Troy A. Dexter [email@example.com], Department of Geosciences, Virginia Polytechnic Institute, Blacksburg, VA 24061, USA; Colin D. Sumrall [firstname.lastname@example.org] and Michael L. McKinney [email@example.com], Department of Earth and Planetary Sciences, University of Tennessee, Knoxville, TN 37996-1410, USA; manuscript received on 03/09/2007; manuscript accepted on 24/02/2008.
The surface area of blastoid respiratory structures (hydrospires) shows positive allometry during ontogeny to offset the exponential increase in volume. Transverse cross-sections of thecae through an ontogenetic series in two blastoid species, Pentremites pyriformis and Pentremites godoni, were used to calculate surface area and volume within the hydrospires. These two congeneric species showed similar allometric change in hydrospire surface area, but this change was accomplished using different mechanisms. In P. godoni, increased hydrospire surface area was developed through an allometric increase in hydrospire length while keeping hydrospire fold count constant. In contrast, P. pyriformis, showed little allometric change in hydrospire length, but instead increased the number of hydrospire folds ontogenetically. This study shows that developmental patterns can be modified in different ways in order to solve the same functional problem.
Blastoids are a group of extinct, stalked echinoderms that range from Late Ordovician to Late Permian (ca. 470–251 Ma). The only modern echinoderm analog to blastoids is the generally deep water, stalked crinoids. Modern crinoids, however, respire through tube feet, or podia, located externally on the feeding arms. In contrast, most blastoid respiration occurred by pumping ambient seawater through the hydrospires within the theca in a method known as endothecal respiration. Consequently, comparisons between the mode of respiration in modern crinoids and extinct blastoids are difficult. On the other hand, blastoid hydrospires represent a general model for endothecal respiration common among many groups of extinct, stalked echinoderms including hemicosmitid rhombiferans, glyptocystitoid rhombiferans, ‘rhombbearing’ crinoids, and parablastoids (Paul 1968; Sprinkle 1973, 1982; Brower 1999; Sumrall & Schumacher 2002). This study, therefore, addresses a generalized respiration type common to many Palaeozoic echinoderm clades.
Biomechanics of extinct animals are difficult to quantify because of the lack of preservation of soft anatomy. In blastoids, such as the spiraculate Pentremites used here, biomechanical studies are facilitated by the mineralized nature of the respiratory structures called hydrospires. Hydrospires are thin, porous folds of high Mg-calcite stereom on the thecal interior (Macurda 1968). Ambient seawater was pumped into hydrospire pores along the edge of the ambulacra, adaxially through the hydrospire folds underneath where oxygen diffusion occurred (Fig. 1). The water was then pumped adorally through bulbous terminals at the end of the hydrospires and exited through spiracles bordering the peristomial opening (Fig. 1). During diagenesis, the hydrospire folds are generally preserved either through filling of the theca by micritic sediment and/or the precipitation of syntaxial calcite spar within the thecal interior. Accordingly, the measurement of surface area and the quantification of respiratory capacity can be calculated through serial sections.
Previous investigations of hydrospire surface area have suggested a linear relationship with thecal volume during ontogeny (Macurda 1965, 1968). However, because respiration takes place across the surface area of the hydrospires, a curvilinear relationship is expected if the hydrospires are to compensate for the cubic rate of increase in body mass (Becker et al. 2000).
By increasing the sample number from previous investigations, this curvilinear relationship becomes more apparent. There are a number of difficulties involved in interpreting the effects of changing respiratory capacity throughout ontogeny. In blastoids, thecal morphology is largely a function of the length of the ambulacra that lie along the theca. The length of the ambulacra, however, not only controls the efficiency of food gathering functions of the organism, but also controls the length of the hydrospires. Regardless, the respiratory structures have to maintain the metabolic requirements of the blastoid as morphology evolves during ontogeny. By studying the hydrospires of two different morphotypes of Pentremites, different solutions to compensate for increased respiratory requirements during ontogeny can be accessed for the change in morphology.
