Carl F. Koch

Prediction of sample size effects on the measured temporal and geographic distribution patterns of species

Few paleontological studies of species distribution in time and space have adequately considered the effects of sample size. Most species occur very infrequently, and therefore sample size effects may be large relative to the faunal patterns reported. Examination of 10 carefully compiled large data sets (each more than 1,000 occurrences) reveals that the species-occurrence frequency distribution of each fits the log series distribution well and therefore sample size effects can be predicted. Results show that, if the materials used in assembling a large data set are resampled, as many as 25% of the species will not be found a second time even if both samples are of the same size. If the two samples are of unequal size, then the larger sample may have as many as 70% unique species and the smaller sample no unique species. The implications of these values are important to studies of species richness, origination, and extinction patterns, and biogeographic phenomena such as endemism or province boundaries. I provide graphs showing the predicted sample size effects for a range of data set size, species richness, and relative data size. For data sets that do not fit the log series distribution well, I provide example calculations and equations which are usable without a large computer. If these graphs or equations are not used, then I suggest that species which occur infrequently be eliminated from consideration. Studies in which sample size effects are not considered should include sample size information in sufficient detail that other workers might make their own evaluation of observed faunal patterns.

On the distribution of species occurrence

The distribution of species abundance (number of individuals per species) is well documented. The distribution of species occurrence (number of localities per species), however, has received little attention. This study investigates the distribution of species occurrence for five large data sets. For modern benthic foraminifera, species occurrence is examined from the Atlantic continental margin of North America, where 875 species were recorded 10,017 times at 542 localities, the Gulf of Mexico, where 848 species were recorded 18,007 times at 426 localities, and the Caribbean, where 1149 species were recorded 6684 times at 268 localities. For Late Cretaceous molluscs, species occurrence is examined from the Gulf Coast where 716 species were recorded 6236 times at 166 localities and a subset of this data consisting of 643 species recorded 3851 times at 86 localities. Logseries and lognormal distributions were fitted to these data sets. In most instances the logseries best predicts the distribution of species occurrence. The lognormal, however, also fits the data fairly well, and, in one instance, better. The use of these distributions allows the prediction of the number of species occurring once, twice, …, n times. Species abundance data are also available for the molluscan data sets. They indicate that the most abundant species (greatest number of individuals) usually occur most frequently. In all data sets approximately half the species occur four or less times. The probability of noting the presence of rarely occurring species is small, and, consequently, such species must be used with extreme caution in studies requiring knowledge of the distribution of species in space and time.

Bias in the published fossil record

The published fossil record has significant bias in favor of common and bio- stratigraphically important taxa when compared with data obtained from a thorough exam- ination of several hundred collections from the Western Interior of North America. Overall species diversity is underestimated by a factor of 3 to 4, and bivalve and gastropod diversity by a factor of 5. The proportion of bivalves increased from 40 to 56% of the fauna, and the proportion of ammonites decreased from 28 to 18%. Thirteen published reports listed 65 species from 203 reported occurrences. Data from all sources showed 170 species for 1050 occurrences. By using abundance data and assuming a log-normal distribution, as many as 200 fossilizable mollusc species may have inhabited the Western Interior during the upper- most biozone of the Cenomanian. The importance of this study is that it quantifies the bias in the published fossil record relative to the potential fossil record for an unusually well studied interval of geologic time. The bias would be greater for less well studied strata.

Preservational effects in paleoecological studies; Cretaceous mollusc examples

The effect of preservational quality on paleoecologic studies is evaluated quantitatively by using data from 83 fossil collections. These collections are from a restricted Cretaceous time interval (Haustator bilira Assemblage Zone) of Maestrichtian Age and are from the Eastern Gulf Coastal Plain Province. In all, 32,335 specimens were identified, resulting in recognition of 643 different taxa. Each collection was categorized into one of six preservational types, ranging from those in which both aragonite and calcite shells are well preserved to those having only calcite shells preserved. Statistical comparisons reveal that preservation affects the faunal makeup of these collections. Specif- ically, collections in which both aragonite and calcite are well preserved have more taxa than collections of poorer preservational quality and contain faunal elements not found in other collections. These two effects can confound paleoecologic studies of endemism, eurytopy vs. stenotopy, species longevity and other studies of the distribution of organisms in space and time. These effects are especially significant for studies based on presence/absence data, such as published faunal lists and selectively collected samples. In such studies, collections of good preservational quality may be interpreted to rep- resent strata of high diversity, taxa having the more durable hard parts will appear to be widespread and long ranging, and taxa that are preserved only in collections of the best preservational quality will appear stenotopic, endemic, and rare.

