.
In each replicate, the ages ased to the terminal taxa are used to calculate the stratigraphic fit e. Since the randomized asments of FAD ages are replicated a given of times e.
Outcome of the randomization procedure replicates applied to the data and trees shown in Figures 2 and 3. This procedure was implemented in the scripting language of TNT Goloboff et al. This script re the dataset containing the age character with their associated step matrixthe topologies to compare, and the minimum and maximum ages of each taxon's FAD i. This implementation includes two options for constraining the age asments of F according to additional stratigraphic information on the relative order of F.
The first option allows forcing the age asment of some terminal taxa to be equal during each replicate rather than as them independently at random. This is necessary if, for example, the F of two or more terminal taxa are recorded at the same horizon, or if there is a high degree of certainty on the correlation of the sediments bearing these F. The second option allows constraining the age asments of some terminal taxa to be necessarily older or younger than those of other taxa.
This is useful when, for example, there is no doubt on the relative age of the F of two fossil taxa e. This option is potentially useful because the relative ages of fossil taxa are usually more precisely known than their absolute ages. The randomization procedure was applied to measure the stratigraphic fit of competing hypotheses for two dinosaur groups. The first case contrasts the stratigraphic fit of two trees based on recently published hypotheses on the early radiation of Sauropodomorpha Yates, ; Galton and Upchurch,one of the major groups of Dinosauria.
These two trees differ markedly in their topology and evolutionary implications Fig. The competing tree depicts Prosauropoda as a paraphyletic arrangement of taxa relative to the clade Sauropoda Fig. Their relative ordering in stratigraphic fit, however, is strongly dependent on the age ased to the F of terminal taxa and, therefore, in absence of further evidence, they must be viewed as having a similar degree of agreement with the temporal information of the fossil record Fig.
Outcome of the randomization procedure applied to two competing hypotheses of the phylogeny of basal sauropodomorph dinosaurs. The original trees of both studies were modified taxa not present in both analyses pruned from trees. The tree shown in B was randomly chosen from the set of most parsimonious trees other trees produced similar.
The second test case is an analysis of trees depicting the long-standing debate surrounding the origin of birds Fig. The data analyzed here were taken from Brochu and Norellwho made a similar comparison but used the midpoint value of the uncertainty interval associated to the age of each taxon's FAD.
These authors concluded that the hypothesis depicting the dinosaurian origin of Aves has a higher stratigraphic fit than any of the proposed alternative hypotheses. Our application of the methods described here demonstrates that this conclusion is robust to the incorporation of age uncertainty in the evaluation of stratigraphic fit to phylogeny Fig.
Outcome of the randomization procedure applied to the competing hypotheses on the evolutionary origins of birds. A Tree depicting the phylogenetic position of Avialae within Diapsida, the tree shows the bird lineage circled in gray deeply nested within Dinosauria. approaches to calculating the stratigraphic fit of phylogenetic trees based on ghost lineages were derived asing an exact age for the FAD of each terminal taxon, irrespective of the actual precision of the chronostratigraphic information on this datum.
The stratigraphic fit of phylogenetic trees should be viewed as a comparison between the temporal content of two independently derived hypotheses—one of toplogy and one of age. It could be argued there is more certainty on the age estimate of a fossil taxon's FAD than on its phylogenetic placement, although this issue depends on the taxon, the method of age estimation, and several other factors. This, however, is a distinction on the precision and degree of support of these hypotheses, not on their status as observations or hypotheses.
We show above that taking rough approximations of chronostratigraphic information, treating this data as precise by rounding to the mean can produce misleading regarding the relative stratigraphic fit of alternative phylogenetic trees. These misleading conclusions will affect most applications of these indices, especially if they are considered as auxiliary optimality criteria. We have focused here on the effects of age uncertainty in these two measures because they are the most sensitive to differences in temporal data.
Other metrics that are solely based on the relative ordering of F, not measuring the extent of the mismatches implied by a tree i. In particular, measures such as SCI Huelsenbeck,SRC Norell and Novacek,or stratocladistic approaches Fisher, could only be affected if there is overlap between uncertainty intervals associated to the F of terminal taxa.
Further refinements of the method proposed here could incorporate more complex models in the age asment process, instead of the randomized equiprobable age asments based on the uncertainty intervals of the F.Fossil record dating assumptions
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