( Springer-Verlag 1997
Geol Rundsch (1997) 86 : 160—167
OR I G I N A L P AP E R
C. A. McRoberts · M. Aberhan
Marine diversity and sea-level changes: numerical tests for association using Early Jurassic bivalves
Received: 15 March 1996/Accepted: 23 October 1996
Abstract Past attempts to substantiate the species-area effect by correlating changes in sea-level and marine diversity have met with limited success. Partial rank correlation and concordance analyses are used as two complementary numerical methods to examine the association between sea-level changes and diversity as predicted by the species-area effect. When applied to Early Jurassic bivalve species from northwestern Europe, the numerical analyses failed to discriminate an association (o"!0.298 for the partial rank correlation and pL "0.45 for the concordance probability). Additional analysis using subsets of the data or recoding periods of anoxic water as periods of reduced habitable area (in addition to marine regression) also failed to show a significant association. The absence of significant correlation is likely to be due to numerous biotic and abiotic factors that cannot directly be measured from sediments or fossil assemblages. A multitude of interrelated cause-and-effect relationships renders the species-area effect a poor predictor of the influence of sea-level changes on marine diversity. Key words Sea-level · Marine diversity · Numerical methods · Early Jurassic · Bivalvia · Northwest Europe
Christopher A. McRoberts ( ) 1 Institut fu¨r Pala¨ontologie der Universita¨t, Pleicherwall 1, D-97070 Wu¨rzburg, Germany Martin Aberhan Institute fu¨r Pala¨ontologie der Universita¨t, Pleicherwall 1, D-97070 Wu¨rzburg, Germany Present address: 1Department of Geological Sciences, Binghamton University, Binghamton, New York 13903-6000, USA Tel.: (607) 777 2264; Fax: (607) 777 2288 E-mail:
[email protected]
Introduction The coincidence between changes in sea-level and changes in marine diversity has been known for some time (e.g. Newell 1967); yet, how these two systems may be related is still fertile ground for speculation. Causal hypotheses are generally centered around two, not mutually exclusive, arguments: (a) that diversity is controlled by species-area relationships in which biotic interactions, such as competition for space or other resources, control diversity (e.g., MacArthur and Wilson 1963, 1967); or (b) that diversity responds to abiotic physical and/or chemical factors, such as water temperature, ocean circulation, or oxygen depletion, which may, albeit indirectly, be related to changes in sea-level (Hallam 1989; Jablonski 1995). Although testing hypotheses for abiotic controls requires data from a variety of sources (e.g., geochemical), the direct effects of area reduction on shallow-shelf faunas is testable given the metrics of diversity and sea level. Despite previous studies identifying associations between sealevel and diversity (Simberloff 1974; Sepkoski 1976), such claims have been criticized for the incorporation of sampling errors in both variables (Flessa and Sepkoski 1978; Jablonski 1980). Recent empirical assessments using specific clades over limited geologic and geographic ranges have shown little, if any, correlation between the two varying systems (Valentine and Jablonski 1991; McGhee 1992). To better assess the relationship between sea-level fluctuations and measures of diversity (or its derivatives of extinction and origination), we apply numerical tests on changes in diversity in European early Jurassic bivalves and the possible correlation with changes in sea-level. The species-area effect follows the principle that a reduction in habitable area leads to increased competition for resources among fauna and hence a reduction in diversity. This relationship can be expressed by the MacArthur-Wilson power function: S"kAz, where S is species richness, A the habitable area, and k and
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z are fitted constants particular for each taxon and geographic region (MacArthur and Wilson 1963, 1967). Associated with a reduction of habitable area are a host of other ecologic factors, such as niche partitioning, that have also been suggested as factors controlling diversity. Although it is generally assumed that lowering sea-level will reduce habitable area, especially on shelves with steeply dipping slopes (Jablonski 1985), any such relationship between regression and area reduction in shallow seas is dependent upon ancient hypsographic curves (Wyatt 1984; Wyatt 1987). Not only is the physiogeographic effect of lowering sea-level on habitable area unclear, but claims of a causal relationship between extinction and regression have come under criticism because regression alone would not decrease shelf