Even as interest renews in characterising Phanerozoic marine global diversity patterns, there is a growing realisation that interesting insights also lie at smaller scales, particularly in spatial patterns of diversity (e.g. Miller 1997; Vermeij and Leighton 2003; Jablonski 2009). Additive diversity partitioning offers palaeobiology a way to dissect global diversity, to rank the relative contributions of diversity at all scales from the patch to the province, and to understand the causes of diversity changes at those scales.
Sampling is the principal hurdle for applying additive diversity partitioning to the fossil record, and the issue presents itself in at least three ways. First, there is the question of sampling within geological units (i.e. beds, depositional facies and sedimentary basins) and how this corresponds to relevant ecological units (Kowalewski et al., 2006; Scarponi and Kowalewski, 2007). In part, geologically defined sampling units are required partly out of necessity; they are what palaeontologists have to work with. There is also a broad correspondence of these geological sampling units with ecologically meaningful units. The scale of a sampled bed is approximately equivalent to the scale of a box core containing time-averaged dead fauna, for example. At least in marine environments, depositional facies are defined by grain size, bedding and sedimentary structures, many of which reflect features that are important to benthic invertebrates, such as shear stress, substrate consistency and oxygen availability. Depositional basins are large-scale sampling units of approximately the same scale as ecological landscapes. Other sampling units may be possible in the fossil record, and it will be critical to evaluate the differences in scale among studies when comparing their results, particularly when dealing with organisms of varying dispersal capabilities (cf. Gaston and Blackburn, 2000).
Second, additive partitioning requires that sampling intensity be equal across all elements at a given scale, in other words, the sampling design should be balanced. For example, in a sampling design consisting of depositional sequences, depositional facies and beds, the size of each sampled bed should be comparable, each facies should have the same number of beds, and each sequence should have the same sampled facies. If sampling is incomplete at one level, such as too few samples within a particular facies, the diversity in that facies will be depressed relative to other facies. This will lower the mean alpha diversity at that level, lowering the beta diversity for the level below and raising the beta diversity at the level above. Conversely, overly intense sampling at one level will raise the mean alpha diversity at that level, elevating beta diversity for the level below and depressing the beta diversity of the level above.
Layou (2007) and Heim (2009) were aware of additive diversity partitioning at the onset of their study and developed balanced sampling designs. The sampling in Patzkowsky and Holland (2007) was conducted prior to learning of additive partitioning and was therefore not balanced. To achieve a balanced design, Patzkowsky and Holland (2007) removed those habitats that could not be sampled consistently through time, removed depositional sequences that lacked a core set of shared habitats and subsampled to equalise the sampling intensity within habitats. A similar strategy could be used in other studies designed without additive diversity partitioning in mind.
Finally, sampling poses a challenge in bridging from regional-scale studies to the global scale. The iconic pattern of global diversity (e.g. Sepkoski 1997) was estimated from tabulations of first and last occurrences of taxa. Such compendia include many taxa so rare that they are known from only a few specimens and are unlikely to be encountered in any bed-scale sampling. For example, an intensive study in the Ordovician of the Cincinnati Arch encountered 57 genera within 1900+ samples (Holland et al. 2001), yet 185 genera have been reported historically from these strata. Although some of these genera may have been encountered in the field yet not recognised as a distinct genus (e.g. some ramose trepostomes), the majority were too rare to be found. These rare taxa dominate genus-level diversity within a compendium-based analysis, but would be absent in a collection-based study. The extent to which rare taxa alter temporal diversity patterns depends on the variation in taxon abundance distributions through time (Kosnik and Wagner 2006; Wagner et al. 2006). Promising approaches to capturing this rare tail have recently been developed (Harnik, 2009).
This compendium effect of rare taxa can be compared to the diversity partitions of Patzkowsky and Holland (2007) using a compilation of all reported taxa from the type Cincinnatian (http://www.uga.edu/strata/cincy/fauna; Text-fig. 5). Among-habitat beta diversity is 16–24 per cent of the within-habitat mean alpha diversity in the sample-based data, but is 33–37 per cent in the compendium-based data. In short, the compendium contains almost double the number of rare taxa limited to a single habitat than a sample-based study indicates. Whether the compendium pattern is a better reflection of reality is difficult to know, as patterns of sampling intensity in that compendium cannot be determined. The more important issue is that compendium-derived diversity estimates cannot be reconciled with sample-based diversity estimates, particularly when they are compiled at greatly different scales (e.g. Sepkoski’s (2002) compendium vs. local collections). For example, the compendium-scale diversity is nearly triple the sample-based diversity in the example above (Text-fig. 5).