Respiration in blastoids
Assuming isometry (no change in shape during ontogeny), as an organism grows, linear dimensions increase at a linear rate, surface areas increase at a squared rate, and volumes increase at a cubic rate (Schmidt-Nielsen 1984). Consequently, during ontogeny, certain properties of organisms should vary linearly (height, length, width), at a squared rate (diffusional membranes, external casing), or at a cubic rate (volume, mass, food intake, respiration). In organisms with isometric growth, an increase in length will cause the surface area to increase as a square function and the volume to increase as a cubic function (Schmidt-Nielsen 1984; Becker et al. 2000). In a living organism, an increase in volume should be proportional to an increase in the number of cells within that individual. Therefore, if the nutrient requirement for each individual cell remains constant, an increase in volume of an individual should produce a cubic relationship for nutrient uptake relative to the length of the individual. However, because diffusion occurs over the surface area of respiratory organs, it should increase as a squared rate relative to the height of the animal unless positive allometric changes in size and shape occur in these organs (Schmidt-Nielsen 1984; Becker et al. 2000). Therefore, ontogenetic increases in blastoid thecal volume should be met with a concomitant increase in respiratory surface area to allow for the metabolism of the increased nutrient uptake.
The generalized respiratory design of blastoids was endothecal respiration in which cilia along the hydrospire walls pumped seawater through thin stereom folds within the theca where gas exchange occurred (Fig. 1). Within the spiraculate blastoid Pentremites, incurrent pores (hydrospire pores) were positioned between pairs of side plates along both sides of the ambulacra (Fig. 1). These pores enter paired hydrospires positioned below each ambulacrum (Figs 1, 2).
The hydrospires were separated into corrugated folds numbering between one and nine. The number of folds is typically maintained and used as a diagnostic characteristic to separate species (Figs 1, 2) (Macurda 1968; Beaver 1968). Water passing in through the hydrospire pores would have been transported inward and upward along these thin, porous hydrospire folds and out through the spiracles surrounding the peristomial opening (Fig. 1) (Macurda 1965). The thin walls of the hydrospire folds were constructed of permeable, mesh-like stereom through which respiration took place (Fig. 2) (Macurda 1968; Beaver 1996). To increase respiratory efficiency, it is likely that coelomic fluid was transported aborally within the visceral cavity along the walls of the hydrospire folds as suggested by Paul (1968) (Fig. 1). This counter-current flow of coelomic fluid versus sea water would increase the gradient between oxygen-depleted coelomic fluid and oxygen-rich sea water, thus increasing the rate of oxygen and carbon dioxide diffusion through the hydrospires (Paul 1968). The significant difference in oxygen diffusion efficiency makes it highly probable that counter-current respiration was employed in blastoids. Because diffusion of gases occurred along the hydrospire folds, the surface area of the hydrospire folds was likely the limiting factor in the amount of oxygen that could be absorbed.
Consequently, increases in total respiratory surface area resulting from exponential increase in body volume during ontogeny could be accomplished by changing any of three parameters for hydrospire folds: number, length or shape (invagination). Previous investigations have indicated that hydrospire fold number tends to remain constant throughout ontogeny within spiraculate blastoids (Macurda 1968; Beaver 1968; J. Sprinkle, personal communication, 2004), although hydrospire fold increase is common in fissiculate blastoids such as Hadroblastus, Koryschisma and Phaenoschisma (Macurda 1968; Sprinkle & Gutschick 1990).
Localities and samples
Two species of the genus Pentremites were collected for this study; Pentremites godoni (Defrance) and Pentremites pyriformis (Say). These species were selected for their close phylogenetic relationship and their different growth strategies resulting in dissimilar morphotypes (Galloway & Kaska 1957). Both populations were collected from individual localities of Late Mississippian, Chesterian Age.
Samples of P. godoni were collected from the Lower Chesterian, Ridenhower Formation of the Paint Creek Group at Floraville, Illinois (Beaver and Fabian 1998). Outcrops were located along the banks of a streambed located at either side of the Prairie Du Long Creek. The outcrops were composed of highly weathered, fissile, fossiliferous, light green shale with minor limestone interbeds. Blastoids found at this locality were primarily P. godoni with fewer P. pyriformis.