area to the extent necessary to account for the magnitude of observed diversity declines (Jablonski 1985). Additionally, there are periods of pronounced regression, such as the mid-Oligocene, which fail to correspond to biotic crises as would be predicted by the species-area effect. An alternative hypothesis is that many diversity reductions (e.g., mass extinctions) occur in response to the spreading of anoxic waters during marine transgression. Apart from the very localized and probably minimal effects on species extinction from toxic poisoning due to anoxic waters, this scenario can also be viewed as falling within the speciesarea hypothesis as a special circumstance of habitat reduction constricting shelf faunas into shallower, oxygenated environments. The optimal way to test the species-area effect is to use an objective measure of habitable area in the MacArthur-Wilson equation. It is unfortunate, albeit expected, that such values for shelf environments which rely upon accurate paleogeographic reconstructions become increasingly inaccurate backwards in geologic time due to tectonic and/or erosional processes. In absence of high-resolution paleogeographic data from
Fig. 1 A Ideal situation where stratigraphic intervals are equally spaced and only one maximum or minimum occurs per stratigraphic interval; B more typically observed situation where the stratigraphic intervals are not equivalent and there occurs more than one sea-level maximum or minimum per stratigraphic interval. Note: curve B must be manipulated by smoothing to reduce the number of peaks to one or none per stratigraphic interval as shown in Fig. 2
which accurate quantitative values for area could be obtained, sea-level curves based on numerous stratigraphic sections can be used. Such curves have the added benefit of greater time resolution and allow the recording of values for an infinite number of horizons in individual stratigraphic sections. The reliability of using sections, rather than cartographic reconstruction of area, is enhanced in sequences which contain biostratigraphically useful and easily correlatable fossils such as the ammonoids. In this paper we describe the methods possible to compare sea-level curves with diversity data and apply such tests on Early Jurassic bivalve mollusks of western Europe. Methods Assuming that accurate measures for habitable area cannot be obtained, the metrics of investigation interest are strictly a measure of sea-level and diversity. However, what might be considered a two-variable problem (sea-level and diversity) can be decomposed into three variables (sea-level, diversity, and time) in which the data are inherently ordered and may be cyclic along a time series. In testing for the association between sealevel and diversity, time, in a strict sense, plays a subordinate role to stratigraphic interval spacing from which both data sets have been derived. As such, an ideal study would have both data sets recorded with similar stratigraphic resolution along equally-spaced time intervals (Fig. 1). Depending on how the data were gathered, it is likely that both sets of data will be collected on different time scales, a problem which must be reconciled by deciding on a common scale of resolution and by lumping data, curve smoothing, or interpolative techniques (Fig. 2). Additionally, if a significant linear trend is observable in the data which can be accounted for by other processes (e.g., long-term trends
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where t is calculated as:
S
n!3 . (2) 1!o2 xy,z Critical values of t can be determined in standard tables with an appropriate a-level and n!3 degrees of freedom. t "o n~3 xy,z
Concordance in change Fig. 2 A,B Preparatory steps necessary to compare curves of sealevel and diversity. A Removing long-term trends by regression; B smoothing curves so that there is no more than one maximum or minimum for each stratigraphic interval
in diversification), the trend can be removed by using the residuals of linear regression, rather than the original data, to further analyses (Fig. 2). It needs to be stressed that randomly varying series can show significant spurious correlations (Raup and Gould 1974), and that a number of unmeasured variables (e.g., climate factors or habitat fragmentation) may be closely linked to both sea-level and diversity and result in spurious correlations between the two. Another problem that can occur is that any biologic response (changes in diversity) will lag behind sea-level changes. This lag period may be ecologically short (years), in which case it might not be detected during the course of a study, or long (thousands or millions of years) in which case cross-correlation techniques can be applied to identify and remove such an effect.
