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PALEOBIOLOGICAL APPLICATIONS OF THREE-DIMENSIONAL BIOMETRY ONLARGER BENTHIC FORAMINIFERA: A NEW ROUTE OF DISCOVERIES

ANTONINO BRIGUGLIO1,3, JOHANN HOHENEGGER

1AND GYORGY LESS

2

ABSTRACT

Four specimens of larger benthic foraminifera (the RecentPalaeonummulites venosus and Operculina ammonoides, andthe phylogenetically related Paleogene Nummulites fabianii andN. fichteli) were investigated by X-ray tomography. Theresulting three-dimensional measurements enabled a compre-hensive, quantitative study of shell morphology to interpret cellgrowth without specific shell preparation and/or destruction.After segmentation and extraction of all scanned lumina, thefollowing characters were measured on all chambers of eachspecimen: chamber volume, septal distance, chamber height, andchamber width. The sequence of chamber lumina follows either alogistic function (Palaeonummulites, Operculina), where thedeceleration in growth rate of the latest chambers could markthe onset of reproduction, or it can be modeled by a series ofstepwise functions with differing constants (Nummulites).Variations around the growth model are either periodic,following external cycles, or random as expressed by abruptdeviations. Therefore, they may reflect the response of the cell toenvironmental changes in terms of cyclic changes (e.g.,seasonality) or single events (e.g., predator attack). Correlationsbetween chamber volume and the other chamber parametersshow that septal distance always matches the sequence inchamber volume and can therefore be used as a proxy forenvironmental analyses in both growth models. Chamber heightand width often remain constant around their function andrarely deviate drastically to accommodate the needed lumen forretaining test size and shape. Chamber width may varyaccording to chamber volume in involute specimens, whereasboth chamber height and width correlate with volume in thosetests following an Archimedean spiral. X-ray-tomography showsparticular promise in determining which parameters that can beassessed routinely in two dimensions primarily reflect environ-mental conditions vs. parameters best used for taxonomicidentification and for systematic lineage reconstruction.

INTRODUCTION

Larger benthic foraminifera (LBF) have hosted endo-symbiotic photosynthetic microalgae for .300 millionyears. Accordingly, they have always provided enoughlight to their partners by living within the photic zone andby building a shell able to host as many symbionts asnecessary (Hohenegger, 2009). While solar energy isabundantly available near the sea surface, light energydeclines rapidly with depth, and yet many LBF taxa thrivenear the lower limits of sufficient light penetration forphotosynthesis. Living in shallow water means dealing with

hydrodynamics, and LBF build their shells to resist suspensionand entrainment (Briguglio and Hohenegger, 2011). Therefore,shape analyses of LBF tests can reveal pivotal information forecologic and environmental reconstructions. Moreover, overgeological time, LBF have experienced biogeographic changes(Renema and others, 2008), environmental stresses (Hallock,2000), and repeated extinctions and diversifications (Hottinger,2001). Successful biological adaptations have allowed forami-nifera to survive such events and have enabled LBF to be oneof the most prominent carbonate producers in shallow-waterenvironments (Hohenegger, 2006) and to be precise indexfossils for biostratigraphic purposes (e.g., Serra-Kiel andothers, 1998). The life and growth strategies, environmentaladaptations, biology, and the taxonomic differentiation ofLBF are fascinating, highly complex, and poorly understoodtopics that require test-shape analysis.

Many methods and techniques have been proposed during thelast decades to address these questions. The results demonstrate thecomplexity and beauty of these protists (e.g., Hottinger, 1960;Schaub, 1981; Less, 1987; Drooger, 1993), which build their tests asgreenhouses (Hallock, 1981; Hallock and others, 1991; Hoheneg-ger and others, 1999; Renema, 2005; Hohenegger, 2009) that resistwater motion (Briguglio and Hohenegger, 2009, 2011).

