Premise of research. Pseudosporochnales (Cladoxylopsida) were conspicuous elements of the Earth's earliest forests. Recent evidence has done much to clarify basic aspects of the pseudosporochnalean architecture, but important questions remain about the developmental processes responsible for growth from juvenile individuals to trees of sometimes considerable size.Methodology. Presented here is combined compression/permineralization evidence of a young member of the group from a late Devonian (early Frasnian) locality also containing Eospermatopteris (Wattieza), currently the largest reconstructed pseudosporochnalean tree. Standard pyrite preparations were made and analyzed with reflected light.Pivotal results. The anatomically preserved portion of the trunk with an expanded base lacking a central vascular column shows abundant evidence of appendages with apparent rooting function supplied by traces comprised of primary and often secondary xylem. Traces arise within parenchyma near the trunk center and follow lax courses with multiple divisions outward and downward to the surface, finally enveloping the plant base for some distance. In the upper portion of the specimen, likely near the transition between the base bearing rooting appendages and the aerial shoot, the traces form a vascular plexus toward the periphery of the stem, with the bulk of vascular tissues comprising secondary xylem. Similar but differently oriented vascularization also occurs near the base.Conclusions. Here we hypothesize a unique form of "bipolar" development in this specimen, and potentially all pseudosporochnaleans, by means of a trunk base bearing an appendicular system of positively geotropic rooting appendages. In addition, we hypothesize that diffuse meristematic activity of the base plus the vascular plexus may have a previously unrecognized role in the development of pseudosporochnaleans from the small specimen observed here to large body size. We also suggest that this tissue offers an explanation for the enigmatic genus Xenocladia known from tissue fragments of large size found in coeval marine sediments of New York State. Given current incomplete understanding of development within the Pseudosprochnales, considering the rooting system as sui generis confers the advantage of adequate description of this organ, without necessarily specifying correspondence or homology with other groups.

For over 150 years, the mid-Devonian Eospermatopteris stump cast localities comprising the "oldest known petrified forest" of Goldring (1927) at Gilboa, New York have rarely been accessible for study. In 2010-2013, we had the opportunity to appraise all three major sites. Presented here are observations focusing on botanical data that may prove useful for interpreting future sites. Eospermatopteris at Riverside Quarry consists of stem base casts/ molds, and corresponding root mounds on a paleosol surface. Sizes, spatial distributions, and unusual occurrences of the root mounds are assessed. Trunks above the base are also observed as compressions showing features of outer cortex and probable vascular tissues, as interpreted fromprevious examples. An arboreal isoetalean is noted on the paleosol along with an enigmatic mound possibly representing a Stigmaria-like root system similar to that described at Cairo NY. Details of aneurophytalean stems on the paleosol surface are presented including evidence of attached lateral branch systems, or possible rooting structures of small size. The paleosol at Gilboa Dam is remarkably similar to that at Riverside Quarry, but with carbonaceous remains much better preserved. Eospermatopteris base casts and root mounds are present along with probable aneurophytalean stems showing abundant evidence of attached lateral branches that are themselves profusely branched. The Manorkill locality exhibits weathered Eospermatopteris casts that outcrop along a ledge offering profile views. The Gilboa localities are significant in providing probably the best botanical data on rooted and close to in place floral elements froma mid-Devonian paleosol to date. (C) 2021 Elsevier B.V. All rights reserved.

The origin of trees and forests in the Mid Devonian (393-383 Ma) was a turning point in Earth history, marking permanent changes to terrestrial ecology, geochemical cycles, atmospheric CO2 levels, and climate. However, how all these factors interrelate remains largely unknown. From a fossil soil (palaeosol) in the Catskill region near Cairo NY, USA, we report evidence of the oldest forest (mid Givetian) yet identified worldwide. Similar to the famous site at Gilboa, NY, we find treefern-like Eospermatopteris (Cladoxylopsida). However, the environment at Cairo appears to have been periodically drier. Along with a single enigmatic root system potentially belonging to a very early rhizomorphic lycopsid, we see spectacularly extensive root systems here assigned to the lignophyte group containing the genus Archaeopteris. This group appears pivotal to the subsequent evolutionary history of forests due to possession of multiple advanced features and likely relationship to subsequently dominant seed plants. Here we show that Archaeopteris had a highly advanced root system essentially comparable to modern seed plants. This suggests a unique ecological role for the group involving greatly expanded energy and resource utilization, with consequent influence on global processes much greater than expected from tree size or rooting depth alone.