Partial correlations
Traditional bivariate correlation and time-series techniques involving Fourier analysis are deemed inappropriate because the sample data usually do not meet the criteria of normality or of equally spaced data points. For most applications involving sea-level data derived from curves where these conditions cannot be met, it is more appropriate to use a nonparametric analog to bivariate partial correlations based on ranks (Kendall 1970). The partial rank correlation coefficient, o , can xy,z be calculated as: o !(o · o ) xy xz yz o " (1) xy,z J(1!o2 ) (1!o2 ) yz xz where o is the partial correlation between the ranxy,z ked variables x and y (sea-level and diversity), holding the contribution from z (time) constant. The bivariate correlations can be either Spearman’s or Kendall’s rank correlation coefficients. The null hypothesis of no correlation between the two data series (o "0) can xy,z be tested for significance utilizing the t distribution,
Given that it may be quite difficult to apply ranks to sea-level curves, and even more difficult to interpret results from ranked sea-level data, an alternate measure of association between sea-level and diversity is by examining the concordance in directions of change, which attempts to capture associations of short-term trends summed over time. Although useful in determining association between transgressive/regressive cycles and increases/decreases in diversity, this method does not discern the magnitudes in such changes and therefore cannot discriminate minor events from major ones that may have a profound effect on the biota. The procedures for testing concordances of direction are outlined by Gordon (1982) and are only briefly summarized herein. Because long-term trends do not affect the analysis, the initial step is to code the concordance, Z , between the two variables from each i stratigraphic interval. Z "1 if *x *y '0 (i.e., the changes are concordant) i i i or Z "0 if *x *y (0 (i.e., the changes are discordant). i i i (3) Assuming that the Z-value of ith stratigraphic level is independent of its neighbors (i$1), each Z takes the value 1, signifying complete concordance with probability p, or the value 0, signifying complete discordance with (1!p). The value of p can be estimated by: m pL " + Z /m (4) i i/1 where m is the number of transitions between stratigraphic levels and is equal to n!1. Because pL behaves as a binomial variable, confidence intervals for pL can be determined for any given risk (a) by calculating a binomial density distribution or by a normal approximation (assuming a large sample size) which is given as: pL $t JpL (1!pL )/m (5) a For example, a 95% confidence interval of a series of 100 transitions where pL "0.75 would, given t"1.96, yield the upper and lower confidence intervals 0.665 and 0.835, respectively. Confidence intervals can be
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examined to determine if the observed probability pL can be distinguished from random roll (where p"0.5).
Case example: Early Jurassic bivalves Geologic setting and data acquisition
Early Jurassic bivalves from western Europe provide an excellent test case to examine the relationship between sea-level change and diversity for a variety of reasons. Most important is that the species-level bivalve data are taxonomically relatively straightforward and stratigraphic control on regional sea-level is unambiguous and recorded over a long interval (20 ammonoid zones). Furthermore, sea-level changes and associated phenomena (spread of anoxic waters) have been invoked as a causal agent in the Early Toarcian extinction event (Hallam 1986; Aberhan and Fu¨rsich, in press) and thus provides a rationale in which to test the effect of sea-level change on species-area effect. Our analyses use the sea-level curve and bivalvespecies-richness data from western Europe compiled by Hallam (1986, 1987). The diversity data are recorded to standard ammonoid zone. To achieve a quantitative measure of sea level, the original sea-level curve was divided into eight partitions of equal magnitude in which the average magnitude for each ammonoid zone was recorded. Our choice of eight magnitude partitions provided an optimal compromise of resolution while avoiding complex transformations into quantitative values of magnitude. Both species data and sea-level magnitudes were converted to ranks and subsequently subjected to bivariate and partial correlation and concordance analyses (see Table 1). Two subsequent analyses were performed to accommodate assumptions about the biotic effects of anoxia and to test ‘‘background’’ changes in diversity. Organic-rich shales are known to occur during several periods in the northwestern European Jurassic. Such times include the earliest Sinemurian, early Late Pliensbachian, and, most pronounced, the Early Toarcian (Fig. 3). Given the assumption that the spread of anoxic waters into shelf areas would reduce habitable area despite an increase in water depth, we deemed it more appropriate to code such intervals as having a negative impact on habitable area. Thus, an additional concordance analysis was conducted where the Early Toarcian was coded negatively for a reduction of ecospace even though it occurs during sea-level rise. A third analysis examined a subset of the data series in which there appears to be a significant covarying signal between sea-level and diversity. This was done because it has been suggested that the Early Toarcian extinction was induced by anoxic marine waters during the peak transgression, at which some threshold may have been