The quantification of such phenomena becomes morecomplex by including ontogenetic shell variation, life cycles(with extreme morphological differences between genera-tions), and intraspecific variability. Despite interestingresults, the actuopaleontological approach is insufficientto completely understand the paleobiology of fossil LBF.The greater complexity in morphogenesis and bauplan infossil taxa requires fully defining an array of complexparameters to effectively model test geometry (Hohenegger,2011; Hohenegger and Briguglio, 2012).

Methods to more effectively describe paleobiological adap-tations of LBF, including those that survived extinction events,would help reconstruct iterative evolutionary tendencies andextreme proliferation at certain times and locations in geologichistory. Previous studies in this direction are based primarily onbiometric observation of two-dimensional parameters oforiented test sections. Such measurements are the startingpoint for species definition and environmental interpretation.Nonetheless, this immense body of work is constrained by itstwo-dimensional character. Each measurement is made fromthin sections, which may not be representative of the whole test.Moreover, destruction of the test is required to obtain thesesections, resulting in the loss of data that could be obtainedfrom specimens cut in other directions.

Internal wall characters (e.g., trabeculae transversae innummulitids), septal width, and chamber height areimpossible to obtain from one oriented section. Commonly,three-dimensional structures, as well as complex chambershapes, are misunderstood in two-dimensional analyses.The splitting of nummulitid shells may help in some cases,but quantifying chamber parameters on half tests still3 Correspondence author. E-mail: [email protected]

1 Institut fur Palaontologie, Universitat Wien, Geozentrum, Althan-strasse 14 A-1090, Wien, Austria

2 University of Miskolc, Institute of Mineralogy and Geology, H-3515 Miskolc-Egyetemvaros, Hungary

Journal of Foraminiferal Research, v. 43, no. 1, p. 72–87, January 2013

72

neglects the third dimension. This is especially relevant indifferentiating between involute and evolute coiling.

In recent years, several instruments and software havebeen developed to tackle some of these problems. Comput-ed tomography, although well-known and broadly used formany years in (bio)medical investigations and materialsciences, involved huge initial costs that made it unafford-able for academia. This method has now become availablefor biological purposes, with advanced and upgradedtechniques yielding impressive, increasingly more preciseand faster results at a more affordable price. The possibilityto quantify any measurable geometric parameter of anorganism’s interior is a great opportunity to tackle LBFstructures, architectures, bauplan, and the many otherquestions addressed above (Briguglio and Benedetti, 2012).The digital resolution at the micrometer level is the onlysolution to the many controversies about the phylogeniesand evolutionary trends in fossil LBF.

The present work was designed to show how computedtomography can be used to overcome previous shortcom-ings (bi-dimensionality, oriented sections, specimen de-struction) to solve problems involving the functionalmorphology, environmental dependence, and ontogeny ofLBF. Several results presented here provide insight intohow this technology can be used to study paleobiology,including ontogeny, life cycle, and paleoenvironmentalreconstructions. Particular attention is given to cell growthand its apparent reaction to environmental changes, and tothe correlation among parameters describing chambershape and the resulting volume variations. Several insightsabout the biology and the ontogeny of recent and fossilLBF can be inferred by measuring the test volume occupiedby protoplasm during growth steps (Briguglio and others,2011), as this may reveal how the cell reacts to environ-mental variations and to local stress. The measurement ofthe chamber volume for LBF geometry is quite timeconsuming, as each chamber is connected to the next one indifferent locations (i.e., foramen, stolons), and this requiresmanual corrections, for each chamber, of all the two-dimensional slices obtained by the scanning process.However, 3-D technology and software engineering is

speeding up the segmentation process, and in the nearfuture it will be possible to scan and measure manychambers in a relatively short time. This study examinesonly four specimens, each belonging to a different species,with the goal of demonstrating the potential of microCTand its application to LBF, with some interesting results.

Because test volume is a combination of severalgeometric characters (chamber height, width, and length;Fig. 1), a correlation between volume and these variables ishere given to demonstrate when and how intensely each cellreacted to various environmental changes.

