Quantitative biochronology of Devonian ammonoids from Morocco and proposals for a refined unitary association method
Abstract
Based on a rich dataset, the biostratigraphy of the late Emsian and the Eifelian (Early–Middle Devonian) ammonoids from the Moroccan Tafilalt is re‐evaluated. We processed this dataset (comprising 53 species from 15 sections) with the unitary association method (UAM), by means of the UA‐graph freeware. This led to the construction of a sequence of 17 UAs (maximal sets of actually or virtually coexisting taxa), which are grouped into 10 laterally reproducible association zones. This biostratigraphical subdivision of this interval is in some parts finer than the classically used empirical stratigraphical scheme and than a previous graphic correlation analysis. It enabled us to measure regional ammonoid diversity of this interval in detail. The UAM is a powerful biochronological method, which benefits from complementary tools to analyse conflicting inter‐taxon stratigraphical relationships inherent to complex biostratigraphical datasets. In cases of under‐constrained superpositional relationships between the taxa, the UAM can yield results, which are not parsimonious in terms of reconstructed virtual coexistences. We suggest several additions to complement the algorithmic steps of the method. The most important is the exhaustive or heuristic reconstruction of possible solutions resolving the observed biostratigraphical contradictions (conflicting inter‐taxon superpositional relationships and cycles between maximal cliques) and the selection among the solutions of the most‐parsimonious one(s) in terms of reconstructed virtual coexistences. Multiple equivalent results may then be processed with standard consensus techniques. Finally, the robustness of the results can be tested by bootstrapping methods to provide confidence estimates on the ranges and associations of studied taxa.
Keywords
The Devonian (∼418 to 361 Ma after Kaufmann 2006) witnessed a major macroecological turnover among marine organisms, namely the Devonian nekton revolution (Klug et al. 2010). This period is characterized by the rapid diversification of land plants and by an explosive trend from planktonic and demersal toward true nektonic marine animals as represented by the radiation of several groups of jawed fish. It is also marked by the origination of important cephalopod groups such as Bactritoidea, Ammonoidea, perhaps Coleoidea and Nautilida (see Erben 1964, 1965, 1966; Dzik 1981, 1984; House 1981, 1996; Bandel & Boletzky 1988; Klug 2001a, 2002a; Korn & Klug 2003; Klug & Korn 2004; Kröger 2005; Fuchs 2006; Kröger & Mapes 2007; Klug et al. 2008a,b; De Baets et al. 2009, 2010). Several significant geo‐events with distinctive sedimentary and/or faunal perturbations also occurred during the Devonian (see House 1985, 2002; Walliser 1986, 1996), including the Choteč‐ and Kačák‐events briefly discussed here. The Devonian is thus a key period, which has received the attention of numerous studies.
Whatever the diverse objectives and approaches of investigation focusing on this period are, they necessarily rely directly or indirectly on available biochronological zonations and correlations. Achieving the best possible biochronological resolution by means of exact and robust correlations has thus direct implications for various geological, geochemical, palaeoclimatic and evolutionary hypotheses related to this period. Ammonoids represent one of the most important groups of macro‐invertebrates for dating Devonian marine rocks. Morocco is a key area for Devonian ammonoid biostratigraphy (Petter 1959; Becker & House 1994, 2000; Belka et al. 1999; Korn 1999; Klug 2001a, 2002a; Becker et al. 2004; Ebbighausen et al. 2004, in press) and research on the Devonian ammonoid faunas of Morocco has begun in the early 20th century ( Clariond 1934a,b; Roch 1934; Termier & Termier 1950). Becker & House (1994, 2000) and Becker (1996) published the ‘standard’ biostratigraphical schemes for Early and Middle Devonian ammonoids (see also Weddige 1996). However, these zonations were established in a classical, non‐quantitative way. Klug (2002a) made a first attempt to produce a biostratigraphical zonation with a quantitative method by applying the graphic correlation method (Shaw 1964), but still with a semi‐empirical approach of successive pairwise correlation of the sections. However, increasing number of datasets and increasing need of higher resolved correlations require the use of quantitative biochronological analyses based on robust algorithms. Furthermore, quantitative stratigraphical approaches are already known to produce results with a much higher resolution potential than (even long standing robust) empirical zonations (e.g. Boulard 1993; Monnet & Bucher 2002, 2007; Sadler 2004; Cody et al. 2008). Hence, the goal of this study is first to revise the zonation of late Emsian and Eifelian (Devonian) ammonoids from Morocco by means of another quantitative biochronological method, namely the unitary association method (UAM), and second to discuss some theoretical and practical aspects of this method.
Material
This study focuses on the Devonian sedimentary successions from Morocco, more precisely the late Emsian and Eifelian of the eastern Anti‐Atlas (Fig. 1). This area provides extensive exposures rich in various fossils, especially in ammonoids (e.g. Becker & House 1994; Belka et al. 1999; Bultynck & Walliser 2000; Klug 2002a). During the Devonian, the eastern Anti‐Atlas experienced an increasing influence of synsedimentary tectonic movements (Wendt 1988). These pre and early Variscan movements left almost no traces in the Early Devonian but already in the Middle Devonian, an increase in facies differentiation is apparent (Kaufmann 1998).
Accordingly, the late Emsian sedimentary sequence begins in the eastern Anti‐Atlas with the clayey deposits of the Daleje‐Event (Bultynck & Walliser 2000; Klug 2001a). The thickness of the subsequent clayey unit varies in most localities in the Tafilalt from 30 to 70 m (Massa 1965; Belka et al. 1999; Klug 2002a; in most localities the entire Emsian varies between 100 and 200 m: Kaufmann 1998). Marls and marly limestones of latest Emsian age containing a diverse anarcestid fauna overlie these late Emsian claystones and clayey marlstones. This anarcestid‐dominated fauna contains the oldest ammonoids included in this study. Above these marls, the clay content and the abundance of limestone nodules increase in many sections. These nodular layers usually contain early Eifelian agoniatitids of the genera Foordites and Fidelites (Klug 2002b).
