Ordinal Diversity Research Articles

Quantifying the diversity of multiple time series with an ordinal symbolic approach.

The main motivation of this paper is to introduce the ordinal diversity, a symbolic tool able to quantify the degree of diversity of multiple time series. Analytical, numerical, and experimental analyses illustrate the utility of this measure to quantify how diverse, from an ordinal perspective, a set of many time series is. We have shown that ordinal diversity is able to characterize dynamical richness and dynamical transitions in stochastic processes and deterministic systems, including chaotic regimes. This ordinal tool also serves to identify optimal operating conditions in the machine learning approach of reservoir computing. These results allow us to envision potential applications for the handling and characterization of large amounts of data, paving the way for addressing some of the most pressing issues facing the current big data paradigm.

Coombs Hill: A Late Devonian fossil locality in the Witpoort Formation (Witteberg Group, South Africa)

Coombs Hill, a new fossil locality in the Witpoort Formation (Witteberg Group) of South Africa, preserves a record of Famennian (Late Devonian) life in Gondwana. Fossil plants collected at Coombs Hill are preliminarily assigned to several classes. Shelly invertebrates include a variety of bivalve mollusc forms, some of which appear to be preserved in life position. Biodiversity at Coombs Hill is comparable to that of the well-known Waterloo Farm lagerstätte in ordinal diversity, but exhibits differences in species composition. Ongoing taxonomic analysis will provide a rare window into the ecology of high-latitude environments during this pivotal stage of Earth history, which immediately preceded the end-Devonian extinction. Sandstone dominated sedimentary facies at Coombs Hill suggest a high-energy coastal marine setting, with brackish back-barrier estuarine/lagoonally derived fossiliferous mudstones. Exact stratigraphic placement within the Witpoort Formation is hampered by structural deformation, and precise age comparisons with Waterloo Farm are currently tenuous.Significance:
 
 A new fossil locality at Coombs Hill comprises the second known site with a suite of well preserved continental and marginal marine fossils from the Witpoort Formation, providing an exceptionally rare example of high-latitude life during the critical latest Devonian Famennian age.
 Several new plant taxa will be diagnosed from this locality, which also gives important insights into the morphology of Archaeopteris notosaria, South Africa’s earliest known tree.
 Discovery of a second palaeontologically significant site in the Witpoort Formation provides impetus for further structural and sedimentary facies analyses to align the unit with datable global eustatic events, and to clarify its internal chronology.

Exploring the impact of RNA editing on mitochondrial phylogenetic analyses in liverworts, an early land plant lineage

AbstractPlant mitochondrial protein‐coding genes are slow evolving, and therefore are less subject to substitution saturation, and therefore perhaps more suitable for resolving deep relationships of high taxonomic categories. Plant mitochondrial genes hold, however, hundreds of RNA editing sites, involving mostly non‐synonymous substitutions in the first and second codon positions, which has been reported to affect phylogenetic reconstructions. We have previously identified ca. 4700 mitochondrial RNA editing sites within a group of liverworts representing the ordinal diversity of liverworts, allowing us to critically evaluate the impacts of RNA editing sites on phylogenetic reconstructions in liverworts. Our phylogenetic inferences are mostly congruent on topology inferred from the original mitochondrial gene dataset, dataset with RNA editing sites corrected, and dataset with RNA editing sites excluded. The RNA editing site excluded dataset recovered a topology identical to that of the RNA editing site corrected dataset, supporting the sister relationship of Ptilidium and Jungermanniales, whereas the original dataset supported the sister relationship of Ptilidium and Jungermanniidae. The controversial placements of Ptilidium could be explained by site‐wise log‐likelihood analysis, as the majority of liverwort RNA editing sites supported the sister relationship of Ptilidium and Jungermanniidae, hence the correction or exclusion of the RNA editing sites changed the tree topology and supported the sister relationship of Ptilidium and Jungermanniales. Our study shows that RNA editing sites potentially impact phylogenetic analyses, suggesting that both genome and transcriptome derived data should be used with caution for phylogenetic reconstruction with genes hosting vast numbers of RNA editing sites such as plant organellar genes.

Measures of Nominal and Ordinal Population Diversity

A measure of population diversity across a set of categories such as racial and ethnic groups is presented that clearly demonstrates how the index captures deviations from a standard of maximum diversity. The measure is applied to subareas of a larger area such as census tracts and is employed to develop 2 alternative measures of neighborhood diversity for the larger area. This and other measures of diversity assume that the population is classified into a nominal, unordered set of categories. The distribution of the population into a set of rank-ordered categories introduces the additional element that the pattern of a distribution across the categories should be considered in assessing levels of diversity. A measure of ordinal diversity and corresponding measures of neighborhood ordinal diversity are presented to address this.

