Cummins, Hays, Powell, Eric N., Newton, H. J., Stanton, Robert J., Jr. & Staff, George : Assessing

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1 Assessing transportation by the covariance of species with comments on contagious and random distributions HAYS CUMMINS, ERIC N. POWELL, H. J. NEWTON, ROBERT J. STANTON, JR. AND GEORGE STAFF IJTHAIA Cummins, Hays, Powell, Eric N., Newton, H. J., Stanton, Robert J., Jr. & Staff, George : Assessing transportation by the covariance of species with comments on contagious and random distributions. Lethaia, Vol. 19, pp Oslo. ISSN The paleoecologist must be able to distinguish a transported assemblage from an in situ one. A method is proposed to assess whether the post-mortem transport of individuals affected their observed spatial (horizontal) distribution. The spatial distribution of a species can be random or contagious. The spatial distribution of individuals of a species in the death assemblage produced by the cumulation of many temporally discrete inputs will be random if the individual inputs are random and contagious if the inputs are contagious. The spatial distribution patterns of several species should not covary in the absence of physical disturbance regardless of their own distributions, however. The degree of covariance between individuals of several species of similar hydrodynamic propensity is dependent on the amount and intensity of postmortem movement. The more species that covary, and the larger the size classes that covary, the more likely that transportation played an important role in the species' distribution patterns. Conversely, the absence of covariance suggests that, for at least some species, biological factors determined the species' spatial distributions. Similarly, covariance of vertical distribution patterns might suggest homogenization. by bioturbational or physical mixing. 0 Paleoecology, transportation, patchiness, distribution, death assemblage. Hays Cummins, Department of Oceanography; Eric N. Powell (person to whom reprint requests should be addressed), Department of Oceanography; H. 1. Newton, Department of Statistics; Robert J. Stanton, Jr., Department of Geology; George Staff, Department of Geology, Texas A&M University, College Station, Texas 77843, U.S.A.; 7th November, Taphonomic processes, such as dissolution (Alexandersson 1979; Koch & Soh1 1983), shell breakage (Driscoll & Weltin 1973; Vermeij 1979) and transportation (Straaten 1956; Trewin 1973) may affect the composition of the fossil assemblage substantially (Boyd & Newell 1972; McCarthy 1977; Bosence 1979). Often, transportation is a critical factor. Both physical factors such as storms and tidal currents (Wilson 1967; Ye0 & Risk 1979) and biological factors such as movement of shells by hermit crabs (Fotheringham 1975; Hazlett 1981) may be involved. Transportation may be primarily lateral (horizontal) or, in the case of bioturbation for example, vertical mixing also may be important (Straaten 1952; Clifton & Hunter 1973; Trewin & Welsh 1976). The degree of shell transport in the marine environment depends upon a shell's hydrodynamic properties such as shape, size and density and the type and strength of the transporting agent (e.g. currents, waves) (Menard & Boucot 1951; Futterer 1978). To interpret the paleoecology of a fossil assemblage requires an assessment of the role transportation played in the assemblages' composition. Boucot (1953), Boucot et al. (1958), Johnson (1960), Fagerstrom (1964) and others used the size-frequency distribution of species to distinguish a transported assemblage from one buried in situ. Leftlright valve ratios (Kornicker et al. 1963), the degree of disarticulation of bivalves (Boucot et al. 1958), the orientation of valves (Salazar-Jimenez et af. 1982), and evidence of abrasion (Driscoll 1967) also were employed. All of these methods proved useful under some circumstances, however Craig & Hallam (1963), Fagerstrom (1964), Trewin (1973), Carter (1974) and others questioned their effectiveness in certain situations. Here, we describe a method for assessing the presence and importance of transportation based on the covariance of species. By the term covariance, we do not imply any statistical result derived from the use of the statistical method designated as analysis of covariance; rather, we use the term in a more general way to indicate coincident variation of species' abundances whereby two or more species' abundances vary similarly from sample to sample. That is, a sample's rank derived from the abundance of one species would be similar to its rank derived from the abundance of a second species. The method is based on the fact that animals typically live contagiously on 1 Lethaia 1/86

2 2 Hays Cummins and others the sea floor, but normally few species distributions are dependent on that of any other. [We use the term contagious as used by Elliott (1977) to indicate a patchy distribution statistically significantly different from what would be expected by a random dispersion of individuals]. Thus, the in situ remains of any one species rarely should have the same spatial distribution as those of any other. If species covary (that is, if two or more species distribution patterns are similar resulting in similar relative abundances in all samples of a death or fossil assemblage) and if a biological interpretation such as commensalism is precluded, then the presence of covariance indicates that transportation determined the species spatial distribution. The degree of covariance in an assemblage provides an estimate of the extent of this physical disturbance. Most death assemblages represent a time-averaged cumulation of temporally discrete inputs from the living community. Probably, each input has a different spatial distribution because consecutive generations of animals are rarely distributed identically on the sea floor. To describe this method, we first examine how the cumulation of these temporally discrete distributions determines the final cumulative or time-averaged distribution of a species in the death assemblage. Then, we examine the significance of the covariance of several time-averaged distribution patterns within a restricted area of the sea floor. Finally we make a number of verifiable predictions concerning the degree of physical disturbance in an assemblage based on distribution patterns and the covariance of distribution patterns which can be tested further in appropriate death and fossil assemblages. Methods Site description. - Two shallow-water, marine benthic communities were studied on the Texas coast. One site, located in the Laguna Madre, was just offshore of Padre Island near South Bird Island. The other site, located in Copano Bay, was near the mouth of the Aransas River. Hedgepeth (1947), Brown et al. (1976) and McGowen et al. (1976) gave a general description of the geology and oceanography of the area. Powell et al. (1982, 1984), Staff et al. (1985) and Cummins et al. (in press) gave details of the sampling location and procedure, environmental parameters of the study sites and additional data on LETHAIA 19 (1986) the composition and biomass of the living community and death assemblage. The Laguna Madre site had a higher salinity regime over the study period, usually above 30%; sediment was a fine to medium well-sorted sand. Ripple marks were present at every sampling period and windrows of grass and associated shell debris were common on the beach in most months. The Copano Bay site frequently experienced salinities below 10%; sediment was a muddy sand, 18% silt and clay by weight. The upper 1 4 cm, however, was a sandy mud: 89.6% by weight was below 120 pm in size. In general, current and wave energy were less than at the Laguna Madre site. Ripple marks were rarely present, for example. Cummins et al. (in press), however, found that considerable sediment erosion and deposition, confined to the upper 1 4 cm muddy layer, occurred during the study period. McGowen et al. (1976) considered both areas to be depositional over the long term. Water level at both sites frequently was affected substantially by wind tides generated by storms. Both sites were subjected to considerable sediment resuspension and movement during these intervals. Thus, storms probably were the primary factor producing shell transport at both sites. Sampling procedure. - Both sites were sampled at six-week intervals. Both sampling locations were approximately 50 m offshore in about 1 m depth. In each case, a 100 m sampling line was established. Each sampling occasion, two transects, perpendicular to the line, were chosen randomly and sampled, however no transect was within f 2 m of any other to eliminate any chance of prior disturbance of the death assemblage by the field crew. Sampling of each transect consisted of 2 box cores of 176 cm2 area and 17 cm depth and one 3 m x 24 cm X 5 cm deep surface scrape during the April-October, 1981 period and 4 box cores and one 1.5 m scrape thereafter. The samples were sieved in the field using a 500 pm screen and preserved in a buffered formalinrose bengal mixture. All organisms were identified. Each bivalve and gastropod was measured. The maximum dimension measured for bivalves was the maximum anterior-posterior length; for gastropods, the length from apex to abapical tip. For the death assemblage, whole organisms were defined as those for which both maximum length and maximum width (height for bivalves) could be measured. Others were designated as fragments if