Samples of P. pyriformis were collected from the Indian Springs Shale Member of the Big Clifty Formation in the Stephensport Group at Sulpur, Indiana (Blake & Elliott 2003). Outcrops were located at road cuts around the intersection of Interstate 64 and Indiana Highway 37. The outcrops were composed of fossiliferous grey shale interbedded with limestone.
Blastoids at this locality were predominantly P. pyriformis with fewer P. godoni. Blastoid specimens at both localities displayed excellent external preservation with limited flattening, distortion, or silicification. Blastoids were preserved with secondarily precipitated calcite spar with or without geopedal micrite infilling. P. godoni is characterized by long, wide ambulacra that extend most of the height of the theca (Galloway & Kaska 1957) (Fig. 3A–C). P. pyriformis has much shorter ambulacra relative to the theca (Galloway & Kaska 1957) (Fig. 3D–F). P. godoni tends to have a wider, squatter theca with an obtuse pelvis angle whereas P. pyriformis tends to be thinner (nearly subconical) with a sharp pelvic angle (Galloway & Kaska 1957) (Fig. 3). In P. pyriformis, the vault-height to pelvis-height ratio (V/P ratio) tends to remain the same throughout ontogeny, growing from 1.0 to a maximum of 1.5 (Waters et al. 1985). P. godoni has a strong allometry in ambulacra with a V/P ratio that starts at around 1.0 in juveniles and increases from 4.0 to 10.0 in adults (Waters et al. 1985). For both samples, specimens belonging to each species were segregated by the above criteria so that each sample was monospecific. This was only problematic in the smallest of specimens because morphometric differences increase ontogenetically. However, limited measurement resolution was a larger source for error than species identification in very early developmental stages.
Specimens were collected individually and from bulk samples gathered at the two localities. All the blastoids were sorted by completeness by discarding fragmented and disarticulated samples because they would have been unacceptable for hydrospire or volumetric measurements. The few flattened or distorted specimens were also removed from the sample population, as they would not have accurately preserved the measured features.
Samples were measured for thecal height, thecal width, pelvis height, vault height, ambulacral length, and mass, and volume was calculated. Mass was measured with 0.1-µg resolution. Volume for the entire theca was calculated by converting the mass of the sample using the density of calcite or 2.71 g cm−3. Although echinoderm stereom is composed of high Mg-calcite, the volume calculated from the mass used the density of pure calcite. Magnesium comprises little of the total mass in high Mg-calcite (approximately 4%). Furthermore, the pores in the stereom are permineralized, and the entire visceral cavity is infilled with calcite, leaving only a minute amount of magnesium in the total mass. The samples selected from the population also had very little silicification present externally. Any minor amount of silicification would not affect the results greatly because the difference in density between silica and calcite is minimal (2.63 g cm−3 compared to 2.71 g cm−3).
The specimens were sectioned transversely, perpendicular to the oral–aboral axis to examine the internal hydrospires. Each section was made by attaching the basal portion of the theca to a glass slide and grinding material from the oral side of the theca. This left a flat internal surface and the remaining aboral portion of the theca, destroying the sample in the process. A low-speed rock saw with a micrometre and a 0.5-mm-thick diamond blade was used to remove sections from the samples. The micrometre was used to determine the thickness of each section removed.
Sections were removed using consistent thicknesses with the exception of the top and occasionally the bottom of the specimen where the section interval was increased to add detail. Hydrospires show extensive change near the top of the specimen where the hydrospire folds are merging together to form the spiracles. Small specimens showed the hydrospires grading down in size rapidly at the bottom of the ambulacra. If the consistent, thicker sections were removed through these locations where the hydrospires go through considerable change, the measurements would underestimate the total hydrospire surface area. Occasional increases in the thickness of sections occurred when the specimen accidentally slipped off the slide arm attachment of the rock saw and a new cut was needed to create an even surface. Seven specimens at an early ontogenetic stage (three P. godoni and four P. pyriformis) were embedded entirely in epoxy and ground by hand because they were too small for the rock saw.
