Age constraints on the dispersal of dinosaurs in the Late Triassic from magnetochronology of the Los Colorados Formation (Argentina)

Significance

Uncertainties in reported ⁴⁰Ar/³⁹Ar dates from the Ischigualasto Formation of Argentina allow its dinosaur-bearing fauna to be Norian in age and possibly contemporaneous with some of the older U-Pb dated dinosaur-bearing units in the Chinle Formation of the American Southwest. Our magnetochronology of the previously undated Los Colorados Formation, which also contains a diverse dinosaur assemblage, constrains its age to the interval from 227 to 213 Ma (Norian) and thereby largely restricts the underlying Ischigualasto Formation to the Carnian. Rise of early dinosaurs was thus diachronous across the Americas with their dispersal from the austral temperate belt blocked until later in the Norian. The breakout may have resulted from critically lowered climatic barriers associated with decreasing atmospheric pCO₂ levels.

Abstract

A measured magnetozone sequence defined by 24 sampling sites with normal polarity and 28 sites with reverse polarity characteristic magnetizations was established for the heretofore poorly age-constrained Los Colorados Formation and its dinosaur-bearing vertebrate fauna in the Ischigualasto–Villa Union continental rift basin of Argentina. The polarity pattern in this ∼600-m-thick red-bed section can be correlated to Chrons E7r to E15n of the Newark astrochronological polarity time scale. This represents a time interval from 227 to 213 Ma, indicating that the Los Colorados Formation is predominantly Norian in age, ending more than 11 My before the onset of the Jurassic. The magnetochronology confirms that the underlying Ischigualasto Formation and its vertebrate assemblages including some of the earliest known dinosaurs are of Carnian age. The oldest dated occurrences of vertebrate assemblages with dinosaurs in North America (Chinle Formation) are younger (Norian), and thus the rise of dinosaurs was diachronous across the Americas. Paleogeography of the Ischigualasto and Los Colorados Formations indicates prolonged residence in the austral temperate humid belt where a provincial vertebrate fauna with early dinosaurs may have incubated. Faunal dispersal across the Pangean supercontinent in the development of more cosmopolitan vertebrate assemblages later in the Norian may have been in response to reduced contrasts between climate zones and lowered barriers resulting from decreasing atmospheric pCO₂ levels.

The leading candidate for the oldest known occurrence of dinosaurs is the tetrapod assemblage of the Ischigualasto Formation of Argentina (1–4) where a preferred recalculated ⁴⁰Ar/³⁹Ar date of 231.4 ± 0.3 Ma (1σ analytical uncertainty as reported) (5) on the Herr Toba tuff from near the base of the formation points to a Carnian age for the dinosaur-bearing fauna. However, two recent studies of high-precision U-Pb zircon dates from the Chinle Formation in the American Southwest, practically the only other Late Triassic strata with radioisotopic age constraints on vertebrate assemblages, arrive at very different interpretations of the timing of the dispersal of dinosaurs depending on the accepted degree of total uncertainty for the Ischigualasto ⁴⁰Ar/³⁹Ar data.

The study by Irmis et al. (6) advocated a diachronous rise of dinosaurs, starting in the Ischigualasto Formation of Argentina in the Southern Hemisphere and appearing only later in the Chinle Formation. They pointed to a new U-Pb zircon date of 211.9 ± 0.7 Ma (2σ uncertainty as conventionally reported for U-Pb dates) for a dinosaur-bearing vertebrate assemblage in Hayden Quarry at Ghost Ranch, New Mexico, that was considerably younger than the nominal dates from the Ischigualasto Formation. The Placerias Quarry in northeastern Arizona apparently contains even older dinosaurs from the Chinle Formation (7), and although it was not dated directly, Irmis et al. (6) suggested that a new U-Pb zircon date of 218.1 ± 0.7 Ma from presumably age-correlative strata in New Mexico would make even the Placerias assemblage much younger than the Ischigualastian fauna if the Herr Toba date is taken at face value.