Systematic analysis of the stable carbon isotopic composition of fossil land plants (delta C-13(p)) has the potential to offer new insights regarding paleoclimate variation and plant-environment interactions in early terrestrial ecosystems. delta C-13(p) was measured for 190 fossil plant specimens belonging to 10 genera of Early to Late Devonian age (Archaeopteris, Drepanophycus, Haskinsia, Leclercqia, Pertica, Psilophyton, Rhacophyton, Sawdonia, Tetraxylopteris, and Wattieza) and 2 genera of Early Carboniferous age (Genselia and Rhodeopteridium) collected from sites located mainly in the Appalachian Basin (22-30 degrees S paleolatitude). For the full carbon-isotopic dataset (n = 309), delta C-13(p) ranges from -20.3 parts per thousand to -30.5 parts per thousand with a mean of -25.5 parts per thousand, similar to values for modern C-3 land plants. In addition to a secular trend, delta C-13(p) exhibits both intra- and intergeneric variation. Intrageneric variation is expressed as a small (mean 0.45 parts per thousand) C-13-enrichment of leaves and spines relative to stems that may reflect differential compound-specific compositions. Intergeneric variation is expressed as a much larger (to similar to 5 parts per thousand) spread in the mean delta C-13(p) values of coeval plant genera that was probably controlled by taxon-specific habitat preferences and local environmental humidity. Among Early Devonian taxa, Sawdonia yielded the most C-13-depleted values (-27.1 +/- 1.7 parts per thousand), reflecting lower water-use efficiency that was probably related to growth in wetter habitats, and Leclercqia, Haskinsia, and Psilophyton yielded the most C-13-enriched values (-23.0 +/- 1.6 parts per thousand, -22.3 +/- 1.3 parts per thousand, and -24.8 +/- 1.6 parts per thousand, respectively), reflecting higher water-use efficiency probably related to growth in drier habitats.

Significance The evolution of trees and forests in the Mid–Late Devonian Period, 393–359 million years ago, profoundly transformed the terrestrial environment and atmosphere. The oldest fossil trees belong to the Cladoxylopsida. Their water-conducting system is a ring of hundreds of individual strands of xylem (water-conducting cells) that are interconnected in many places. Using anatomically preserved trunks, we show how these trees could grow to a large size by the production of large amounts of soft tissues and new wood around the individual xylem strands and by a controlled structural collapse at the expanding base. We have discovered a complex tree growth strategy unique in Earth history, but with some similarity to that of living palms.

We present the rationale for a cross-disciplinary investigation addressing the Devonian plant hypothesis' which proposes that the evolutionary appearance of trees with deep, complex rooting systems represents one of the major biotic feedbacks on geochemical carbon cycling during the Phanerozoic. According to this hypothesis, trees have dramatically enhanced mineral weathering driving an increased flux of Ca2+ to the oceans and, ultimately, a 90% decline in atmospheric CO2 levels through the Palaeozoic. Furthermore, experimental studies indicate a key role for arbuscular mycorrhizal fungi in soil-plant processes and especially in unlocking the limiting nutrient phosphorus in soil via Ca-phosphate dissolution mineral weathering. This suggests co-evolution of roots and symbiotic fungi since the Early Devonian could well have triggered positive feedbacks on weathering rates whereby root-fungal P release supports higher biomass forested ecosystems. Long-standing areas of uncertainty in this paradigm include the following: (1) limited fossil record documenting the origin and timeline of the evolution of tree-sized plants through the Devonian; and (2) the effects of the evolutionary advance of trees and their insitu rooting structures on palaeosol geochemistry. We are addressing these issues by integrating palaeobotanical studies with geochemical and mineralogical analyses of palaeosol sequences at selected sites across eastern North America with a particular focus on drill cores from Middle Devonian forests in Greene County, New York State.