Table 1 Early Jurassic bivalve diversity and extinction metrics for western Europe. (Data from Hallam 1986, 1987) Ammonoid zone Levesquei Thouarsense Variabilis Bifrons Falciferum Tenuicostatum Spinatum Margaritatus Davoei Ibex Jamesoni Raricostatum Oxynotum Obtusum Turneri Semicostatum Bucklandi Angulata Liasicus Planorbis
Species richness 44 27 23 28 18 26 60 59 55 53 54 50 44 43 41 42 40 41 36 33
Diversity rank 13.5 4 2 5 1 3 20 19 18 16 17 15 13.5 12 9.5 11 8 9.5 7 6
Sea-level scale 7 7 7 8 8 6.5 6 5.5 4.5 5 4 3.5 4 4 4 4 3 2.5 3 1.5
Fig. 3 Bivalve species diversity and sea-level curve from northwestern Europe. Asterisk on sea-level curve represents periods of anoxic shale deposition which were especially prevalent during the early Toarcian. (Data from Hallam 1986, 1987)
breached. It may therefore be more appropriate to examine ‘‘background’’ relationships between sea-level and diversity before the crises during a time of gradual sea-level rise.
164 Table 2 Numerical results of concordance analysis (pL ) with lower and upper 95% confidence limits in parentheses and of correlation analyses. Note that o and q are Spearman’s and Kendall’s coefficients, respectively Data set
Concordance (pL )
Correlation
n"20
0.47 (0.29—0.67)
nTax — sea-level nTax — time sea-level — time nTax— sea-level, time
n"14
0.54 (0.31—0.75)
o
q
!0.210 !0.039 !0.104 0.111 0.923* 0.777* !0.298 !0.232
nTax — sea-level 0.813* nTax — time 0.980* sea-level — time 0.847* nTax — sea-level, !0.161 time
0.670* 0.922* 0.693* 0.111
*Significant (p(0.1)
level. Further analyses considering the effects of anoxia and testing a subset of the data also fail in discriminating any association between sea-level and diversity. Possible explanations for this apparent lack of correlation between sea-level changes and changes in diversity are discussed below.
Discussion There is a range of possible explanations which may explain the failure to identify any relationship between sea-level and diversity changes in the Jurassic bivalve data. We focus the discussion on three possible reasons: (a) our methods were not appropriate for the data; (b) our methods correctly indicated no association between sea-level and marine diversity; or (c) there is a complex association with many competing factors.
Results A failure in methods?
Table 2 shows the results of the numerical tests for the Early Jurassic bivalve data. In general, the concordance is low (pL "0.47) indicating no association between directions of change in sea-level and diversity. Surprisingly, there is an overall slight negative Spearman’s partial correlation (o "!0.298) between sea-level 1!35*!and diversity. The absence of relationship is in contrast to the very strong bivariate Spearman’s correlation (o"0.923) between sea-level and stratigraphic position illustrating the overall trend of sea-level rise over time. The results of the concordance analysis, which codes periods of anoxia as a reduction in habitable area (regardless of the direction of change in sea-level), produced similar results (pL "0.55), and indicate no association between increasing diversity and increasing ecospace that could be discerned from random roll. Furthermore, in the pre-extinction subset of the data (Planorbis to Spinatum zones) the concordance probability was only slightly increased (pL "0.54) and likewise failed to statistically associate changes between sea-level and diversity. Bivariate correlations between sea-level and diversity on the pre-extinction data become significant (o"0.813, q"0.670) attesting to the visual correspondence between the two systems before the Toarcian (Fig. 3). Despite these high bivariate correlations, the partial correlation, still negative, remains very low (o "!0.161) and is statistically insignificant, per1!35*!haps due to the strong intercorrelations between the three variables. The association between sea-level and time are due more to their stratigraphic position (time) or some other unmeasured variable, rather than an inherent cause—effect relationship. In summary, both the non-parametric partial correlation and concordance analyses suggest no relationship between the diversity of bivalve species and sea-
