Abstract:  Palaeodiversity curves are constructed from counts of fossils collected at outcrop and thus potentially biased by variation in the rock record, specifically by the amount of sedimentary rock representative of different time intervals that has been preserved at outcrop. To investigate how much of a problem this poses we have compiled a high-resolution record of marine rock outcrop area in Western Europe for the Phanerozoic and use this to generate a model that predicts the sampled diversity curve. We find that we can predict with high accuracy the variance of the marine genus diversity curve (itself dominated by European taxa) from rock outcrop data and a three-step model of diversity that tracks supercontinent fragmentation, coalescence and fragmentation. The size and position of two of the five major mass extinction spikes are largely predicted by rock outcrop data. We conclude that the long-term trends in taxonomic diversity and the end-Cretaceous extinction are not the result of rock area bias, but cannot rule out that rock outcrop area bias explains many of the short-term rises and falls in sampled diversity that palaeontologists have previously sought to explain biologically.

Sedimentary rocks cropping out on land form the primary source of information about past environments and biotas, and geologists and palaeontologists have built up a detailed view of the history of life through the study of this record. Yet ever since the work of Raup (1972, 1976), it has been recognized that the amount of rock available at outcrop, and the relative representation of environments this captures, are not the same for different geological time periods. The ratio of terrestrial to marine sediments preserved from any given time-interval, for example, depends upon where sea level stood then compared with today. For the early Late Cretaceous, when sea level reached its post-Palaeozoic maximum (Miller et al. 2005), we have a very limited terrestrial rock record, whereas in the Early Triassic, when sea level stood well below that of today, the opposite is true. The area of marine rock preserved at outcrop today reflects the continental area over which marine sediments were originally deposited and the amount of subsequent erosion and deformation to which they have been subjected. Thus, the rock record at outcrop is initially generated by large-scale cycles of continental flooding driven by plate tectonics and climate change (Dewey and Pitman 1998; Miller et al. 2005), and subsequently degraded through burial or erosion over time.

Because the geological history of marine diversity has traditionally been deduced from counts of the number of fossils that have been recorded from each time interval (e.g. Sepkoski et al. 1981; Benton 1995; Sepkoski 1997) it is likely to be highly sensitive to fluctuations in the amount of rock surviving from different time periods and preserved at outcrop. Higher diversity is expected to be recorded when there is a greater amount of marine rock preserved at outcrop simply because more fossil collections can be made by palaeontologists. The worry has therefore arisen that much of the observed change in sampled diversity recorded over geological time might just be reflecting rock availability and collecting opportunity (Raup 1972, 1976; Peters and Foote 2001, 2002; Smith 2001; Smith et al. 2001; Crampton et al. 2003, 2006a, b; Foote 2003; Peters 2005; Smith and McGowan 2005; Smith in press).

Here we present new data on the outcrop area of marine and terrestrial sediments at stage level for the Phanerozoic of Western Europe using an equal-grid sampling method. We use this to identify the major sedimentary sequences that the rock record is constructed from, and then test how much of the Phanerozoic diversity curve of marine genera (Sepkoski 2002) can be attributed to rock outcrop area effects. Our approach thus asks the question: How much of the Phanerozoic diversity curve cannot be explained simply by variation in the rock record? Our stance is that we have to be able to reject the null hypothesis (that rock area effects on sampling potential explains all) before proposing biological explanations for changes in observed diversity. A strong correlation between rock area and sampled diversity does not necessarily imply that sampling alone has driven diversity, but it does undermine the assumption that the Phanerozoic diversity curve can be taken at face value. We chose to focus on Western Europe because of the availability of high-quality, large-scale geological maps with accompanying memoirs. Furthermore, simply for historical reasons, fossil first and last occurrences in databases are dominated by Northern Hemisphere records, especially those from Western Europe (Smith 2001; Kidwell and Holland 2002), where fossil collecting has been pursued more extensively and over a longer time than for any other region. For example, 33 out of the 49 (67 per cent) first occurrence records at ordinal level listed by Jablonski and Bottjer (1990) are from Western Europe. Palaeodiversity curves are thus likely to be most heavily influenced by the European rock record.