We consider a class of dynamic tournaments in which two contestants are faced with a choice between two courses of action. The first is a riskless option (“hold”) of maintaining the resources the contestant already has accumulated in her turn and ceding the initiative to her rival. The second is the bolder option (“roll”) of taking the initiative of accumulating additional resources, and thereby moving ahead of her rival, while at the same time sustaining a risk of temporary setback. We study this tournament in the context of a jeopardy race game (JRG), extend the JRG to \(N > 2\) contestants, and construct its equilibrium solution. Compared to the equilibrium solution, the results of three experiments reveal a dysfunctional bias in favor of the riskless option. This bias is substantially mitigated when the contestants are required to commit in advance how long to pursue the risky course of action.

Mapping of Eospermatopteris root systems within ‘the Earth’s earliest forest’ clarifies its palaeoecology, produces a new interpretation of aneurophytaleans and extends the range for arborescent lycopsids.

We study batch queueing systems with continuous time, finite commuter populations, single server, and endogenously determined arrival times. Symmetric equilibrium solutions in mixed strategies are constructed and subsequently tested in two experiments that examine two different batch queueing systems, one with a fixed server capacity, and the other with a variable server capacity. With experience in playing the stage queueing game repeatedly, experimental results from groups of twenty subjects support equilibrium play on the aggregate level when the server capacity is fixed and commonly known. When it is known to be variable, randomly changing from round to round, subjects diverge from equilibrium play and increase their individual payoffs substantially by significantly shortening their waiting time.

Two auction mechanisms are studied in which players compete with one another for an exogenously determined prize by independently submitting integer bids in some discrete and commonly known strategy space specified by the auctioneer. In the unique lowest (highest) bid auction game, the winner of the prize is the player who submits the lowest (highest) bid provided that this bid is unique, i.e., unmatched by other bids. Assuming a commonly known finite population of players, a non-negative cost of entry, and an option to stay out of the auction if the entry cost is deemed too high, we propose an algorithm for computing symmetric mixed-strategy equilibrium solutions to the two variants of the auction game, illustrate them, and examine their properties.

A new method is developed to simulate the triangular distribution. The result is of interest from a practical as well as a theoretical viewpoint. The new method is surprisingly simple and is more efficient than the standard method of simulation by inversion of the cumulative distribution function. The method is also generalized to simulate the two-sided power distribution.

This paper presents a stochastic model of an individual patient’s experience during a visit to a doctor’s office. The stochastic model is based on tracking the visit of patients at a local family practice clinic. A rigorous, iterative procedure for model development allows the stochastic model to be constructed, evaluated, and validated to establish consistency with both the theoretical stochastic assumptions and the clinic’s actual operating environment. This model extends the use of stochastic models in health care in two important respects. First, the stochastic model represents an application of semi-Markov processes in outpatient health care settings. Second, through the use of the infinitesimal generator associated with the transition probability matrices governing patient flow, numerical predictions for first passage times are easily obtained.

The Blenheim-Gilboa locality in New York contains Rellimia thomsonii specimens preserved as both compressions and permineralizations that offer an unusually complete perspective on the reproductive structures, primary body, and secondary anatomy of this Middle Devonian plant. Here we describe the vegetative appendages, axis and branch size relationships, and trace departure as well as primary anatomy, including phloem sieve cells of interconnected axis orders of vegetative and fertile specimens. At least five orders are present, and each axis order is approximately half the diameter of the parent axis. Three-ribbed protosteles are evident in all axes. Protoxylem in transverse section is a continuous three- ribbed sheet one or two tracheids wide, enveloped by several cell layers of metaxylem in turn surrounded by primary phloem. Sieve cells have vertically arranged sieve areas. Trace departure to axes is similar in vegetative and fertile axes. Traces are apparent proximally as radial elongations of the tip of the parent primary xylem rib. In distal sections, the rib tip is tangentially elongated; ultimately, the trace becomes three- ribbed. Traces to vegetative appendages and fertile organs divide dichotomously. The new features described here allow us to expand and complement previous work and to discuss our whole- plant concept of Rellimia.