One reason for the failure to statistically recognize an association is that the methods we used are not appropriate for the data. Although coding sea-level data directly from hypothesized sea-level curves may be criticized, we defend the technique because such curves are derived from a large number of stratigraphic sections and are not subject to inaccurate calculations of paleogeographic areas where spatial relationships are likely to have been altered by tectonic or erosional processes. One must nevertheless acknowledge the assumptions in constructing such regional curves which must be viewed as averages of individual local sections and rely on accurate temporal correlations. It may also be true that sample size was insufficient to distinguish between true signals and noise. Ideally, a high number of data points in combination with a well-established relative sea-level curve and clear signals in the diversity record are desired. Provided the error in calculating sea-level ranks or diversity were minimized, the 20 data points in our study would be sufficient to discriminate an association. Both numerical methods should have been able to detect a correlation. The concordance analysis is admittedly insensitive to the magnitude of changes between successive intervals; thus, minor fluctuations in diversity, such as the transitions between the Hettangian into the uppermost Pliensbachian, is given the same weight as the pronounced drop in diversity from the Pliensbachian into the Toarcian. However, the partial correlation analysis takes into account the magnitude of both diversity trends and sea-level changes. The use of partial correlations, rather than simple bivariate algorithms, is also warranted on the grounds that timesequentially arranged data are inherently ordered and not randomly distributed. This point is illustrated by
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the bivariate correlations, especially in the lower portion of the sequence, in which the stratigraphic position is highly correlated with the other two variables. No association?
It is also possible that changes in habitable area as a function of sea-level are not a key factor in controlling the diversity of marine benthic invertebrates. Valentine and Jablonski (1991) argue that most benthic-shelf species along the modern California shelf are widely distributed parallel to the shoreline, but have only a limited expansion in an onshore—offshore direction, and thus, a reduction in shelf width due to sea-level fall may have no or only little impact on the diversity of marine invertebrate species. It can be argued that shelf gradients were much less in northwestern Europe than on the Recent California shelf, and that parallel distributions of fossil species may have been broader and more subject to constriction of habitable area during periods of marine regression. Complex relationships
The third possibility for the failure to recognize an association between sea-level and diversity is that the relationships are more complex than simple speciesarea effects, involving a multitude of interrelated processes of which the habitable-area effect is just one. This is illustrated in Fig. 4, which depicts some of the major expected environmental and biologic responses to sealevel changes and the resulting changes in marine diversity. The list includes aspects of species-area relationships, i.e., changes in habitable area as well as niche diversity, as potential parameters. In addition, changes in sea-level are thought to be associated with climatic
Fig. 4 Summary of biotic and abiotic factors induced by sealevel that may affect diversity
changes. For example, the extensive flooding of continents tends to produce a more equable climate with a lower thermal gradient between high and low latitudes and a reduced seasonality (e.g., Hallam 1992). This enhances overall environmental stability, which in turn favors K-selected organisms and finally increases marine species diversity. It should be noted, however, that the correlation between environmental stability and increased diversity may not be true for all ecosystems (e.g. Connell 1978). Furthermore, a rise in sea-level is likely to facilitate faunal migrations by connecting formerly isolated shelf areas and by forming new marine corridors. The immigration of new species into a particular basin will increase species richness within this region. For example, the Early Jurassic Hispanic Corridor, connecting the western Tethys with the East Pacific, was open at least intermittently from the Pliensbachian onwards. Paleobiogeographic evidence suggests that faunal migrations took place at different times and in both directions (e.g. Damborenea and Mancen8 ido 1979; Hillebrandt 1981; Hallam 1983; Smith and Tipper 1986). The same biotic and abiotic factors are involved during sea-level fall, working, however, the other way around and leading to a diversity decrease. Note that similar effects can be expected with the spread of anoxic bottom waters across epicontinental seas as with regression. For example, both processes would result in a reduction of habitable shelf area, the loss of habitat heterogeneity, increasing environmental stress with the promotion of r-selected generalists, and eventually the emigration of established species into areas with more favorable living conditions. In addition to the processes discussed above, we expect the effects of transgressions and regressions on marine species diversity to strongly depend on the scale of change, the rate of sea-level change, and the conditions prior to sea-level change. Obviously, not all major