Material and methods

Rock outcrop area estimation

Sedimentary rock outcrop area was derived from outcrop patterns in 1265 geological maps of Spain, France, England and Wales. The geological maps of France and Spain are all 1 : 50,000 scale, older maps of England and Wales are at 1 : 63,630 (1 inch to 1 mile), whereas more recent maps are 1 : 50,000 scale. Each map was scored for the presence or absence of rocks dated to one of 71 time intervals on a modified version of the Gradstein et al. (2004) time scale. The overall average size of time interval is 7·5 myr (s.d., 4·61), with Palaeozoic bins averaging 9·8 myr (s.d., 5·75) and Mesozoic–Cenozic bins averaging 6·0 myr (s.d., 2·93). Rock outcrops were assigned to terrestrial or marine, and scored as either fossiliferous or non-fossiliferous based upon the accompanying memoirs. If in one map both terrestrial and marine strata were represented in the same time interval, each was scored as present. An additional 117 French maps at 1 : 80,000 and partially covering the same area as the 1 : 50,000 maps were also scored to assess the impact of differences in map scales.

Genus diversity data are derived from Sepkoski's Online Genus Database maintained by S. E. Peters (, which reproduces the data from Sepkoski (2002). This is not strictly sampled diversity because that database lists only first and last occurrences and thus derives standing diversity estimates from taxa that range through time intervals even though they have not always been sampled from those intervals. However, it is the best estimate we have currently of total recorded marine diversity. Where there was not sufficient temporal resolution in the Cenozoic some values were obtained from secondary estimates derived from Sepkoski's genus-level diversity and published by Rohde and Muller (2005). In some cases, owing to differences in stratigraphic nomenclature, it was necessary to combine values for some stages and take the arithmetic mean. We analysed both maximum and minimum estimated sampled diversity by using both the total number of taxa known from a single time interval (maximum) and the sum of taxa with a recorded first or last occurrence in a single time interval (minimum), as recommended by Peters and Foote (2001), to see if this altered our results.

Data manipulation

In order to identify the long-term trend in the data we smoothed the rock-outcrop time-series data by taking a nine-point moving average, chosen to remove prominent short-term cycles that recurred every 6–10 time bins. The long-term trend was removed from the data by plotting either first differences or the residuals from a regression of raw data against its smoothed curve. Spectral analysis of the residual data from the smoothed time series was performed using the program PAST (Hammer et al. 2001). PAST implements the Lomb-Scargle Fourier transform, which overcomes the problem of uneven temporal spacing of our data.

Generating a long-term model of diversity that accounts for rock outcrop bias

Sampling bias created by variation in outcrop area of marine sedimentary rocks of different ages was removed from the Phanerozoic diversity curve of marine genera as follows:

  • 1A model in which rock area at outcrop was a perfect predictor of sampled diversity was constructed in the following way. Rock outcrop area and sampled diversity were each sorted independently from low to high values and a linear model of the form y = mx + c fitted to the ordered data, where x is the amount of rock, m is the gradient of the straight line and c is a constant.
  • 2This equation was then applied to the rock outcrop data in their original order to derive a time series of predicted diversity from rock outcrop area.
  • 3The predicted diversity was next subtracted from the observed maximum or minimum sampled diversity curve to obtain a residual ‘unexplained diversity signal’, which represents variation in diversity that cannot be accounted for by rock outcrop area.
  • 4Finally, least-squares regression analyses were run to derive a simple best-fit model for this time series of residuals. For reasons explained below, four time intervals that had marine sediments cropping out in 12 or fewer maps (< 1 per cent of total area: Early and Middle Permian, Early Triassic and Norian), and which therefore provided poor estimators of global marine diversity, were omitted. The remaining residuals clearly fall along three successive trajectories that can be simplified to a three-phase model: rising by log10 0·02 at each time interval between the Late Cambrian and Mid-Devonian, falling by log10 0·04 from the Mid-Devonian to end-Triassic, then rising again by log10 0·03 between the Early Jurassic and Pliocene.