We study both theoretically and experimentally the decisions players make in two queueing games with batch service. In both games, players are asked to independently decide when to join a discrete-time queue to receive service, or they may simply choose not to join it at all. Equilibrium solutions in pure and mixed strategies are constructed for two games where balking is prohibited and where it is allowed. They are then tested experimentally in a study that varies the game type (balking vs. no balking) and information structure (private vs. public information) in a 2X2 between-subject design. With repeated iterations of the stage game, all four experimental conditions result in aggregate, but not individual, behavior approaching mixed-strategy equilibrium play.

A new consistency measure, the harmonic consistency index, is obtained for any positive reciprocal matrix in the analytic hierarchy process. We show how this index varies with changes in any matrix element. A tight upper bound is provided for this new consistency measure when the entries of matrix are at most 9, as is often recommended. Using simulation, the harmonic consistency index is shown to give numerical values similar to the standard consistency index but it is easier to compute and interpret. In addition, new properties of the column sums of reciprocal matrices are obtained.

Forest stump is crowned The evolution of the tree habit was fundamental to the Earth's terrestrial ecosystem. The earliest known evidence for forests consists of fossil tree stumps, about 385 million years old, from Gilboa in Upstate New York. These have been known since the 1870s and named ' Eospermatopteris '. But in the absence of the aerial portions of these trees, the affinities and significance of these stumps has remained unknown. Stein et al . now describe a spectacular tacular fossil tree from Schoharie County, New York, showing for the first time an intact crown belonging to a previously known plant type called Wattieza , attached to an Eospermatopteris trunk and base. This complete fossil of a tree-like fern provides the evidence needed for a detailed reconstruction of the appearance of the world's earliest forests.

Two types of auction were introduced on the Internet a few years ago and have rapidly been gaining widespread popularity. In both auctions, players compete for an exogenously determined prize by independently choosing an integer in some finite and common strategy space specified by the auctioneer. In the unique lowest (highest) bid auction, the winner of the prize is the player who submits the lowest (highest) bid, provided that it is unique. We construct the symmetric mixed-strategy equilibrium solutions to the two auctions, and then test them in a sequence of experiments that vary the number of bidders and size of the strategy space. Our results show that the aggregate bids, but only a minority of the individual bidders, are accounted for quite accurately by the equilibrium solutions.

For well over 50 years, the telome theory of Walter Zimmermann has been extremely influential in interpreting the evolutionary history of land plant architecture. Using the "telome/mesome" distinction, and the concept of universal "elementary processes" underlying the change in form in all plants, the theory was an ambitious synthesis based on the proposition that evolutionary change might be understood by a simple set of developmental or evolutionary rules. However, a major problem resides in deciding exactly how assertions of change are to span both developmental and evolutionary domains simultaneously, and, we argue, the theory critically fails testability as a scientific theory. Thus, despite continued popularity for the descriptive terms derived from the theory in evolutionary studies of early land plants, time has come to replace it with a more explicit, testable approach. Presented here is an attempt to clarify perhaps the most important issue raised by the telome theory-whether simple changes in basic developmental processes suffice to describe much of early land plant evolution. Considering the morphology of Silurian-Devonian fossil members, it is hypothesized that early land plants possessed a common set of developmental processes centered on primary growth of shoot apical meristems. Among these were (1) the capacity to monitor and act upon internal physiological status here modeled as "apex strength," (2) a mechanism for allocation of apex strength in a context-dependent way at each point of branching, (3) a rule for context-dependent apex angle for branches, (4) a largely invariant phyllotaxis unrelated to physiological status, and (5) a simple switch for terminating primary growth, based in part on genetics. Implemented as a set of developmental rules within a simple L-system model, these aspects of primary development in plants determine a sizable range of resultant morphologies, some of which are highly reminiscent of the early fossils. Thus, some support is found, perhaps, for Zimmermann's intuition. However, traditional concepts of growth patterns in plants, including the contrast between epidogenesis and apoxogenesis, require updating. In our reformulation, developmental processes, stated as rules of developmental dynamics, together constitute what we term the plant's developmental state. Using a hypothetico-cleductive format, one may hypothesize intrinsic (or genetic) developmental processes that play out as realized developmental activity in specific spatial/temporal contexts, as modified by multiple context factors. The resultant plant morphology is highly dependent on multiple and simultaneous pathway ontogenetic trajectories. Within a likely set of developmental rules reasonably inferred from plant development, some of Zimmermann's elementary processes are perhaps recognizable whereas others are not. Progressively "overtopped" morphologies are easily produced by modifying intrinsic branch allocation. However, even so, the other developmental rules have a profound effect on final architectures. Planate architectures and circination vernation, often treated as special cases by plant morphologists, are perhaps better understood in terms of recurrent or iterative developmental relationships. Much analytic work remains before a completely specified system of rules will emerge. A well-articulated relationship between ontogeny and phylogeny remains fundamentally important in assessing evolutionary change.Fossil and living plants make it abundantly clear that current evolutionary concepts involving modification of a sigle ontogenetic trajectory from ancestor to descendant need to be greatly expanded into consideration of the entire logical geometry of causation in development. A mechanism for testing is also required that need not wait for complete elucidation at the molecular level. The relative simplicity of plant development, combined with an outstanding fossil record of early members, offers unique opportunities along these lines.