MATERIALS AND METHOD

Single specimens of Palaeonummulites venosus, Opercu-lina ammonoides, Nummulites fabianii, and N. fichteli wereinvestigated with micro-computed tomography at theUniversity of Vienna, Austria. The scans were done at theDepartment of Theoretical Biology, with image processingat the Department of Palaeontology. Detailed descriptionof this method and its possible application to foraminiferahave been described by Speijer and others (2008), Briguglioand others (2011), and Gorog and others (2012). The list ofscanned specimens is reported in Table 1 with informationon the sample and scan properties.

Samples were scanned in small cylindrical plasticcontainers (a polypropylene pipette tip). Most plastics arerelatively transparent to X-rays and thus suitable to scanmineralized specimens. The specimens were scanned invertical position to reduce thickness crossed by X-rayradiation, thus yielding more contrast. Paperboard wasused to maintain them in position during rotation.

The reconstruction process, which creates the black andwhite X-ray stack from X-ray images provided by the CTscanner, aligns pixels from the top of the scanned object tothe bottom. This procedure may take several hours andproduces a stack of slices normal to the equatorial plane.To reconstruct the geometry of scanned specimens, thesequence of virtual axial sections requires a huge number ofslices, which increases the visualization time even foradvanced computer stations; the image stack can reach

FIGURE 1. Measurements of chamber height, septal distance, and chamber width on each chamber lumen.

TOMOGRAPHY ON LARGER FORAMINIFERA 73

20–35 Gb depending on the resolution and scan quality.The reconstructed stacks are normally smaller (,10–15 Gb),but still too large to run fast three-dimensional visualiza-tions and elaborations. To reduce the number of slices, adedicated program allows re-slicing along arbitrarilydefined planes. An exact re-slicing along the equatorialplane drastically reduces the stack size and speeds up theworking process, segmentation, and successive rendering ofthe volumes. Such size reduction affects neither data qualitynor image resolution; it only reduces the amount of datawithout information. The computer used for manipulatingthe image stacks was equipped with an IntelHCore (TM) 2Quad CPU Q9400 at 2.66 GHz, 8 GB of RAM with aMicrosoft Windows XP Professional 364 system, providedby the Department of Palaeontology, University of Vienna,Austria.

The software ImageJ (http://rsbweb.nih.gov/ij), perhapsthe most popular open-source imaging software in neuro-science, was used to measure 2-D images and to basicallyvisualize a 3-D dataset through plug-in, including VolumeViewer (http://rsb.info.nih.gov/ij/plugins/volume-viewer.html) and VolumeJ (http://webscreen.ophth.uiowa.edu/bij/vr.htm). We used Image Surfer (another open-sourceprogram; http://cismm.cs.unc.edu/) for volume rendering,quantifications, slicing at arbitrary orientations, measure-ments in 2-D and 3-D, and taking snapshots suitable forpublication.

Scan resolution depends on several variables that reflectthe distance of the object from the X-ray source anddetector; the scanner type also plays a role. Scan qualitydepends on scan intensity (kV and mA) and the density ofimaging.

After calibration, all chambers were segmented andextracted for each specimen. The following parameterswere measured for each chamber: chamber volume, septaldistance, chamber width, and chamber height, as displayedin Figure 1. For further statistical analyses, the volume datawere linearized using the cubic root. To determine potentialsignificant correlation between volume increase and thetwo-dimensional parameters measured on each chamber,correlations were calculated for each specimen and arerepresented as correlation matrices.

To recognize and quantify periodic deviations and cyclicvariations of the cell growth around the regression function

yy~axzb ð1Þ

or the constant

yy~aj, ð2Þ

where j indicates the different stepwise functions, wecalculated residuals r from the linear function for eachmeasured value yi as

ri~yi{(axizb) ð3Þ

and from stepwise functions as

rij~yij{aj, ð4Þ

where

aj~1=nj

Xi~nj

i~1

yij ð5Þ

Because the linear regression increases due to chambernumber x, deviations from the linear functions are small inearlier growth stages and large in later stages. Therefore, allresiduals ri have to be standardized by

rs, i~ yi{axi{bð Þ= axizbð Þ:100 ð6Þ

to make the intensity of deviations comparable for allgrowth stages i (chamber number). Standardized residualshave also been calculated in case of stepwise functions as

rs,ij~ yij{aj

� �=aj:100: ð7Þ

The three-dimensional chamber models of the scannedspecimens, the data measured on each chamber, theresiduals calculated for the measured parameters and theircorresponding standardized values are reported for P.venosus (Figs. 2, 3), O. ammonoides (Figs. 4, 5), N. fabianii(Figs. 6, 7) and N. fichteli (Figs. 8, 9). The latter two arefossil species commonly believed to be in an ancestor (N.fabianii)-descendant (N. fichteli) relationship (e.g., Schaub,

