Modelling forest dynamics: a perspective from point process methods

This paper reviews the main applications of (marked) point process theory in forestry including functions to analyse spatial variability and the main (marked) point process models. Although correlation functions do describe spatial variability at distinct range of scale, they are clearly restricted to the analysis of few dominant species since they are based on pairwise analysis. This has over-simplified the spatial analysis of complex forest dynamics involving "large" number of species. Moreover, although process models can reproduce, to some extent, real forest spatial patterns of trees, the biological forest-ecological interpretation of the resulting spatial structures is difficult since these models usually lack of biological realism. This problem gains in strength as usually most of these point process models are defined in terms of purely spatial relationships, though in real life, forest develop through time. We thus aim to discuss the applicability of such formulations to analyse and simulate "real" forest dynamics and unwrap their shortcomes. We present a unified approach of modern spatially explicit forest growth models. Finally, we focus on a continuous space-time stochastic process as an alternative approach to generate marked point patterns evolving through space and time.     

Do Triplets Have Enough Information to Construct the Multi-Labeled Phylogenetic Tree?

The evolutionary history of certain species such as polyploids are modeled by a generalization of phylogenetic trees called multi-labeled phylogenetic trees, or MUL trees for short. One problem that relates to inferring a MUL tree is how to construct the smallest possible MUL tree that is consistent with a given set of rooted triplets, or SMRT problem for short. This problem is NP-hard. There is one algorithm for the SMRT problem which is exact and runs in time, where is the number of taxa. In this paper, we show that the SMRT does not seem to be an appropriate solution from the biological point of view. Indeed, we present a heuristic algorithm named MTRT for this problem and execute it on some real and simulated datasets. The results of MTRT show that triplets alone cannot provide enough information to infer the true MUL tree. So, it is inappropriate to infer a MUL tree using triplet information alone and considering the minimum number of duplications. Finally, we introduce some new problems which are more suitable from the biological point of view.     

Phylogenetic tree construction using sequential stochastic approximation Monte Carlo

Monte Carlo methods have received much attention recently in the literature of phylogenetic tree construction. However, they often suffer from two difficulties, the curse of dimensionality and the local-trap problem. The former one is due to that the number of possible phylogenetic trees increases at a super-exponential rate as the number of taxa increases. The latter one is due to that the phylogenetic tree has often a rugged energy landscape. In this paper, we propose a new phylogenetic tree construction method, which attempts to alleviate these two difficulties simultaneously by making use of the sequential structure of phylogenetic trees in conjunction with stochastic approximation Monte Carlo (SAMC) simulations. The use of the sequential structure of the problem provides substantial help to reduce the curse of dimensionality in simulations, and SAMC effectively prevents the system from getting trapped in local energy minima. The new method is compared with a variety of existing Bayesian and non-Bayesian methods on simulated and real datasets. Numerical results are in favor of the new method in terms of quality of the resulting phylogenetic trees.     

Complexity of the simplest phylogenetic estimation problem

The maximum-likelihood (ML) solution to a simple phylogenetic estimation problem is obtained analytically The problem is estimation of the rooted tree for three species using binary characters with a symmetrical rate of substitution under the molecular clock. ML estimates of branch lengths and log-likelihood scores are obtained analytically for each of the three rooted binary trees. Estimation of the tree topology is equivalent to partitioning the sample space (space of possible data outcomes) into subspaces, within each of which one of the three binary trees is the ML tree. Distance-based least squares and parsimony-like methods produce essentially the same estimate of the tree topology, although differences exist among methods even under this simple model. This seems to be the simplest case, but has many of the conceptual and statistical complexities involved in phylogeny estimation. The solution to this real phylogeny estimation problem will be useful for studying the problem of significance evaluation.     