3 LETHAIA 19 (1986) Assessing transportation in fossil assemblages 3 Mulinia lateralis (All size classes) 70( r 3 50 N E v) - m 3 U.-.- > U 600 5oa 40C I z X u- U I300 0 L- a, a E 3 z 2oo U U u- 0 L a, loo a E 3 \t 50 0 Apr May June Aug Sept Oct Dec Jan Mar Apr June July Sept Oct Fig. I. Temporal changes in the number of Mulinia loferulis in the living community and death assemblage at the Laguna Madre site. beaks (for bivalves) and apexes (for gastropods) were intact. For bivalves, left, right, and articulated valves were enumerated separately. To calculate the total number of valves collected, articulated valves were counted twice, free left or right valves once each (Powell et al. 1984). Statistical techniques. - Covariance was assessed in two ways: The Spearman s rank correlation and a technique based on the Kolmogorov-Smirnov test described by Powell et al. (1984). The Spearman s rank correlation (two-sided tests in all cases) (Daniel 1978) was used to assess the covariance of species by using the sampling period totals (the cumulative totals of 4 to 8 box cores or 2 scrapes) as input data. The low number of sam- ples taken per sampling period, and the frequency of samples with few or no individuals of less common species prohibited use of this test on data from each individual box core within a single sampling period. Thus, the method assumes that sampling period to sampling period differences in abundance were produced by the random sampling of species spatial distributions rather than the coincidence of species temporal cycles which also might change their abundances simultaneously. In each test, the null hypothesis stated that the rank orders of the samples based on the number of individuals of species A and of species B were independent; that is, the rank order of the samples for species A was dissimilar from the rank order for species B. The alternative hypoth-

4 4 Hays Cummins and others LETHAIA 19 (1986) I I Apr May June Aug Sept Oct Dec Jan Mar Apr June July Sepf Ocf Dec Jan Mar Apr June July Sepf Oct Fig. 2. Number of individuals collected each six weeks in the death assemblage at the Copano Bay site for four species never collected living during the study period. esis stated that the rank orders of the samples were either directly or inversely correlated; that is, knowing the rank order for species A provided a more or less exact estimate of the rank order for species B. Potentially, this analysis was compromised by the coincidence of temporal cycles in some species. At the Laguna Madre site, for example, most species settled in the living community during the summer. Each produced a pulse in the death assemblage in late summer which decayed during the fall (Fig. 1) (Powell et al. 1984). At the Copano Bay site, the top 1 4 cm of the sediment was periodically eroded and redeposited. Erosion occurred in the fall: deposition occurred in the spring. This affected the number of individuals collected for those species whose depth distribution was not uniform. For example, Acteocina canaliculata s (Fig. 2) abundance increased with depth. Sampling during erosional periods effectively was deeper yielding higher abundances of A. canaliculata in the fall and winter months (Cummins et al. in press). Such temporal cycles, of course, would not be present in fossil assemblages, so that a Spearman s rank analysis could be used without qualification. In our case, we checked the results of the Spearman s rank analysis by a second method that was not affected by temporal events. The method, which could only be used on the most abundant species, consistently supported the Spearman s rank analyses and allowed us to use

5 LETHAIA 19 (1986) Assessing transportation in fossil assemblages 5 the latter test with confidence for less common species as described above. In this analysis, four box cores per sampling occasion were ranked separately from 1 to 4 based on the relative abundance of each of two species. To compare the species, each box core s rank derived from the relative abundance of one species in the 4 samples was subtracted from the box cores rank derived from the relative abundance of the second species. Then, the absolute values of the four differences (one for each box core) for each sampling occasion were summed. If the order of the four box cores is fixed by the ranks of one species (e.g. box-cores a, b, c, d are ranked 1, 2, 3, 4), the four ranks of the second species can be distributed in only 24 ways relative to the first (e.g. for box-cores a, b, c, d respectively: 1, 2, 3, 4 v. 1, 4, 3, 2 etc.) and the sums only can take the values 0,2,4,6 or 8 (4 in the above example). If the first species ranks are randomly distributed with respect to the second (i.e. the relative abundances of the two species are independent), the 24 combinations produce the following frequency of occurrence of sums: 0, 4.17%; 2, 12.50%; 4, 29.17%; 6,37.50%; 8,16.67%. If the two species tend to covary, sums of 0, 2 or 8 should be more common than expected by random chance; 0 and 2 if low ranks of one species coincide with low ranks of a second; 8 if low ranks of one coincide with high ranks of a second. The actual distributions of sums present were compared to the distribution expected from random combinations of the rankings by two-sided Kolmogorov-Smirnov one-sample tests using approximate significance levels for continuous distributions [the test is conservative for discontinuous distributions (Daniel 1978)l. Computer simulation. - Species might be distributed contagiously or randomly on the sea floor. To investigate the effect of distribution patterns on covariance, we developed a model to generate ideal distribution patterns for comparison with the actual data collected in the field. The model generated yearly inputs (one run was one year) into the model s death assemblage that were distributed either contagiously or randomly (as if living individuals died in place and were added to the death assemblage each year) and cumulated these inputs for many years. Each year s distribution pattern was independent of any preceding or succeeding year s. For a random distribution pattern, the GGUW [uniform (0, 1) random number generator with shuffling] random number routine from the International Mathematical and Statistical Libraries, Inc. was used to locate random points (individuals) on a field (sea floor). For patchy distributions, the random number routine was used to locate cluster centers on the field [we used 40 clusters (or cluster centers) per field]. The number of individuals per clump was varied within and between years by generating random numbers and keeping only those which fell within a specified range around each cluster center. Thus, the spatial area of each cluster was the same, but the clusters location on the field (or sea floor) and the number of individuals per cluster varied between runs (i.e. from year to year). After each year, the field was sampled using a grid to determine the spatial location and distribution of individuals. For contagious distributions, the patches were located randomly and independently with respect to the location of the grid. In each case, the sampled field was well within the boundaries of the actual field to exclude edge effects. Variance to mean ratios for the yearly contagious distributions varied between 2.9 and Finally, the number of individuals per year in each sampled grid square was cumulated over many years (we used 50 years = 50 runs). The final output was a model of the distribution of a species in the death assemblage produced by yearly inputs, distributed contagiously or randomly, using the assumption that each year s distribution was independent of all other year s. Probably, this is accurate for yearly species with planktonic larvae which include the bulk of the species collected at both of our collecting sites, but certainly other, longer-lived species might be different. Computer simulations were run for five contagiously distributed species and five randomly distributed species. Different species were determined by using a different randomly-generated seed number at the beginning of run 1 to assure that each set of 50 yearly runs was potentially different from all other sets. Spearman s rank tests were run on the cumulative totals for each species using a grid of 24 squares to provide a sample number of 24. The death assemblage-background description. - Cummins et al. (in press) found that individuals of a species were added to the death assemblage in pulses and that these pulses gradually decayed as taphonomic processes destroyed the constituent individuals. For example, in Fig. 1, a pulse of living individuals of the bivalve Mulinia lateralis