Slice thickness was measured directly on the specimen using calipers. Several of the samples were unmeasurable because the hydrospire folds were not clearly preserved within the theca. The best specimens had sparry calcite infilling within the visceral cavity. Problematic specimens included those with geopedal micrite fill that obscured the outline of the hydrospires, or recrystallization of the internal cavity that destroyed the hydrospires. A sample was considered unusable unless a minimum of three hydrospire fields were visible. Of 48 specimens sectioned in this study, 33 were useable, of which 18 were P. pyriformis and 15 were P. godoni.
Samples were photographed using a digital camera after each serial section. The ambulacrum was marked on the slides, and the position of each slide was kept consistent. Each picture was scaled to calibrate measures in the image analysis software. Approximately ten sections were analysed throughout the length of the hydrospires for each sample but the number varied with the height of the specimen being sectioned.
The images captured for each sample were measured using the image analysis program Scion Image (Scion Corporation, Frederick, MD, USA). For each section, all hydrospire folds along each half of the hydrospire pair as well as the hydrospiralium cleft on a single hydrospire were outlined, and measurements of area and perimeter were recorded. Each serial section of an individual blastoid generates a truncated cylinder in which the surface area and volume were calculated by multiplying the area and perimeter by the averaged section thickness. These cylinders were then summed to determine the total hydrospire surface area and volume for the specimen. A corrected thecal volume was calculated by subtracting the total hydrospire volume from the total thecal volume (calculated from the mass) for each individual. Because the hydrospires were cavities open to the outside environment, their volume would not add to the respiratory need of the individual. This adjusted volume is a closer representation of the total organic volume of the theca. In order to determine the growth factors during ontogeny for both species, power functions (exponents of log-log plots) were calculated. The power function, Y = a Xb, uses Y and X as the variables (the characteristics under comparison), with a as the intercept and the exponent b as the ratio of allometric growth (Huxley & Teissier 1936; Gould 1967, 1968; Brower 1987; see also Gayon 2000 for the history of allometry). The exponent of allometric growth represents the change in the rate between Y and X. Thecal height was used to determine relative stage of ontogeny among the individuals in both species.
The primary morphological distinctions between P. godoni and P. pyriformis are the shape of the theca and the length of the ambulacra. P. godoni shows strong positive allometric change in ambulacral length, whereas P. pyriformis shows weak positive allometric change. Ambulacral length to thecal height was significantly different between the species (P < 0.0001) (Fig. 4A). Thecal height to volume for both species shows the expected cubic relationship (Fig. 4B). The power function for P. pyriformis was Y = 1.4 X3.0 and for P. godoni was Y = 2.8 X2.9, where Y was total thecal volume and X was thecal height. The exponents of growth for P. pyriformis and P. godoni were 3.0 and 2.9 respectively, both of which were extraordinarily close to the expected cubic rate of volume increase.
Hydrospire surface area increased at an exponential rate compared to height (Fig. 5A). The equation of the power function for P. pyriformis was Y = 0.71 X2.5 and the equation for P.godoni was Y = 0.76 X2.7 where X is the height and Y is the hydrospire surface area (Fig. 5A). The r2 values for the power function for P. pyriformis was 0.9746 and for P. godoni was 0.9874.
The ratio of hydrospire surface area to volume was not significantly different between the two species (P = 0.261). When hydrospire surface area was compared to volume, linear regression produced the equation Y = 0.94 (± 0.03)X + 26.21 (± 21.37) for P. pyriformis and Y = 0.83 (± 0.03)X + 63.98 (± 32.00) for P. godoni (Fig. 5B). The r2 correlation for the linear regression in P. pyriformis was 0.9833 and for P. godoni was 0.9835 (Fig. 5B). When the curve of the graph was fit to a power function, the equation for P. pyriformis was Y = 2.9 X0.84 and for P. godoni was Y = 2.1 X0.88, where Y is the hydrospire surface area and X is the thecal volume (Fig. 5B). The exponent of a power curve where X is the volume and Y is the hydrospire surface area produced an exponent of 0.84 for P. pyriformis and 0.88 for P. godoni. The r2 correlation of the power function was 0.9816 for P. pyriformis and 0.9882 for P. godoni. The linear r2 value of the line for P. pyriformis is 0.9849 and for P. godoni is 0.9840. The comparison of hydrospire surface area to mass presented similar results as volume, which would be expected since volume was derived from mass. The exponent of a power curve where X is the mass and Y is the hydrospire surface area produced an exponent of 0.83 for P. pyriformis and 0.88 for P. godoni. The r2 correlation for the power function was 0.9834 for P. pyriformis and 0.9888 for P. godoni.