TABLE 1. Scanning properties for the investigated specimens and additional information on their provenance.

Palaeonummulites venosus(Fichtel and Moll, 1798)

Operculina ammonoides(Gronovius, 1781)

Nummulites fabianii(Prever in Fabiani, 1905)

Nummulites fichteli(Michelotti, 1841)

Code V0 ammonoides 1 fabianii 3 fichteli 14Camera temperature 255uC 255uC 255uC 255uCImage size 510 3 512 504 3 512 1024 3 1024 1024 3 1024kV 80 77 80 80mA 46 45 50 50Pixel size 4,258 mm 4,645 mm 4,228 mm 4,228 mmSlices 276 178 258 268Size 66.4 Mb 43.3 Mb 231 Mb 238 MbProvenance Sesoko, Japan.

50-m water depthMotobu Town, MotobuPeninsula, Okinawa, Japan.18-m water depth

Baciu Quarry, Cluj-Napoca,Romania.

Biarritz, Rocher de la Vierge,France.

Age Recent Recent Latest Eocene, SBZ 20 Earliest Oligocene, SBZ 21Reference Hohenegger, 1994 Hohenegger and others, 1999 Papazzoni and Sirotti,1995 Boussac, 1911; Schaub, 1981;

Mathelin and Sztrakos, 1993

74 BRIGUGLIO AND OTHERS

FIGURE 2. Palaeonummulites venosus. A equatorial and B axial views of chamber lumina, C axial view of chamber lumina covered by the test (notealar prolongations reaching the umbonal area), D chamber volume, E cubic root of chamber volume, F septal distance, G chamber width, H chamberheight; all measurements in mm. I correlation matrix: correlation coefficients in the lower left portion of the matrix and probabilities of independence(no correlation) in the upper right portion of the matrix. Bold and underlined fonts represent extreme and significant correlations.


FIGURE 3. Palaeonummulites venosus. Residuals and standardized residuals (in %) for linearized chamber volume (A, B), septal distance (C, D),chamber width (E, F), and chamber height (G, H).


FIGURE 4. Operculina ammonoides. A equatorial and B axial views of chamber lumina, C axial view of chamber lumina covered by the test (notealar prolongations reaching the umbonal area), D chamber volume, E cubic root of chamber volume, F septal distance, G chamber width, H chamberheight; all measurements in mm. I correlation matrix: correlation coefficients in the lower left portion of the matrix and probabilities of independence(no correlation) in the upper right portion of the matrix. Bold and underlined fonts represent extreme and significant correlations.


FIGURE 5. Operculina ammonoides. Residuals and standardized residuals (in %) for linearized chamber volume (A, B), septal distance (C, D),chamber width (E, F), and chamber height (G, H).


FIGURE 6. Nummulites fabianii. A equatorial and B axial views of chamber lumina, C axial view of chamber lumina covered by the test (note alarprolongations reaching the umbonal area), D chamber volume, E cubic root of chamber volume, F septal distance, G chamber width, H chamberheight; all measurements in mm. I correlation matrix: correlation coefficients in the lower left portion of the matrix and probabilities of independence(no correlation) in the upper right portion of the matrix. Bold and underlined fonts represent extreme and significant correlations.


FIGURE 7. Nummulites fabianii. Residuals and standardized residuals (in %) for the linearized chamber volume (A, B), septal distance (C, D),chamber width (E, F) and chamber height (G, H).