To isolate the effects of variation in diversity based on rock area from variation in observed diversity based on this model, the rock series was randomized 1000 times and new predicted values were calculated following steps 2 and 3 above.


The effect of map scale on estimates of rock outcrop area

The marine rock outcrop area curves derived from 1 : 80,000 and 1 : 50,000 maps of the same area generated highly congruent results (see supplementary data: The two plots differ only in their relative amplitude of variation, with the analysis carried out at a smaller scale generating a lower amplitude time series than the larger-scale analysis. Critically, the shapes of the two curves are almost indistinguishable, allowing us to combine maps of different scale.

The Phanerozoic sedimentary rock record of Western Europe

The amount of sedimentary rock (terrestrial and marine combined) preserved at outcrop in Western Europe does not follow a simple trend over time (Text-fig. 1). As expected, there is much less Palaeozoic sedimentary rock than post-Palaeozoic, presumably because older strata have been through more cycles of uplift and erosion than younger strata. However, preserved rock area at outcrop can drop to Palaeozoic levels even in the early Cenozoic. Furthermore, the proportion of sedimentary rocks that can be dated accurately declines back in time, primarily because a greater proportion is affected by metamorphism. Poorly dated rocks also become common in the Late Palaeozoic, but these are primarily clastic deposits lacking fossils that have not been specifically assigned to terrestrial or marine in the accompanying sheet memoirs.

Figure TEXT‐FIG. 1..

 Surface area of sediments (numbers of maps with outcrop) surviving at outcrop derived from 1265 geological maps of Spain, France, England and Wales. A, absolute values. B, relative values. Time along the x-axis. Cam, Cambrian; Ord, Ordovician; Sil, Silurian; Dev, Devonian; Car, Carboniferous; Per, Permian; Tri, Triassic; Jur, Jurassic; Cre, Cretaceous; Pal, Palaeogene; Neo, Neogene.

Two long-term cycles first recognized by Stille (1924) are easily picked out by the changing ratio of terrestrial to marine sediments. These are signatures from global tectonic cycles of supercontinent assemblage and fragmentation (Fischer 1984; Worsley et al. 1986; Dewey and Pitman 1998), with marine rocks dominating during rifting phases of supercontinents (break-up of Pannotia and Pangea in the Early Palaeozoic and Mesozoic, respectively) and terrestrial rocks dominating at times of continental assembly.

On a time scale of tens of millions of years there are well-defined cycles in marine rock outcrop area that repeat on average every 50 myr (Text-fig. 2A). These cycles are clearer after removal of the long-term trend (Text-fig. 2B) and show strong autocorrelation. The post-Palaeozoic cycles correspond to second-order sequences as defined from independent seismic data (de Graciansky et al. 1998) and thus record major transgression/regression cycles. Furthermore, the individual cycles are repeated with high fidelity across the region, with the rock record curves for Spain, France and, to a lesser extent, the UK all highly congruent (results not shown).

Figure TEXT‐FIG. 2..

 Marine rock outcrop area for Western Europe plotted against geological time. A, raw data and trend line (nine-point moving average). B, residuals with the ten major sequence cycles numbered. Abbreviations as in Text-figure 1.

Such detrended rock record plots thus give a simple and independent means of defining the major (second order) sequences through the Phanerozoic of Western Europe, with minimum rock outcrop areas defining system bases and maximum rock outcrop areas maximum flooding surfaces. These cycles, though appearing regular, are not strictly periodic and spectral analyses of the marine rock outcrop record fail to pick out a strong signal, the only marginally significant peak being at 38·6 myr (Text-fig. 3). Thus, sea-level variation is best described as oscillatory rather than strictly cyclical.

Figure TEXT‐FIG. 3..

 Spectral analysis of the area of European marine rock at outcrop time series using the Lomb-Scargle fourier transform from PAST (Hammer et al. 2001).