6 6 Hays Cummins and others present in June and August, 1981 produced, by their mortality, a pulse in the death assemblage in August, September and October. During the next six months, this pulse gradually decayed away. At both sites two types of species were present; those that were present as living individuals and which died and proceeded through a pulse and decay mode similar to that of M. lateralis, and those that were never found alive and so had no input into the death assemblage during the study period. Interestingly, these latter species also did not decay measurably; that is, their continued presence in the death assemblage throughout the study period was due to their relative immunity to taphonomic loss rather than to any input from the living community. Curiously, Cummins et al. (in press) also found that species, such as M. lateralis, which were found alive and which did generate pulses in the death assemblage comprised individuals of two types. Some individuals were components of pulses added during the study period. These decayed rapidly after input. Other individuals were present at the beginning of the study and apparently did not decay away. That is, a portion of the individuals of these species also was relatively immune to taphonomic loss. Over a period of 4 to 8 months, most of the individuals added during a pulse disappeared from the death assemblage, but the background number of individuals, those present at the study's inception, never declined measurably. For example, note that for M. lateralis (Fig. l), the number present in the death assemblage prior to the August-October, 1981 pulse is approximately the same as the number present after the pulse had decayed away (March-April, 1982). Decay never removed all M. lateralis from the death assemblage. Only those individuals added in the August-October pulse decayed away. Thus, the death assemblage consisted of two components; a dynamic component composed of individuals added by mortality and destined to decay away and a static component composed of individuals present at the study's inception and conclusion which decayed little if at all during the study. It is unlikely that shells of a species added by pulses of mortality were distributed as was the species' background component. Unfortunately, the two components could not be separated during the analysis. Thus, further consideration of the distribution of species in the death assemblage requires the recognition that the overall distribution of some species remained fairly constant LETHAIA 19 (1986) during the study while the distribution pattern of other species changed gradually as pulses were added and decayed away. Results To determine a species' spatial distribution, we analyzed each individual month's collections as suggested by Elliott (1977) (Table 1). Contagious distribution patterns were the rule. The analysis is provisional, however, because the number of samples (4 or 8) per sampling period is low. To enlarge this number, we considered further species for which data from consecutive sampling occasions could be grouped together as if taken simultaneously because no sampling period to sampling period changes in abundance occurred to compromise the statistical analysis. Necessarily, only those species, indicated by an asterisk in Table 1, which had no recruitment into the death assemblage from the living community during the study, could be used. At Copano Bay, the erosionalldepositional cycle prohibited use of the entire data set for the top six of these species in Table 1. For these, we considered together only Table 1. Statistical results of tests for contagious or random distribution patterns for n = 4 or 8 using the method of Elliott (1977). Data used were total individuals (whole shells and fragments) collected per box core. * indicates cases where data from several sampling occasions were combined (as explained in the text) and a chi-square goodness-of-fit test performed on the combined data. In each case, the distribution was contagious (a for a Poisson distribution; a > 0.20 for a negative binomial distribution). Copano Bay *Caecum pulchellum 'Chione cancellara 'Acreocina canaliculata * Brachidonres exustus * Laevicardium morroni * Diastoma varium * Tagelus plebeius Litroridina sphinctostoma Mulinia lateralis Individual collections Number random Number contagious Laguna Madre 'Anomalocardia auberiana 0 14 Laevicardium mortoni 2 12 Tellina tampaensis 0 14 Diasroma varium 0 12

7 LETHAIA 19 (1986) Assessing transportation in fossil assemblages I Table 2. Numbers of individuals collected per m2 during each sampling occasion. Additional data used herein but reported by Cummins et al. (in press) are indicated by + for all size classes and * for size class mm. Except where noted, all data came from box-core collections only. For bivalves, the number of valves collected is given. Laguna Madre Apr May June Aug Sept Oct Dec Jan Mar Apr June July Sept Oct Acteocina canaliculata All size classes Anomalocardia auberiana' All size classes mm mm [includes scrape samples] % Caecum pulchellum All size classes 1.6S2.64 mm Crepidula convexa* Diasroma varium" mm mm mm Laevicardium mortoni All size classes mm mm mm mm mm mm mm [includes scrape samples] % Mulinia Iateralisf' mm mm mm [includes scrape samples] Mysella planulatat' Syrnola sp. All size classes mm

8 8 Hays Cummins and others LETHAIA 19 (1986) Table 2. (continued) Laguna Madre Apr May June Aug Sept Oct Dec Jan Mar Apr June July Sept Oct Tellina tampaensis' mm mm mm mm mm mm mm [includes scrape samples] Tagelus divisus' mm mm Copano Bay Apr May June Aug Sept Oct Dec Jan Mar Apr June July Sept Oct Dec Jan Acreocina canaliculalat mm 1.6%2.64 mm mm Brachidonres e.rustus Caecum pulchellum' mm mm Chione cancellata' 0.bl.68 mm mm Diasroma varium All size classes mm mm mm Luevicardium mortoni+ Littoridina barred

9 LETHAIA 19 (1986) Assessing transportation in fossil assemblages 9 Table 2. (continued) Copano Bay Apr May June Aug Sept Oct Dec Jan Mar Apr June July Sept Oct Dec Jan Linoridina sphinctosroma mm 1.6q2.64 mm mm mm % % % Mulinia lateralis mm mm % Tagelus plebeius All size classes mm mm samples collected in late spring-early summer when neither erosion nor deposition affected the number of individuals collected. For Tagelus plebeius and Anomalocardia auberiana, we considered all sampling collections together, because neither species was affected by the erosionaudepositional cycle. No distribution calculated from this enlarged data set was significantly different from a negative binomial distribution for any species (Chi-square goodness of fit test, a = 0.10, Elliott 1977). Thus, all of these species were contagiously distributed on the sea floor, as were all other numerically important species at both sites. Table 2 contains data not previously reported by Cummins et al. (in press) that were used, together with the latter data, to generate the Spearman s rank analyses reported in Tables Table 14 contains a key to the full species names as abbreviated in Tables Significant results reported in Tables 3-13 indicate cases where the rank order of the samples for one species was similar to that of another. That is, the two species were present in more or less the same relative proportions in all samples regardless of their absolute numbers. Most species covaried at the Laguna Madre site. If the comparisons are based on the total number of individuals (or valves) collected, only three comparisons show a clear absence of covariance (Table 3). All involved Mulinia lateralis, a species which was present in the living com- munity during the study and was added in pulses to the death assemblage (Fig. 1) (Powell et al. 1984). These pulses, present only periodically during the study, were sufficiently large that their presence and decay determined the rank order of the samples for this species. Other species found living which generated pulses in the death assemblage, such as Tellina tampaensis and Laevicardium mortoni, nevertheless covaried consistently with species with no input or decay (e.g. Anomalocardia auberiana). In these cases, the background concentrations of the former species, which apparently are relatively immune to taphonomic loss, were sufficiently large that the addition of input pulses and their decay did not affect substantially the samples rank order. Besides Mulinia lateralis, the only hard-bodied organism that did not covary with all others was tubes produced by spirorbid polychaetes (similar to those pictured in Nicol & Jones 1982) (Table 4). These tubes drifted in on floating sea grass during the study period (Powell et al. 1982), generating input pulses which, like M. lateralis, determined the sample s rank order. The total number of individuals collected can be separated into whole individuals and fragments. At the Laguna Madre site, one species fragments covaried with those of another in all comparisons (Table 5). A species whole shells covaried with those of another less well, but still only 7 of 55 comparisons were not significant