Bivalve Species Duration, Areal Extent and Population Size in a Cretaceous Sea

Geographic distribution, species duration, and population size of 41 bivalve species which coexisted during the uppermost biozone ( Sciponoceras gracile zone) of the Cenomanian were measured. Average species duration and correlation between geographic distribution, species duration, and population size were computed for five groups: total, infaunal, epifaunal, cemented epifaunal, and uncemented epifaunal bivalves. Average species duration for all bivalves is less than 2 Myr. Infaunal bivalves averaged slightly higher, epifaunal slightly lower. Positive correlation was measured between species duration and geographic distribution for all five groups and statistical significance of the relationships was demonstrated for all but infaunal forms. In general no correlation was found between species duration and population size, and between population size and geographic distribution with the following exceptions: species duration and population size were significantly correlated for infaunal bivalves and uncemented epifaunal bivalves, and population size and geographic distribution were correlated for uncemented bivalves. Because these 41 fossil species coexisted at the same time and were distributed in the same space, differences in the relationships of species duration, geographic distribution and population among the various life habits indicate differences in ecological strategy and the evolutionary consequences of that difference.

Evaluating Paleontologic Data Relating to Bio-Events

Measurements of diversity and extinction intensity around bio-events in local stratigraphic sections and global taxonomic data bases include some degree of uncertainty, or potential error. Sources of uncertainty involve failure to sample rarer species in all collections and imprecise age correlations and species counts, among others. This chapter presents several methods for evaluating this paleontologic uncertainty. For fossil ranges in local sections, methods are reviewed that might help to discriminate between true gradual (or stepwise) extinction and apparent gradual decline resulting from sampling effects. For tabulated extinctions in regional or global data bases, methods are evaluated for measuring extinction intensity and procedures are presented for calculating relative uncertainty.

Species extinction across the cretaceous‐tertiary boundary: Observed patterns versus predicted sampling effects, stepwise or otherwise?

Stepwise extinction and origination patterns have been reported around the Cenomanian‐Turonian, Cretaceous‐Tertiary, and the Eocene‐Oligocene boundaries. Some of these observed stepwise patterns may result from only sampling effects. It is possible to test whether or not the observed stepwise patterns result from sampling effects if the appropriate information is known. An example of such a test involves the molluscan species from the Maastrichtian Prairie Bluff Chalk at Bragg, Alabama. Species abundances are known and sample sizes are 2144, 558, and 680 specimens from the lower, middle, and upper portions of the Prairie Bluff at Braggs. The observed ranges are not significantly different from the predicted values. These molluscs are representative of the Campanian‐Maastrichtian temperate fauna distributed from northern Mexico, through the U.S. coastal plain, to eastern Europe. This test suggests that this species‐rich and widely distributed fauna persisted unchanged until the latest Cretaceous.

Sampling effects, species-sediment relationships, and observed geographic distribution: An uppermost Cretaceous bivalve example

Abstract When bivalve specimens from Campanian and Maastrichtian age sediments in Europe are compared to speciesdocumented for similar sediments of the Atlantic and Gulf coastal Plain of North America, 78 species are recognized as being the same on both continents. The North American data set results from examination of 502 bulk collections and the european data set is based on examination of specimens from 61 locations which are housed in 12 European museums. A sampling effects model which accounts for the disparity in data set size, predicts that 115 rather than 78 of the 164 North American bivalve species should be found if the two data sets are in fact samples of the same fauna. The difference of 37 species is mainly attributed to species-sediment interaction and the fact that 15% of the North American collections are from carbonates whereas 77% of the European collections are from carbonates. When the sampling effect model uses species occurrence frequency for the 74 North American carbonate collections, the observed similarity values are close to those predicted. The model predicts 82–87 species and 75 species are observed. It can be concluded that species-sediment relationships are strong for these bivalve species, that the sampling effect model is valid if proper attention is given to the sediment make-up of the two data sets, and that the areal distribution of these bivalve species which lived just prior to the K/T boundary should be reanalyzed.