The shape of the long-term Phanerozoic diversity curve after correcting for rock outcrop area bias

Maximum and minimum estimates of sampled marine diversity through the Phanerozoic, derived from counts of the number of genera, are shown in Text-figure 4 together with the amount of marine rock at outcrop in Western Europe. To remove potential bias created by variation that exists in the amount of rock representing different times we have to collect from, we first modelled what a sampled diversity curve would look like if it were perfectly predicted by rock outcrop area in Western Europe (see ‘Methods’) and diversity were constant over time. This generated a partial fit (Text-fig. 5A), but markedly underestimates sampled diversity in the Permian and Cenozoic while overestimating diversity in the Jurassic. Bivariate correlation of the model prediction against sampled diversity produces only a very low and non-significant level of correspondence (r2 = 0·04).

Figure TEXT‐FIG. 4..

 Marine rock outcrop area for Western Europe plotted against minimum and maximum estimated marine genus diversity (from Sepkoski 2002). Eu M, marine sedimentary rock outcrop area for Western Europe; Max Div, maximum estimated sampled genus diversity; Min Div, minimum estimated sampled genus diversity; other abbreviations as in Text-figure 1.

Figure TEXT‐FIG. 5..

  A, maximum sampled Phanerozoic marine genus diversity (‘observed’) compared with predicted diversity based on marine sediment outcrop area with uniform diversity through time (‘predicted’). B, residuals remaining after removing predicted diversity model curve from observed diversity curve. Open circles represent time intervals where rock outcrop area falls to less than 1 per cent and which are omitted from the linear fit calculation (NB, the Lower Triassic point lies off the scale and is not shown). C, maximum sampled Phanerozoic marine genus diversity (‘observed’) compared with predicted diversity based on marine sediment outcrop area incorporating the three-phase diversification model derived from B. D, residuals after removing the predicted three-phase diversity model curve from observed diversity curve. Horizontal axis, time; EP, Early Permian; MP, Middle Permian; Nor, Norian; other abbreviations as in Text-figure 1.

Removing the predicted rock record bias effect from the observed diversity curve leaves the residual ‘unexplained signal’, which cannot be accounted for by changes in rock outcrop area (Text-fig. 5B). This residual signal must be generated by variation in diversity over time or by other biases as yet unaccounted for, and is what we predict a diversity time series would look like were each time interval to have exactly the same area of sedimentary rock at outcrop for sampling. Taking the maximum sampled diversity data first, the residuals define clear trends, rising from the Cambrian to the mid Devonian, then falling through to the Triassic (though with high variance in the Permo-Triassic), and rising again steadily from the Early Jurassic to Pliocene. Regression lines through these three phases (ignoring the four outliers where a marine rock record is absent or almost so) provided us with our model of diversity change over time. We tested the cost of these additional parameters in our model using Akaike Information Criterion (AIC) analysis (Hilborn and Mangel 1997) and found they gave a strong increase in the power of explanation of our model (Table 1).

Table 1.   The results of Akaike Information Criterion (AIC) analysis of the improvement in model fit. The simplified version of AIC based on the residual sum of squares (RSS) of the fit of the predicted to observed data (see Hilborn and Mangel 1997, pp. 159–160) was used. The AIC column summarizes the improvement in fit of the model while penalizing the addition of parameters (k), as extra parameters always improve the fit of a model when measured by the coefficient of correlation (R2). Values of ΔAIC < 2 are regarded as strong support for increased explanatory power of the model. As the values calculated for our model with three additional parameters are negative, there is strong support for the use of these additional parameters. n = number of observations.
No incremental rise in diversity3·66712−207·53 
With three-phase model of diversity2·927110−212·57−5·04

We obtained a very similar result using the minimum sampled diversity data, though this showed a slightly more gradual rise in the Early Palaeozoic and slightly steeper drop from the Devonian to end Triassic. The same four points in the Permo-Triassic stand out as major outliers, but are joined by the Turonian, Priabonian, Rupelian and Late Miocene. These latter points have significantly lower sampled diversity than estimated from marine rock area.