One unexpected result of this study is the documentation of an increasing number of hydrospire folds in P. pyriformis late in ontogeny. All blastoids add folds early in ontogeny, but it is generally assumed that except for rare cases, blastoid hydrospire folds reach a fixed adult number early in ontogeny. There were a limited number of samples in each size category for this study. P. godoni developed five hydrospire folds at a minimum height of 8.7 mm and maintained this fold number through maturity (Fig. 6A–C). In contrast, P. pyriformis developed additional folds at the mature stages of ontogeny, one fold at a time (Fig. 6D–F). From thecal heights less than 13.5 mm, P. pyriformis had five or six hydrospire folds. All samples above a thecal height of 13.5 mm in P. pyriformis had six to eight hydrospire folds depending on the individual (Fig. 6E, F).
Hydrospire surface area
Using thecal height as a proxy for ontogenetic stage, many characters approximate isometric growth. In P. pyriformis, thecal width, ambulacral length and vault height all increase at a linear rate. The pelvis height in P. pyriformis was nearly isometric, confirming previous studies of P/V ratio throughout ontogeny (Waters et al. 1985). The pelvis height in P. godoni, however, showed no correlation with thecal height. There is a slight trend of increasing pelvis height with thecal height at the juvenile stages, but this pattern is lost in mature stages as a result of allometric growth in the vault. Pelvis shape in mature P. godoni grew outward in width with little to no increase in height. Visual inspection suggests that intraspecific variation controls pelvis height in mature specimens.
The theoretical Euclidean relationship between height and volume in an isometric shape should correspond to a cubic increase in volume. Although certain characteristics of blastoids display considerable allometry, these data suggest that the individuals as a whole are rather isometric. Since volume increases at a cubic rate relative to height, the expected allometric exponent is three. The experimental result is extraordinarily close to the theoretical expectation with the exponent of P. pyriformis and P. godoni calculated to be 3.0 and 2.9, respectively (Fig. 4B). When hydrospire surface area was compared to height, the expected exponent assuming pure isometric growth would equal 2.0. However, the exponents were 2.5 and 2.7 for P. pyriformis and P. godoni, respectively (Fig. 5A). In other words, height and volume progressed isometrically during ontogeny, whereas surface area of the hydrospires shows strong allometric growth in both species. We suggest that the positive allometry in the hydrospires was an adaptation to compensate for the increased volume with respect to surface area seen in ontogeny.
Comparing hydrospire surface area volume, the allometric exponents showed somewhat negative allometry with values of 0.84 for P. pyriformis and 0.88 for P. godoni. Although the results indicate that volume is increasing more rapidly than the hydrospire surface area, the rate of increase is not far from the expected value of 1.0 if surface area is synchronously changing with volume.
It is possible that thecal volume exceeds the hydrospire surface area because thecal volume is not a perfect proxy for the total respiratory need. A more precise measure of the total respiratory requirement for an individual would be the total visceral volume within the theca where all the organs are held. The respiratory system was necessary for providing oxygen to all the cells not in contact with seawater; consequently, external plates, brachioles, stems and rootlets should be excluded. The visceral cavity was also not composed entirely of living tissue.
Modern echinoderms transport coelomic fluids within the visceral cavity to carry oxygen and nutrients to the cells (Brusca & Brusca 2003). These fluid-filled areas would not add to the total metabolic requirement as they lack cells. Furthermore, the digestive system was open to the external water column and filled with food; therefore, it also lacks any mass that would add to respiratory need. Because these structures are not preserved and the entire volume of the theca was measured, the volume was most likely overestimated.