FIGURE 8. Nummulites fichteli. A equatorial and B axial views of chamber lumina, C axial view of chamber lumina covered by the test (note alarprolongations reaching the umbonal area), D chamber volume, E cubic root of chamber volume, F septal distance, G chamber width, H chamberheight; all measurements in mm. I correlation matrix: correlation coefficients in the lower left portion of the matrix and probabilities of independence(no correlation) in the upper right portion of the matrix. Bold and underlined fonts represent extreme and significant correlations.


FIGURE 9. Nummulites fichteli. Residuals and standardized residuals (in %) for the linearized chamber volume (A, B), septal distance(C, D), chamber width (E, F) and chamber height (G, H).


1981). As the standardized residuals were calculated inpercentages and all ordinate axes were constructed identi-cally, comparisons among the measured parameters arepossible. For all investigated specimens, the proloculus anddeuteroloculus measurements were excluded to avoidincorrect data interpretation due to their exceptionallylarge dimensions compared with the following chambers.

RESULTS

PALAEONUMMULITES VENOSUS

The chamber-volume sequences can be fitted by logisticgrowth (Fig. 2D). Two major lower peaks are evident whenthe chamber-lumina sequence is linearized by cubic roots(Fig. 2E): the first at chamber 30 and the second atchamber 40. At the same locations, strong deviations fromthe linear trend are visible in the septal-distance sequence(Fig. 2F). Moreover, the only deviation in the chamber-width sequence is visible at chamber 40 (Fig. 2G) and inchamber-height sequence only at chamber 30 (Fig. 2H).

The correlation matrix (Fig. 2I) indicates that the volumesequence highly correlates with septal distances and second-arily with chamber widths. Consequently, septal distanceand chamber width are also significantly correlated.

In P. venosus, the residuals of the linearized volume(Fig. 3A) and their standardized values (Fig. 3B) show that,besides the deviations at chambers 30 and 40, the firstchambers of this specimen were characterized by strongdeviations. Although they are completely hidden in thevolume sequence by the logistic function, they are visible inthe residuals sequence and correctly displaced in size in thestandardized volume sequence. Also, documented by thestandardized residuals of chamber width and height(Figs. 3F, H), these deviations are due to larger initialvalues in the test. Standardized chamber volume (Fig. 3B)oscillates around the expected trend, never varying morethan 10–15%, whereas the initial deviations and atchambers 30 and 40 reach 40%.

The sequence of the standardized septal-distance residu-als (Fig. 3D) shows how strongly such parameters mayvary, with deviations up to 40–60% from the expectedtrend. The strong deviation in chambers 30 and 40 isreflected in septal-distance residuals and in their standard-ized values. In the sequence of chamber-width residuals(Fig. 3E), the major deviation at chamber 40 is visible, andin the standardized sequence (Fig. 3F) an additionaldeviation appears at chamber 10, which is representedneither in the volume sequence nor in its residuals. Thedeviation at chamber 30 is also visible in the chamber-height residuals (Fig. 3H). The standardized residuals ofchamber heights (Fig. 3F) and widths (Fig. 3H) show thatthese parameters remain constant around the calculatedlinear function and do not vary by .20% of the expectedtrend (except for the deviations in the initial chambers).

OPERCULINA AMMONOIDES

The volume sequence shows logistic growth in O.ammonoides (Fig. 4D). Major deviations from the logisticgrowth function are visible around chambers 14–18 for thelinearized volumes (Figs. 4D, E). Strong deviations from

the linear function are visible at the same life stages in theseptal-distance sequence (Fig. 4F), although much lessprominent in the chamber-width sequence (Fig. 4G).Chamber-height values are extremely variable (Fig. 4H).A major disturbance is visible in the growth of thisspecimen from chambers 15–35 (see fig. 2 in Briguglioand others, 2011). This disturbance produced chamberswith reduced height, resulting in an irregular spiral.Notably, such extreme deviations, which can reach 260%

from the expected values, do not result in visible volumedeviations. Because of this morphological characteristicproducing a negative disturbance on the cell growth in theinvestigated specimen, the calculated linear function hasbeen obtained by omitting chambers 16–34 (Fig. 4H). Thecorrelation matrix (Fig. 4I) shows that the septal-distancesequence is the only character that mirrors the chamber-volume sequence.

