Mathematical Models and Biological Meaning: Taking Trees Seriously

We compare three basic kinds of discrete mathematical models used to portray phylogenetic relationships among species and higher taxa: phylogenetic trees, Hennig trees and Nelson cladograms. All three models are trees, as that term is commonly used in mathematics; the difference between them lies in the biological interpretation of their vertices and edges. Phylogenetic trees and Hennig trees carry exactly the same information, and translation between these two kinds of trees can be accomplished by a simple algorithm. On the other hand, evolutionary concepts such as monophyly are represented as different mathematical substructures are represented differently in the two models. For each phylogenetic or Hennig tree, there is a Nelson cladogram carrying the same information, but the requirement that all taxa be represented by leaves necessarily makes the representation less efficient. Moreover, we claim that it is necessary to give some interpretation to the edges and internal vertices of a Nelson cladogram in order to make it useful as a biological model. One possibility is to interpret internal vertices as sets of characters and the edges as statements of inclusion; however, this interpretation carries little more than incomplete phenetic information. We assert that from the standpoint of phylogenetics, one is forced to regard each internal vertex of a Nelson cladogram as an actual (albeit unsampled) species simply to justify the use of synapomorphies rather than symplesiomorphies.Comment: 15 pages including 6 figures [5 pdf, 1 jpg]. Converted from original MS Word manuscript to PDFLaTe

Action potential energy efficiency varies among neuron types in vertebrates and invertebrates.

The initiation and propagation of action potentials (APs) places high demands on the energetic resources of neural tissue. Each AP forces ATP-driven ion pumps to work harder to restore the ionic concentration gradients, thus consuming more energy. Here, we ask whether the ionic currents underlying the AP can be predicted theoretically from the principle of minimum energy consumption. A long-held supposition that APs are energetically wasteful, based on theoretical analysis of the squid giant axon AP, has recently been overturned by studies that measured the currents contributing to the AP in several mammalian neurons. In the single compartment models studied here, AP energy consumption varies greatly among vertebrate and invertebrate neurons, with several mammalian neuron models using close to the capacitive minimum of energy needed. Strikingly, energy consumption can increase by more than ten-fold simply by changing the overlap of the Na+ and K+ currents during the AP without changing the APs shape. As a consequence, the height and width of the AP are poor predictors of energy consumption. In the Hodgkin–Huxley model of the squid axon, optimizing the kinetics or number of Na+ and K+ channels can whittle down the number of ATP molecules needed for each AP by a factor of four. In contrast to the squid AP, the temporal profile of the currents underlying APs of some mammalian neurons are nearly perfectly matched to the optimized properties of ionic conductances so as to minimize the ATP cost

Sea surface temperature contributes to marine crocodylomorph evolution

During the Mesozoic and Cenozoic, four distinct crocodylomorph lineages colonized the marine environment. They were conspicuously absent from high latitudes, which in the Mesozoic were occupied by warm-blooded ichthyosaurs and plesiosaurs. Despite a relatively well-constrained stratigraphic distribution, the varying diversities of marine crocodylomorphs are poorly understood, because their extinctions neither coincided with any major biological crises nor with the advent of potential competitors. Here we test the potential link between their evolutionary history in terms of taxic diversity and two abiotic factors, sea level variations and sea surface temperatures (SST). Excluding Metriorhynchoidea, which may have had a peculiar ecology, significant correlations obtained between generic diversity and estimated Tethyan SST suggest that water temperature was a driver of marine crocodylomorph diversity. Being most probably ectothermic reptiles, these lineages colonized the marine realm and diversified during warm periods, then declined or became extinct during cold intervals

New remains ofMachimosaurus hugiivon Meyer, 1837 (Crocodilia, Thalattosuchia) from the Kimmeridgian of Germany

The fourth complete skull of the marine crocodilian Machimosaurus von Meyer, 1837 is hereby described together with an associated complete mandible and disarticulated postcranial elements from the Kimmeridgian of Neuffen, Germany. Although the genus has been described fairly recently on the basis of two nearly complete skulls, their state of preservation did not allow a thorough examination of the entire skull anatomy. Here, we add new information with the description of nicely preserved cranial and mandibular elements of a single individual attributable to Machimosaurus hugii von Meyer, 1837. The diagnosis is updated for the genus and for the species M. hugii and challenges the validity of the second species M. mosae (Liénard, 1876). Moreover, previous assumption that Steneosaurus obtusidens Andrews, 1913 is a junior synonym of Machimosaurus hugii is not supported by our observations. Notably, M. hugii differs from S. obtusidens by a lower tooth count, the morphology of the dentition, the shape of the supratemporal fenestrae and the absence of an antorbital fenestra. Comparative anatomy and a phylogenetic analysis show that Machimosaurus is more closely related to the genus Steneosaurus than to Teleosaurus cadomensis (Lamouroux, 1820).doi:10.1002/mmng.20130000

