A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling

1. A first step in the analysis of complex movement data often involves discretisation of the path into a series of step-lengths and turns, for example in the analysis of specialised random walks, such as Lévy flights. However, the identification of turning points, and therefore step-lengths, in a tortuous path is dependent on ad-hoc parameter choices. Consequently, studies testing for movement patterns in these data, such as Lévy flights, have generated debate. However, studies focusing on one-dimensional (1D) data, as in the vertical displacements of marine pelagic predators, where turning points can be identified unambiguously have provided strong support for Lévy flight movement patterns. 2. Here, we investigate how step-length distributions in 3D movement patterns would be interpreted by tags recording in 1D (i.e. depth) and demonstrate the dimensional symmetry previously shown mathematically for Lévy-flight movements. We test the veracity of this symmetry by simulating several measurement errors common in empirical datasets and find Lévy patterns and exponents to be robust to low-quality movement data. 3. We then consider exponential and composite Brownian random walks and show that these also project into 1D with sufficient symmetry to be clearly identifiable as such. 4. By extending the symmetry paradigm, we propose a new methodology for step-length identification in 2D or 3D movement data. The methodology is successfully demonstrated in a re-analysis of wandering albatross Global Positioning System (GPS) location data previously analysed using a complex methodology to determine bird-landing locations as turning points in a Lévy walk. For this high-resolution GPS data, we show that there is strong evidence for albatross foraging patterns approximated by truncated Lévy flights spanning over 3·5 orders of magnitude. 5. Our simple methodology and freely available software can be used with any 2D or 3D movement data at any scale or resolution and are robust to common empirical measurement errors. The method should find wide applicability in the field of movement ecology spanning the study of motile cells to humans.

Evolution of the diatoms: major steps in their evolution and a review of the supporting molecular and morphological evidence.

Over the years, many reviews of different aspects of diatom biology, ecology and evolution have appeared. Since 1993 many molecular trees have been produced to infer diatom phylogeny. In 2004, Medlin & Kaczmarska revised the systematics of the diatoms based on more than 20 years of consistent recovery of two major clades of diatoms that did not correspond to a traditional concept of centrics and pennates and established three classes of diatoms: Clade 1 = Coscinodiscophyceae (radial centrics) and Clade 2 = Mediophyceae (polar centrics + radial Thalassiosirales) and Bacillariophyceae (pennates). However, under certain analytical conditions, an alternative view of diatom evolution, a grades of clades, has been recovered that suggests a gradual evolution from centric to pennate symmetry. These two schemes of diatom evolution are evaluated in terms of whether or not the criteria advocated by Medlin & Kaczmarska that should be met to recover monophyletic classes have been used. The monophyly of the three diatom classes can only be achieved if (1) a secondary structure of the small subunit (SSU) rRNA gene was used to construct the alignment and not an alignment based on primary structure and (2) multiple outgroups were used. These requirements have not been met in each study of diatom evolution; hence, the grade of clades, which is useful in reconstructing the sequence of evolution, is not useful for accepting the new classification of the diatoms. Evidence for how these two factors affect the recovery of the three monophyletic classes is reviewed here. The three classes have been defined by clear morphological differences primarily based on gametangia and auxospore ontogeny and envelope structure, the presence or absence of a structure (tube process or sternum) associated with the annulus and the location of the cribrum in those genera with loculate areolae. New evidence supporting the three clades is reviewed. Other features of the cell are examined to determine whether they can also be used to support the monophyly of the three classes.

Evolution of the diatoms: major steps in their evolution and a review of the supporting molecular and morphological evidence.