We combined our simple three-step model of diversity with the observed marine rock record to derive a predicted Phanerozoic diversity curve. A highly significant match was found between our rock-based estimate and maximum sampled diversity (Text-fig. 5C; regression r2 = 0·58), with a much lower correlation obtained from minimum sampled diversity (r2 = 0·015). Particularly noteworthy is the high fidelity with which the model derived from rock outcrop area captures the small rises and falls of the maximum sampled diversity curve. Randomizing the rock series shows that the probability of obtaining such a good match by chance is less than 0·01. Only between the Early Permian and Late Triassic does the correspondence between prediction and observed diversity break down, with modelled diversity sometimes greatly underestimating the Sepkoski diversity curve. This time interval has very few marine sedimentary deposits surviving in Western Europe, so it follows that this part of the diversity curve must be dominated by non-European data. Furthermore, there is a greater preponderance of through-ranging, long-lived taxa in the Sepkoski database that have not necessarily been sampled for times when the rock record is poor. It is thus only when marine sedimentary rocks are very poorly represented in Western Europe that our prediction from rock outcrop area fails to provide an excellent explanation for sampled diversity. Excluding the four Permo-Triassic intervals that have almost no marine sedimentary record in Western Europe, we find that our simple diversity model explains almost 80 per cent of the variance (r2 = 0·781) of the maximum sampled genus diversity curve.

Rock outcrop area and Last Occurrences (‘Extinctions’)

Mass extinctions have been widely thought to play a major role in defining the palaeodiversity curve (Sepkoski et al. 1981; Benton 1995; Sepkoski 1996, 1997; Foote 2005; Jablonski 2005). However, the great majority of drops in sampled diversity occur when the rock record becomes poorer (Peters and Foote 2002), and thus might be created by rock record bias. We can test this with our independent data. Major extinctions should all stand out as significant negative excursions against our rock model prediction since sampled diversity at times of extinction will drop much more than predicted by our rock area model (diversity being the balance between origination and extinction). A time series of first differences highlights when rock record model and observed diversity shift out of step (Text-fig. 6). Over a large part of the time series the two move in remarkable parallel.

Figure TEXT‐FIG. 6..

 Time-series plot of first differences for observed marine genus diversity and predicted diversity derived from marine rock outcrop area. Correlation of the two curves is significant at P < 0·001, r2 = 0·177. The five major mass extinctions widely accepted are marked with arrows. Asterisks mark time intervals where the drop in observed diversity is larger than predicted from the rock record; abbreviations as in Text-figure 1.

Subtracting the rise or fall in rock area moving from one time interval to the next, from the rise or fall in diversity between the same two time intervals is illuminating. Under our null hypothesis, if the change in marine rock outcrop area were solely responsible for changes in diversity then, for any stage, the resultant value should be zero. We find two time intervals where the resultant plot diverges significantly from observed pattern. One is a single-stage excursion coincident with the end-Cretaceous extinction, the other a cluster of four time intervals during the Permo-Triassic where marine outcrop commonly drops below 1 per cent of surface area. If we remove those four time intervals with poor marine rock record and then calculate 95 per cent confidence intervals (Text-fig. 7), only the end-Cretaceous stands out as a time interval when diversity dropped significantly more than predicted from rock record alone. Otherwise, the magnitude and position of variation in sampled diversity through time are, for the most part, predicted from the area of rock that is preserved in Western Europe.

Figure TEXT‐FIG. 7..

 Plot of residuals after subtracting first differences for predicted diversity based on rock outcrop area model from observed marine diversity. Dashed lines equal two standard deviations around the mean after removal of four Permo-Triassic outliers, where the rock record is extremely sparse in Western Europe and a poor predictor of diversity. Anis, Anisian; Ash, Ashgillian; Cam, Cambrian; Camp, Campanian; Car, Carnian; Chat, Chattian; Dan, Danian; E, Early; L, Late; Ldvry, Llandovery; Len, Lenian; Lut, Lutetian; M, Middle; Maas, Maastrichtian; Perm, Permian; Nor, Norian; Tri, Triassic; Rup, Ruppelian; West, Westphalian; Ypr, Ypresian.


