A test of the reserve meristem hypothesis using Verbascum thapsus (Scrophulariaceae)

The reserve meristem hypothesis predicts that latent meristems may act as a bet-hedging strategy given high-cost, predictable herbivory. Under this hypothesis, damage to a plant should elicit greater branching. This prediction was tested in Verbascum thapsus with three experiments manipulating the intensity and type of damage to reproductive tissue. In the first experiment, seed set was prevented in the treatment group by stigma excision and lanolin application to 80% of the flowers of each plant. In the second experiment, a minimum of two mating pairs of weevils were added to treated plants prior to the onset of flowering. In the third experiment, all fruits were sliced lengthwise twice. All three treatments significantly reduced seed set. In the first two experiments, treated plants significantly increased degree of branching (branch number and total branch length). This supports the reserve meristem hypothesis as an explanation for greater branching in larger plants of V. thapsus. Interestingly, the fruit destruction experiment failed to elicit a branching response, which suggests that the timing of damage is important.     

An empirical assessment of tree branching networks and implications for plant allometric scaling models

Several theories predict whole‐tree function on the basis of allometric scaling relationships assumed to emerge from traits of branching networks. To test this key assumption, and more generally, to explore patterns of external architecture within and across trees, we measure branch traits (radii/lengths) and calculate scaling exponents from five functionally divergent species. Consistent with leading theories, including metabolic scaling theory, branching is area preserving and statistically self‐similar within trees. However, differences among scaling exponents calculated at node‐ and whole‐tree levels challenge the assumption of an optimised, symmetrically branching tree. Furthermore, scaling exponents estimated for branch length change across branching orders, and exponents for scaling metabolic rate with plant size (or number of terminal tips) significantly differ from theoretical predictions. These findings, along with variability in the scaling of branch radii being less than for branch lengths, suggest extending current scaling theories to include asymmetrical branching and differential selective pressures in plant architectures.     

Quantitation of 3D ureteric branching morphogenesis in cultured embryonic mouse kidney

The growth and branching of the epithelial ureteric tree is critical for development of the permanent kidney (metanephros). Current methods of analysis of ureteric branching are mostly qualitative. We have developed a method for measuring the length of individual branches, and thereby the total length of the ureteric tree in 3 dimensions (3D). The method involves confocal microscopy of whole-mount immunostained metanephroi and computer-based image segmentation, skeletonisation and measurement. The algorithm performs semi-automatic segmentation of a set of confocal images and skeletonisation of the resulting binary object. Length measurements and number of branch points are automatically obtained. The final representation can be reconstructed providing a fully rotating 3D perspective of the skeletonised tree. After 36 h culture of E12 mouse metanephroi, the total length of the ureteric tree was 6103 +/- 291 microm (mean +/- SD), a four-fold increase compared with metanephroi cultured for just 6 h (1522 +/- 149 microm). Ureteric duct length increased at a rate of 153 microm/h over the first 30 h period and was maximal between 18 and 24 h at 325 microm/h. The distribution of branch lengths at the six time points studied was similar, suggesting tight control of ureteric lengthening and branching. This method will be of use in analysing ureteric growth in kidneys cultured in the presence of specific molecules suspected of regulating ureteric growth. The method can also be used to analyse in vivo kidneys and to quantify branching morphogenesis in other developing organs.     

Phylogenetic test of the molecular clock and linearized trees

To estimate approximate divergence times of species or species groups with molecular data, we have developed a method of constructing a linearized tree under the assumption of a molecular clock. We present two tests of the molecular clock for a given topology: two-cluster test and branch-length test. The two-cluster test examines the hypothesis of the molecular clock for the two lineages created by an interior node of the tree, whereas the branch-length test examines the deviation of the branch length between the tree root and a tip from the average length. Sequences evolving excessively fast or slow at a high significance level may be eliminated. A linearized tree will then be constructed for a given topology for the remaining sequences under the assumption of rate constancy. We have used these methods to analyze hominoid mitochondrial DNA and drosophilid Adh gene sequences.      