In contrast, Ramezani et al. (8) suggested that the rise of dinosaurs may have occurred at about the same time across the Americas. Their new U-Pb zircon dates for seven tuffaceous horizons in the Chinle Formation at Petrified Forest National Park, Arizona, indicated that the entire succession spans from ∼225.0 to 207.8 Ma (or younger), with the Adamanian–Revueltian faunal transition (9) between 219 and 213 Ma. More pertinently, their assessment of the full dating error envelope for the Ischigualasto Formation, including ⁴⁰Ar/³⁹Ar data in a thesis (10), suggested that an age of ∼218 Ma (or younger) cannot be excluded for its contact with the overlying Los Colorados Formation. Such a younger age would allow a closer temporal correspondence between the geographically separated assemblages, signifying that the Adamanian was effectively the age equivalent of the Ischigualastian (11) and thus that there was virtually parallel development of early dinosaurs across the Americas. Olsen et al. (12) also expressed doubts about the reliability of the dating of the Ischigualastian vertebrate assemblages that would necessarily make them of Carnian age.

There are only two dated levels to formally constrain the numerical age of the Late Triassic epoch: a 230.1 ± 0.06 Ma U-Pb zircon date on a volcanic ash in late Carnian marine strata from southern Italy (13) and an age of 201.3 ± 0.18 Ma calculated for the Triassic–Jurassic boundary from U-Pb zircon dates on volcanic ashes bracketing the boundary in ammonite-bearing sediments from Peru (14). In the current absence of other reliable radioisotopic age controls on fossiliferous marine strata that are the basis for a global chronostratigraphy, correlations to the Newark astrochronological polarity time scale [APTS (15)] have provided important constraints on ages for standard subdivisions of the Late Triassic (16–18), which have largely been adopted in recently published geologic time scales (19, 20). High-precision U-Pb geochronology on earliest Jurassic volcanics of the Central Atlantic Magmatic Province (CAMP) interbedded with sediments in the upper part of the Newark continental rift sequence strongly affirms the astrochronological methodology (21).

Over the entire ∼35-My-long Late Triassic epoch, there are only four land vertebrate biozones recognized in North America and just two in South America (11). The low temporal resolution combined with endemism of faunas for the Late Triassic make it difficult to disentangle temporal and spatial components governing the distribution of dispersed vertebrate assemblages and for progress requires age control aside from biostratigraphy. In this regard, dating of the Los Colorados Formation would help determine if the underlying Ischigualasto Formation extends into the Norian or is confined to the Carnian and if the temporal range of the dinosaur-bearing Coloradian fauna actually extends to the end of the Triassic as sometimes supposed (e.g., 11). The apparent absence of volcanic ash layers suitable for radioisotopic dating in the Los Colorados Formation motivated this magnetostratigraphic study of the unit and enabled us to address these objectives.

Magnetochronology of the Los Colorados Formation

The ∼600-m-thick Los Colorados Formation occurs in the upper part of the more than 3,500 m of continental deposits in the Triassic Ischigualasto–Villa Union basin of western central Argentina and consists of red-colored, fine- to medium-grain–size fluvial sandstones together with siltstones and ancillary floodplain mudstones with early calcisol development (22, 23) (Fig. 1). The lower contact of the Los Colorados Formation is delineated by a gradational transition from the gray, green, and purple floodplain and fluvial sandstones and overbank mudstones of the underlying ∼700-m-thick Ischigualasto Formation (25–27) (Fig. S1). The age of the Ischigualasto Formation and its associated Ischigualastian fauna (28) is bracketed by ⁴⁰Ar/³⁹Ar dates on two volcaniclastic layers: the Herr Toba tuff from near the base of the formation at 231.4 ± 0.3 Ma (1, 5) and an unnamed tuff (sample ISCH-6-611) from its uppermost part at 225.9 ± 0.9 Ma (5). There are no radioisotopically dated horizons in the conformably overlying Los Colorados Formation, whose faunal assemblage (28) is usually considered Norian and even thought to contain elements of both Late Triassic and Early Jurassic aspects (29–31). Fluvial and eolian deposits and interbedded conglomerates of the overlying Cerro Rajado Formation are in erosional contact with the Los Colorados Formation and, although barren of fossils, regarded as Cretaceous or even younger in age (32, 33).

Fig. 1.