Regional to global patterns in Late Cretaceous selachian (Chondrichthyes, Euselachii) diversity

ABSTRACT Although selachian fossil remains have been studied for nearly three centuries, little is known about their evolutionary history. Recent studies have suggested different timings of early diversification events in the Late Triassic, Jurassic, and Early Cretaceous. However, Late Cretaceous selachian diversity has remained little explored despite numerous and diversified selachian assemblages known from this time interval. Sampling standardization, origination/extinction rates, and raw ordinal diversity were examined based on taxonomic occurrences in three data sets representing distinct geographical areas (Anglo-Paris Basin, northwestern Europe, and Western Interior Seaway) spanning the Cenomanian-Campanian interval. This examination allowed the identification of regional diversity events, previously reported for some invertebrate groups, but presented for the first time for a marine vertebrate group. The local mid-Cenomanian diversity drop (Anglo-Paris Basin) is interpreted as a possible consequence of changes in bottom seawater conditions related to the rapid mid-Cenomanian transgression. The Cenomanian/Turonian faunal turnover is likely to be due to various sampling biases (Anglo-Paris Basin and northwestern Europe), but a genuine extinction in the Western Interior Seaway cannot be excluded. The Santonian diversity peak synchronous with a marked global increase in seawater temperatures contrasts with the rapid temperature decrease linked with low diversity in the early Campanian. SUPPLEMENTAL DATA—Supplemental materials are available for this article for free at www.tandfonline.com/UJVP

A NEW GENUS OF ARCHIPOLYPODAN MILLIPEDE FROM THE COSELEY LAGERSTATTE, UPPER CARBONIFEROUS, UK

: A new archipolypodan millipede, Anaxeodesmus diambonotus gen. et sp. nov., is described from the Upper Carboniferous (Westphalian B) Coseley Lagerstatte, West Midlands, UK. This taxon is unique amongst Archipolypoda in having tergites unornamented by spines or tubercles. It appears to have archidesmidan affinities as it shares similarities in sternal morphology with the Early Devonian archipolypodan Palaeodesmus tuberculata (Brade-Birks) from the Midland Valley of Scotland. Anaxeodesmus diambonotus significantly increases the ordinal diversity of Archipolypoda in the Late Carboniferous as all other Archipolypoda from this time period belong to the spiny Euphoberiida.

Woody plants in Kenya: expanding the Higher-Taxon Approach

Information on species diversity is urgently needed but often unavailable. Conservation biologists have therefore used the ‘Higher-Taxon Approach’ to predict the distribution of α-diversity of species from the diversities of higher taxa. We expanded this approach. We studied the Kenyan woody plant flora on a 56×56 km grid basis and found that the distribution of species α-diversity could be predicted precisely even from ordinal diversity. In contrast, the distribution of species β-diversity was difficult to predict even from the genus level, although within biogeographic zones the prediction improved. The spatial scale of species α-diversity could be predicted precisely only from genus level, and was hardly predictable from ordinal level. The spatial scale of species β-diversity was roughly predictable from genus to ordinal levels. Overall, the Higher-Taxon Approach could be expanded to a rough prediction of the spatial scale of species diversities. But, the approach only poorly predicted the spatial distribution of species β-diversity.

Patterns of faunal turnover and diversity in the Siwalik Neogene record in relation to regional and global events

The fluvial Neogene Siwalik formations of northern Pakistan contain one of the longest and richest sequences of terrestrial vertebrate faunas known. The complete sequence extends from ca. 18 Ma to 1 Ma, with the interval between 18 and 7 Ma being best sampled. Throughout this best known interval vertebrate remains are frequently abundant in channel fills and less common in large channel sands, levees, and paleosols. Although the abundance and quality of fossil preservation varies, all stratigraphic levels have some fossils and the record of most subintervals is good to excellent. As a consequence the patterns of faunal turnover and changes in diversity can be documented and analyzed for 0.5 my long subintervals.Thirteen orders of Siwalik mammals have been identified, with well sampled subintervals typically having 50 or more species. Despite the ordinal diversity, however, most Siwalik mammal species belong to just three orders: rodents, artiodactyls, and perissodactyls. Among the larger mammals, the bovids and equids are the most common and have the most species, while the murid and cricetid rodents dominate the small mammal assemblages. These Siwalik abundance and diversity patterns differ markedly from those of the Paleogene and are a result of Neogene radiations in these four families and extinction of Paleogene groups.Between 18 and 7 Ma species diversity varies considerably. Among artiodactyls and rodents the number of species first increases between 15 and 13 Ma and then falls after 12 Ma. Significant changes in relative abundance are also known, including an increase in the abundance of bovids between 16.5 and 15 Ma and a very abrupt increase of murids at 12 Ma.Data on stratigraphic ranges of rodents and artiodactyls show that faunal change in the Siwaliks was episodic, occurring as short intervals with high turnover, followed by longer periods with considerably less change. Maxima of first appearances occur at approximately 13.5 and 8.5 Ma, while maxima of last appearances come at 12.0, 9.5, and 8.0 Ma. It is thus apparent that in the Siwaliks increased extinction did not accompany or closely follow maxima of first appearances.Correlations of these faunal events to global climatic trends are ambiguous. However, it is apparent that the middle Miocene diversification of Siwalik faunas occurred during a period of global cooling, while the late Miocene decline in diversity preceded a second episode of cooling and increasing aridity.