Over the years, many reviews of different aspects of diatom biology, ecology and evolution have appeared. Since 1993 many molecular trees have been produced to infer diatom phylogeny. In 2004, Medlin & Kaczmarska revised the systematics of the diatoms based on more than 20 years of consistent recovery of two major clades of diatoms that did not correspond to a traditional concept of centrics and pennates and established three classes of diatoms: Clade 1 = Coscinodiscophyceae (radial centrics) and Clade 2 = Mediophyceae (polar centrics + radial Thalassiosirales) and Bacillariophyceae (pennates). However, under certain analytical conditions, an alternative view of diatom evolution, a grades of clades, has been recovered that suggests a gradual evolution from centric to pennate symmetry. These two schemes of diatom evolution are evaluated in terms of whether or not the criteria advocated by Medlin & Kaczmarska that should be met to recover monophyletic classes have been used. The monophyly of the three diatom classes can only be achieved if (1) a secondary structure of the small subunit (SSU) rRNA gene was used to construct the alignment and not an alignment based on primary structure and (2) multiple outgroups were used. These requirements have not been met in each study of diatom evolution; hence, the grade of clades, which is useful in reconstructing the sequence of evolution, is not useful for accepting the new classification of the diatoms. Evidence for how these two factors affect the recovery of the three monophyletic classes is reviewed here. The three classes have been defined by clear morphological differences primarily based on gametangia and auxospore ontogeny and envelope structure, the presence or absence of a structure (tube process or sternum) associated with the annulus and the location of the cribrum in those genera with loculate areolae. New evidence supporting the three clades is reviewed. Other features of the cell are examined to determine whether they can also be used to support the monophyly of the three classes.

A timescale for diatom evolution based on four molecular markers: reassessment of ghost lineages and major steps defining diatom evolution.

ABSTRACT. – Phylogenies and molecular clocks of the diatoms have largely been inferred from SSU rDNA sequences. A new phylogeny of diatoms was estimated using four gene markers SSU and LSU rDNA rbcL and psbA (total 4352 bp) with 42 diatom species. The four gene trees analysed with a maximum likelihood (ML) and Baysian (BI) analysis recovered a monophyletic origin of the new diatom classes with high bootstrap support, which has been controversial with single gene markers using single outgroups and alignments that do not take secondary structure of the SSU gene into account. The divergence time of the classes were calculated from a ML tree in the MultliDiv Time program using a Bayesian estimation allowing for simultaneous constraints from the fossil record and varying rates of molecular evolution of different branches in the phylogenetic tree. These divergence times are generally in agreement with those proposed by other clocks using single genes with the exception that the pennates appear much earlier and suggest a longer Cretaceous fossil record that has yet to be sampled. Ghost lineages (i.e. the discrepancy between first appearance (FA) and molecular clock age of origin from an extant taxon) were revealed in the pennate lineage, whereas those ghost lineages in the centric lineages previously reported by others are reviewed and referred to earlier literature.

A timescale for diatom evolution based on four molecular markers: reassessment of ghost lineages and major steps defining diatom evolution.

ABSTRACT. – Phylogenies and molecular clocks of the diatoms have largely been inferred from SSU rDNA sequences. A new phylogeny of diatoms was estimated using four gene markers SSU and LSU rDNA rbcL and psbA (total 4352 bp) with 42 diatom species. The four gene trees analysed with a maximum likelihood (ML) and Baysian (BI) analysis recovered a monophyletic origin of the new diatom classes with high bootstrap support, which has been controversial with single gene markers using single outgroups and alignments that do not take secondary structure of the SSU gene into account. The divergence time of the classes were calculated from a ML tree in the MultliDiv Time program using a Bayesian estimation allowing for simultaneous constraints from the fossil record and varying rates of molecular evolution of different branches in the phylogenetic tree. These divergence times are generally in agreement with those proposed by other clocks using single genes with the exception that the pennates appear much earlier and suggest a longer Cretaceous fossil record that has yet to be sampled. Ghost lineages (i.e. the discrepancy between first appearance (FA) and molecular clock age of origin from an extant taxon) were revealed in the pennate lineage, whereas those ghost lineages in the centric lineages previously reported by others are reviewed and referred to earlier literature.