Columnar section of rock formations (Left) and location and geologic sketch map (Right) of the Ischigualasto–Villa Union basin where map patterns for formations in the basin are keyed to the columnar section (with basalts near Morado Hill shown as gray fill). The Valle Fertil megafault represents Neogene tectonic inversion activity that exhumed the Mesozoic basin (24). Paleomagnetic sampling sites for the La Sal section are shown by filled circles and listed in Table S1. The starting point of the Gallinita section of the Ischigualasto Formation (25) is indicated by a purple square. The La Esquina fauna of the upper Los Colorados Formation (22) comes from the northern part of the basin as labeled (see also Fig. S2). The dated tuffs from near the base and toward the top of the Ischigualasto Formation (5) are indicated by purple stripes in the stratigraphic column.

A magnetostratigraphic profile for the entire Los Colorados Formation at the La Sal section was constructed from 52 sites with acceptable data (Table S1) and is delineated by a sequence of 15 geomagnetic polarity intervals labeled LC1r to LC8n in ascending order from the base of the measured section (Fig. 2). Magnetozones LC1 and LC4/LC5 include polarity intervals based on single sites that should thus be regarded as tentative. Nevertheless, available age constraints, including that the 14 polarity intervals should collectively represent roughly 5–15 My according to long-term polarity reversal rates for the Late Triassic (15), lead us to correlate Los Colorados magnetozones LC1r–LC8n to Newark APTS chrons E7r–E15n (Fig. 2). This magnetic correlation requires that only the two shortest chrons in this interval (E11n and E13n.1r) are not represented in the La Sal section dataset, plausibly because of small sampling gaps or depositional hiatuses. With these caveats, and taking the single-site polarity intervals at face value, our magnetic correlation produces a remarkably linear plot of sediment thickness versus age for the Los Colorados Formation (Fig. 3). The correlation indicates an overall sediment accumulation rate of approximately 35 m/My over a total duration of ∼14 My from around 227 to 213 Ma. Given that the Carnian–Norian boundary in Tethyan marine sections has been correlated to Newark Chron E7r (16, 17), the base of the Los Colorados Formation in correlative chron LC1r would essentially correspond chronostratigraphically to the Carnian–Norian boundary. The magnetochronological age estimate of ∼227 Ma for the base of the Los Colorados Formation is in reasonable agreement with the ⁴⁰Ar/³⁹Ar date of 225.9 ± 0.9 Ma for the tuff (sample ISCH-6-811) in the uppermost Ischigualasto Formation (5), which becomes more strongly constrained to be predominantly Carnian in age. The top of the Los Colorados Formation in the La Sal section extends to latest Norian (chron E15n, ∼213 Ma), a few million years before the Rhaetian–Norian boundary that has been correlated to chron E16n (18). Accordingly, the ∼600-m-thick sampled section of the Los Colorados Formation falls entirely within the Norian.

Fig. 2.

Magnetic polarity stratigraphy of the La Sal section of the Los Colorados Formation (Left) with the preferred correlation to the Newark APTS (15, 34) adjusted to a U-Pb date (rounded to nearest 0.5 My) of 201.5 Ma for the beginning of CAMP volcanism in the Newark basin that is close to the end-Triassic extinction level (21). Magnetic polarity stratigraphy of the Los Colorados Formation section was based on the latitude of the site-mean VGPs with respect to the mean north paleopole (VGP rLat), where rLat approaching +90° is regarded as normal polarity, and rLat approaching −90° as reverse polarity. Filled or open bars in polarity columns denote intervals of normal or reverse polarity; chrons comprised of successive main normal and reverse polarity-paired intervals are designated by LC prefix for Los Colorados, E prefix for Newark, and H prefix for Hartford sequences. Tick marks next to the APTS chron column are for 405-ky Milankovitch cycles used for apportioning durations (12). Geologic time scale (GTS) (20) adjusted for magnetic correlations to Newark APTS (16, 18, 35).

Fig. 3.

Stratigraphic level versus age for correlation of magnetostratigraphy of the Los Colorados Formation to the Newark APTS shown in Fig. 2 (solid circles connected by solid lines, dashed over intervals including an unresolved short magnetozone) and ⁴⁰Ar/³⁹Ar dates on two tuffs from the Ischigualasto Formation (labeled ISCH-6-611 and Herr Toba) shown with 1σ analytical (internal) uncertainties [solid error bars (5)] and including external uncertainties (dashed error bars) suggested by ref. 8. Overall sediment accumulation rates implied by these data are indicated for each formation.