On top of these nodular layers, the commonly dark and more clayey deposits of the Choteč transgression are overlain by usually massive limestone beds, often rich in ammonoids of genera such as Pinacites and Fidelites as well as bactritoids and orthocerids (Kröger 2008). In most sections in the eastern Anti‐Atlas, the following sediments have rather high carbonate content up to the Kačák transgression (House 1985; Walliser 1985; Truyóls‐Massoni et al. 1990; Klug 2002a). In the layers below these transgression deposits, the genera Cabrieroceras, Exopinacites and Subanarcestes are variably common in many localities. The transgression sediments themselves have a markedly higher clay content and locally contain a rich limonitic ammonoid fauna including, for example, Cabrieroceras and Subanarcestes. The overlying sediments are much more carbonated and usually contain a much less diverse ammonoid fauna with representatives of the genus Agoniatites and early tornoceratids as well as trace fossils. These layers mark roughly the end of the Eifelian sequence. They correspond also to the upper bound of the dataset used here.
Sediments of late Emsian age belong to the Amerboh Group and those of Eifelian age to the Bou Tchrafine Group ( Hollard 1974, 1981). A vast amount of bed‐by‐bed ammonoid collections have been sampled during the last decades (C.K.) leading to thousands of ammonoid specimens scattered in 15 sections (Fig. 1). For the detailed description of the sections, see Klug (2002a). The dataset contains 24 genera and 53 species whose taxonomy has been revised (see Klug 2002a; Ebbighausen et al. 2004).
Quantitative biochronology and the unitary associations
Several quantitative biochronological methods have been published (for a review, see Boulard 1993; Sadler 2004): e.g. unitary associations (UAs) ( Guex 1977, 1991); constrained optimization ( Kemple et al. 1989, 1995) using the programme CONOP (Sadler & Cooper 2003; Cody et al. 2008) which roughly corresponds to a multidimensional automatic version of graphic correlation (Shaw 1964; Miller 1977; Edwards 1989; Carney & Pierce 1995; Zhang & Plotnick 2006); appearance event ordination and its programme CONJUNCT ( Alroy 1992, 1994, 2000; Domingo et al. 2007); or probabilistic methods (Hay 1972; Agterberg & Nel 1982; Agterberg & Gradstein 1999; Halekoh & Vach 2004; Fortelius et al. 2006; Puolomäki et al. 2006). These methods are not based on the same assumptions and constraints (e.g. occurrence‐based vs. event‐based such as first and last occurrences (FOs and LOs, respectively)), consequently leading to different results. This means that when reconstructing the zonation of a fossil group the biostratigrapher must make a choice given the properties of each available method. Among the available quantitative methods, we apply the method of UAs. This choice is prompted by the fundamental properties of the method (see below), by positive comparative studies (Baumgartner 1984; Boulard 1993; Galster et al. 2010), and by the availability of a user‐friendly freeware of the method (UA‐graph; Hammer, Guex & Savary; <http://folk.uio.no/ohammer/uagraph/>).
Properties of the method
The unitary association method (UAM; Guex 1977, 1991) has several advantages compared with other methods of quantitative stratigraphy. It is a quantitative and deterministic method based on the coexistence of species, which is the primary state of data available from the fossil record. It produces discrete (discontinuous) biozones in agreement with the discontinuous nature of the fossil record. It preserves the integrity of the original dataset, in the sense that all initially documented associations of taxa (coexistence in space) are preserved. Its efficiency in resolving complicated biochronological problems has been demonstrated with taxonomic groups that are differing in the completeness of their fossil record (e.g. ammonites, brachiopods, mammals, nannoplankton or radiolarians; Angiolini & Bucher 1999; Boulard 1993; Baumgartner et al. 1995; Guex & Martinez 1996; Monnet & Bucher 2002, 2007; Baumgartner 2006; Brühwiler et al. 2010; Carter et al. 2010). It usually leads to a significant improvement of biochronological resolution, even in the case of ammonites (e.g. Monnet & Bucher 2002, 2007), which have traditionally been acknowledged as one of the leading groups for dating Mesozoic marine rocks. It allows also an objective assessment of the diachronism of the studied taxa and the choice of actual characteristic taxa of each zone. Finally, yet importantly, it has been demonstrated that the unknown duration of discrete biochronozones produced by the UAM does not involve ceteris paribus, a methodological bias when computing fluctuations of taxonomic richness through time (Escarguel & Bucher 2004).
Brief description of the method
The UAM ( Guex 1977, 1991; Guex & Davaud 1984; Savary & Guex 1991, 1999) constructs zonations composed of a sequence of time‐ordered, discrete, maximal sets of actually or virtually coexisting taxa (association zones), called UAs. UAM differs from other association methods (Oppel, Concurrent Range, or Assemblage Zones) in that it exploits conflicting biostratigraphical relationships that commonly occur among FOs and LOs of taxa to infer virtual associations (i.e. coexistence in time but not necessarily in space). A strict association zone such as produced by the UAM is characterized either by the taxa occurring only within this zone or by the intersecting ranges of taxa observed within the zone. The biochronozones produced by the UAM thus significantly differ from the commonly used continuous Interval Zones based on the FOs and/or LOs of index taxa.
The major principles and steps of the UAM are illustrated here with an imaginary and somewhat simplistic example (for additional details see Guex 1991; Savary & Guex 1991, 1999), based on the occurrences of eight taxa within four sections (Fig. 2A).
1.
The first step is the construction of the biostratigraphical graph G* (Fig. 2B), which compiles and represents all observed biostratigraphical relationships (associations, superpositions and exclusions); its edges and arcs represent associations (overlapping range of two taxa in a stratigraphical section) and superpositions (separated succession of two taxa in a stratigraphical section) of taxa (vertices), respectively.
2.