Another issue to consider is that thecal volume to hydrospire surface area calculations included a wide range of ontogenetic stages. It is believed that blastoids had a free-swimming larval stage before they developed into their stalked, hydrospire-bearing stage (Sevastopulo 2005). The minute size of these early stages would have allowed oxygen to passively diffuse into the visceral cavity, and it is likely that diffusion through the plates provided oxygen even into the later juvenile stages. Consequently, the theca attains some volume prior to the development of hydrospires resulting in the curve not passing through the origin (Fig. 5B). Because of the lack of hydrospires in the early post-larval stages, the addition of the juveniles likely decreases the precision of the thecal volume to hydrospire surface area relationship in adult forms.
Hydrodynamic flow through the hydrospires was considered to be equivalent for both species throughout ontogeny. The limiting factor on how rapidly water could be transported into the respiratory system would likely be the diameter of the hydrospire pores. Visual inspection between the species of individuals at the similar ontogenetic stages seemed to indicate that hydrospire pore size was comparable. It is possible that oxygen diffusion became more efficient at older stages as flow rate through the wider hydrospire pores becomes less restricted. However, the hydrospire surface area in P. godoni was a closer match to volume than P. pyriformis. P. godoni had longer ambulacra and thus an increased number of hydrospire pores. If a decrease in restriction in the hydrospire pores allowed for an increase in oxygen uptake, P. godoni would be expected to have less surface area relative to volume than P. pyriformis. Because this is not the case, it appears as though hydrodynamic flow remains unchanged throughout ontogeny.
Positive allometric growth in hydrospire surface area can be accomplished in three ways; increasing the length of the hydrospires, increasing the number of hydrospire folds, or increasing the complexity of the hydrospire folds. The hydrospires extend slightly below the spiracles to the bottom of the ambulacra, and because the hydrospire folds are pinned to the ambulacra, the ambulacral length is a proxy for the length of the hydrospires. The ambulacra, and consequently the hydrospires, are appreciably longer in P. godoni than in P. pyriformis (Fig. 3) with a substantial concomitant ontogenetic increase in vault to pelvis ratio in P. godoni compared to virtually no change in V/P ratio in P. pyriformis (Waters et al. 1985). Even so, the morphotypes are not significantly different in the relationship between hydrospire surface area and thecal volume. The morphological difference between the two species suggests that another factor was involved in ontogenetic increase in hydrospire surface area.
In P. godoni, the ambulacra increase in length with positive allometry allowing the hydrospire length to increase disproportionately with thecal height (Figs 3, 4A). This occurs because the height growth vector in P. godoni is predominantly in the vault. Hydrospire fold number was maintained as hydrospire length increases through later ontogeny (Fig. 6A–C). However, in P. pyriformis, the ambulacra length shows a nearly isometric increase and consequently little disproportionate increase in hydrospire length during ontogeny. This occurs because the isometric growth in P. pyriformis is equally contained in both the vault and the pelvis through the ontogeny. With shorter hydrospires, P. pyriformis ontogenetically increases hydrospire surface by adding new hydrospire folds late in ontogeny (Fig. 6D–F). This is contrary to the previous investigations, suggesting that hydrospire fold number tends to remain constant during ontogeny (Macurda 1968; Beaver 1968; J. Sprinkle, personal communication, 2004). Any occurrence of increasing hydrospire fold number had previously been observed only in fissiculate blastoid species (Macurda 1968).