10 10 Hays Cummins and others LETHAIA 19 (1986) Table3. Spearman s rank comparisons for the total number of individuals (whole shells and fragments) collected per sampling occasion for taxa at the Laguna Madre site. P <P < P CrepidulalLaevicardium CrepidulalSyrnola CrepidulalA cteocina ActeocinalSymola ActeocinalMysella ActeocinalLaevicardium ActeocinalAnomalocardia AcreocinalT. divisus T. divisusllaevicardium T. divisuslmysella T. divisusltellina AnomalocardialLaevicardium AnomalocardialSyrnola DiastomalMyseNa LaevicardiumlMyseNa LaevicardiumlSyrnola Laevicardiuml Tellina Mysellal Rllina MysellalSy rnola TellinalSymola CrepidulalT. divisw CrepidulalAnomalocardia CrepidulalMysella Acteocinal Tellina T. divisusldiastorna T. divisuslsyrnola T. divisuslmulinia MulinialDiastoma AnomalocardialMysella AnomalocardialCaecum Anomalocardial Tellina Diastomal Tellina Diastomal Laevicardium CrepidulalTellina ActeocinalCaecum MulinialMysella LaevicardiumlCaecum MysellalCaecum 0.02 < P cr < P P>O.lO CrepidulalCaecum MulinialTellina Mulinial Laevicardium A nomalocardialdiastoma DiastomalCaecum DiastomalSyrnola CaecumlSyrnola Crepidulal Diastoma CrepidulalMulinia T. divisuslcaecum T. divisuslanomalocardia ActeocinalDiastoma MulinialSyrnola TellinalCaecum Acteocinal Mulinia MulinialCaecum MulinialA nomalocardia (Table 6). Comparisons of one species fragments to whole specimens of another yield similar results (Table 7). If the species are compared size class by size class, the smaller size classes of different species ( mm and mm) covaried in most cases (38 of 42 comparisons) (Table 8). These smaller size classes dominated Table 4. Spearman s rank comparisons of spirorbid tubes with the total number of individuals of the indicated taxa collected per sampling occasion from the Laguna Madre site. P <P50.10 PZO.10 (none) Tellina Caecum T. divisus Diastoma Mulinia Anomalocardia Acteocina Mysella Laevicardium Crepidula the total numbers of most species (Powell et al. 1984) and largely determined the results of comparisons in Tables 3-7. Covariance was less common in the larger size classes. Still, 10 of 14 comparisons were significant for shells mm. The Laguna Madre scrape samples were analyzed to provide data on the largest size classes (24.64 mm); those too rare to be sampled adequately by the box-core sampling regimen. Onehalf of these comparisons were not significant. Thus, covariance decreased substantially in the largest size classes of those species with the largest maximum size. At the Copano Bay site, most species (whole shells plus fragments) also covaried (39 of 45 comparisons, Table 9).?kro species, Tagelus plebeius and Littoridina barretti, accounted for the 6 non-significant results. One of these, T. plebeius, was collected in life position in most cases; the other, like Mulinia lateralis at the Laguna Madre site, was an important component of the living community and generated pulses in the death as-

11 LETHAIA 19 (1986) Assessing transportation in fossil assemblages 1 1 Table 5. Spearman s rank comparisons of the total number of fragments collected per sampling occasion for taxa from the Laguna Madre site. P <P < P50.02 MulinialDiastoma LaevicardiumlDiastoma LaevicardiumlT. divisus Anomalocardial Tellina DiastomalT. divisus LaevicardiumlTellina MulinialT. divisus MulinialLaevicardium TellinalDiastoma TellinalT. divisus LaevicardiumlAnomalocardia DiastomalAnomalocardia MulinialA nomalocardia 0.02 < Ps < PS 0.10 P>O.IO MulinialTellina AnomalocardialT. divisus (none) (none) semblage during the study period (Cummins et al. in press). If only whole shells were considered, just 26 of 45 comparisons were significant (Table 10). Most non-significant results again involved T. plebeius, L. barretti, and a third species which also generated pulses in the death assemblage, Littoridina sphinctostoma. In contrast, the species fragments covaried in nearly every comparison (Table 11). If fragments were compared to whole specimens, however, 25 comparisons Table 6. Spearman s rank comparisons of the total number of whole shells collected per sampling occasion for taxa from the Laguna Madre site. P < P <P50.02 CrepidulalA cteocina CrepidulalLaevicardium CrepidulalSyrnola AnomalocardialLaevicardium AnomalocardialSyrnola T. divbuslacteocina T. divisuslmysella T. divisusllaevicardium DiastomalMysella ActeocinalMysella ActeocinalLaevicardium ActeocinalSyrnola SyrnolalLaevicardium SyrnolalMysella SyrnolalTellina TellinalMysella TellinalLaevicardium LaevicardiumlMysella CrepidulalT. divisus CrepidulalAnomalocardia CrepidulalMysella MulinialT. divisus MulinialDiastoma AnomalocardialActeocina T. divisusltellina ActeocinalTellina A cteocinalcaecum MysellalCaecum Crepidulal Tellina MulinialTellina Mulinial Mysella Anomalocardial Tellina AnomalocardialCaecum T. divisuslsyrnola 0.02 < P < P P>O.IO T. divirusldiastoma Diastomal Tellina SyrnolalCaecum LaevicardiumlCaecum MysellalAnomalocardia CrepidulalMulinia CrepidulaKaecum MulinialActeocina MulinialLaevicardium AnornalocardialDiastoma T. divisuslcaecum DiastomalSyrnola DiastomalCaecum DiastomalActeocina CrepidulalDiastoma MulinialCaecum MulinialSyrnola MulinialA nomalocardia AnomalocardialT. divisus DiastomalLaevicardium TellinalCaecum