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regressions in the Phanerozoic are associated with severe diversity declines (e.g., the mid-Oligocene), whereas others (e.g., the Permo-Triassic) approximately coincide with mass extinctions (e.g., Hallam 1992; Erwin 1993). Similarly, on a smaller scale, not all transgressive episodes during the Jurassic produce a diversity decline (and widespread anoxia) as experienced during the Early Toarcian of northwest Europe and the Andean basin, even if sea-level peaks of the same order of magnitude are compared to each other (Aberhan and Fu¨rsich, in press). This suggests that the magnitude of sea-level change is not the only controlling parameter, but that threshold effects may override any simplistic species-area effects. Furthermore, often interrelated factors, which may be important in this context, are: 1. The tempo at which sea-level changes proceed. For example, the lack of severe diversity declines during the rapid glacio-eustatic sea-level changes of the Pleistocene has been explained by the duration of lowstands being too short to cause extinctions (Hallam 1981; Jablonski 1985). 2. The relative position of sea-level prior to change. 3. The topographic relief (and size) of continents, which—in combination with (2)—controls the degree of continental flooding. For example, Wyatt (1995) suggested that late Ordovician regressions actually increased habitable areas in the shallow seas (although it is unlikely that this controlled diversity). 4. The paleogeographic setting. This concerns, for example, the existence of marine corridors or physical barriers, and the presence and number of islands within the study area, which may serve as refugia. 5. The kind of organic adaptations prior to sea-level change. For example, faunas with high degrees of endemism and stenotopy are more likely to suffer extinctions during periods of environmental stress (be it regressions or anoxia) than more eurytopic faunas with a low percentage of geographically restricted forms. 6. The regional and temporal scale. Clearly, an analysis on a global scale has to consider more potentially influential factors than a study on a basinwide scale. Thus, the overprinting of eustatic sea-level fluctuations by regional tectonics may hamper a straightforward correlation of sea-level with diversity. Similarly, if long time periods are analyzed, plate tectonic processes, such as the fragmentation and amalgamation of continents, global climatic changes, and shifts in the number of faunal provinces, add to the complexity of an analysis. Consequently, we suggest that there is no straightforward way to predict the impact of sea-level changes on the diversity of marine shelf faunas.
Conclusions We have set forth in this paper numerical methods with which to test the association between metrics of taxonomic diversity and sea-level as determined from com-
posite curves. Although applying such tests to Early Jurassic bivalves has resulted in fairly high bivariate correlations between sea-level and diversity, there are more appropriate measures of association such as: (a) nonparametric partial correlation factoring out any influence from the time dimension and (b) concordance analyses which tests for trends in direction of change. Both analyses suggest no relationship between the diversity of bivalve species and sea-level as experienced in Early Jurassic bivalves of western Europe. Further analyses considering the effects of anoxia and testing a subset of the sequence also failed to discriminate any association between sea-level and diversity. Rises and falls in diversity may have a multitude of different and connected causes, some of which may be linked to changes in sea-level. For any example, we expect it will be difficult to decipher which of the various interconnected parameters are more important than others, or to even isolate a specific variable. We conclude that because some of the abiotic/biotic factors associated with changing sea-level may not be obvious or even measurable in the historical record, the speciesarea effect cannot be applied unambiguously to the ancient record. Acknowledgements We thank A. Swan and J. Scallan for commenting on a previous draft of the manuscript, and we appreciate a review by W. Oschmann leading to a better paper. This contribution was written while C.A.M. was supported as an Alexander von Humboldt-Stiftung Fellow; the foundation’s support and research facilities provided by the Institut fu¨r Pala¨ontologie, Universita¨t Wu¨rzburg, are gratefully acknowledged.
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