Increasing spanning forests in graphs and simplicial complexes

Let G be a graph with vertex set {1,...,n}. A spanning forest F of G is increasing if the sequence of labels on any path starting at the minimum vertex of a tree of F forms an increasing sequence. Hallam and Sagan showed that the generating function ISF(G, t) for increasing spanning forests of G has all nonpositive integral roots. Furthermore they proved that, up to a change of sign, this polynomial equals the chromatic polynomial of G precisely when 1,..., n is a perfect elimination order for G. We give new, purely combinatorial proofs of these results which permit us to generalize them in several ways. For example, we are able to bound the coef- cients of ISF(G, t) using broken circuits. We are also able to extend these results to simplicial complexes using the new notion of a cage-free complex. A generalization to labeled multigraphs is also given. We observe that the de nition of an increasing spanning forest can be formulated in terms of pattern avoidance, and we end by exploring spanning forests that avoid the patterns 231, 312 and 321

Variation in Resource Acquisition and Utilization Traits Between Native and Invasive Perennial Forbs

Understanding the functional traits that allow invasives to outperform natives is a necessary first step in improving our ability to predict and manage the spread of invaders. In nutrient-limited systems, plant competitive ability is expected to be closely tied to the ability of a plant to exploit nutrient-rich microsites and use these captured nutrients efficiently. The broad objective of this work was to compare the ability of native and invasive perennial forbs to acquire and use nutrients from nutrient-rich microsites. We evaluated morphological and physiological responses among four native and four invasive species exposed to heterogeneous (patch) or homogeneous (control) nutrient distribution. Invasives, on average, allocated more biomass to roots and allocated proportionately more root length to nutrient-rich microsites than did natives. Invasives also had higher leaf N, photosynthetic rates, and photosynthetic nitrogen use efficiency than natives, regardless of treatment. While these results suggest multiple traits may contribute to the success of invasive forbs in low-nutrient environments, we also observed large variation in these traits among native forbs. These observations support the idea that functional trait variation in the plant community may be a better predictor of invasion resistance than the functional group composition of the plant community

Examining student ICT ownership, use and preferences towards electronically delivered learning resources in Nakhon Phanom University and Sakon Nakhon Rajabhat University

The objectives of this research were 1) to find students’ ownership of technology devices, ownership, soft-ware facility, and preferences, 2) to find out what devices instructors use in the classroom, 3) to find out how the students use the online learning that the university provided for them, and 4) to examine students’ software skills. The questionnaire and the interview instruments were designed to clarify participants’ attitudes, and used a Likert scale. Surveys and qualitative research design were developed using Qualtrics software, which is an online research survey tool that can be used for a whole range of data gathering purposes applicable to Higher Degree Research. The samples were the students in both universities (Nakhon Phanom University and Sakon Nakhon Rajabhat University), a total of 977 people. A statistical computer program was employed

Counting Arithmetical Structures on Paths and Cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag (d) - A) r=0 , where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag (d) - A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients ((2n-1)/(n-1)) , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

Counting Arithmetical Structures on Paths and Cycles

Let G be a finite, connected graph. An arithmetical structure on G is a pair of positive integer vectors d, r such that (diag (d) - A) r=0 , where A is the adjacency matrix of G. We investigate the combinatorics of arithmetical structures on path and cycle graphs, as well as the associated critical groups (the torsion part of the cokernels of the matrices (diag (d) - A)). For paths, we prove that arithmetical structures are enumerated by the Catalan numbers, and we obtain refined enumeration results related to ballot sequences. For cycles, we prove that arithmetical structures are enumerated by the binomial coefficients ((2n-1)/(n-1)) , and we obtain refined enumeration results related to multisets. In addition, we determine the critical groups for all arithmetical structures on paths and cycles

Relating Detonation Parameters to the Detonation Synthesis of Silicon Carbide

Detonation synthesis of silicon carbide (SiC) nanoparticles from carbon liberated by negatively oxygen balanced explosives was evaluated in a 23 factorial design to determine the effects of three categorical experimental factors: (1) cyclotrimethylene-trinitramine (RDX)/2,4,6-trinitrotoluene (TNT) ratio, (2) silicon (Si) additive concentration, and (3) Si particle size. These factors were evaluated at low and high levels as they relate to the detonation performance of the explosive and the solid Si-containing phases produced. Detonation velocity and Chapman-Jouguet (C-J) detonation pressure, which were measured using rate stick plate dent tests, were evaluated. Solid detonation product mass, silicon carbide product concentration, and residual silicon concentration were evaluated using the x-ray diffraction analysis. The factors of Si concentration and the RDX:TNT ratio were shown to affect detonation performance in terms of detonation velocity and C-J pressure by up to 10% and 22%, respectively. Increased concentration of Si in the reactants improved the average SiC concentration in the detonation products from 1.9 to 2.8 wt. %. Similarly, increasing the ratio of RDX to TNT further oxidized detonation products and reduced the average residual Si remaining after detonation from 8.6 to 2.8 wt. %. A 70:30 mass ratio mixture of RDX to TNT loaded with 10 wt. % \u3c 44 μm silicon powder produced an estimated 1.33 g of nanocrystalline cubic silicon carbide from a 150-g test charge. Using a lower concentration of added silicon with a finer particle size reduced SiC yield in the residue to 0.38 g yet improved the SiC to residual Si ratio to 1.64:1