12 12 Hays Cummins and others LETHAIA 19 (1986) Table 7. Spearman s rank comparisons of the total number of fragments of one species to the total number of whole shells of another for taxa from the Laguna Madre site. In each pair the species for which the number of fragments was used in the analysis is on the left. P < P < P T. divisuslt. divisus T. divisusltellina T. divisuslcrepidula T. divisuslacleocina T. divisuslsyrnola T. divisuslmulinia T. divisuslmysella TellinalCrepidula Tellinal Caecum T. divisusllaevicardium TellinalDiastoma MulinialLaevicardiwn Tellinal Tellina TellinalT. divisus MulinialCaecum TellinalActeocina MulinialMysella MulinialSyrnola TellinalSyrnola DiaslomalCrepidula MulinialCrepidula TellinalMysella DiasromalCaecum MulinialT. divisus TellinalAnomalocardia Laevicardiuml Diastoma DiastomalAnomalocardia Tellinal Laevicardium LaevicardiumlCaecum DiasromalSyrnola DiastomalLaevicardium LaevicardiumlCrepidula LaevicardiumlMulinia DiasromalT. divisus AnomalocardialMysella DiastomalActeocina AnomalocardialCrepidula DiastomalMysella AnomalocardialCaecum LaevicardiumlLaevicardium AnomalocardialA creocina LaevicardiumlSy rnola LaevicardiumlA cteocina LaevicardiumlTellina LaevicardiumlT. divisus LaevicardiumlMysella A nomalocardiala nomalocardia A nomalocardialsyrnola A nomalocardiallaevicardiltm 0.02 < P S < P PZO.10 T. divisuslcaecum T. divirusldiastoma MulinialMulinia MulinialA nomalocardia MulinialDiastoma MulinialA cteocina Diastomal Diasroma LaevicardiumlAnomalocardia T. divisuslanomalocardia TellinalMulinia DiastomalMulinia Diasromal Tellina AnomalocardialT. divisus AnomalocardialTellina AnomalocardialDiastoma MulinialTellina AnomalocardialMulinia were non-significant (Table 12). If the whole individuals are compared by size class, approximately half of all comparisons were significant (Table 13). Most non-significant results involved T. plebeius or the two Littoridina species. Simultaneously occurring temporal cycles could compromise this statistical analysis. At the Laguna Madre site, most species settled and produced pulses in the death assemblage in the summer, for example. The cyclic pattern of erosion and deposition produced a similar temporally coincident pattern in many species at the Copano Bay site. Certainly some of the observed covariance is due to these phenomena, however several types of evidence suggest that most of the covariance cannot be so easily explained. For example, species that did not covary tended to be those that settled and produced pulses. Thus, temporally coincident annual cycles of settlement could not have produced much of the observed covariance. Furthermore, we examined covariance sampling period by sampling period using a second technique for species sufficiently abundant to do so (Table 15). In this latter analysis, data were compared within each sampling period only; thus, the analysis was immune to the effects of temporally coincident changes in abundance. These results clearly demonstrate that, for these taxa, instances where the ranks of box cores for two species were identical or nearly identical (i.e. instances where covariance occurred) occurred consistently with higher frequency than what might be expected from random chance. The results agreed with the results of the Spearman s

13 LETHAIA 19 (1986) Assessing transportation in fossil assemblages 13 Table 8. Spearman s rank comparison, size class by size class, of the total number of whole individuals collected per sampling occasion for taxa from the Laguna Madre site. The size class restriction listed applies to both taxa in each pair. Data are from boxcore samples only except S 4.64 mm which includes scrape samples. Species comparisons mm 0.W1.68mm mm Anomalocardial Tellina 0.01<P <P50.10 P>O.lO AnomalocardidT. divisus 0.05<Ps <P50.10 Anomalocardial Laevicardium P P P Anomalocardial Mulinia P>O.IO pzo.10 Anomalocardial Mysella Anomalocardial Syrnola Anomalocardial Caecum Anomalocardial 0.002<P <P <P50.05 Diastoma P>O.lO pzo.10 P>O.lO TellindLaevicardium P P TellindMulinia 0.002<P <PS0.01 TellinalT. divisus P <P50.01 TellinalMysella TellinalDiastoma 0.02<P50.05 P <P <P50.05 TellinalSyrnola TeNinalCaecum LaevicardiumlMysella Laevicardiuml Diastoma 0.02<P50.05 P pzo.10 P< <P50.10 Pz0.10 LaevicardiumlMulinia 0.002<PS <P50.01 LaevicardiumlT. divisus P LaevicardiumlSyrnola LaevicardiumlCaecum P P <P50.02 MulinialDiastoma 0.002<P <P50.05 MulinialT. divisus P P MulinialSyrnola MysellalDiastoma MysellalT. divisus MysellalSyrnola 0.002<P <P <P50.01 P DiastomalT. divisus 0.002<P <P50.10 DiastomalCaecum P>O.lO DiastomalSyrnola SyrnolalT. divisw 0.05<P50.10 P< mm 22.12mm 23.20mm 24.64mm pzo P>O.IO P <P50.02 pzo.10 P>O.IO 0.05<P50.10 pzo <P <P <P <P <P50.02 P PSO <P <PS0.02 pzo.10 rank analysis in all cases at the Laguna Madre site (Powell et al. 1984) and in all but 4 cases from the Copano Bay site [given the test s conservatism for discrete data (Conover 1972), these 4 are only marginal exceptions]. Additionally, the four exceptions all involved at least one species that settled and produced a pulse in the death assemblage during the study period. As expected, these newly dead individuals did not covary. In fact, 11 of 12 cases withp values <0.02 (Table 15) involved only species which did not settle in the living community during the study and, thus, had no input into the death assemblage. Such taxa might be expected to show the greatest degree of covariance because potentially they had been exposed to physical processes for a longer period of time. Thus, the temporal coincidence of cyclic phenomena as the primary explanation for the observed covariance accrues little support from the data. Clearly, the spatial distributions of most species were nearly identical. In contrast, individual computer species essen-

14 14 Hays Cummins and others LETHAIA 19 (1986) Table 9. Spearman s rank comparisons for the total number of individuals (whole shells and fragments) collected per sampling occasion for taxa at the Copano Bay site. PSO <P~ <P50.02 BrachidonteslChione BrachidonteslA cteocina ChionelL. sphinctostoma Brachidontesl Diastoma BrachidonteslT. plebeius L. sphinctostomall. barretti BrachidonteslCaecum Brachidontesl Laevicardium L. sphinctostomalt. plebeius Brachidontesl Mulinia LuevicardiumlMulinia Diastomal T. plebeius LaevicardiumlCaecum LnevicardiumlL. sphinctostoma CaecumlActeocina LaevicardiumlChione LaevicardiumlT. plebeius ChionelDiastoma LaevicardiumlActeocina ChionelCaecum Laevicardiuml Diastoma ChionelMulinia ChionelActeocina DiastomalCaecum ChionelT. plebeius DiastomalActeocina L. sphinctostomalmulinia DiastomalMulinia MulinialCaecum L. sphinctostomaldiastoma DiastomalL. barretti MulinialActeocina CaecumlT. plebeius ActeocinalL. barretti 0.02<Ps <P50.10 P10.10 BrachidonteslL. sphinctostoma L. sphinctostomalcaecum BrachidonteslL. barretti L. sphinctostomalacteocina MulinialL. barretti LaevicardiumlL. barretti MulinialT. plebeius ChionelL. barretti CaecumlL. barretti T. plebeiusll. barretti T. plebeiuslacteocina tially never covaried regardless of whether the two species compared were both distributed contagiously, both randomly or one of each (Table 16). The few significant results are no more than expected by chance at the a = 0.05 or a = 0.10 level (binomial test). Spatial distribution pattern Species might be expected to be distributed contagiously or randomly. An analysis of the covariance of species distributions requires an understanding of what processes control the post-mortem distribution patterns of the individual species. Certainly, the distribution of individuals from temporally discrete events (catastrophic burial, for example) could be interpreted relatively easily, however death assemblages and fossil assemblages rarely originate from single discrete events. More commonly, the individuals present in the death assemblage represent the time-averaged cumulation of many years inputs [although Cummins et al. (in press) question the validity of assuming that death assemblages form strictly from the gradual accumulation of yearly inputs by settlement and mortality in the living community]. We propose that random distributions can only be biologically produced, whereas contagious distributions may be of biological or physical origin. If of physical origin, covariance also should be observed. The significant question is, can time-averaging change the distribution patterns? That is, is the distribution pattern derived from the cumulation of individual inputs distributed as were the individual inputs themselves (i.e. random or contagious)? Clearly, cumulating individual inputs consisting of randomly distributed individuals yields a random distribution because the addition of randomly distributed individuals to a population of randomly distributed individuals simply increases the number of randomly distributed individuals. Interestingly, the cumulation of individual inputs consisting of contagiously distributed individuals remains contagious even if the patches themselves are randomly distributed. To prove this, we considered cluster processes as described in Cox & Isham (1980). A cluster process consists of