Residual statistics better show the deviations of chambervolumes from the linear function (Fig. 5A) compared withthe linearized sequence (Fig. 4E), and the deviations atchambers 14–18 are easily recognizable. The rest of thestandardized volume sequence oscillates around the expect-ed values (deviation ,10%).

The septal-distance residuals show several deviations,which may attain negative values #50% of those expectedand positive values at chambers 14–18 exceeding 100% ofthe expected values (Fig. 5D). The strong volume deviationat chamber 14 is partly accommodated by a modifiedseptal-distance parameter.

Chamber-width residuals show positive peaks at cham-bers 18 and 32 (Fig. 5E), exceeding 30% of the expectedvalues (Fig. 5F). The first part of the sequence ischaracterized by very high positive deviations for the firsttwo chambers. The terminal part of the standardizedchamber-width residuals constantly oscillates around 10–15% of the expected values.

The deviations in chamber-height residuals are enormousand divert very prominently from chambers 14–35(Fig. 5G). The standardized-values sequence points to astrong deviation in the initial chambers, attaining negativepeaks #60% where the growth disturbance took place(Fig. 5H).

NUMMULITES FABIANII

In N. fabianii the logistic function, as reflected in thechamber volume, is not representative of growth. Rather, asequence of linear functions with insignificant multiplica-tive constants remains more or less parallel to the x-coordinate. After 25 chambers (Figs. 6D, E) the additiveconstant of the linear function changes instantaneously,producing a distinctive step that is also repeated afterchamber 50. This particular geometric trend cannot beexpressed by a linear regression line; a sequence of threeconstant functions y 5 aj (j 5 function number) must,therefore, be calculated (Fig. 6E) and applied to obtainconsistent residuals (Figs. 7A, B).

The stepwise trend is well documented in the septal-distance sequence (Fig. 6F) and visible in both otherparameters (Figs. 6G, H). This sequence is the character


that best mirrors the volume sequence, as documented inthe correlation matrix (Fig. 6I).

Residual chamber-volume statistics based on theirfunction constants show that deviations rarely attain+40% of the expected values (Fig. 7B), but are normallyconfined between the limits of +20%. The stepwise growthtrend in these calculations is not visible because residualshave been calculated according to their correspondingfunction constant a. Septal distances are much lesspredictable than chamber volumes; they often reach values+40% than expected (Fig. 7D). The residuals of chamberwidths and chamber heights are highly variable (Figs. 7E,G), but the deviations are not significant. Standardizedresiduals for these characters remain constant within thelimits of +20% (Figs. 7F, H).

NUMMULITES FICHTELI

The chamber-volume sequence of the N. fichteli specimen(Fig. 8D) is similar to N. fabianii. Though less visible,stepwise growth is recognizable in all measured parameters.Almost 90 chambers are divided into four steps withconstant functions (Fig. 8E) that are used to subdivide thechamber-volume, septal-distance, chamber-height, andchamber-width sequences.

Major deviations from the expected volume trends arevisible at chambers 40, 46, 70, and 87 (Fig. 8E). The septal-distance sequence deviates prominently at the samelocations where volume deviations were also observed(Fig. 8F). The chamber-width sequence does not deviatestrongly from the function constants, and the onlysignificant deviation corresponds to chamber 70 (Fig. 8G).Chamber-height sequence shows an oscillation around thefunction constants and deviates slightly more than chamberwidth. Major deviations are visible at chambers 40 and 46(Fig. 8H). A very high correlation was found betweenvolume and septal distance in this specimen. Chamberheights and widths also highly correlate with the volumes(Fig. 8I).