Late Triassic Biochronology

The vertebrate fauna in the lower part of Ischigualasto Formation includes a taxonomically diverse group of dinosaurs constituting about 11% of recorded specimens (5). The La Esquina fauna from the upper third of the Los Colorados Formation also contains dinosaurs that are taxonomically diverse, making up about 1/3 of recorded vertebrate taxa (5). Projecting laterally from the La Sal section (Fig. S2), the La Esquina fauna is most probably no younger than ∼213 Ma (latest Norian), or ∼11 My before the Triassic–Jurassic boundary. This unexpected result, which needs to be verified by direct magnetostratigraphic study of the La Esquina section (30 km along-strike to the northwest traced by cliff exposures; Fig. 1 and Fig. S2), is at variance with some interpretations of the faunal assemblage as transitional, containing Late Triassic and Early Jurassic elements (e.g., 30).

We can now compare this record with geochronologic data from the Chinle Formation to address the question of a diachronous (6) versus simultaneous (8) rise of dinosaurs across the Americas. Although the Chinle Formation is one of the richest and best studied terrestrial records of Late Triassic biota, dinosaurs are a rare component of most faunas (36). The oldest directly dated dinosaur fauna from the Chinle Formation (or apparently anywhere else outside the Ischigualasto–Villa Union basin) is Hayden Quarry at Ghost Ranch in New Mexico. This is where Chindesaurus, the only known example of a herrerasaurid theropod dinosaur from outside South America, has been described (37, 38). U-Pb zircon dating at Hayden Quarry places a maximum age of 211.9 ± 0.7 Ma for Chindesaurus (6), consistent with its occurrence in the Petrified Forest Member in the northern part of Petrified Forest National Park in Arizona (39) whose age is constrained between ∼210 and 214 Ma by U-Pb zircon dating (8).

There may be older dinosaurs at Placerias Quarry in Arizona, regarded as the oldest Adamanian strata (40) and currently assigned to the upper part of the Blue Mesa Member (39). Irmis et al. (6) obtained a U-Pb zircon date of 218.1 ± 0.7 Ma from a tuffaceous sandstone in the upper part (although previously reported in various abstracts as at the base) of the Blue Mesa Member in the Six Mile Canyon area of New Mexico (39). At about the same time, Ramezani et al. (8) published a significantly older U-Pb zircon date of 223.036 ± 0.027 Ma from the upper part of the Blue Mesa Member at its type locality in Petrified Forest National Park. The discrepancy points to the difficulty in making correlations based on lithology in such widely distributed but discontinuously exposed deposits. Nevertheless, because the Adamanian–Revueltian transition is placed in the upper part of the overlying Sonsela Member (9), the Chinle U-Pb geochronology of Ramezani et al. (8) would place the faunal transition sometime between 219 and 213 Ma, which is not inconsistent with the results of Irmis et al. (6) for the Adamanian.

The earliest documented dinosaur occurrences in North America (Chinle Formation) according to these data are thus demonstrably younger and thus diachronous with respect to those in South America (∼231 Ma, basal Ischigualasto Formation) by around 13 My (using ∼218 Ma for the Placerias Quarry) and as much as 19 My if the more secure ∼212-Ma date for Chindesaurus from Hayden Quarry ends up as the operative oldest age of Chinle dinosaurs.

Late Triassic Paleogeography

The confirmed earlier rise of dinosaurs in the Ischigualasto Formation and the subsequent provinciality between the abundant and diverse dinosaur fauna from the overlying Los Colorados Formation (5, 30) compared with the very sparse and species-poor dinosaur fauna of the nominally coeval (Norian) Chinle Formation (6) may be related to contrasting paleogeographic settings. Most of the world landmasses in the Late Triassic were assembled in the supercontinent of Pangea with no major internal seaways to act as barriers to dispersal of land vertebrates. So what could have impeded by millions of years the rise of dinosaurs in North America and accounted for the large disparity in their diversity and abundance between South and North America when dinosaurs become more widespread in the Norian? We suggest that an important contributing factor was climate zonation and spatiotemporal changes with continental drift modulated by varying concentrations of greenhouse gases.