15 LETHAIA 19 (1986) Assessing transportation in fossil assemblages 15 Table 10. Spearman s rank comparisons of the total number of whole shells collected per sampling occasion for taxa from the Copano Bay site. PSO <Ps0.01 o.ol<ps0.02 MulinidChione MulinialBrachidontes A cteocinalchione ActeocinalCaecum Caecuml Brachidontes ChionelBrachidontes MulinialActeocina MulinidCaecum MulinialLaevicardium LaevicardiumlChione CaecumlChione DiastomdChione L. barrettilacteocina L. barrettilchione LaevicardiumlCaecum Laevicardiuml Brachidontes L. sphinctostomoldiastoma 0.02<Ps <Ps0.10 F70.10 MulinidDiastoma LaevicardiumlActeocina MulinialT. plebeius L. sphinctostomall. barretti Laevicardiuml Diastoma MulinialL. barretti A cteocinaldiastoma MdinidL. sphinctostoma Acteocinal Brachidontes LaevicardiumlL. barretti Caecuml Diastoma LuevicardiumlT. plebeius Diastomal Brachidontes LaevicardiumlL. sphinctostoma L. barrettildiastoma L. sphinctostomalt. plebeius L. sphinctostomalchione L. sphinctostomalbrachidontes L. sphinctostomalacteocina L. sphinctostomdcaecum T. plebeiuslchione T. plebeiuslbrachidontes T. plebeiusldiastoma T. plebeiustacteocina T. plebeiusll. barretti L. barrettilcaecum L. barrenilbrachidontes L. barrenilt. plebeius Table 11. Spearman s rank comparisons of the total number of fragments collected per sampling occasion for taxa from the Copano Bay site. P <Ps0.01 o.o1<pso.m ActeocinalL. sphinctostoma Brachidon testchione Brachidontest Diastoma BrachidonteslMulinia BrachidonteslT. plebeius L. sphinctostomalmulinia L. sphinctostomalchione L. sphinctostomallaevicardium Chionel Diastoma ChionelT. plebeius LaevicardiumlChione LaevicardiumlActeocina ActeocinalMulinia A cteocinaldiastoma A cetocindchione BrachidonteslActeocina BrachidonteslCaecum L. sphinctostomalt. plebeius L. sphinctostomalbrachidontt-s T. plebeiuslmulinia T. plebeiusldiastoma ChionelMulinia LaevicardiumlMulinia LaevicardiumlT. plebeius ActeocinalT. plebeills BrachidonteslLaevicardium L. sphinctostomaldiastoma LaevicardiumlDiastoma P>O.IO CaecumlChione CaecumlAcfeocina CaecumlMulinia Caecuml T. plebeius Caecumlhevicardium

16 ~ 16 Hays Cummins and others LETHAIA 19 (1986) Table 12. Spearman s rank comparisons of the total number of fragments of one species (first name in each pair) to the total number of whole shells of another (second name in each pair) for taxa from the Copano Bay site. p5o.m 0.002<P~ <P50.02 MulinialLaevicardiwn ActeocinaIActemina ActeocinalLaevicardium ActeocindCaecum LnevicardiumlCaecum BrachidonteslBrachidontes BrachidonteslCaecum CaecumlMulinia CaecumlBrachidontes BrachidonteslMulinia BrachidonteslA cteocina MulinialChione TageluslCaecum ChionelLaevicardium ChionelCaecum ChionelBrachidontes ChionelMulinia MulinialMulinia MulinialCaecum MulinialA cteocina L. sphinctostomalcaecum L. sphinctostomallaevicardium Laevicardiumlbevicardium BrachidonteslLaevicardium BrachidonteslChione ActeocinalChione MulinialDiastoma T. plebeiuslbrachidontes ChionelActeocina MulinialBrachidontes CaecumlCaecum CaecumlChione T. plebeiuslmulinia T. plebeiuslacteocina ChionelChione ActeocindBrachidontes L. sphinctostomall. sphinctostoma L. sphinctosromall. barretti LnevicardiumlActeocina ActeocinalMulinia ActeocinalL. barretti L. sphinctostomalacteocina L. sphinctostomalchione T. plebeiusllaevicardium T. plebeiuslt. plebeius MulinialL. sphinctostoma MulinialL. barretti LaevicardiumlBrachidontes BrachidonteslL. barretti BrachidonteslDiastoma LaevicardiumlChione ActeocinalDimtoma L. sphinctostomaldiastoma T. plebeiusll. sphinctostoma T. plebeiusll. barretti T. plebeiusldiastoma T. plebeiuslchione ChionelL. barretti ChionelL. sphinctostoma ActeocinalL. sphinctostoma L. sphinctostomalbrachidontes LaevicardiumlL. barretti CaecumlL. barretti CaecumlActeocina CaecumlL. sphinctostoma BrachidonteslT. plebeius BrachidonteslL. sphinctostoma LaevicardiumlMulinia LaevicardiumlL. sphinctostoma LaevicardiumlT. plebeius LaevicardiumlDiastoma ActeocinalT. plebeius L. sphinctostomalmulinia L. sphinctostomalt. plebeius MulinialT. plebeius ChionelT. plebeius ChionelDiastoma DiastomalT. plebeius a point process of cluster centers, each center having associated with it a random number of points forming a subsidiary process or cluster (the patch). Particular types of cluster processes (or the spatial structure and characteristics of patches of individuals) are determined by the distribution of centers, the distribution of the membes of a cluster about the center, and the distribution of the number of members per cluster among the various cluster centers. We assume that the distribution of organisms on the sea floor is a Neyman-Scott (1972) cluster process. In such a cluster process, the location of centers follows a Poisson process; that is, the probability that a center falls within a particular region is proportional to the size of that region and the location is independent of the number of centers in any other non-overlapping region. Furthermore, the location of the elements of a cluster about its center also follows a Poisson process. Whereas it is difficult to determine for cluster processes the distribution of the number of points in a given physical region, this is not required to show that the long-run distribution of points (i.e.