The residuals statistics highlight the most prominentdeviations in the volume sequence (Fig. 9A), and thenormalization of these values shows how they deviate by#40% of the expected values (Fig. 9B). The deviations at

chambers 40, 46, 70, and 87 are again evident. In septal-distance residuals and in their standardized values, the majordeviations are clearly visible; they deviate by .60% of theexpected value. Other values are still far from the expectedconstant, oscillating around 40% in both directions(Figs. 9C, D). Chamber-width and chamber-height residualsare much less saw-toothed than septal-distance ones(Figs. 9E, G), and their standardized values do not deviateby .10–20% from the expected values. The four majordeviations observed in the volume sequence are visible, andthey deviate #50% in standardized residuals for chamberwidth and height (Figs. 9F, H). The procedure used here tocalculate separated linear functions for the stepwise growth(instead of one single regression line) has been statisticallychecked for both fossil specimens (Fig. 10).

DISCUSSION

Ontogenetic changes in chamber shape (e.g., volumes)represent the reaction of the cell to internal and externalfactors, the growth program, and the limitations due toenvironmental conditions. Thus, all disturbances, devia-tions, or interruptions of the genetically controlled growthprogram are manifested in the test morphology andchemistry.

External factors operate either constantly, such astemporary environmental fluctuations (temperature, illumi-nation, etc.), or instantaneously, as in catastrophic events(in the sense of Poston and Stewart, 1978) such as storms,unsuccessful food capture, or the presence of competitors.Internal factors, which may be related to the morphogeneticprogram, may abruptly alter growth similarly, as demon-strated in ammonites (Kullmann and Scheuch, 1970).

The calculation of test growth in nummulitids is a goodexample to show how growth reacts to external factors. Themethod of standardized residuals visualizes variations fromgiven growth functions and yields interesting results such asconsistent (periodic) or chaotic (instantaneous) growthdeviations.

Two questions concerning cyclicity can be asked. Whatexternal phenomena induce periodicity, and what param-eter or combination of parameters reacts to these external

FIGURE 10. Comparison of residual variances between linear regression, stepwise functions, F-values, and probabilities of variance in Nummulitesfabianii and N. fichteli.


variations? Finding such correlations is crucial in paleobi-ological studies of LBF to understand their ontogeny andlife cycles. Some attempts have been made to study the shellchemistry (Wefer and Berger, 1980; Sarswati, 2012), andothers are trying to tackle LBF cyclicity by laser-ablation-plasma mass spectrometry (Evans and others, 2011, 2012),yet without published results. Coupling chamber-volumemeasurements with such data, once available, will providean interesting direction for further research.

Chamber-volume cyclicity reflects the interaction be-tween growth (modeled by a mathematical function) andenvironment (subjected to regular and abrupt changes). If afactor forces a growing cell to deviate from its normalgrowth function pattern, then the cell itself will build a newchamber to accommodate the new volume of protoplasm.In this process, the cell may modify one or more of the threeparameters defining the chamber: septal distance, chamberheight, and chamber width. Biologically, changing theseptal distance is the easiest solution to accommodate adefined volume. The modification of chamber height orchamber width, in contrast, will result in a more compli-cated bauplan deviation, such as in a change from aninvolute to evolute coiling system (or vice versa). Therefore,slight modifications of chamber volumes (e.g., cyclicity) areaccommodated by septal-distance modifications, whileabrupt volume deviations (e.g., resulting from predation,longer environmental stress, competition), may also requiremodification of chamber height and width.

This interpretation is supported by the present observa-tions that for the investigated specimens the septal-distancesequence always matches the volume sequence with highsignificance. This means that the septal distance is theprimary parameter for defining the size of each chamber.As shown, all major deviations in the volume sequence arealways visible in the septal-distance sequence and at thesame position.

For involutely coiled species (e.g., P. venosus), chamberwidth also clearly matches the volume sequence (Fig. 2I).The alar prolongations (in the sense of Hottinger, 2006) arethus probably used to create the needed lumen toaccommodate cell growth by varying their extensionaround the previous whorl. Where alar prolongations areabsent (e.g., O. ammonoides), the correlation betweenchamber width and volume is consequently very weak.