Pangea can be reconstructed from relative fits of the now dispersed continental elements (41). However, positioning in latitude requires control from paleomagnetic pole positions in the context of the geocentric axial dipole (GAD) hypothesis. We use the 220-Ma reference pole of the global composite apparent polar wander path (APWP) of Kent and Irving (42), which is based on the mean of eight entries from igneous rocks and sedimentary rocks corrected for inclination error ranging in age from 211 to 227 Ma. This age window coincides well with our estimated age range of the Los Colorados Formation, and we note that the 220-Ma–mean pole is one of the best defined (A95 = 2.3°) in the global composite APWP for the Mesozoic and early Cenozoic (42). The predicted paleolatitude for the Ischigualasto basin locality (∼30°S, 68°W) is 48.4°S, corresponding to a GAD inclination of 68.0°. The characteristic remanent magnetization (ChRM) mean inclination for the Los Colorados Formation (60.4 ± 3.8°) is appreciably shallower (by 7.6 ± 4.7°). This is most probably due to sedimentary inclination error as is often found associated with early-acquired red-bed magnetizations with sufficient data for direct analysis (43, 44).

Pangea was characterized by a nearly pole-to-pole extent of landmass at 220 Ma (Fig. 4). There is no evidence of polar ice caps in the Triassic, a period characterized by generally equable climate (46) whereby latitudinal variations in the difference between precipitation and evaporation (P-E) may have been especially important in defining climate belts. As a leading-order estimate of climate belts, we use the zonal-mean annual values of P-E based on a general circulation model with idealized geography, an annual-mean insolation, and a high (8× preindustrial level) atmospheric pCO₂ concentration (45). More elaborate climate models (e.g., 47) give similar spatial patterns. In this context, the Ischigualasto–Villa Union basin at 48°S paleolatitude would place it in the austral temperate humid belt (Fig. 4). At about the same time (220 Ma), the Chinle depocenter in the American Southwest (as well as some other important fossil localities like the Newark rift basin in eastern North America and the Argana basin in northern Africa) was migrating into the boreal tropical arid belt while the Keuper (Germanic) basin of Europe and Jameson Land of Greenland had entered into the boreal temperate humid belt. Local continental faunas and floras would have become well-adapted to their particular climate settings whose loci changed slowly as Pangea drifted northward by ∼15° over the Late Triassic. At the same time, the terrestrial assemblages would have differed markedly among the climate belts, whose contrasting environments may have presented effective hurdles to dispersal.

Fig. 4.

Reconstruction of Pangea for the Norian based on continental rotation parameters (41) and positioned in latitude using a 220-Ma–mean global pole (42). Some key Late Triassic vertebrate fossil localities are indicated by filled circles connected to their relative positions at 200 Ma by open circles, with relative positions of localities at 230 and 210 Ma indicated by crosses. Idealized zonal belts (45) of precipitation (P) relative to evaporation (E) are indicated by darker green shading for P > E (more humid) and lighter green shading for P < E (more arid).

Prolonged residence within the austral temperate belt seems to be associated with the development of terrestrial vertebrate assemblages that included dinosaurs from their first appearance in the Carnian Ischigualastian fauna to the Norian Coloradian (La Esquina) fauna. In the latter, the first numerical dominance of the herbivorous dinosaurs over other groups is documented and seems to be correlated with their increase in taxonomic diversity and size (48). The breakout of dinosaurs from the austral temperate humid belt to the tropics and beyond may have required lowering of climate barriers; for example, a reduction in P-E contrasts whereby the vast zonal deserts became less arid and perhaps at least intermittently more traversable. Reduced P-E contrasts could have resulted from decreased concentrations of atmospheric pCO₂ (45, 49). Modeling (47) supported by similarly age-registered paleosol carbon isotope analyses (50) points to generally decreasing levels of atmospheric pCO₂ over the Late Triassic and into the Early Jurassic when terrestrial faunas became much more cosmopolitan (51). Interestingly, an interval of particularly low atmospheric pCO₂ values has been reported in the Ghost Ranch section of the Chinle Formation (52) where the early dinosaur Chindesaurus was constrained to be no older than ∼212 Ma (6). This marked dip in atmospheric pCO₂ speculatively may coincide with a dispersal event of dinosaurs into tropical regions like the Chinle depocenter.

Magnetic polarity stratigraphy of the Ischigualasto Formation and especially the La Esquina section of the Los Colorados Formation and U-Pb zircon dating of tuffaceous layers in these units as well as those more directly associated with dinosaur-bearing levels in the Chinle Formation (and elsewhere) would be desirable to confirm the chronology of events outlined here.