17 LETHAIA 19 (1986) Assessing transportation in fossil assemblages 17 Table 13. Spearman s rank comparisons, size class by size class, of the total number of whole individuals collected per sampling occasion for taxa from the Copano Bay site. The size class restriction listed applies to both taxa in each pair. Species comparisons mm mm mm mm CaecumlActeocina CaecumlL. sphinctostoma CaecumlDiastoma Caecum1 Mulinia CaecumlChione CaecumlT. plebeius ActeocinalL. sphinctostoma ActeocinalDiastoma ActeocinalMulinia A cteocinalchione ActeocinalT. plebeius 0.01cPs <P50.02 P>O.lO t <P tPs <P50.01 pzo.10 t50.10 t50.10 P>O.IO 0.05<P50.10 P>O.lO 0.02<P <P <P~0.oz 0.02tP50.05 P>O.lO DiastomalL. sphinctostoma DiastomalMulinia DiastomalChione DiastomalT. plebeius 0.01<P tP tP50.05 P>O.IO 0.02tP <P50.02 P>O.lO MulinialL. sphinctostoma MulinialChione MulinialT. plebeius P>O.IO 0.05tP50.10 P>O.lO P>0.10 T. plebeiusll. sphinctostoma T. plebeiuslchione P>O.lO P>O. 10 L. sphinctostomalchione 0.01cP50.02 the distribution of points as the number of clusters approaches infinity, or in this case the distribution of individuals after the cumulation of many yearly contagious inputs) in a cluster process is not uniform (i.e. Poisson). Thus, if we let NA(t) denote the number of points in region A after t clusters, Cox & Isham (1980) show for a Neyman-Scott process that the ratio of the variance of NA(t) to the mean of NA(t) coverages (as t + m) to a number that is greater than or equal to Table 14. Full species names for the taxa listed in Tables The abbreviated.form used in Tables >13 is in parentheses. Copano Bay (Caecum) pulchellum (Acteocina) canaliculata (Diastoma) varium (Brachidontes) exustus (Chione) cancellata (T)agelus (plebeius) (Mulinia) lateralis (L)ittoridina (barretti) (L)ittoridina (sphinctostoma) (Laevicardium) mortoni Laguna Madre (Caecum) pulchellum (Diastoma) varium (T)agelus (divisus) (Mysella) planulata (Mulinia) lateralis (Laevicardium) mortoni (Tellina) tampaensis (Anomalocardia) auberiana (Syrnola) sp. (Crepidula) convexa (Acteocina) canaliculata one, with equality if and only if the clusters are of size one. Thus, one achieves a random distribution (a mean to variance ratio not significantly different from 1) if and only if there is, in essence, no clustering. In other words, only in the absence of contagiously distributed individuals can the cumulative distribution of such individuals added over many years be random. Therefore, the observation of randomly or contagiously distributed individuals in a fossil assemblage implies that the preponderance of the individuals were initially put in as random or contagious inputs respectively or were distributed so after death regardless of whether the individuals were derived from a single input event or the cumulation of many discrete input events. Most organisms are distributed contagiously on the sea floor (Gardefors & Orrhage 1968; Green & Hobson 1970; Reys 1971; Rosenberg 1974; Hockin 1982), although random distribution patterns also can occur (Lie 1968; Findlay 1982; Moller & Rosenberg 1983). [Some random distribution patterns can be ascribed to inappropriate sampling methodology, however (Elliott 1977; Jumars et al. 1977; Findlay 1982; Kac 1983)l. It is unlikely that random distributions in death or 2 Lethaia 1/86

18 18 Hays Cummins and others LETHAIA 19 (1986) Table IS. Comparisons of species from the Copano Bay site (whole shells plus fragments, except where noted) using the Kolmogorov-Smirnov method described in the Methods section. n indicates the number of sampling periods used, each of which yielded a sum of the absolute values of the differences between the ranks of 4 box cores for each of the species indicated. Numbers given are the fraction of each n yielding the indicated sum. P values given are for continuous distributions from Daniel (1978). Possible sums of ranks Expected percentage of runs if randomly distributed BrachidonteslChione BrachidonteslLaevicardium Brachidontesl Mulinia BrachidonteslCaecum BrachidonteslDiastoma Chionel Laevicardium ChionelDiastoma CaecumlLaevicardium MulinialDiastoma Mulinial Laevicardium CaecumlDiastoma MulinialCaecum MulinialChione L. sphinctostomalchione BrachidonteslActeocina ChionelA cteocina L. sphinctostomalacteocina LaevicardiumlActeocina MulinialA cteocina DiastomalActeocina CaecumlA cteocina CaecumlActeocina (whole shells only) n=15 n= 14 n=17 n= 16 n=14 n=14 n=16 n=16 n=18 n=16 n= 16 n=17 n=17 n=17 n=17 n=15 n=16 n=15 n=19 n=17 n=19 n= P<O.OI P<O.OI P<O.O1 0.01<P<0.02 P<O.OI 0.02<P<0.05 P< <Pc <P< <P<0.10 RO <P< <P<0.20 P>0.20 P<O.Ol P< <P<0.02 P<O.OI 0.02<P<0.05 P<O.O1 P>0.20 P<O.O1 fossil assemblages, not solely due to sampling error, can be produced non-biologically. Physical processes, such as currents and waves, consistently generate patchy distributions. The spatial variation in grain size produced by waves and currents, the accumulation of shells in ripple Table 16. Spearman's rank comparisons generated by the computer model. Species A-E were contagiously distributed; species F-J were randomly distributed. Comparisons were made between both types of distributions. * indicates a negative correlation which never occurred in the species correlations in Tables P5O.M 0.02<PC0.05 O.OS<P50.10 P>O.lO (none) EJG DIG AIB AIF FIG ClH 'BIG WH AIC AIGF~H UI AIDAIHFII UJ AIE AII FIJ DIF BIC BIF GIHDIH BID BIH G/I DII BIE BII GIJ DIJ UD BIJ H/I E/F UE c/f H/J EJI DIE UG UJ EJJ troughs, and the distribution of shells on a beach are examples (Kornicker et al. 1963; Yasso 1966; Behrens & Watson 1969; Mothersill 1969; Wells & Ludwick 1974; Reineck & Singh 1980). Thus, we predict that shells distributed randomly in the horizontal in a fossil assemblage, in all probability, result from the in situ burial of randomly distributed individuals. Covariance Unfortunately, animals rarely are randomly distributed and contagious distributions can be of biological or physical origin. Covariance provides a way to distinguish between the latter two alternatives. All species at both sites were contagiously distributed. Furthermore, the spatial distributions of most species at the two study sites were nearly identical; that is, they covaried in space such that they occurred in about the same relative proportions numerically in all samples regardless of their absolute abundance. Covariance occurred even though all samples were