In all investigated specimens, negative peaks in theresiduals are much more abundant than positive peaks.This is logical because, during growth, a rapid increase inprotoplasm would be accommodated by increased rate ofchamber formation, thereby avoiding creation of chamberswith larger lumina. In contrast, under stress, there may beinsufficient protoplasm to build normal-sized lumina,resulting in chambers with smaller lumina.

According to logarithmic and Archimedean spirals,however, chamber heights have fixed geometries andcannot be modified unless a major accident disturbs thegrowth rate. Based on an Archimedean spiral that keepschamber heights constant, the increase in cell volumecannot strictly follow a logistic growth connected with alogarithmic spiral. As clearly evident in N. fabianii, the needto grow faster and/or with larger lumina induces anincidental increase in chamber height; this increase is

reflected in test growth by a sequence of linear functionswith stepwise increasing additive constants, thus approxi-mating exponential growth. Therefore, an abrupt positiveshift in chamber height can be a successful solution toaccommodate the increased volume for a longer time.Consequently, the correlations are good between volumeresiduals and chamber height and width for both fossilspecimens featuring an Archimedean coiling geometry.

Stronger deviations were observed in initial chambers foralmost all standardized residuals in chamber widths. Even ifthe proloculus and the deuteroloculus are not included inthe sequences, the first three or four chambers may embracethe relatively larger proloculus by increasing their width forbetter accommodation. This stabilizes them in creating thefirst part of the marginal chord where the main canalsystem is located.

CONCLUSIONS

The chamber sequence in nummulitids mirrors individualgrowth and makes such growth measurable by calculatingthe chamber lumina using a microCT scan. Such measure-ments accurately show the growth form of the foraminiferalcell and mark the deviation from a latent mathematicalgrowth function due to external and internal factors.

Minor disturbances in cell growth and all deviations inoscillatory growth are manifested in septal distance. This isbecause chamber height and width strictly follow themorphogenetic program to retain test shape, with veryfew possibilities for stronger deviations from that shape.Observed deviations in chamber height and width arealways related to growth impedances caused by majorfactors such as competitors, predators, or adverse localecological conditions.

This makes studying the chamber-volume sequences—and their relationship to septal-distance, chamber-width,and chamber-height sequences—of primary interest in cellbiology and shell morphology. Using residual statistics andtheir standardization for all measured parameters can bepivotal to assess deviations and to quantify them in relationto overall cell growth. Quantifying septal distances andchamber heights and widths on other specimens might showhow they vary during growth and how much they candeviate from given mathematical growth models toaccommodate the needed cell volume. These results areimportant to define those characters that are correlated tothe volume sequence and therefore act as proxies forecological variations and environmental reconstructions.This approach also helps separate these characters fromthose whose sequence is more constant and is thereforebetter suited for taxonomic identification and for phyloge-netic lineage reconstructions, if measured on entire popu-lations.

The results of this study show that septal distances andtheir sequence during the cell’s life can provide muchinformation on the paleobiology of the cell itself as they arewell correlated to the volume sequence. Using three-dimensional studies to identify the optimum parametersto study in two dimensions, including oriented thin-sectionmeasurements, can increase the speed at which multiplespecimens can be studied in equatorial sections.


The study of chamber height and width can also provideimportant information on major environmental changesreflected in volume growth in taxa possessing a logarith-mic spiral or extended alar prolongations. In shellsfollowing Archimedean spirals (i.e., almost all fossilnummulitids), chamber width and height can be used fortaxonomic identifications and for systematic lineagereconstructions.

ACKNOWLEDGMENTS

This work was developed within the project P 23459-B17‘‘Functional Shell Morphology of Larger Benthic Forami-nifera’’ of the Austrian Science Fund. We thank GerdMuller and Brian Metcher, University of Vienna, formaking the use of MicroCT possible. We thank theInstitute of Palaeontology, University of Vienna, whichprovided a dedicated working station to analyze thedatasets. Michael Stachowitsch, University of Vienna,revised the English text as a native English-speakingscientific copy editor. We thank four anonymous reviewersfor their comments. Special thanks are due to PamelaHallock and Paul Brenckle for their help in preparing themanuscript.

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Received 13 February 2012Accepted 11 October 2012


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