A genome evolution-based framework for measures of originality for clades

To evaluate the originality of a species for determining its conservation priority, most indices use the branching pattern and the branch length of a phylogenetic tree to represent the diversification pattern and the number of characters. One limitation of these indices is their lack of consideration of the dynamic process, such as character changes and distribution along lineages during evolution. In this study, we propose a robust framework incorporating the underlying dynamic processes under a framework of genome evolution to model character changes and distribution along different lineages in a given phylogenetic tree. Our framework provides a more transparent modeling, instead of the simple surrogates of branching pattern and branch length previously employed. Nonrandom extinction has been found to be clustered within old and species-poor clades, thus it is desirable to combine the evaluation of originality of clades, which will provide a more complete picture and a useful tool for setting global conservation priorities. Using a phylogenetic tree consisting of 70 species of New World terrestrial Carnivora, we demonstrate that the index derived from our framework can discern the difference in originality of clades. Moreover, we demonstrate that the originality of clades and species in a tree changes with different scenarios of dynamic processes, which were neglected by previous indices. We find that the originality of clades should be one of the criteria for setting global conservation priorities.     

Inferring phylogenetic relationships avoiding forbidden rooted triplets

To construct a phylogenetic tree or phylogenetic network for describing the evolutionary history of a set of species is a well-studied problem in computational biology. One previously proposed method to infer a phylogenetic tree/network for a large set of species is by merging a collection of known smaller phylogenetic trees on overlapping sets of species so that no (or as little as possible) branching information is lost. However, little work has been done so far on inferring a phylogenetic tree/network from a specified set of trees when in addition, certain evolutionary relationships among the species are known to be highly unlikely. In this paper, we consider the problem of constructing a phylogenetic tree/network which is consistent with all of the rooted triplets in a given set C and none of the rooted triplets in another given set F. Although NP-hard in the general case, we provide some efficient exact and approximation algorithms for a number of biologically meaningful variants of the problem.     

Crown alterations induced by decline: a study of relationships between growth rate and crown morphology in beech (Fagus sylvatica L.)

One of the first symptoms expressed by declining trees is reduced growth in stem diameter and length increment. The possibility of a relationship between length increment and crown thinning in beech (Fagus sylvatica L.) was investigated by developing a computer model to simulate first order branching patterns of the apical 2 m of monopodially branching beech trees, 70–100 years old, for a range of length increment rates. The model was based on values for branching angle, main axis and branch length increment, number of branches produced per year and branch mortality rates for six healthy and declining trees. Shoot growth rates in the apical 2 m of the sample trees ranged from about 5 cm/year (decline class 3) to 43 cm/ year (healthy). Simulations of branching patterns in the apical 2 m of trees growing at different rates indicated that, when growth rate exceeded about 20 cm/year, total first order branch length and area explored were independent of growth rate. When growth rates fell below this value there was a reduction in total area explored and first order branch length due primarily to the formation of fewer branches. More acute branching angles contributed to a reduction in the area explored. Growth rate-related crown thinning could increase the risk of bark necrosis and secondary pathogen infection during dry and/or hot spells.     

Identifying site-specific substitution rates

A maximum likelihood framework for estimating site-specific substitution rates is presented that does not require any prior assumptions about the rate distribution. We show that, when the branching pattern of the underlying tree is known, the analysis of pairs of positions is sufficient to estimate site-specific rates. In the abscense of a known topology, we introduce an iterative procedure to estimate simultaneously the branching pattern, the branch lengths, and site-specific substitution rates. Simulations show that the evolutionary rate of fast-evolving sites can be reliably inferred and that the accuracy of rate estimates depends mainly on the number of sequences in the data set. Thus, large sets of aligned sequences are necessary for reliable site-specific rate estimates. The method is applied to the complete mitochondrial DNA sequence of 53 humans, providing a complete picture of the site-specific substitution rates in human mitochondrial DNA.     

Quantifying the degree of self-nestedness of trees: application to the structural analysis of plants

In this paper, we are interested in the problem of approximating trees by trees with a particular self-nested structure. Self-nested trees are such that all their subtrees of a given height are isomorphic. We show that these trees present remarkable compression properties, with high compression rates. In order to measure how far a tree is from being a self-nested tree, we then study how to quantify the degree of self-nestedness of any tree. For this, we define a measure of the self-nestedness of a tree by constructing a self-nested tree that minimizes the distance of the original tree to the set of self-nested trees that embed the initial tree. We show that this measure can be computed in polynomial time and depict the corresponding algorithm. The distance to this nearest embedding self-nested tree (NEST) is then used to define compression coefficients that reflect the compressibility of a tree. To illustrate this approach, we then apply these notions to the analysis of plant branching structures. Based on a database of simulated theoretical plants in which different levels of noise have been introduced, we evaluate the method and show that the NESTs of such branching structures restore partly or completely the original, noiseless, branching structures. The whole approach is then applied to the analysis of a real plant (a rice panicle) whose topological structure was completely measured. We show that the NEST of this plant may be interpreted in biological terms and may be used to reveal important aspects of the plant growth.     