Respiratory rates in other echinoderms
When the exponent of hydrospire surface area to mass in P. pyriformis and P. godoni is compared to the metabolic rate to body mass of modern echinoderms, the values fall into a similar range as a majority of these species (Table 1). Most modern species show a slight negative allometry for respiratory rate relative to body mass, with exponents below one (Table 1). This seems to indicate that total respiratory surface area is a valid proxy for determining metabolic rate in ancient echinoderms. The other modern species in Table 1 whose respiratory rates show nearly equal isometry or a slight positive allometry relative to body mass are the asteroid Aphelasterias japonica with an exponent of 1.075 to 1.160 and the holothuroidean Cucumaria frondosa at 1.051 (Ryabushko 1978). One experiment on the echinoid Strongylocentrotus droebachiensis also had the upper range of its exponent reach isometry. The metabolism of these species may be higher than in other species, requiring that oxygen diffuse at a rate matching body mass increase. The other ancient echinoderm listed in Table 1 is the rhombiferan Pleurocystites strimplei in the order Glyptocystitida (Brower 1999). Like blastoids, hemicosmitid rhombiferans, parablastoids, and certain crinoids, glyptocystitoid rhombiferans utilize internal canal structures for respiration (Paul 1968; Sprinkle 1973, 1982; Brower 1999; Sumrall & Schumacher 2002).
Table 1. Respiration rates relative to body size for a variety of echinoderm species and their sources (table modified from Lawrence & Lane 1982).
One would expect the results for Pleurocystites strimplei to be similar to the blastoids and have an exponent slightly less than one, yet this species has positive allometry with an exponent of 1.33 (Brower 1999). Brower's (1999) explanation for respiration increasing at a rate greater than body mass was that this rhombiferan spent much of its time in the sediment and utilized a deposit feeding lifestyle (but see Sumrall 2000 for a refutation of this). It is possible that the metabolism in rhombiferans was much higher for its mass or that oxygen uptake through the pectinirhombs was less efficient. Individual pectinirhombs are arranged along plate boundaries and have an incurrent and excurrent side (Paul 1968). It is possible that external water currents would flow counter to the pectinirhomb currents, making some of the pectinirhombs on an individual rhombiferan far less efficient than others. This would make total surface area of the respiratory structures in rhombiferans an overestimate of actual oxygen diffusion rates.
Hydrospires increase in surface area during ontogeny in a manner that nearly matches the cubic rate of increase in volume. This suggests that the hydrospires were indeed structures designed primarily for respiration. The external structures (brachioles, stem) likely scaled to thecal size through ontogeny, and apparently had no effect on the allometric relationships. Blastoid morphology affects the manner in which positive allometry in hydrospire surface area was attained. For P. godoni, positive allometry of the ambulacra allows for positive allometry in hydrospire length. In P. pyriformis, ambulacral length does not increase markedly during ontogeny, and this species accommodates the nearly isometric hydrospire length by increasing the number of hydrospire folds throughout ontogeny. This study indicates that increasing hydrospire fold number in later ontogeny is likely more common in spiraculate blastoid species than previously suspected. Spiraculate species with low V/P ratios have to maintain metabolism by increasing hydrospire surface area, and the limited length would tend to require increasing fold number. Hydrospire surface area to volume measurements in blastoids give respiratory rate values that fall well within the range of modern echinoderms. This indicates that using the surface area of the respiratory structures in ancient stemmed echinoderms is a valid proxy for determining respiratory capacity.
This project was conducted as part of the senior author's master's thesis at the University of Tennessee, Knoxville. Support for this project was provided by the Geological Society of America's 2005 Student Grant and the Paleontological Society's Stephen Jay Gould Grant. Further assistance for this research was provided by the Mayo Foundation and the Department of Earth and Planetary Sciences at the University of Tennessee. We would like to thank Ed Perfect for his assistance with the revisions and his knowledge of hydrodynamics which was necessary for the interpretation of hydrospire biomechanics. Larry Taylor, Allen Patchen, Bill Deane, Kula Misra, Claudia Mora, and Zheng-Hua Li all graciously allowed the use of their equipment, much of which did not survive this project. We would also like to thank Linda Kah, Jonathon Evenick, Jeff Nettles, and Whitney Kocis for their help and advice on this project. Furthermore, the numerous talks with Johnny Waters and James Sprinkle about the project's focus and potential difficulties were essential for its completion. We would also like to thank Michal Kowalewski, James Schiffbauer, and Peter Voice for reviewing early drafts of this paper.