The next step is the extraction of all unique maximal sets (i.e. not contained in a larger set) of mutually coexisting species, called ‘maximal cliques’ (Fig. 2C). The example proposed here contains six maximal cliques among which is one that includes taxa 3, 5 and 7 coexisting (but not necessarily in the same section) and thus constitute a maximal clique (‘mc4’, Fig. 2C).
3.
Then, a crucial step of the method is to resolve the superpositional relationships between these maximal cliques. These relationships are inferred by pairwise comparison of raw stratigraphical relationships between their taxa in the biostratigraphical graph G*. Given the discontinuous nature and incompleteness of the fossil record and thus of the data (sedimentary gaps, unfavourable facies, insufficient sampling, selective preservation, ecological exclusion, reworking, etc.), there occur nearly inevitably conflicting stratigraphical relationships between the taxa (called also ‘biostratigraphical contradictions’). For instance, Figure 2D reports one case (left) in which the superpositional relationships between the taxa are congruent (arcs in the same direction) and another one (right) in which the relationships are contradictory (arcs of opposed directions). The UAM solves such conflicting stratigraphical relationships by assuming that one of these opposed arcs is wrong and actually the result of a virtual coexistence (i.e. inter‐taxa coexistence that is real in time but not observed physically in the stratigraphical samples). The choice of the supposed incorrectly oriented arc (or set of arcs) follows a ‘majority rule’ (see Guex 1991, p. 82; Galster et al. 2010, p. 244). This rule counts the number of arcs plus their frequency in both directions separately and then considers the highest number to reflect the correct stratigraphical order (Fig. 2D).
4.
Once all superpositional relationships between the maximal cliques have been resolved, one can construct the graph Gk that compiles all these relationships (Fig. 2E). From this, the method now extracts the longest sequence (path) of superposed maximal cliques (Fig. 2F). This is also a crucial step of the method, because maximal cliques, which do not belong to the longest path, are merged (if possible) with contemporary maximal cliques of the path. This sequencing can also be complicated by the presence of cycles in the superpositional relationships of the maximal cliques (‘strongly connected components’; see discussion).
5.
Finally, one can transcribe the sequence of maximal cliques into the sequence of UAs (Fig. 2G). A UA is thus defined as a maximal set of mutually coexisting species, be it actually or virtually. The sequence of UAs is called the ‘protoreferential’ and along with the reproducibility matrix (a sections vs. UAs matrix), they constitute the zonation used to correlate the fossiliferous content of sections (Fig. 2H).
Devonian ammonoid zonation
Results
The UAM was automated previously in the computer programmes DV‐86 (Guex & Davaud 1984) and BioGraph ( Savary & Guex 1991, 1999). It is now replaced by a more robust implementation either as a stand‐alone software UA‐graph (Hammer, Guex & Savary; <http://folk.uio.no/ohammer/uagraph/>) or integrated in the versatile and widely distributed palaeontological analysis freeware PAST (Hammer et al. 2001; <http://folk.uio.no/ohammer/past/>). We analysed the dataset of Devonian ammonoids from Morocco by means of the UA‐graph version 0.28. Figure 3 reports and illustrates the graphical user interface of the programme and the tools discussed below. The biochronological analysis is pre‐processed with the removal of taxa found in only one section (‘singletons’; Fig. 3A, ‘Null endemic taxa’ checkbox), because they are known to significantly increase the amount of biostratigraphical contradictions while being of no help for correlation purposes (Boulard 1993; Monnet & Bucher 1999; Savary & Guex 1999). The Devonian ammonoid dataset contains 17 such singleton taxa.
The analysis of the raw dataset leads to 18 UAs (Fig. 4A) based on 53 species scattered within 15 sections. The dataset contains 66 conflicting stratigraphical relationships between 25 maximal cliques. Note that without removing the singletons, the dataset contains 93 biostratigraphical contradictions. Importantly, the dataset contains six maximal cliques implicated in cycles (Fig. 5A; see discussion below). These numbers roughly characterize the quality of a dataset (e.g. Boulard 1993; Monnet & Bucher 2002) and the software reports them directly on its interface (Fig. 3B).
The major result of the biochronological analysis is a composite range chart representing the succession of the 18 discrete maximal sets of mutually coexisting species (UAs; Figs 3C, 4A). This sequence synthesizes the association, superposition and exclusion relationships of the ammonoid taxa included in the analysis. It clearly defines the characteristic content of each biostratigraphical unit (UA). It is worth noting that this sequence of UAs integrally preserves all of the observed associations documented in the original dataset without creating reversed sequences of taxon ranges. It means that the UAM preserves entirely the integrity of the data (this is not necessarily the case with other quantitative biochronological methods). This is an important point because all locally witnessed coexistences are considered trustworthy (in the absence of reworking, taxonomic misidentification, etc.) and thus must appear in the range chart produced by a biochronological analysis (Guex 1991; Sadler 2004).
Optimization
The UAM will always calculate and provide a result (UA sequence) even with poor quality data. Because biostratigraphical contradictions always occur in the raw data and may lead to arbitrary results in the worst case, the user must always check the validity of the final interpretation. As already highlighted by the authors of the UAM (Savary & Guex 1999), a source of uncertainties can arise with data having cycles between their maximal cliques (e.g. Fig. 5A). In this case, their destruction can be quasi‐arbitrary (Savary & Guex 1999) and may, consequently, lead to different and potentially questionable virtual coexistences. The presence of cycles in the superpositional relationships between the maximal cliques suggests that some of these superpositions are incorrectly oriented. Because the Devonian ammonoid dataset contains six cliques in such cycles, we conducted an additional empirical analysis to solve these cycles in order to obtain results that are more robust.