Bayes estimators for phylogenetic reconstruction

Tree reconstruction methods are often judged by their accuracy, measured by how close they get to the true tree. Yet, most reconstruction methods like maximum likelihood (ML) do not explicitly maximize this accuracy. To address this problem, we propose a Bayesian solution. Given tree samples, we propose finding the tree estimate that is closest on average to the samples. This "median" tree is known as the Bayes estimator (BE). The BE literally maximizes posterior expected accuracy, measured in terms of closeness (distance) to the true tree. We discuss a unified framework of BE trees, focusing especially on tree distances that are expressible as squared euclidean distances. Notable examples include Robinson-Foulds (RF) distance, quartet distance, and squared path difference. Using both simulated and real data, we show that BEs can be estimated in practice by hill-climbing. In our simulation, we find that BEs tend to be closer to the true tree, compared with ML and neighbor joining. In particular, the BE under squared path difference tends to perform well in terms of both path difference and RF distances.     

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.     

Local Diameter Fully Constrains Dendritic Size in Basal but not Apical Trees of CA1 Pyramidal Neurons

Computational modeling of dendritic morphology is a powerful tool for quantitatively describing complex geometrical relationships, uncovering principles of dendritic development, and synthesizing virtual neurons to systematically investigate cellular biophysics and network dynamics. A feature common to many morphological models is a dependence of the branching probability on local diameter. Previous models of this type have been able to recreate a wide variety of dendritic morphologies. However, these diameter-dependent models have so far failed to properly constrain branching when applied to hippocampal CA1 pyramidal cells, leading to explosive growth. Here we present a simple modification of this basic approach, in which all parameter sampling, not just bifurcation probability, depends on branch diameter. This added constraint prevents explosive growth in both apical and basal trees of simulated CA1 neurons, yielding arborizations with average numbers and patterns of bifurcations extremely close to those observed in real cells. However, simulated apical trees are much more varied in size than the corresponding real dendrites. We show that, in this model, the excessive variability of simulated trees is a direct consequence of the natural variability of diameter changes at and between bifurcations observed in apical, but not basal, dendrites. Conversely, some aspects of branch distribution were better matched by virtual apical trees than by virtual basal trees. Dendritic morphometrics related to spatial position, such as path distance from the soma or branch order, may be necessary to fully constrain CA1 apical tree size and basal branching pattern.     

Confounding factors in HGT detection: statistical error, coalescent effects, and multiple solutions.

Prokaryotic organisms share genetic material across species boundaries by means of a process known as horizontal gene transfer (HGT). This process has great significance for understanding prokaryotic genome diversification and unraveling their complexities. Phylogeny-based detection of HGT is one of the most commonly used methods for this task, and is based on the fundamental fact that HGT may cause gene trees to disagree with one another, as well as with the species phylogeny. Using these methods, we can compare gene and species trees, and infer a set of HGT events to reconcile the differences among these trees. In this paper, we address three factors that confound the detection of the true HGT events, including the donors and recipients of horizontally transferred genes. First, we study experimentally the effects of error in the estimated gene trees (statistical error) on the accuracy of inferred HGT events. Our results indicate that statistical error leads to overestimation of the number of HGT events, and that HGT detection methods should be designed with unresolved gene trees in mind. Second, we demonstrate, both theoretically and empirically, that based on topological comparison alone, the number of HGT scenarios that reconcile a pair of species/gene trees may be exponential. This number may be reduced when branch lengths in both trees are estimated correctly. This set of results implies that in the absence of additional biological information, and/or a biological model of how HGT occurs, multiple HGT scenarios must be sought, and efficient strategies for how to enumerate such solutions must be developed. Third, we address the issue of lineage sorting, how it confounds HGT detection, and how to incorporate it with HGT into a single stochastic framework that distinguishes between the two events by extending population genetics theories. This result is very important, particularly when analyzing closely related organisms, where coalescent effects may not be ignored when reconciling gene trees. In addition to these three confounding factors, we consider the problem of enumerating all valid coalescent scenarios that constitute plausible species/gene tree reconciliations, and develop a polynomial-time dynamic programming algorithm for solving it. This result bears great significance on reducing the search space for heuristics that seek reconciliation scenarios. Finally, we show, empirically, that the locality of incongruence between a pair of trees has an impact on the numbers of HGT and coalescent reconciliation scenarios.     