Competition-dependent modelling of foliage biomass in forest stands

Currently, foliage biomass is estimated based on stem diameter or basal area. However, it is questionable whether the relations between foliage and stem observed from plantations of a single tree species can be applied to stands of different structure or species composition. In this paper, a procedure is presented to simulate foliage and branch biomass of tree crowns relative to crown size and light competition. Crowns are divided into layers and segments and each segment is divided into a foliated and an unfoliated fraction. Depending on the competitive status of the segment, leaf area density, specific leaf area and foliated branch fraction are determined. Based on this information, foliage biomass is calculated. The procedure requires a crown shape function and a measure to characterise competition for light and space of each individual segment within the canopy. Simple solutions are suggested for both requirements to enable an application with data that can be measured non-destructively in the field; these were stem position, tree height, crown base height, crown radii and some general crown shape information. The model was parameterised from single trees of Norway spruce and European beech and partly evaluated with independent data close to the investigation plot. Evaluations showed that the model can attribute the ecology of the different crown forms. Modelled foliage distribution for beech and spruce as well as total needle biomass of spruce agreed well with measurements but foliage biomass of beech was underestimated. The results are discussed in the context of a general model application in structured forests.     

Retinal Vessel Width Measurement at Branchings Using an Improved Electric Field Theory-Based Graph Approach

The retinal vessel width relationship at vessel branch points in fundus images is an important biomarker of retinal and systemic disease. We propose a fully automatic method to measure the vessel widths at branch points in fundus images. The method is a graph-based method, in which a graph construction method based on electric field theory is applied which specifically deals with complex branching patterns. The vessel centerline image is used as the initial segmentation of the graph. Branching points are detected on the vessel centerline image using a set of detection kernels. Crossing points are distinguished from branch points and excluded. The electric field based graph method is applied to construct the graph. This method is inspired by the non-intersecting force lines in an electric field. At last, the method is further improved to give a consistent vessel width measurement for the whole vessel tree. The algorithm was validated on 100 artery branchings and 100 vein branchings selected from 50 fundus images by comparing with vessel width measurements from two human experts.     

Evaluating a non-destructive method for calibrating tree biomass equations derived from tree branching architecture

Key message

Functional branch analysis (FBA) is a promising non-destructive method that can produce accurate tree biomass equations when applied to trees which exhibit fractal branching architecture.

Abstract

Functional branch analysis (FBA) is a promising non-destructive alternative to the standard destructive method of tree biomass equation development. In FBA, a theoretical model of tree branching architecture is calibrated with measurements of tree stems and branches to estimate the coefficients of the biomass equation. In this study, species-specific and mixed-species tree biomass equations were derived from destructive sampling of trees in Western Kenya and compared to tree biomass equations derived non-destructively from FBA. The results indicated that the non-destructive FBA method can produce biomass equations that are similar to, but less accurate than, those derived from standard methods. FBA biomass prediction bias was attributed to the fact that real trees diverged from fractal branching architecture due to highly variable length–diameter relationships of stems and branches and inaccurate scaling relationships for the lengths of tree crowns and trunks assumed under the FBA model.     

Distribution of end-points of a branching network with decaying branch length

The geometry of the human bronchial tree has been described as a network formed by successive dichotomous branching with constant branching angles and geometrically decaying branch lengths. Models having these properties and with randomly distributed branching planes are constructed. The distribution of the end points of the model networks are described by computing the variance of the distributions in the direction of the axis of the network and in the transverse directions. It is found that, for a given decay ratio, there is a branching angle for which the volume filled by the end points is a maximum. The advantages of the network with the decay ratio and branching angle of the human bronchial tree are discussed.     

Estimating species trees using approximate Bayesian computation

Development of methods for estimating species trees from multilocus data is a current challenge in evolutionary biology. We propose a method for estimating the species tree topology and branch lengths using approximate Bayesian computation (ABC). The method takes as data a sample of observed rooted gene tree topologies, and then iterates through the following sequence of steps: First, a randomly selected species tree is used to compute the distribution of rooted gene tree topologies. This distribution is then compared to the observed gene topology frequencies, and if the fit between the observed and the predicted distributions is close enough, the proposed species tree is retained. Repeating this many times leads to a collection of retained species trees that are then used to form the estimate of the overall species tree. We test the performance of the method, which we call ST-ABC, using both simulated and empirical data. The simulation study examines both symmetric and asymmetric species trees over a range of branch lengths and sample sizes. The results from the simulation study show that the model performs very well, giving accurate estimates for both the topology and the branch lengths across the conditions studied, and that a sample size of 25 loci appears to be adequate for the method. Further, we apply the method to two empirical cases: a 4-taxon data set for primates and a 7-taxon data set for yeast. In both cases, we find that estimates obtained with ST-ABC agree with previous studies. The method provides efficient estimation of the species tree, and does not require sequence data, but rather the observed distribution of rooted gene topologies without branch lengths. Therefore, this method is a useful alternative to other currently available methods for species tree estimation.     