One of the major strengths of the UAM and of its implementation UA‐graph is the accompanying tools available (Fig. 3) for assessing the quality of the dataset itself and tracing back the possible origin of the conflicting stratigraphical relationships between taxa. Several of these tools greatly help to evaluate the clique cycles. For instance, UA‐graph has tools for providing the list of maximal cliques and their taxonomic content (Fig. 3D, ‘Maximal cliques’ button) and more importantly to display the relationships between these cliques (Fig. 3D, ‘Graph of cliques’ button). Figure 5A, B reports this information for the Devonian ammonoid dataset. From these data, the conflicting superpositional relationships implicated in the cliques cycles can now be extracted (Fig. 5C). This enables to estimate the frequency of superposed pairs of cliques involved in the cycles and to identify the minimal sets of clique superpositions to correct for in order to break all cycles (Fig. 5C). Then, one can see the detailed conflicting inter‐taxon relationships (Fig. 3E, ‘Contradictions’ button) between the maximal cliques of these minimal sets (Fig. 5D). This enables to identify the possible origin of these contradictions (e.g. which taxa in which sections) and if the minimal sets involve conflicting relationships with a weak ‘majority rule’.
In the case of the Early and Middle Devonian ammonoids, this pinpoints that the origin of the cycles results from the following problems: (1) very poor documentation of the species 49sph, which is documented only twice in two different sections (Fig. 3F, ‘Taxon frequency’ and ‘Taxon distribution’); and, (2) poorly constrained superpositional relationship between the cliques 16 and 17 (Fig. 5D). We thus modified the dataset (Fig. 5E) by removing the species 49sph and by forcing the virtual coexistence between the species 16tes and 20occ (the arc between these two species is involved in numerous biostratigraphical contradictions in addition to the clique pair 16–17).
The run with this modified dataset still yields 18 UAs (Fig. 4B), but only 37 conflicting superpositional relationships between the cliques (compared to 66 previously) and no more cycles between the cliques. The two sequences of UAs are nearly the same (Fig. 4A, B); the single difference is the inversion of two UAs (16 and 17) due to the inversion of the superpositional relationship between the species 14len and 32mag. This inversion results from the poorly constrained relationship between these two species, which is indeterminate in the initial raw data and resolved indirectly by the conflicting superpositions between the maximal cliques.
The Devonian ammonoid dataset currently contains occurrences with some taxonomic uncertainties (‘cf.’). We tested the influence of these uncertainties by looking for anomalies of distribution (see procedures in Guex 1991, p. 92). Occurrences of such taxonomic uncertainties, which create additional biostratigraphical contradictions and have a disjunctive range compared to occurrences with a well‐defined taxonomy, were discarded from the dataset. In our case, this leads to the removal of three occurrences (20occ from BouTchrafineWest, 33emi from HassiChebbiWest, and 33emi from upper JebelOuafilalEast). The run with this modified dataset yields 17 UAs (Fig. 4C) for 30 conflicting superpositional relationships between the cliques and zero cycles again. The two sequences of UAs remain roughly equivalent (Fig. 4B, C). The major difference is the shortening of the two taxa whose specimens where poorly identified. These shorter ranges are due to the non‐confirmation of some coexistences (e.g. taxon 33emi with taxa 17sin and 30atr; see Fig. 4C). This absence of some coexistences also indirectly causes the disappearance of one maximal association (i.e. one UA at the end of the process).
The previous run (taxonomic uncertainties) is the final step of our ‘optimization’ procedure. The basic results of a biochronological analysis is a composite range chart (Fig. 3C, ‘UAs’) displaying the associations and successions of studied taxa (Fig. 6A‐left). In the case of UAs, a distinct marker underlines the virtual associations. This range chart, which thus defines the content of each UA, is complemented by its reproducibility matrix (Fig. 3C, ‘UA reproducibility’). It is a UAs vs. sections matrix (Fig. 6A‐right), which indicates which UAs are identified in which sections. This enables to assess the lateral (geographical) reproducibility of each UA. This set of information is important, because the goal of a biochronological analysis is to construct a zonation for correlations. Since some UAs have a poor lateral reproducibility and thus a poor correlation potential, the UAs are merged into unitary association‐zones (UAZ) of higher geographical reproducibility (Fig. 6A‐mid). Note that UA‐graph automatically attributes (if possible) a UA or set of UAs to each sample of the dataset based on the resulting range chart produced by the method (Fig. 3C, ‘Correlation table’).
Finally, we empirically extended the ammonoid range chart by adding additional information, not automatically produced by the software UA‐graph. First, the singleton taxa removed before the biochronological analyses were dated by means of this last sequence of UAs and reintegrated in the range chart (Fig. 6B). The same applies to the occurrences with a poor taxonomic identification, which had been previously removed. Third, we analysed the reproducibility of the relative order of the FOs and LOs of the studied taxa and we reported on the range chart a majority consensus of their relative order (Fig. 6B).
Description of UAZ
In the following, we describe the properties of the UAs we managed to discriminate. UA 1 follows the classical Latanarcestes noeggerathi Zone and UA 17 is overlain by the Holzapfeloceras circumflexiferum Zone of at least partially Givetian age. Therefore, UA 1 to 17 comprise much of the late Emsian and the entire Eifelian. In the zonation outlined below, the species representing each UA‐zone was selected by the following criteria (where applicable and reasonable): 1, species used as index species in older zonations; 2, species occurring in many sections; 3, abundant forms; 4, easily determinable forms. We also indicate the equivalence of the UA‐zones compared with the ‘standard’ interval‐based zones of Becker & House (1994), Becker (1996) and Klug (2002a), which are abbreviated as BH94, B96 and K02 in the remainder of the text.
UAZ 1 Sellanarcestes tenuior Zone (UA 1)
Content.– Anarcestes plebeius, Latanarcestes noeggerathi, Sellanarcestes solus.
Equivalence.– Topmost Noeggerathi to basal Wenkenbachi Zones (BH94, B96, K02).
Distribution.– Northern Gondwana and central Europe.
UAZ 2 Sellanarcestes wenkenbachi Zone (UAs 2–4)
Content.– Achguigites tafilaltense, Anarcestes latissimus, An. plebeius, An. simulans, Chlupacites praeceps, Latanarcestes noeggerathi, Sellanarcestes ebbighauseni, Sell. neglectus, Sell. tenuior.