Log Transformation Improves Dating of Phylogenies

Phylogenetic trees inferred from sequence data often have branch lengths measured in the expected number of substitutions and therefore, do not have divergence times estimated. These trees give an incomplete view of evolutionary histories since many applications of phylogenies require time trees. Many methods have been developed to convert the inferred branch lengths from substitution unit to time unit using calibration points, but none is universally accepted as they are challenged in both scalability and accuracy under complex models. Here, we introduce a new method that formulates dating as a nonconvex optimization problem where the variance of log-transformed rate multipliers is minimized across the tree. On simulated and real data, we show that our method, wLogDate, is often more accurate than alternatives and is more robust to various model assumptions.     

Reconstructible Phylogenetic Networks: Do Not Distinguish the Indistinguishable

Phylogenetic networks represent the evolution of organisms that have undergone reticulate events, such as recombination, hybrid speciation or lateral gene transfer. An important way to interpret a phylogenetic network is in terms of the trees it displays, which represent all the possible histories of the characters carried by the organisms in the network. Interestingly, however, different networks may display exactly the same set of trees, an observation that poses a problem for network reconstruction: from the perspective of many inference methods such networks are indistinguishable. This is true for all methods that evaluate a phylogenetic network solely on the basis of how well the displayed trees fit the available data, including all methods based on input data consisting of clades, triples, quartets, or trees with any number of taxa, and also sequence-based approaches such as popular formalisations of maximum parsimony and maximum likelihood for networks. This identifiability problem is partially solved by accounting for branch lengths, although this merely reduces the frequency of the problem. Here we propose that network inference methods should only attempt to reconstruct what they can uniquely identify. To this end, we introduce a novel definition of what constitutes a uniquely reconstructible network. For any given set of indistinguishable networks, we define a canonical network that, under mild assumptions, is unique and thus representative of the entire set. Given data that underwent reticulate evolution, only the canonical form of the underlying phylogenetic network can be uniquely reconstructed. While on the methodological side this will imply a drastic reduction of the solution space in network inference, for the study of reticulate evolution this is a fundamental limitation that will require an important change of perspective when interpreting phylogenetic networks.     

Multipolar consensus for phylogenetic trees

Collections of phylogenetic trees are usually summarized using consensus methods. These methods build a single tree, supposed to be representative of the collection. However, in the case of heterogeneous collections of trees, the resulting consensus may be poorly resolved (strict consensus, majority-rule consensus, ...), or may perform arbitrary choices among mutually incompatible clades, or splits (greedy consensus). Here, we propose an alternative method, which we call the multipolar consensus (MPC). Its aim is to display all the splits having a support above a predefined threshold, in a minimum number of consensus trees, or poles. We show that the problem is equivalent to a graph-coloring problem, and propose an implementation of the method. Finally, we apply the MPC to real data sets. Our results indicate that, typically, all the splits down to a weight of 10% can be displayed in no more than 4 trees. In addition, in some cases, biologically relevant secondary signals, which would not have been present in any of the classical consensus trees, are indeed captured by our method, indicating that the MPC provides a convenient exploratory method for phylogenetic analysis. The method was implemented in a package freely available at http://www.lirmm.fr/~cbonnard/MPC.html     

Evaluating the performance of a successive-approximations approach to parameter optimization in maximum-likelihood phylogeny estimation

Almost all studies that estimate phylogenies from DNA sequencedata under the maximum-likelihood (ML) criterion employ an approximateapproach. Most commonly, model parameters are estimated on someinitial phylogenetic estimate derived using a rapid method (neighbor-joiningor parsimony). Parameters are then held constant during a treesearch, and ideally, the procedure is repeated until convergenceis achieved. However, the effectiveness of this approximationhas not been formally assessed, in part because doing so requirescomputationally intensive, full-optimization analyses. Here,we report both indirect and direct evaluations of the effectivenessof successive approximations. We obtained an indirect evaluationby comparing the results of replicate runs on real data thatuse random trees to provide initial parameter estimates. Forsix real data sets taken from the literature, all replicateiterative searches converged to the same joint estimates oftopology and model parameters, suggesting that the approximationis not starting-point dependent, as long as the heuristic searchesof tree space are rigorous. We conducted a more direct assessmentusing simulations in which we compared the accuracy of phylogeniesestimated using full optimization of all model parameters oneach tree evaluated to the accuracy of trees estimated via successiveapproximations. There is no significant difference between theaccuracy of the approximation searches relative to full-optimizationsearches. Our results demonstrate that successive approximationis reliable and provide reassurance that this much faster approachis safe to use for ML estimation of topology.     