Materials and Methods

The La Sal section was chosen for a sampling transect through the Los Colorados Formation on the basis of fresh exposures in a stream cut through the cliff outcrop of strata that are in clear structural continuity and stratigraphic superposition with the Ischigualasto Formation (Fig. 1 and Fig. S1). The La Esquina section with its rich tetrapod fauna from the upper part of the Los Colorados Formation [La Esquina local fauna or Upper Coloradense (30, and references therein)] is about 30 km along-strike to the northwest and linked by essentially continuous cliff exposures; the Los Colorados Formation may be somewhat thicker there than in the La Sal section, but the lower part of the formation is virtually inaccessible at La Esquina to make a complete reference section there. In contrast to the Ischigualasto Formation, which forms a badlands landscape triggered by its drab clay-rich floodplain deposits, the more indurated red siltstones and sandstones of the Los Colorados Formation crop out as prominent cliffs. We attempted to obtain three oriented samples at each site using a cordless drill with a water-cooled 2.5-cm-diameter diamond bit and a magnetic compass for orienting the cores. The finer-grained red mudstone and siltstone facies were preferentially sampled, whereas the coarser-grained sandstones were avoided after measurements on the first sample collection showed that this lithology tended not to yield interpretable results. The various sampling campaigns produced nearly 150 oriented samples from 58 sites that represent most of the lithologic intervals suitable for paleomagnetic analysis in this section.

Thermal demagnetization data from a dozen or more treatment steps up to 685 °C using a 2G cryogenic magnetometer and large-capacity ovens in a shielded room were used to identify the ChRM component of each sample’s natural remanent magnetism. After removal of generally small spurious or overprint components, demagnetization trajectories typically revealed a high unblocking temperature magnetization that converged toward the origin directed either northerly and up or southerly and down from site to site (Fig. 5 A and B). Principal component analysis (53) of the last six or more treatment steps between 300 and 600° up to 685 °C anchored to the origin was used to estimate the direction of the ChRM in each sample; component estimates with a maximum angular deviation greater than 15° were rejected as poorly defined except in a few cases where a demagnetization trend was obvious and a stable end-point direction could be identified. We also excluded results from a handful of samples with anomalously shallow directions that may reflect undue influence of depositional processes, especially in the initially sampled medium- to coarser-grained sandstones and a handful of samples with widely aberrant directions that were most probably misoriented. As indicated by the high unblocking temperatures that typically range to 685 °C, the magnetizations are carried predominantly by hematite, which may be of detrital or early diagenetic origin.

Fig. 5.

Paleomagnetic results from Los Colorados Formation. (A and B) Vector end-point demagnetization diagrams of representative samples with reverse (A) and normal (B) polarity characteristic magnetizations. Open (closed) circles are projections of the vector end points onto the vertical (horizontal) planes, with thermal treatment steps in degrees Celsius shown next to open symbols in B. (C) Equal-area plot of 52 site-mean ChRM directions from the Los Colorados Formation, where open/closed symbols are plotted on the upper/lower hemisphere of the projection. Site and formation statistics are given in Table S1.

In all, 104 of the 142 samples analyzed, representing 52 (88%) of the 58 sites, provided acceptable paleomagnetic data (Table S1). With all directions corrected for a regional stratal tilt with a strike of 320° and dip of 12° to the northeast, the site-mean ChRM directions fall into two nearly antipodal populations (Fig. 5C): 24 sites of normal polarity clustered around a mean of Declination, D = 14.8°, Inclination, I = −58.7° (A95 = 5.0°) and 28 sites of reverse polarity with a mean of D = 195.9°, I = 61.9° (A95 = 5.8°). The populations are antipodal at 95% confidence (3.3° departure compared with critical angle of 7.7°) giving a positive reversal test [Class B (54)]. Converted to common (normal) polarity, the 52 ChRM site means are aligned along a mean axis of D = 15.4°, I = −60.4° (A95 = 3.8°).

Virtual geomagnetic pole (VGP) latitudes calculated for the accepted 52 site-mean directions and gauged with respect to the mean (north) VGP position (71.8 °N, 70.8 °E, A95 = 5.0°) delineate a magnetostratigraphic sequence of 14 polarity intervals, which are labeled LC1r to LC8n in ascending order from the base of the measured section (Fig. 2).