Figure TEXT-FIG. 5.. Additive diversity partitions during a Late Ordovician biotic invasion in the eastern United States, illustrating the differences between diversity partitions calculated from field censuses (upper figure, modified from Patzkowsky and Holland 2007) and from a compendium of reported genera (lower figure). Diversity partitions reflect alpha diversity within a habitat (equal to sum of collection-level alpha diversity and among-collections beta diversity of Text-fig. 3) and among-habitat beta diversity. Note that the relative contributions of the shallow subtidal (ss) and deep subtidal (ds) to among-habitat beta diversity are shown for the compendium-based analysis, based on the new approach to calculating diversity partitions presented in this paper. The faunal invasion prior to and during the C5 sequence marks a substantial reversal in the relative contributions to beta diversity of these two habitats.
Download figure to PowerPoint
More recently, global diversity has been estimated through sample standardisation techniques applied to compilations of local occurrences (e.g. Alroy et al. 2008). Such approaches ease the problem of comparing diversity at greatly different scales by maintaining a constant sampling effort through time, but so far have not been balanced with respect to provinces or sedimentary environments. The structure of the Paleobiology Database makes balanced subsampling feasible, and conducting it will require targeted addition of new data from specific sedimentary environments. A promising development is the shareholder quorum subsampling method (Alroy, 2010), which provides an objective and consistent way to define sampling quality, makes sampling intensity equivalent at different scales and corrects for unbalanced sampling.
Changes that could be investigated
Modern ecologists are increasingly interested in the question of diversity partitioning, both from the aspect of documenting the spatial scaling of diversity to guide conservation policy and from the perspective of understanding how ecological processes shape diversity at a range of scales. Additive diversity partitioning is an exciting and timely opportunity for palaeobiologists because palaeobiological data are uniquely suited for understanding the evolution of diversity partitioning. Many aspects at the regional scale are easily within reach, such as changes in onshore–offshore partitioning and changes in partitioning within habitats. In particular, it is relatively easy to address how these change in response to external factors such as migration and extinction (e.g. Layou 2007; Patzkowsky and Holland 2007; Heim 2009), or relative to global-scale phenomena such as Ordovician radiation, the Palaeozoic plateau in diversity, or the Mesozoic–Cenozoic rise in diversity. Larger-scale issues such as provinciality (e.g. Valentine 1971; Valentine et al. 1978; Miller et al. 2009) or latitudinal gradients (Roy et al. 2000; Valentine et al. 2008) could also be addressed through additive diversity partitioning, although the larger spatial scale will make balanced sampling more difficult.
Not only can taxonomic diversity be addressed through additive partitioning, but other forms of diversity can as well. Ecologists have noted how differing patterns of functional and taxonomic diversity indicate substantial functional redundancy among taxa. Existing methods of describing marine functional diversity are well developed (e.g. Bambach et al. 2007; Novack-Gottshall 2007) and lend themselves to additive partitioning. Such approaches could address how functional redundancy is affected, for example, by immigration events and regional extinctions.
Several modern ecologists have asked questions about the relative importance of seasonal variations versus spatial variations in diversity, particularly of insects. These studies pose interesting palaeobiological counterparts, such as how much was a particular extinction or migration event worth compared to the increase in diversity achieved by sampling another habitat. These questions have particular relevance for the interpretation of diversity patterns in single sections or small regions, where facies changes at a boundary can overwhelm the true patterns of origination or extinction (e.g. Holland 2000; Smith et al. 2001).
Revisiting Sepkoski’s question
Sepkoski (1988, p. 221) famously asked ‘Alpha, beta, or gamma – where does all the diversity go?’ The ultimate goal of additive diversity partitioning in the marine fossil record is the complete partitioning of Phanerozoic diversity into all of its components. Such a partitioning would greatly facilitate the interpretation of Phanerozoic diversity by reducing the question to scales at which diversity may be more interpretable, such as the number of provinces, the latitudinal configuration of habitable space, the intensity of onshore–offshore gradients and the complexity of local habitats.