Molecular and Morphological Phylogenies of Mammals: Congruence with Stratigraphic Data

Tests of a sample of 206 cladograms of mammals show that morphological data seem to predict phylogenies that match the known fossil record better than molecular trees. Three metrics that assess the rank order of branching points, the stratigraphic consistency of those nodes, and the ratio of ghost range to known range show a considerable diversity of values. Some published trees show excellent matching with fossil-record data; others show almost no correspondence whatsoever. Morphological trees are nearly twice as good as molecular trees in terms of matching of the rank orders of nodes and oldest fossils, while morphological trees are 10% better than molecular in terms of stratigraphic consistency of the nodes. The ratios of ghost range to known range are lower for molecular trees. Among the molecular trees, those based on gene data are considerably better than those based on protein sequences, at least in terms of the rank order of nodes and the stratigraphic consistency of nodes. Protein trees, however, were best of all in terms of minimizing the proportion of ghost range. These findings probably indicate real phenomena, but the match of molecular trees to the expectations of stratigraphy may improve as the study of molecular phylogeny matures.     

On encodings of phylogenetic networks of bounded level

Phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees, such networks canonically induce collections of phylogenetic trees, clusters, and triplets, respectively. Thus it is not surprising that many network approaches aim to reconstruct a phylogenetic network from such collections. Related to the well-studied perfect phylogeny problem, the following question is of fundamental importance in this context: When does one of the above collections encode (i.e. uniquely describe) the network that induces it? For the large class of level-1 (phylogenetic) networks we characterize those level-1 networks for which an encoding in terms of one (or equivalently all) of the above collections exists. In addition, we show that three known distance measures for comparing phylogenetic networks are in fact metrics on the resulting subclass and give the diameter for two of them. Finally, we investigate the related concept of indistinguishability and also show that many properties enjoyed by level-1 networks are not satisfied by networks of higher level.     

Teleonomical optimization of a fractal model of the pulmonary arterial bed

Modeling the pulmonary arterial tree (PAT) is considered here as an optimal synthesis problem. Firstly, a class of candidate models is specified: the three-dimensional symmetric dichotomous fractal trees of elastic tubes described by Womersley's equations. Secondly, the parameters are shown to be constrained by interactions of PAT with the rest of the body; these constraints are used to limit the volume of the parametric space to which attention will be directed in the synthesis step. Thirdly, a teleonomical hypothesis is proposed: a naturally selected PAT must have a minimal input impedance under conditions keeping total arterial volume and distensibility as small as possible. This hypothesis is translated in mathematical terms and the resulting cost-function minimized in the limited parametric volume. The optimal model has parameter values and an impedance spectrum corresponding satisfactorily with real data. Moreover this model gives a clear picture of the internal hemodynamic behavior of PAT as an impedance matching device.     

Fast optimal genome tiling with applications to microarray design and homology search.

In this paper, we consider several variations of the following basic tiling problem: given a sequence of real numbers with two size-bound parameters, we want to find a set of tiles of maximum total weight such that each tiles satisfies the size bounds. A solution to this problem is important to a number of computational biology applications such as selecting genomic DNA fragments for PCR-based amplicon microarrays and performing homology searches with long sequence queries. Our goal is to design efficient algorithms with linear or near-linear time and space in the normal range of parameter values for these problems. For this purpose, we first discuss the solution to a basic online interval maximum problem via a sliding-window approach and show how to use this solution in a nontrivial manner for many of the tiling problems introduced. We also discuss NP-hardness results and approximation algorithms for generalizing our basic tiling problem to higher dimensions. Finally, computational results from applying our tiling algorithms to genomic sequences of five model eukaryotes are reported.     