Equivalence.– Middle to late part of the Wenkenbachi Zone (BH94, B96, K02).
Remarks.– Sellanarcestes draensis most likely also occurs here. This interval has some potential for a further subdivision with additional data and after a sound revision of the genera Anarcestes and Sellanarcestes.
Distribution.– Northern Gondwana and central Europe.
UAZ 3 Anarcestes lateseptatus Zone (UA 5)
Content.– Achguigites tafilaltense, Anarcestes latissimus, An. plebeius, An. simulans, Latanarcestes noeggerathi, Sellanarcestes tenuior, Mimagoniatites bohemicus.
Equivalence.– Anarcestes (+ Sellanarcestes) Zone and parts of the Anarcestes (− Sellanarcestes) Zone (BH94); part of the Anarcestes lateseptatus Zone (B96, K02).
Distribution.– Northern Gondwana and central Europe.
UAZ 4 Fidelites clariondi/Pinacites jugleri Zone (UAs 6–7)
Content.–Fidelites fidelis, Fid. verna, Foordites veniens, Mimagoniatites bohemicus, Subanarcestes marhoumense.
Equivalence.–Foordites platypleura/F. veniens to early Pinacites jugleri Zones (BH94, B96, K02).
Remarks.– We chose two taxa for this zone since Fidelites clariondi is very abundant, but Pinacites jugleri is distributed nearly globally and has a very characteristic morphology (Klug & Korn 2002). The early Eifelian Choteč‐Event lies within this zone. The preceding stratigraphical interval surrounding the Emsian/Eifelian boundary is often poor in ammonoids and cannot be assigned to UAZ 4 with certainty. Usually, the characteristic representatives of UAZ 4 appear first slightly above this boundary. Further detailed studies of the boundary interval might perhaps yield sufficient data to introduce an additional UA zone at this level, corresponding to the Foordites platypleura and F. veniens Zones (B96, K02).
Distribution.– Nearly cosmopolitan (at least northern Gondwana, Euramerica, S‐China).
UAZ 5 Subanarcestes macrocephalus Zone (UAs 8–10)
Content.– Agoniatites bicanaliculatus, Crispoceras tureki, Diallagites testatus, Fidelites clariondi, Fid. fidelis, Fid. occultus, Fid. verna, Parafidelites atrousense, Pinacites jugleri, Sobolewia inflata, Subanarcestes marhoumense, Wendtia ougarta.
Equivalence.– Late Pinacites jugleri Zone to Subanarcestes macrocephalus Zone (BH94, B96); late Pinacites jugleri Zone to early Cabrieroceras housei Zone (K02).
Distribution.– At least northern Gondwana and southern as well as central Europe.
UAZ 6 Cabrieroceras crispiforme Zone (UA 11)
Content.– Agoniatites bicanaliculatus, Crispoceras tureki, Diallagites testatus, Fidelites clariondi, Fid. occultus, Fid. verna, Pinacites eminens, Sobolewia inflata, Subanarcestes marhoumense, Wendtia ougarta.
Equivalence.– Part of the Cabrieroceras crispiforme plebeiforme Zone (BH94, B96); late Cabrieroceras housei Zone (K02).
Distribution.– At least northern Gondwana as well as central Europe.
UAZ 7 Exopinacites singularis Zone (UAs 12–14)
Content.– Agoniatites bicanaliculatus, Ag. vanuxemi, Cabrieroceras crispiforme, Cab. housei, Crispoceras tureki, Diallagites testatus, Fidelites clariondi, Fid. occultus, Fid. verna, Sobolewia inflata, Subanarcestes coronatus, Sub. macrocephalus, Sub. marhoumense.
Equivalence.– Late Cabrieroceras crispiforme plebeiforme to Agoniatites vanuxemi Zone (BH94, B96); Agoniatites vanuxemi to Agoniatites obliquus Zones (K02).
Remarks.– A detailed revision of the genera Cabrieroceras and Subanarcestes might help to further refine the ammonoid biostratigraphical scheme.
Distribution.– At least northern Gondwana as well as central Europe.
UAZ 8 Diallagites lenticulifer Zone (UA 15)
Content.–Agoniatites vanuxemi, Cabrieroceras crispiforme, Cab. housei, Diallagites testatus, Exopinacites singularis, Fidelites clariondi, Subanarcestes macrocephalus.
Equivalence.– Late Agoniatites vanuxemi and/or Cabrieroceras crispiforme n. ssp. Zone (BH94); late Agoniatites vanuxemi Zone (B96); Agoniatites obliquus Zone (K02).
Distribution.– At least northern Gondwana.
UAZ 9 Parodiceras magnosellaris Zone (UA 16)
Content.– Agoniatites vanuxemi, Cabrieroceras crispiforme, Cab. housei, Fidelites clariondi, Subanarcestes macrocephalus.
Equivalence.–Cabrieroceras crispiforme n. ssp. Zone (BH94); late Agoniatites vanuxemi Zone (B96); Agoniatites obliquus Zone (K02).
Distribution.– At least northern Gondwana as well as central Europe.
UAZ 10 Agoniatites obliquus Zone (UA 17)
Content.– Agoniatites vanuxemi, Cabrieroceras crispiforme, Cab. housei.
Equivalence.– Cabrieroceras crispiforme n. ssp. Zone (BH94); late Agoniatites vanuxemi Zone (B96); Agoniatites obliquus Zone (K02).
Distribution.– At least northern Gondwana, Euramerica as well as central Europe.
Discussion
The only available quantitative Devonian ammonoid zonation of Morocco has been constructed by means of classical empirical successive pairwise correlation of the sections using the method of graphic correlation (see Klug 2002a). This empirical zonation contains ten interval zones (Fig. 7A‐left) and is based on nearly the same dataset (except the two sections of Bou Tchrafine).
