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Abstract Migration independently evolved numerous times in animals, with a myriad of ecological and evolutionary implications. In fishes, perhaps the most extreme form of migration is diadromy, the migration between marine and freshwater environments. Key and long-standing questions are: how many times has diadromy evolved in fishes, how frequently do diadromous clades give rise to non-diadromous species, and does diadromy influence lineage diversification rates? Many diadromous fishes have large geographic ranges with constituent populations that use isolated freshwater habitats. This may limit gene flow between some populations, increasing the likelihood of speciation in diadromous lineages relative to nondiadromous lineages. Alternatively, diadromy may reduce lineage diversification rates if migration is associated with enhanced dispersal capacity that facilitates gene flow within and between populations. Clupeiformes (herrings, sardines, shads, and anchovies) is a model clade for testing hypotheses about the evolution of diadromy because it includes an exceptionally high proportion of diadromous species and several independent evolutionary origins of diadromy. However, relationships among major clupeiform lineages remain unresolved, and existing phylogenies sparsely sampled diadromous species, limiting the resolution of phylogenetically informed statistical analyses. We assembled a phylogenomic dataset and used multi-species coalescent and concatenation-based approaches to generate the most comprehensive, highly resolved clupeiform phylogeny to date, clarifying associations among several major clades and identifying recalcitrant relationships needing further examination. We determined that variation in rates of sequence evolution (heterotachy) and base-composition (nonstationarity) had little impact on our results. Using this phylogeny, we characterized evolutionary patterns of diadromy and tested for differences in lineage diversification rates between diadromous, marine, and freshwater lineages. We identified 13 transitions to diadromy, all during the Cenozoic Era (10 origins of anadromy, 2 origins of catadromy, and 1 origin of amphidromy), and 7 losses of diadromy. Two diadromous lineages rapidly generated nondiadromous species, demonstrating that diadromy is not an evolutionary dead end. We discovered considerably faster transition rates out of diadromy than to diadromy. The largest lineage diversification rate increase in Clupeiformes was associated with a transition to diadromy, but we uncovered little statistical support for categorically faster lineage diversification rates in diadromous versus nondiadromous fishes. We propose that diadromy may increase the potential for accelerated lineage diversification, particularly in species that migrate long distances. However, this potential may only be realized in certain biogeographic contexts, such as when diadromy allows access to ecosystems in which there is limited competition from incumbent species. 

Context:Compilers are the fundamental tools for software development. Thus, compiler defects can disrupt development productivity and propagate errors into developer-written software source code. Categorizing defects in compilers can inform practitioners and researchers about the existing defects in compilers and techniques that can be used to identify defects systematically. Objective:The goal of this paper is to help researchers understand the nature of defects in compilers by conducting a review of Internet artifacts and peer-reviewed publications that study defect characteristics of compilers. Methodology:We conduct a multi-vocal literature review (MLR) with 26 publications and 32 Internet artifacts to characterize compiler defects. Results:From our MLR, we identify 13 categories of defects, amongst which optimization defects have been the most reported defects in our artifacts publications. We observed 15 defect identification techniques tailored for compilers and no single technique identifying all observed defect categories. Conclusion:Our MLR lays the groundwork for practitioners and researchers to identify defects in compilers systematically. 

A k-dispersed labelling of a graph G on n vertices is a labelling of the vertices of G by the integers 1,...,n such that d(i,i+1) ≥ k for 1 ≤ i ≤ n − 1. Here DL(G) denotes the maximum value of k such that G has a k-dispersed labelling. In this paper, we study upper and lower bounds on DL(G). Computing DL(G) is NP-hard. However, we determine the exact value of DL(G) for cycles, paths, grids, hypercubes and complete binary trees. We also give a product construction and we prove a degree-based bound. 

In the first partial result toward Steinberg’s now-disproved three coloring conjecture, Abbott and Zhou used a counting argument to show that every planar graph without cycles of lengths 4 through 11 is 3-colorable. Implicit in their proof is a fact about plane graphs: in any plane graph of minimum degree 3, if no two triangles share an edge, then triangles make up strictly fewer than 2/3 of the faces. We show how this result, combined with Kostochka and Yancey’s resolution of Ore’s conjecture for k = 4, implies that every planar graph without cycles of lengths 4 through 8 is 3-colorable. 

Abstract Birth–death stochastic processes are the foundations of many phylogenetic models and are widely used to make inferences about epidemiological and macroevolutionary dynamics. There are a large number of birth–death model variants that have been developed; these impose different assumptions about the temporal dynamics of the parameters and about the sampling process. As each of these variants was individually derived, it has been difficult to understand the relationships between them as well as their precise biological and mathematical assumptions. Without a common mathematical foundation, deriving new models is nontrivial. Here, we unify these models into a single framework, prove that many previously developed epidemiological and macroevolutionary models are all special cases of a more general model, and illustrate the connections between these variants. This unification includes both models where the process is the same for all lineages and those in which it varies across types. We also outline a straightforward procedure for deriving likelihood functions for arbitrarily complex birth–death(-sampling) models that will hopefully allow researchers to explore a wider array of scenarios than was previously possible. By rederiving existing single-type birth–death sampling models, we clarify and synthesize the range of explicit and implicit assumptions made by these models. [Birth–death processes; epidemiology; macroevolution; phylogenetics; statistical inference.]