Recent argument has revolved around whether Phanerozoic diversity has followed an exponential or an equilibrium growth trajectory (see Benton and Emerson 2007 for a review). Once rock outcrop bias has been removed, however, the pattern of marine diversity is seen to be neither, but rises and falls incrementally, following the well-known Wilson cycles of supercontinent assembly and fragmentation (Fischer 1984; Worsley et al. 1986). Diversity rises at times of continental fragmentation as sea levels spill over subsiding blocks and falls when continents are drained. Thus, we return to the view, first developed by Newell (1952, 1967) and championed more recently by Peters (2005), that long-term diversity trends are driven by first-order global tectonic cycles of continental accretion and fragmentation. Since the marine fossil record is overwhelmingly dominated by faunas of the continental shelf, it is not surprising that the marine diversity curve should follow the history of continental flooding. On a shorter time-scale, however, changes in rock outcrop area are sufficient to explain almost all rises and falls in the sampled diversity curve, except for the end-Cretaceous extinction (our data are too sparse in the Permo-Triassic to draw any firm conclusions). Thus our data, which differ significantly from other proxies of rock record quality through time developed by Peters and Foote (2001, 2002) and Peters (2005), point to the same important conclusion that they reached: that short-term fluctuations in apparent diversity may simply be driven by rock availability and sampling. This null hypothesis needs to be taken seriously and disproved before biological explanations are sought for such events, exactly as Crampton et al. (2006a) did when comparing relationships between second-order sequence-stratigraphic cycles and sampling probability in New Zealand.

There is one notable anomaly to this correspondence between sea level and maximum sampled marine genus diversity: over the last 90 myr diversity has continued to rise in the face of falling sea level. There are three possible explanations. Firstly, it is possible that diversity really has expanded dramatically in the seas over the last 90 myr despite the loss of epicontinental seas. A second possibility is that marine diversity has declined in Western Europe as epicontinental seas have retreated, but that the rise in genus-level diversity is driven by non-European data. This seems unlikely because the onset of polar ice in the Cenozoic caused sea level to fall world-wide, and Jackson and Johnson (2001) have argued that the highest diversity faunas from the tropics have, if anything, become more poorly represented in the fossil record towards the present. Finally, several workers (e.g. Alroy et al. 2001; Peters and Foote 2001; Crampton et al. 2006b) have argued recently that the Cenozoic rise in diversity is an artefact of better sampling. Our data show marine rock outcrop area bias cannot be responsible at a global scale, but there are several other possible biases, such as the ‘Pull of the Recent’ (Peters and Foote 2001) and increased ability to carry out bulk sampling (Cooper et al. 2006; Crampton et al. 2006a) that remain to be factored out. Because minimum sampled diversity follows the fall in rock outcrop area more closely during the Cenozoic than maximum sampled diversity, there may indeed be a major effect of the ‘Pull of the Recent’ on through-ranging estimates of diversity. However, there is currently much debate about the size and effect of such sampling biases (e.g. Jablonski et al. 2003; Smith in press). We predict that once other sampling and taxonomic biases are properly taken into account, the true marine Phanerozoic diversity curve may provide an even closer match to plate tectonic history than it currently does.

Finally, why should rock outcrop area in such a small part of the globe be such as strong predictor of the Sepkoski genus-diversity curve? Two possibilities spring to mind. Either the pattern of rock outcrop area over time really is driven by eustatic sea-level change and thus represents a global signature, or the Sepkoski database is dominated by European data (albeit with contributions from elsewhere) and thus summarizes regional rather than global diversity. We are currently working on distinguishing between these two hypotheses.

Acknowledgements.  We are grateful to Mike Foote, Shanan Peters, James Crampton, Mike Benton, Phil Donoghue and two anonymous referees for helpful comments on an earlier draft. This work was funded by a Leverhulme Grant.