Cluster analysis and correspondence analysis of Late Silurian (Ludlovian and Pridolian) land-plant macrofossil genera and morphological traits yielded four phytogeographic units: 1) a North Laurussian unit (Bathurst Island), which lay near the palaeoequator; 2) a South Laurussian-Northwest Gondwanan unit (Great Britain, Podolia, and Bolivia), which stretched from 18 degrees S palaeolatitude to 60-75 degrees S palaeolafitude; 3) a Kazakhstanian unit, which probably lay north of the palaeoequator; and 4) a Northeast Gondwanan (Australian) unit, at 10 degrees S palaeolafitude. Phytogeographic analyses based on both genera and morphological traits yielded the same phytogeographic units, suggesting that the observed differentiation does not result from regional taxonomic usage. A data set composed of Pridolian assemblages and 'range-through' assemblages (i.e. assemblages composed of taxa, that crossed the Siluro-Devonian boundary in each region lacking unequivocal Pridolian [late Late Silurian] assemblages) yielded the same four phytogeographic units, as did a data set composed of range-through assemblages from all six regions having Late Silurian land-plant macrofossils. Thus, the observed phytogeographic differentiation does not result from regional differences in the age of floral assemblages. Zosterophylls (Zosterophyllum, Distichophytum and Bathurstia) characterize assemblages from the equatorial North Laurussian unit. The near-equatorial East Gondwanan (Australian) unit containsZosterophyllum, an undescribed endemic zosterophyll genus, Hedeia, the lycopsid Baragwanathia and one additional undescribed endemic genus, which is probably a lycopsid [Tims, J.D.J., 1980. The Early Land Flora of Victoria. PhD Thesis, University of Melbourne, Melbourne, Australia.]. Thus, in the Late Silurian, zosterophylls and large lycopsids were most common in equatorial assemblages. The endemic genera Jugumella (a possible zosterophyll) and Cooksonella (a possible rhyniophyte) characterize the Kazakhstanian unit. Rhyniophytes and rhyniophytoids (Steganotheca, Pertonella, and the form genus, Tarrantia) characterize the wide-ranging South Laurussian-Northwest Gondwanan unit. This unit may reflect the ecological constraints of Late Silurian land plants. If many Late Silurian land plants belonged to ruderal species with wide dispersal capability that flourished only during the growing season, plants growing in seasonally dry and seasonally cold regions may have been quite similar. However, the morphological simplicity of Late Silurian land plants could cause assemblages from seasonally dry and seasonally cold regions to appear similar, even though they shared few biological genera. (c) 2006 Elsevier B.V. All rights reserved.