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Elliptic Fourier shape analysis is a powerful, though under‐utilized, biometric tool that is particularly suited for the description of fossils lacking many homologous landmarks, such as several common bivalve groups. The method is conceptually more parsimonious than more traditional biometric methods based on discrete linear and angular measurements. Most importantly, however, shape analysis captures a much higher proportion of the morphological information resident in any fossil than analyses based on discrete measurements. The number of harmonics required in an elliptic Fourier analysis can be estimated from a series of inverse Fourier reconstructions, or from the power spectrum. In most studies it is appropriate to normalize Fourier coefficients for size, although this information can be reincorporated at a later stage. The coefficients should probably not be standardized, unless there is evidence to suggest that high‐frequency information was genetically as important as low‐frequency information. Depending upon the aims of a particular study and the morphological disparity of the fossils in question, it might be appropriate to eliminate the first harmonic (‘best‐fitting’) ellipse from an analysis. Meaningful comparison of the left and right valves of bivalves requires the digitized coordinates of one or other to be mirrored prior to computation of the Fourier coefficients. □Biometric analysis, Bivalvia, elliptic Fourier analysis, morphometrics.

In the time between speciation and extinction, a species' ecological and biogeographic footprint-its occupancy-will vary in response to macroecological drivers and historical contingencies. Despite their importance for understanding macroecological processes, general patterns of long-term species occupancy remain largely unknown. We documented the occupancy histories of Cenozoic marine mollusks from New Zealand. For both genera and species, these show a distinct pattern of increase to relatively short-lived peak occupancy at mid-duration, followed by a decline toward extinction. Thus, species at greatest risk for extinction are those that have already been in decline for a substantial period of time. This pattern of protracted rise and fall stands in contrast to that of incumbency, insofar as species show no general tendency to stay near maximal occupancy once established.

A B S T R A C TThe late Paleocene to early Eocene was marked by major changes in Earth surface temperature and carbon cycling. This included at least two, and probably more, geologically brief (!200-k.yr.) intervals of extreme warming, the Paleocene-Eocene thermal maximum (PETM) and the Eocene thermal maximum-2 (ETM-2). The long-term rise in warmth and short-term "hyperthermal" events have been linked to massive injections of 13 C-depleted carbon into the ocean-atmosphere system and intense global climate change. However, the causes, environmental impact, and relationships remain uncertain because detailed and coupled proxy records do not extend across the entire interval of interest; we are still recognizing the exact character of the hyperthermals and developing models to explain their occurrence. Here we present lithologic and carbon isotope records for a 200-m-thick sequence of latest Paleoceneearliest Eocene upper slope limestone exposed along Mead Stream, New Zealand. New carbon isotope and lithologic analyses combined with previous work on this expanded section shows that the PETM and ETM-2, the suspected H-2, I-1, I-2, and K/X hyperthermals, and several other horizons are marked by pronounced negative carbon isotope excursions and clay-rich horizons. Generally, the late Paleocene-early Eocene lithologic and d 13 C records at Mead Stream are similar to records recovered from deep-sea sites, with an important exception: lows in d 13 C and carbonate content consistently span intervals of relatively high sedimentation (terrigenous dilution) rather than intervals of relatively low sedimentation (carbonate dissolution). These findings indicate that, over ∼6 m.yr., there was a series of short-term climate perturbations, each characterized by massive input of carbon and greater continental weathering. The suspected link involves global warming, elevated greenhouse-gas concentrations, and enhanced seasonal precipitation.

To interpret changes in biodiversity through geological time, it is necessary first to correct for biases in sampling effort related to variations in the exposure of rocks and recovery of fossils with age. Data from New Zealand indicate that outcrop area is likely to be a reliable proxy of rock volume in both stable cratonic regions, where the paleobiodiversity record is strongly correlated with relative sea level, and on tectonically active margins. In contrast, another potential proxy, the number of rock formations, is a poor predictor of outcrop area or sampling effort in the New Zealand case.

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ABSTRACT. Fourier outline shape analysis is a powerful tool for the morphometric study of two-dimensional form in organisms lacking many biologically homologous landmarks. Several improvements to the method are described herein; these modi®cations are incorporated into the new computer programs HANGLE, HMATCH and HCURVE. First, automated tracing of outlines using image capture software, although desirable, results in high frequency pixel`noise' that can corrupt the Fourier analysis. Program HANGLE eliminates this noise using optional and variable levels of outline smoothing. Secondly, a widely used Fourier technique, elliptic Fourier analysis (EFA, Kuhl and Giardina 1982), yields coef®cients that are not computationally independent of each other, a condition that hampers and compromises statistical analysis. In addition, EFA increasingly downweights successively more detailed features of the outline. Program HANGLE solves both of these problems. Lastly, Fourier methods in general are sensitive to the placement of the starting position of the digitized trace. This problem is acute when the organisms under study have no unambiguously de®ned, homologous point on the outline from which to start the trace. Program HANGLE allows the user to normalize for starting position using various properties of individual outlines. Alternatively, HMATCH takes a new approach and can be used to normalize using properties of the entire population under study.