Branch lengths, support, and congruence: testing the phylogenomic approach with 20 nuclear loci in snakes

Many authors have claimed that short branches in the Tree of Life will be very difficult to resolve with strong support, even with the large multilocus data sets now made possible by genomic resources. Short branches may be especially problematic because the underlying gene trees are expected to have discordant phylogenetic histories when the time between branching events is very short. Although there are many examples of short branches that are difficult to resolve, surprisingly, no empirical studies have systematically examined the relationships between branch lengths, branch support, and congruence among genes. Here, we examine these fundamental relationships quantitatively using a data set of 20 nuclear loci for 50 species of snakes (representing most traditionally recognized families). A combined maximum likelihood analysis of the 20 loci gives strong support for 69% of the nodes, but many remain weakly supported, with bootstrap values for 20% ranging from 21% to 66%. For the combined-data tree, we find significant correlations between the length of a branch, levels of bootstrap support, and the proportion of genes that are congruent with that branch in the separate analyses of each gene. We also find that strongly supported conflicts between gene trees over the resolution of individual branches are common (roughly 35% of clades), especially for shorter branches. Overall, our results support the hypothesis that short branches may be very difficult to confidently resolve, even with large, multilocus data sets. Nevertheless, our study provides strong support for many clades, including several that were controversial or poorly resolved in previous studies of snake phylogeny.     

Identifying the rooted species tree from the distribution of unrooted gene trees under the coalescent

Gene trees are evolutionary trees representing the ancestry of genes sampled from multiple populations. Species trees represent populations of individuals—each with many genes—splitting into new populations or species. The coalescent process, which models ancestry of gene copies within populations, is often used to model the probability distribution of gene trees given a fixed species tree. This multispecies coalescent model provides a framework for phylogeneticists to infer species trees from gene trees using maximum likelihood or Bayesian approaches. Because the coalescent models a branching process over time, all trees are typically assumed to be rooted in this setting. Often, however, gene trees inferred by traditional phylogenetic methods are unrooted. We investigate probabilities of unrooted gene trees under the multispecies coalescent model. We show that when there are four species with one gene sampled per species, the distribution of unrooted gene tree topologies identifies the unrooted species tree topology and some, but not all, information in the species tree edges (branch lengths). The location of the root on the species tree is not identifiable in this situation. However, for 5 or more species with one gene sampled per species, we show that the distribution of unrooted gene tree topologies identifies the rooted species tree topology and all its internal branch lengths. The length of any pendant branch leading to a leaf of the species tree is also identifiable for any species from which more than one gene is sampled.     

The probability of a gene tree topology within a phylogenetic network with applications to hybridization detection

Gene tree topologies have proven a powerful data source for various tasks, including species tree inference and species delimitation. Consequently, methods for computing probabilities of gene trees within species trees have been developed and widely used in probabilistic inference frameworks. All these methods assume an underlying multispecies coalescent model. However, when reticulate evolutionary events such as hybridization occur, these methods are inadequate, as they do not account for such events. Methods that account for both hybridization and deep coalescence in computing the probability of a gene tree topology currently exist for very limited cases. However, no such methods exist for general cases, owing primarily to the fact that it is currently unknown how to compute the probability of a gene tree topology within the branches of a phylogenetic network. Here we present a novel method for computing the probability of gene tree topologies on phylogenetic networks and demonstrate its application to the inference of hybridization in the presence of incomplete lineage sorting. We reanalyze a Saccharomyces species data set for which multiple analyses had converged on a species tree candidate. Using our method, though, we show that an evolutionary hypothesis involving hybridization in this group has better support than one of strict divergence. A similar reanalysis on a group of three Drosophila species shows that the data is consistent with hybridization. Further, using extensive simulation studies, we demonstrate the power of gene tree topologies at obtaining accurate estimates of branch lengths and hybridization probabilities of a given phylogenetic network. Finally, we discuss identifiability issues with detecting hybridization, particularly in cases that involve extinction or incomplete sampling of taxa.     