The UA method produces discrete sequences in which the FO or LO of taxa may occur anywhere within the association. Consequently, such a zonation cannot be superimposed precisely on a zonation defined on individual events. Because graphic correlation focuses on the FOs/LOs of studied taxa whereas the UAM focuses on coexistences of taxa, the range chart produced by graphic correlation is converted into a set of equivalent maximal associations (Fig. 7A‐right) which can be compared directly with the results of the UAM. Interestingly, this yields 14 maximal associations whereas only ten interval zones were defined with the same range chart.
In terms of maximal sets of mutually coexisting taxa, both methods produce roughly the same number of biochronological units (17 UAs compared with 14 GCs). However, their correlation and comparison are not straightforward. A tentative correlation is shown in Figure 7B. The correlation between the two zonations proposed here enables us to highlight the different sets of virtual associations created by both methods (circles and crosses in Fig. 7B). This comparison demonstrates that the empirical pairwise graphic correlation reconstructed three to five times more virtual coexistences than the quantitative UAM (Fig. 7B): 29 to 53 additional virtual coexistences for the graphic correlation, against only nine to ten additional virtual coexistences for the UAs (the variation depends on the correlation which is uncertain in some parts). These very different sets of reconstructed virtual coexistences between the two methods reflect a well‐known problem of graphic correlation, which tends to increase the range of studied taxa as a side effect of the calculation of the line of correlation. The comparison of both zonations is thus hampered by the fact that graphic correlation extended the range of most taxa more than necessary and thus created unnecessary virtual coexistences. The UAM thus clearly produces a more parsimonious solution (in terms of inferred virtual coexistences compared to the raw data) than graphic correlation. Note that this drawback of empirical graphic correlation may be resolved (at least partly) by its quantitative, recent derivative known as constrained optimization (CONOP, Sadler & Cooper 2003).
Ammonoid diversity fluctuations
The UAM has the great advantage that it produces a stratigraphical scheme, which does not distort counts of species and generic richness. Especially for a regional diversity signal, an accurate biotratigraphical scheme is required to obtain sound information on diversity. Using the resulting species ranges of the 17 UAs from late Emsian to Eifelian, we counted (following the procedure of Monnet et al. 2003 which avoid boundary artefacts on diversity curves derived from association zones) the values of total species richness, agoniatitid species richness (including mimagoniatitids), anarcestid species richness (including tornoceratids), species turnover, origination and extinction, and produced two bivariate plots of these data, shown in Figure 8. The resulting curves differ from the species richness and FOs/LOs‐curves of Klug (2002a) by, for instance, the reduced length of the low diversity interval around the Emsian/Eifelian boundary. However, as discussed previously, the graphic correlation artificially lengthened the stratigraphical range of several species, thus leading to biased diversity curves. Yet, the biodiversity curves based on the more robust (see Escarguel & Bucher 2004) UA range chart enable us to document the following regional diversity patterns.
The late Emsian anarcestid radiation. – In this interval, agoniatitids and mimagoniatitids played only a subordinate role while the anarcestids underwent a radiation. As in most ammonoid groups, intraspecific variability is still poorly studied and parts of this radiation as well as the subsequent extinction might seem more intense in terms of diversity than it actually was. This lack of clarity certainly requires further research. By contrast, the abundance of anarcestids in this interval is high and in most localities of the eastern Anti‐Atlas, representatives of this group can be found within a few minutes in the right layers.
The late Emsian anarcestid extinction. – In most sections in the eastern Anti‐Atlas, where the late Emsian is exposed, the abundance of ammonoids decreases rapidly towards the Emsian/Eifelian boundary. This coincides with a transgressive phase, which is interrupted by a short, smaller transgressive/regressive cycle (Lubeseder et al. 2010). In the course of this extinction, not all anarcestid taxa disappear at the same time; Anarcestes survived apparently longer than Sellanarcestes and gave rise to the Eifelian anarcestids.
The early Eifelian agoniatitid radiation. – Shortly after the anarcestid extinction, the agoniatitids diversified and the Pinacitidae originated (Klug & Korn 2002). At least on a regional level, this change from anarcestid‐dominated to agoniatitid‐dominated associations appears like a case of short‐term intra‐ammonoid incumbency, possibly indicating differences in the ecological requirements and/or habitats of the two groups (compare Klug 2001b, 2002b). As far as the pinacitids are concerned, the evolution of their conch morphology suggests an adaptation towards rapid swimming (Klug & Korn 2002). Possibly, the shell morphology reflects a predominantly pelagic habitat, which would also explain the nearly cosmopolitan distribution of Pinacites jugleri, the type species of the genus. A global transgression of the Eifelian ( Johnson et al. 1985, 1996; Lubeseder et al. 2010) was named after this widespread taxon, the Jugleri‐Event (= Choteč‐Event, Walliser 1985; Chlupáč 1985; House 1985; Chlupáč & Kukal 1986; Belka et al. 1999; Bultynck & Walliser 2000; Klug 2002a), reflecting the temporary ecological success of the Agoniatitida. The basal Choteč‐Event lies within the Eifelian at the base of the Polygnathus costatus costatus conodont zone (see Berkyová 2009 and references therein) and does not correspond with the boundary between the Emsian and Eifelian, which lies at the base of the Polygnathus costatus partitus zone. Some consider the Jugleri‐Event and the basal Choteč‐Event, which are commonly combined as the Choteč‐Event, as two separate events (e.g. Pedder 2010). Therefore, this event is situated within UAZ 4. Sea‐level changes most likely played a role in this event ( Johnson et al. 1985, 1996). Berkyová (2009) reports both a facies change and algal blooms reflected in abundant prasinophyte remains in the corresponding layers of several sections in the Prague basin.
Identification of the precise position of the Emsian/Eifelian boundary in Morocco based on ammonoids is not possible yet, since the interval around the boundary is very poor in fossils in general and especially in ammonoids. UAZ 4 commences probably above the boundary with the appearance of the agoniatitid genera Fidelites and Foordites and thus does not include the boundary level anymore.