Although the complete partitioning of Phanerozoic diversity is not at hand (but may soon be), preliminary data suggest that provinciality may be by far the most dominant single source of global diversity. Using two intervals of the Late Ordovician from the compendium of genera from the type Cincinnatian and comparing these to global genus diversity from Sepkoski (1997) suggest that mean within-habitat alpha diversity and among-habitat beta diversity comprise <20 per cent of global diversity, with the remaining 80 per cent reflecting provinciality (Text-fig. 6). In this analysis, the mean habitat diversity is based on shallow subtidal, deep subtidal and offshore habitats and therefore spans much of the fossiliferous habitat for this time. The analysis assumes that the type Cincinnatian is a reasonable proxy for global within-habitat and among-habitat diversity. Given the exceptional preservation, abundance and diversity of fossils from this region, it is likely that the size of these two partitions is overestimated relative to most regions and that the estimate of beta diversity because of provinciality is a minimum estimate.
Figure TEXT-FIG. 6.. Global diversity partitioning during the Late Ordovician. Global genus diversity is based on Sepkoski (1997). Regional mean within-habitat diversity (alpha h) and among-habitat diversity (beta h) are based on an unpublished compendium of genus occurrences from the Late Ordovician of the Cincinnati Arch, USA. Provincial-scale beta diversity (beta p) dominates global diversity during the Late Ordovician.
Download figure to PowerPoint
This estimated 20 per cent contribution of the onshore–offshore gradient to global diversity is far less than Sepkoski’s (1988) 50 per cent estimate. Part of this discrepancy may reflect differences between collection-based approaches like Sepkoski (1988) and compendium-based approaches, such as presented here.
In terms of additive diversity partitioning, global diversity could change in two ways. First, one or more of the diversity partitions could change in absolute size, while also changing its proportional size relative to the other partitions. Such a change would indicate a basic restructuring of how global diversity is assembled. Alternatively, the absolute size of all of the diversity partitions could change by the same proportional amount, such that their relative proportions remained constant. This type of change would imply that there is a relatively fixed structure to global diversity. Observed modern variation in partitions among taxa, habitats and geographical regions, coupled with observed ancient changes in the sizes of diversity partitions, favours the first scenario, whereas parallel changes in mean within-collection (α) and global diversity (e.g. Sepkoski et al. 1981; Alroy et al. 2008) argue for the latter scenario.
The relative sizes of these diversity partitions imply their relative contributions to changes in global diversity. Large changes in diversity would require a large change in partition size and larger partitions are more likely to show large variance in their size through time. For example, even if global (γ) diversity and local (alpha-collection) diversity show similar trajectories (e.g. Sepkoski et al. 1981) or show similar per cent changes through time (e.g. Alroy et al. 2008), local diversity per se cannot be driving the global diversity pattern because the changes in mean alpha diversity are so much smaller than global diversity. For example, if mean alpha diversity increased by ten genera, with no accompanying change in any beta diversity, that is, by adding ten cosmopolitan genera, then global diversity would increase by only ten genera. If, however, the ten genera added to each local collection were endemic in some way, either by environmental restriction or provinciality, then the beta diversity terms will increase, leading to a much greater rise in global diversity.
Thus, the relative sizes of the diversity partitions suggest that large Phanerozoic changes in diversity are driven primarily by changes in the degree of provinciality (cf. Valentine 1970, 1971; Valentine et al. 1978; Heim 2008), to lesser degree by onshore–offshore variation, and to a still lesser degree by changes in local alpha diversity (cf. Kowalewski et al. 2002; Crampton et al. 2006). None of the among-habitat or smaller-scale partitions in Layou (2007), Patzkowsky and Holland (2007), or Heim (2009 are substantial at the scale of global diversity, even though all of these studies were conducted over intervals of substantial ecological change. Counting the number of provinces has been notoriously difficult, and a recent approach has sought to measure directly the degree of geographical differentiation, called geodisparity (Miller et al. 2009). Their analysis indicates that the amount of geodisparity has not changed substantially over the scale of the Phanerozoic, but holds out the possibility that geodisparity may have changed substantially over shorter timescales. Identifying the dominant sources of Phanerozoic diversity and their changes remain open questions, and additive diversity partitioning is a promising avenue for answering them.