The Gene-Duplication Problem: Near-Linear Time Algorithms for NNI-Based Local Searches

The gene-duplication problem is to infer a species supertree from a collection of gene trees that are confounded by complex histories of gene-duplication events. This problem is NP-complete and thus requires efficient and effective heuristics. Existing heuristics perform a stepwise search of the tree space, where each step is guided by an exact solution to an instance of a local search problem. A classical local search problem is the {tt NNI} search problem, which is based on the nearest neighbor interchange operation. In this work, we 1) provide a novel near-linear time algorithm for the {tt NNI} search problem, 2) introduce extensions that significantly enlarge the search space of the {tt NNI} search problem, and 3) present algorithms for these extended versions that are asymptotically just as efficient as our algorithm for the {tt NNI} search problem. The exceptional speedup achieved in the extended {tt NNI} search problems makes the gene-duplication problem more tractable for large-scale phylogenetic analyses. We verify the performance of our algorithms in a comparison study using sets of large randomly generated gene trees.     

Multiple maxima of likelihood in phylogenetic trees: an analytic approach

Maximum likelihood (ML) is a widely used criterion for selecting optimal evolutionary trees. However, the nature of the likelihood surface for trees is still not sufficiently understood, especially with regard to the frequency of multiple optima. Here, we initiate an analytic study for identifying sequences that generate multiple optima. We concentrate on the problem of optimizing edge weights for a given tree or trees (as opposed to searching through the space of all trees). We report a new approach to computing ML directly, which we have used to find large families of sequences that have multiple optima, including sequences with a continuum of optimal points. Such data sets are best supported by different (two or more) phylogenies that vary significantly in their timings of evolutionary events. Some standard biological processes can lead to data with multiple optima, and consequently the field needs further investigation. Our results imply that hill-climbing techniques as currently implemented in various software packages cannot guarantee that one will find the global ML point, even if it is unique.     

Genomic duplication problems for unrooted gene trees

Background

Discovering the location of gene duplications and multiple gene duplication episodes is a fundamental issue in evolutionary molecular biology. The problem introduced by Guigó et al. in 1996 is to map gene duplication events from a collection of rooted, binary gene family trees onto theirs corresponding rooted binary species tree in such a way that the total number of multiple gene duplication episodes is minimized. There are several models in the literature that specify how gene duplications from gene families can be interpreted as one duplication episode. However, in all duplication episode problems gene trees are rooted. This restriction limits the applicability, since unrooted gene family trees are frequently inferred by phylogenetic methods.

Results

In this article we show the first solution to the open problem of episode clustering where the input gene family trees are unrooted. In particular, by using theoretical properties of unrooted reconciliation, we show an efficient algorithm that reduces this problem into the episode clustering problems defined for rooted trees. We show theoretical properties of the reduction algorithm and evaluation of empirical datasets.

Conclusions

We provided algorithms and tools that were successfully applied to several empirical datasets. In particular, our comparative study shows that we can improve known results on genomic duplication inference from real datasets.

     

Long-term stability of marker gene expression in Prunus subhirtella: a model fruit tree species

Transgenic trees currently are being produced by Agrobacterium-mediated transformation and biolistics. Since trees are particularly suited for long-term evaluations of the impact of the technology, Prunus subhirtella autumno rosa (PAR) was chosen as model fruit tree species and transformed with a reporter gene (uidA) under the control of the 35S promoter. Using Southern and GUS fluorometric techniques, we compared transgene copy numbers and observed stability of transgene expression levels in 34 different transgenic plants, grown under in vitro, greenhouse and screenhouse conditions, over a period of 9 years. An influence of grafting on gene expression was not observed. No silenced transgenic plant was detected. Overall, these results suggest that transgene expression in perennial species, such as fruit trees, remains stable in time and space, over extended periods and in different organs, confirming the value of PAR as model species to study season-dependent regulation in mature stone fruit tissues. While the Agrobacterium-derived Prunus transformants contained one to two copies of the transgenes, 91% of the transgenic events also contained various lengths of the bacterial plasmid backbone, indicating that the Agrobacterium-mediated transformation is not as precise as previously perceived. The implications for public acceptance and future applications are discussed.