The early–middle Eifelian anarcestid radiation. – Again, anarcestid diversity pattern was unlike that of the agoniatitids. Compared to the rapid radiation of the agoniatitids, the anarcestid recovery after the Choteč‐Event was slow, but they later reached a higher diversity. The genera Subanarcestes and Cabrieroceras can also be extremely common locally; anarcestids dominate many layers of the middle Eifelian in the Anti‐Atlas in terms of relative abundance (compare Klug 2002b). As far as extinctions are concerned, the late early and middle Eifelian is characterized by a low rate of background extinction.
The late Eifelian ammonoid diversity decrease. – Both the anarcestid and the agoniatitid lineages decrease in diversity in the course of the late Eifelian, although the extinction is dominated by the anarcestid diversity‐decrease. This diversity decrease has apparently two phases, which are probably linked with two or more pulses of the late Eifelian transgression ( Johnson et al. 1985, 1996; Wendt 1988; Lubeseder et al. 2010). These pulses comprise the transgression of the Kačák‐Event (= ‘otomari’ and ‘rouvillei’‐Event in Walliser 1985; House 1985; Walliser et al. 1995; Schöne 1997; = ‘Late Eifelian Events 1 + 2’ and ‘Odershausen Events’ in Weddige & Struve 1988). As far as abundance is concerned, ammonoids stay rather abundant until the Kačák‐Event, at least in several sections of the Tafilalt. In the layers overlaying the sediments of the Kačák‐transgression, low diversity agoniatitid‐dominated faunas occur. In the Givetian, the rediversification of anarcestids was apparently similarly slow as following the Choteč‐Event.
Remarks on the UAM
The UAM is a very powerful method to resolve biochronological problems, to produce robust zonations quickly, and to assess critically the quality of the dataset. The basic principle of the method (conflicting stratigraphical relationships are interpretable as virtual coexistences) is concordant with the raw state of the biostratigraphical data (the only objective information is the occurrence of a taxon). In our opinion, this is currently the best approach for solving biochronological problems. Furthermore, its integration in the mathematical frame of the graph theory ensures a rigorous and consistent treatment of the data. However, the currently available computer implementation of the UAM (UA‐graph) may lead to approximations in some algorithmic steps. As previously pointed out (Fig. 2), the crucial points are: 1, the resolution of the conflicting stratigraphical relationships between the maximal cliques; and, 2, the treatment of cycles involved between maximal cliques.
Superposition of the maximal cliques and the ‘majority rule’
The goal of the approach to solve conflicting stratigraphical cliques’ relationships by a ‘majority rule’ in UA‐graph is to minimize the number of superpositions replaced by virtual coexistences; it is globally and generally sufficient. However, if the data are too loosely constrained, most superpositional relationships are nearly indeterminate with a ratio of the majority rule close to 1. In such cases, the single solution adopted by the UAM is quasi‐arbitrary. Yet, the UAM offers no test or alternative algorithm to handle this problem, and the different solutions must be checked empirically and manually. A ‘cascade effect’ can thus be generated when dealing with under‐constrained data. One error in the superpositional relationship between two maximal cliques is likely to propagate as a cycle in the sequencing of maximal cliques. This effect is illustrated in the correction of cycles yielded by the Devonian ammonoid dataset (Figs 4, 5). One solution proposed here to avoid this problem is to calculate all possible relationships of the conflicting superpositions and to select a posteriori the most parsimonious solution in terms of virtual coexistences created.
Cycles between maximal cliques and the ‘weakest link’
Another source of uncertainties can arise from the case of data leading to cycles between the maximal cliques (‘strongly connected components’). Unfortunately, such cycles occur frequently in poorly constrained data and again their destruction can be quasi‐arbitrary (Guex 1991; Savary & Guex 1999). UA‐graph currently solves these contradictions by using the ‘weakest link’ rule (i.e. the clique superposition supported by the fewest inter‐taxon relationships is destroyed; see Guex 1991, p. 82). Given the uncertainties related to this type of resolution, the unique result produced by the UAM is likely to be partly wrong. Figure 9 reports an imaginary example (Fig. 9A) containing cycles between its maximal cliques where the automatic resolution by the software UA‐graph yields a result (Fig. 9B), which is clearly not the most parsimonious compared to what can be found empirically (Fig. 9C). This example clearly illustrates and demonstrates that the ‘weakest link’ rule is not adequate in such cases. One way to avoid this problem is to calculate all possible minimal sets of clique superpositional relationships necessary to break the cycles and then select the most parsimonious solution in terms of reconstructed virtual coexistences (see Fig. 5 and ‘Optimization’ section).
As seen above, there are several sources of uncertainties when processing poorly constrained datasets and equally parsimonious solutions (different sets of virtual coexistences) may sometimes compete against one another. However, the current implementation of the method yields necessarily a single solution without further indication. Because the method should rather not become to some kind of ‘black box’, we suggest that the software could be improved by providing the user with the possible solutions of a biochronological problem, thus clearly indicating all uncertainties associated with each solution. In the case of multiple solutions, the UAM should be completed with tools that calculate consensus solutions and confidence intervals on the ranges of studied taxa by means of bootstrapping on the raw data. The purposes of these additional tools are intended to help users to assess both the robustness of the results and the quality of the data. It is likely that the differences among the set of solutions will pinpoint the problematic occurrences of taxa and hence help the user to judge his data or at least encourage him to treat those occurrences with more caution. The UAM was already differing from other quantitative methods by allowing the user to evaluate the origin of the conflicting stratigraphical relationships and will thus be even more powerful by allowing the user to evaluate robust and weak parts of the produced zonation. Nevertheless, the implementation of the proposed solutions is not trivial. Indeed, finding all solutions between the conflicting superpositional relationships is well‐known to be a difficult combinatorial approach (as already suggested by Guex & Davaud 1984), which may be impossible to solve if too many taxa are involved. However, using heuristic approaches may still be relevant and adequate in finding a solution more parsimonious than the one currently produced by the UAM in the case of under‐constrained data. These tools are routinely used in phylogenetic reconstructions for instance (Felsenstein 1985; Penny & Hendy 1986; Holmes 2003; Soltis & Soltis 2003) and they would equally be useful implements for the UAM.