Evolution and Radiation of Mammals in the Eocene, and the Diversification of Modern Orders

The Eocene was an especially interesting and important time in the history of mammals. Whereas the Paleocene witnessed the rise of mammals from their previously subordinate position among terrestrial vertebrates, it was during the Eocene that the second major radiation of eutherian mammals took place. Many of the modern orders diversified and achieved dominance on land, and mammals even began to invade the seas and take to the air. By the late Eocene, this explosive radiation had produced the greatest ordinal diversity of mammals known at any time in their history (Lillegraven, 1972). If we could travel back to the Paleocene, we would see few familiar mammals; most belonged to archaic groups that long ago became extinct. But a visitor to the Eocene (given wide latitude in space and time, of course) might recognize many of the denizens of Eocene forests and floodplains—bats, prosimian primates, squirrel-like rodents, rabbits, moles, armadillos, and miniature hoofed animals resembling mouse deer. Along the shore, our hypothetical Eocene naturalist might spot a whale or a primitive sea cow. A closer look would reveal that these animals differed in many ways from living forms, of course, but the resemblances are real and, in some cases, striking. In fact, at least 10 orders of mammals alive today appeared in the fossil record for the first time, or experienced major radiations of modern groups, in the Eocene. Not all Eocene mammals belonged to modern orders, however. There was still a considerable proportion of archaic mammals, many representing lines that had begun in the Paleocene or, in some instances, before. And some of them were highly successful too.

A kinetic model of Phanerozoic taxonomic diversity I. Analysis of marine orders

A simple equilibrial model for the growth and maintenance of Phanerozoic global marine taxonomic diversity can be constructed from considerations of the behavior of origination and extinction rates with respect to diversity. An initial postulate that total rate of diversification is proportional to number of taxa extant leads to an exponential model for early phases of diversification. This model appears to describe adequately the “explosive” diversification of known metazoan orders across the Precambrian-Cambrian Boundary, suggesting that no special event, other than the initial appearance of Metazoa, is necessary to explain this phenomenon. As numbers of taxa increase, the rate of diversification should become “diversity dependent.” Ecological factors should cause the per taxon rate of origination to decline and the per taxon rate of extinction to increase. If these relationships are modeled as simple linear functions, a logistic description of the behavior of taxonomic diversity through time results. This model appears remarkably consistent with the known pattern of Phanerozoic marine ordinal diversity as a whole. Analysis of observed rates of ordinal origination also indicates these are to a large extent diversity dependent; however, diversity dependence is not immediately evident in rates of ordinal extinction. Possible explanations for this pattern are derived from considerations of the size of higher taxa and from simulations of their diversification. These suggest that both the standing diversity and the pattern of origination of orders may adequately reflect the behavior of species diversity through time; however, correspondence between rates of ordinal and species extinction may deteriorate with progressive loss of information resulting from incomplete sampling of the fossil record.

ORDINAL AND FAMILIAL DIVERSITY OF CENOZOIC MAMMALS

SummaryVarious kinds of data concerning changes in total mammalian ordinal and familial diversity through the Cenozoic are graphed for the world and for each of the continents from which a mammalian fossil record is known. Ordinal and familial diversity increased rapidly through the Paleocene and Eocene to reach respective all‐time highs of 26 orders in the late Eocene and 116 families in the early Oligocene (bats and odontocete plus mys‐ticete whales excluded). The major continents suffered a decline in total ordinal and familial diversity in the latter half of the Oligocene with a secondary rejuvenation in the early Miocene. A remarkable uniformity in total number of orders and families per continent has obtained from the early Oligocene to Recent, and no apparent relationship exists between total diversity and continental size.A series of striking correlations exists between the times of first appearances of many mammalian and angiospermous orders and families. High numbers of first appearances (a kind of index to rates of evolutionary diversification) occurred in both mammals and flowering plants in the late Eocene to early Oligocene and in the earlier half of the Miocene. These specific times of high taxonomic diversification also correlate closely with the times of first appearance of “modern” (present at some time during the Quaternary) families of mammals and extinction of archaic families. Major mammalian faunal “turnovers” occurred in the Late Cretaceous, Eocene through early Oligocene, and early Miocene. Nevertheless, total familial and ordinal diversity of mammals on any given continent at any given time has remained remarkably stable. Some sort of faunal equilibrium is suggested.The dramatic taxonomic changes of the earlier parts of the Oligocene (i. e., high rates of appearance of new mammalian and plant taxa plus high rate of extinction of archaic mammals) correlate well with a general deterioration of the world's climate (lowering of mean annual temperature and decrease of equability) ar that time. Contemporaneous adjustments can be observed between climatic change, rates of evolutionary diversification in plants and mammals, and rates of extinction in mammals.