19 LETHAIA 19 (1986) Assessing transportation in fossil assemblages 19 taken from the death assemblage within a fairly restricted area of the same habitat and in spite of the contagious nature of the species individual distribution patterns within that habitat. Furthermore, the background component of individuals of species that were collected alive during the study period, which were present at the study s inception and its conclusion, apparently had a nearly identical distribution pattern in almost all cases, whereas the individuals that actually died during the study period and which created an observable pulse in the death assemblage frequently were not distributed similarly. Of course, one might expect biologically produced covariance among some species when samples come from different habitats as most cluster analyses imply (e.g. Bloom et al. 1972; Stephenson et al. 1972) or if samples were collected across an environmental gradient so that species distributions were affected, at least in part, by the relationship of species to the environmental gradient (e.g. Elliott 1977). In both cases, either negative (inverse) or positive covariance should be observed between most species pairs. That is, some species distributions should be similar to others whereas other species should be distributed inversely (so that, in samples where one species was more abundant, a second species consistently would be less abundant). Cases of negative covariance were never observed in this study because all samples were collected from the same habitat. Most species, when living, are contagiously distributed and should be after death given more or less in place mortality. Even so, covariance of species distributions is not dependent on the species type of distribution pattern. Species, whether randomly or contagiously distributed, may or may not covary, as the computer simulations show. The differentiation of contagious and random distributions requires careful sampling. Sample size must approximate patch size (Elliott 1977). Covariance is much less dependent on sample size because it only requires a knowledge of the coincidence of distribution patterns, rather than the distribution patterns themselves. Thus, most sampling programs should be adequate to assess covariance, provided that all samples come from the same habitat, whereas the investigation of individual distribution patterns frequently would require a more restrictive sampling regimen. A number of biological factors could produce covariance among contagiously distributed spe- cies after death within any single habitat. These include commensalism and predatodprey interactions (e.g. Ankel 1959; Robertson & Mau- Lastovicka 1979; White el al. 1984) and the interaction of micro-habitat with distribution (e.g. Chapman & Newell 1949; Young & Rhoads 1971; Lewis & Stoner 1983; Reise 1983). Negative interactions which might yield inverse correlations (which were never observed by us) also are described (e.g. Bell 1983; Wilson 1983). In general, however, a relatively small percentage of the entire community is affected; normally only one preservable individual is. Ankel s (1959) description of three preservable species which might be expected to covary is an extreme case. At our two sites, nearly all species in the death assemblage covaried together. That is, all species had essentially the same distribution pattern. Covarying species included those that were living during the study period and those that were not. They included both filter feeders and deposit feeders, bivalves and gastropods, primary and secondary consumers, and epifauna and shallow infauna. It is difficult to envision a biological cause for such a coincidence of distribution patterns. Physical transportation must be involved. The computer simulations support this argument. These species were not affected by transportation, but accumulated in the computer s death assemblage in life position. Essentially no covariance was observed. Further support comes from those real species which did not covary. Only four species consistently did not do so based on the Spearman s rank test. Three of these generated, by larval settlement and subsequent growth and mortality, pulses in the death assemblage which gradually decayed away during the study period. The individuals in a pulse, at least initially, would have died more or less in place and probably were collected before a significant transporting event had occurred. The numerical and spatial variability so generated prevented a statistically significant result for these species. The fourth, Tagelus plebeius, was the only species consistently collected in life position. Significantly, it covaried with few other species at the Copano Bay site. That is, the one species that clearly was not transported also did not covary. Furthermore, the fragments of this species, which are more likely to have been transported than the whole shells, did covary with all other species tested. Finally, in comparisons of species from the Copano Bay site using the Kolmogorov-Smirnov 2

20 20 Hays Cummins and others LETHAIA 19 (1986) technique (Table 15), nearly all comparisons involving two species which did not settle and produce pulses during the study produced p values < In contrast, all but one comparison yielding p values > 0.10 involved at least one species that did generate a pulse by larval settlement and mortality. Thus, covariance was present much more frequently between those species for which all individuals were present at the study s inception. Certainly, a higher proportion of the individuals of these species had been exposed to physical processes for a long period of time, whereas many individuals of species with pulses were new additions to the death assemblage. Thus, the hypothesis that transportation produced the observed covariance is supported consistently by several different data analyses. If transportation produced covariance, then variation in the degree of covariance should be observed between localities with different current and wave regimes and between species or size classes having different hydrodynamic properties. A comparison of the two study sites is instructive. The Laguna Madre site is the more physically disturbed of the two. The majority of whole and fragmented individuals collected at both study sites were 1 cm or less in size. Thus, most shells could respond to the physical regime present at both sites. At both sites, fragments always covaried consistently and always covaried more than whole shells. This might be expected because fragments are generally about the same size and might respond in roughly the same manner to physical disturbance. Furthermore, at least a portion of the fragments probably originated from physical processes (e.g. Driscoll 1967; Driscoll & Weltin 1973). If whole shells are analyzed separately, covariance at the Laguna Madre site is much more widespread than at the Copano Bay site. Shells tended to be smaller, on the average, and presumably more easily transported at the Laguna Madre site and the energy level was higher. Importantly, covariance decreased substantially in the higher size classes of species at the Laguna Madre site. When fragments are compared to whole shells, fragments covaried with whole shells in most cases at the Laguna Madre site, but only a little over half of the comparisons were significant at the Copano Bay site. The data agree with the observed physical regime. There is more covariance between species at the Laguna Madre site. Transportation of shells after death produces covariance and the degree of covariance provides a quantitative assessment of transportation. Conclusions Many criteria, such as size-frequency distributions, the number of articulated valves and leftright valve ratios, have been proposed for assessing the role played by transportation in the formation of a fossil assemblage. Most proved useful in some circumstances but not in others. Thus, additional criteria might be usefully employed. We propose that within-habitat species distributions and the covariance of species are useful criteria for assessing transportation. From our data, we make the following testable predictions. (1) A random distribution is of biological origin. (2) A contagious distribution without widespread covariance is of biological origin. (3) Widespread covariance among species within habitat is indicative of the physical transport of shells. The degree of covariance is dependent upon the amount and intensity of the physical disturbance in that increased covariance indicates an increased role of transportation in the determination of species distributions. The Spearman s rank correlation can be used as a measure of this covariance. On the other hand, significant covariance does not imply that transport of shells from outside the habitat occurred. Nearby grass beds contributed only a few species to the death assemblage at the Laguna Madre site (Powell et al. 1982) and only one obviously allochthonous species was present at the Copano Bay site. Most species that covaried were indigenous to the studied habitats. (4) Differences in the degree of covariance among size classes and hydrodynamically different shell shapes might be present. In general, there should be a tendency for smaller size classes to covary more frequently than larger ones. As the intensity of the physical process increases more larger size classes should covary. (5) Infaunal molluscs should covary less frequently than epifaunal molluscs. Covariance among deep infauna indicates substantial sediment resuspension and transportation if in place mortality can be assumed. (6) The spatial distributions examined are horizontal spatial distributions. Vertical distributions also might be considered. Vertical covariance might be indicative of physical or biological mix-

21 LETHAIA 19 (1986) Assessing transportation in fossil assemblages 21 ing of successive inputs from a single community or the presence of a vertical sequence of discrete community types where abundance changes in a certain suite of species occurred more or less contemporaneously. In some cases, a rough measure of the effect of time averaging might result. The interpretations presented are based on data from only two physical regimes and, in most cases, a relatively narrow range of size classes; nevertheless, they suggest the usefulness of measuring covariance. The above predictions can be tested both in modern death assemblages and in fossil assemblages where other data provide clear evidence for transportation or the lack thereof. Covariance should be relatively independent of other taphonomic processes and a species inherent spatial distribution. 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