Less important, the UAM could also be supplemented with two other sets of information: 1, multiple solutions originating from the merging of ‘isolated’ maximal cliques; and, 2, relative order of the taxa datums.
Longest path of Gk and merging of remaining maximal cliques
It often happens that several maximal cliques do not belong to the longest sequence L of superposed maximal cliques from Gk due to indeterminate superpositional relationships (Fig. 2). Generally, there are parallel paths and even disconnected maximal cliques. The solution adopted by the UAM is to merge (if possible) the cliques, which are not contained in the longest path, with cliques in the longest path based on a ‘best fit’ criterion (Guex 1991) such that a clique is merged with its most similar clique in L if it is also bracketed between cliques of L (Fig. 2F). This step of the method (called here the ‘full‐merging approach’) intrinsically induces the creation of virtual coexistences between all taxa belonging to the merged cliques. However, this solution can lead to the creation of more virtual coexistences than necessary. Figure 10 reports an imaginary example (Fig. 10A) and the corresponding result of UA‐graph (Fig. 10B). In this case, it induces the virtual coexistence of taxon 8 with taxa 1 and 3. However, there exist two other possible solutions if we create virtual coexistences only between some of the taxa involved (called here the ‘partial‐merging approach’): either taxon 8 remains below taxon 3 and coexists with taxon 1, or taxon 8 remains above taxon 1 and coexists with taxon 3 (Fig. 10C). Note that these two solutions involve only one virtual coexistence contra two for the solution of the UAM. Hence, the ‘full‐merging approach’ has the advantage of providing a single solution to the user, but this procedure does not yield the most parsimonious solution in terms of the number of created virtual coexistences and more importantly, it does not reflect the fact that multiple solutions (assuming different sets of virtual coexistences) exist. Note that from a purely biochronological point of view, the proposed partial‐merging approach provides no additional power of correlation. However, it has an important influence on the diversity counts, which can be derived from the zonation provided by the method. For instance, in the example of Figure 10, it appears that the taxon richness of UA 2 may be overestimated and that only two taxa really coexisted. The partial‐merging approach can thus provide the user an index of potential errors in the derived diversity curves.
Relative order of the datums of taxa
The UAM focuses on associations of taxa to reconstruct a biochronological zonation. Given the incompleteness of the fossil record and thus of the raw stratigraphical data, this is a better approach than focusing on FOs and LOs as currently done in other methods (see discussion in Guex 1991). Yet, although FOs and LOs are highly susceptible to diachronism (see e.g., Monnet & Bucher 2002, 2007), their relative order can still be partly congruent in a dataset. Hence, instead of discarding this information, the UAM could report at least a majority consensus of the relative order of these datums with their confidence intervals (their reproducibility should be tested) in order to present the most complete results (e.g. Fig. 6B).
Conclusions
We propose a new regional late Emsian and Eifelian (Devonian) ammonoid zonation based on a quantitative biochronological analysis of a large dataset obtained from 15 sections of the eastern Anti‐Atlas (Morocco) and comprising 53 species. The UAM was selected for this revision. It has the property of attributing equal weight to each species occurrence, it is based on a deterministic mathematical model, and it provides reliable counts of taxonomic diversity. A discrete sequence of seventeen coexistence intervals of species (UAs) was constructed for the Devonian dataset. These 17 UAs were grouped into 10 UAZ to increase their geographical reproducibility. This zonation is compared to a previous zonation erected using the graphic correlation method. In addition to providing supplementary biochronological subdivisions, the UAM enables to underline the main drawback of graphic correlation: it often artificially lengthens the stratigraphical range of species and thus creates unnecessary virtual coexistences between some species.
The UAM is a method with a sound and efficient mathematical frame (graph theory). It efficiently solves the encountered biostratigraphical contradictions by assuming the virtual coexistence of some taxa (coexistence in time but not necessarily in space). Yet, as underlined by Guex (1991) among others, the quality of the results strongly depends on the quality of the raw data analysed. That is why the UAM is completed with several appropriate analytical tools that help to understand and to detect the possible origin of observed conflicting stratigraphical relationships. Despite this, the UAM and its software implementation UA‐graph do not provide tools for assessing the quality of the results. The method does not report the uncertainties of the results and lacks an optimization of these results. Indeed, some steps of the method arbitrarily select a single solution, which is not necessarily the most parsimonious one. If the stratigraphical data contains too many indeterminate superpositional relationships, different solutions (i.e. different sets of virtual coexistences) may appear a priori equally good and yet finally correspond to significantly different, possibly conflicting interpretations of the same dataset. Hence, we propose that the method should be supplemented by the search (exhaustively or heuristically, according to the number of conflicting relationships) of the possible solutions between the cycles and conflicting superpositional relationships of the maximal cliques, and by the a posteriori selection of the most parsimonious solution in terms of reconstructed virtual coexistences. In this case, the method should also provide the user with consensus and bootstrapping methods to evaluate the robustness of the results. Such additions would make the UAM an even more powerful tool for biochronological correlations. Note that these propositions are research directions expected to improve the results of the UA‐method, to identify the uncertainties in these results, as well as to support the biostratigrapher with the critical evaluation of the quality of the studied dataset and of its associated biochronological zonation(s), but the detailed algorithmic procedures are not necessarily trivial and remain to be investigated.
Acknowledgements
Reviews by J. Guex and Ø. Hammer helped improving an earlier version of this work. This study was funded by the Swiss National Science Foundation (Project number to H.B.: 200021‐129919; project number to C.K.: 200021‐113956/1 and 200020‐25029). Working permits for Morocco as well as sample exportation permissions were kindly provided by the colleagues of the Ministère de l’Energie et des Mines (Rabat).
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