The relationships of post-Palaeozoic echinoids at family level are established through phylogenetic analysis of 169 taxa and 306 skeletal characters (excluding pedicellariae). Previous phylogenetic analyses of echinoids have either examined specific subgroups in detail or have looked at a relatively small number of taxa selected from across the class, with sparse sampling potentially affecting the reliability of results adversely. Our new analyses represent a compromise between encompassing the diversity of form that exists, while keeping the number of taxa to a level that does not make rigorous analysis impossibly time-consuming. In constructing the taxon-character data matrix we have encountered a surprising lack of primary data on plating pattern, lantern, and girdle structure for many supposedly "well-known" taxa. A well-resolved phylogenetic hypothesis was obtained and is used as the basis for a formal classification. Characters generally have a high retention index (>0.7) but low consistency index (<0.25) suggesting that, although characters are largely retained after they first evolve, most also undergo occasional reversal or convergence. Although parts of the resulting trees are only weakly supported (e.g. the precise sister group of the Irregularia), other parts are unambiguously resolved. Not unexpectedly, deep nodes are often not supported by unique apomorphies and higher taxa acquire their characteristic set of features over time. Diagnoses based on crown group taxa thus often fail to encompass fossil stem-group members adequately. Establishing the relationships of taxa at the root of large groups is hampered by limited character resolution. The influence of fossil taxa on the topology was explored by comparing the tree topologies obtained with and without their inclusion. We show that removal of fossils from stem groups makes no difference where their crown group is morphologically conservative, but has a major influence where extant sister groups are separated by large morphological gaps. Completeness of the echinoid record and its match to the stratigraphical record of first occurrences is tested using various metrics and found to be highly congruent, with irregular echinoids showing a higher congruence than regular ones.

Patterns of origination, extinction and standing diversity through time have been inferred from tallies of taxa preserved in the fossil record. This approach assumes that sampling of the fossil record is effectively uniform over time. Although recent evidence suggests that our sampling of the available rock record has indeed been very thorough and effective, there is also overwhelming evidence that the rock record available for sampling is itself distorted by major systematic biases. Data on rock outcrop area compiled for post-Palaeozoic sediments from Western Europe at stage level are presented. These show a strongly cyclical pattern corresponding to first- and second-order sequence stratigraphical depositional cycles. Standing diversity increases over time and, at the coarsest scale, is decoupled from surface outcrop area. This increasing trend can therefore be considered a real pattern. Changes in standing diversity and origination rates over time-scales measured in tens of millions of years, however, are strongly correlated with surface outcrop area. Extinction peaks conform to a random-walk model, but larger peaks occur at just two positions with respect to second-order stratigraphical sequences, towards the culmination of stacked transgressive system tracts and close to system bases, precisely the positions where taxonomic last occurrences are predicted to cluster under a random distribution model. Many of the taxonomic patterns that have been described from the fossil record conform to a species-area effect. Whether this arises primarily from sampling bias, or from changing surface area of marine shelf seas through time and its effect on biodiversity, remains problematic.

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 highresolution 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.

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The phylogenetic relationships of 46 echinoids, with representatives from 13 of the 14 ordinal-level clades and about 70% of extant families commonly recognized, have been established from 3 genes (3,226 alignable bases) and 119 morphological characters. Morphological and molecular estimates are similar enough to be considered suboptimal estimates of one another, and the combined data provide a tree that, when calibrated against the fossil record, provides paleontological estimates of divergence times and completeness of their fossil record. The order of branching on the cladogram largely agrees with the stratigraphic order of first occurrences and implies that their fossil record is more than 85% complete at family level and at a resolution of 5-Myr time intervals. Molecular estimates of divergence times derived from applying both molecular clock and relaxed molecular clock models are concordant with estimates based on the fossil record in up to 70% of cases, with most concordant results obtained using Sanderson's semiparametric penalized likelihood method and a logarithmic-penalty function. There are 3 regions of the tree where molecular and fossil estimates of divergence time consistently disagree. Comparison with results obtained when molecular divergence dates are estimated from the combined (morphology + gene) tree suggests that errors in phylogenetic reconstruction explain only one of these. In another region the error most likely lies with the paleontological estimates because taxa in this region are demonstrated to have a very poor fossil record. In the third case, morphological and paleontological evidence is much stronger, and the topology for this part of the molecular tree differs from that derived from the combined data. Here the cause of the mismatch is unclear but could be methodological, arising from marked inequality of molecular rates. Overall, the level of agreement reached between these different data and methodological approaches leads us to believe that careful application of likelihood and Bayesian methods to molecular data provides realistic divergence time estimates in the majority of cases (almost 80% in this specific example), thus providing a remarkably well-calibrated phylogeny of a character-rich clade of ubiquitous marine benthic invertebrates.