Vertical stratification in the spatial distribution of the beech scale insect (Ultracoelostoma assimile) in Nothofagus tree canopies in New Zealand

Abstract. 1. The degree of infestation by New Zealand sooty beech scale insects (Ultracoelostoma assimile, Homoptera: Margarodidae) varies dramatically among adjacent southern beech trees (Nothofagus spp., Fagaceae), but has previously been assumed to be uniformly or randomly distributed within individual host trees. In this study, a full‐census survey was conducted from ground level to canopy level on 14 naturally occurring, canopy‐dominant red beech (Nothofagus fusca) trees (size range 38.7–107.6 cm diameter at breast height) to determine the degree of within‐tree heterogeneity in herbivore density. 2. The within‐tree distribution of the sooty beech scale was vertically stratified and highly heterogeneous, with the greatest densities occurring on bark surfaces in the canopy rather than on the trunk, and on the lower rather than upper sides of the branches. The spatial distribution was strongly negatively correlated with trunk and branch diameter, and increasing bark thickness (as a function of diameter) provides a plausible explanation for differences in the establishment and population density of sooty beech scale insects with trunk and branch size. Furthermore, there was a significant change in the spatial distribution of scale insect populations on trunks and branches of trees of increasing diameter at breast height. This indicates a strong temporal component to the spatial dynamics of the sooty beech scale insect driven by changing host phenology. Future studies on phytophagous insects infesting large host trees need to consider more explicitly changes in population dynamics through space and time. 3. Because of the high degree of within‐tree heterogeneity in population density, the total population size of scale insects on an individual tree could not be predicted from any measure of population density low on the trunk. However, the dry weight biomass of sooty mould fungi growing on the ground beneath infested trees was a remarkably accurate predictor of the total population size of scale insects. The use of sooty mould fungi as a relative measure of population size could be incorporated into studies of other honeydew‐producing hemipterans, since the growth of sooty mould is a distinctive feature synonymous with high concentrations of honeydew production worldwide.     

Gene tree distributions under the coalescent process

Under the coalescent model for population divergence, lineage sorting can cause considerable variability in gene trees generated from any given species tree. In this paper, we derive a method for computing the distribution of gene tree topologies given a bifurcating species tree for trees with an arbitrary number of taxa in the case that there is one gene sampled per species. Applications for gene tree distributions include determining exact probabilities of topological equivalence between gene trees and species trees and inferring species trees from multiple datasets. In addition, we examine the shapes of gene tree distributions and their sensitivity to changes in branch lengths, species tree shape, and tree size. The method for computing gene tree distributions is implemented in the computer program COAL.     

Reprint of: Tree-tree interactions and crown complementarity: the role of functional diversity and branch traits for canopy packing

Previous studies have shown that tree species richness increases forest productivity by allowing for greater spatial complementarity of tree crowns (crown complementarity), which in turn results in more densely packed canopies. However, the mechanisms driving crown complementarity in tree species mixtures remain unclear. Here, we take advantage of a high-resolution, three-dimensional terrestrial laser scanning approach in the context of a large-scale biodiversity-ecosystem functioning experiment in subtropical China (BEF-China) to quantify the extent to which functional dissimilarity and divergences in branch traits between neighbouring trees affect crown complementarity at the scale of tree species pairs (i.e., two adjacent trees). Overall, we found no support that functional dissimilarity (divergence in morphological flexibility, specific leaf area and wood density) promotes crown complementarity. However, we show that the effects of functional dissimilarity (the plasticity of the outer crown structure) on crown complementarity vary in their magnitude and importance depending on branch trait divergences. Firstly, crown complementarity tended to be highest for tree species pairs that strongly differed in their functional traits, but were similar in branch density. In contrast, heterospecific pairs with a low functional trait divergence benefitted the most from a large difference in branch density compared with pairs characterised by a large functional dissimilarity. Secondly, the positive effects of increasing divergence in branching intensity (the plasticity of the inner crown structure) on crown complementarity became most important at low levels of functional dissimilarity, i.e. when species pairs were similar in their branch packing and vice versa. This suggests that species mixing allows trees to occupy canopy space more efficiently mainly due to phenotypic changes associated with crown morphology and branch plasticity. Our findings highlight the importance of considering outer and inner crown structures (e.g. branching architecture) to deepen our understanding of tree-tree interactions in mixed-species communities.