Long branch effects distort maximum likelihood phylogenies in simulations despite selection of the correct model

The aim of our study was to test the robustness and efficiency of maximum likelihood with respect to different long branch effects on multiple-taxon trees. We simulated data of different alignment lengths under two different 11-taxon trees and a broad range of different branch length conditions. The data were analyzed with the true model parameters as well as with estimated and incorrect assumptions about among-site rate variation. If length differences between connected branches strongly increase, tree inference with the correct likelihood model assumptions can fail. We found that incorporating invariant sites together with Γ distributed site rates in the tree reconstruction (Γ+I) increases the robustness of maximum likelihood in comparison with models using only Γ. The results show that for some topologies and branch lengths the reconstruction success of maximum likelihood under the correct model is still low for alignments with a length of 100,000 base positions. Altogether, the high confidence that is put in maximum likelihood trees is not always justified under certain tree shapes even if alignment lengths reach 100,000 base positions.     

Drivers of stem radial variation and its pattern in peatland Scots pines: A pilot study

Dendrometers are useful tools to analyze intra-annual variation of radial growth in trees, but have rarely been applied in marginal environments. Our aim in this study was to explore stem radial variation (SRV) of Scots pines (Pinus sylvestris L.) growing in a marginal environment on top of a peatland and compare it with stem radial variation of Scots pines growing in a nearby forest. We compared high-resolution (30 min) tree-growth of the peatland and forest pines in two consecutive years in two ways. First, we modeled raw SRV using site and weather parameters as predictors, to determine if and in what way stem radial variation depends on the site type. Second, we split the SRV signal into sub-series of varying length to test for differences between the time-series pattern of peatland and forest SRV with clustering methods and classifier models. We found indications that site type is influencing raw stem radial variation as: 1) an intercept, i.e. forest trees tended to grow more than peatland trees (as expected); 2) an interaction factor with structural and weather parameters, i.e. response of the forest trees to changing environmental parameters was different than the response of the peatland trees. Conversely, with regard to the temporal pattern of the stem radial variation, we found that the conditions within one year, e.g. weather patterns, were more important than site conditions, especially at short time scales. However, with increasing length of the sub-series the relative accuracy of the classifier models increased. Our results indicate that the site type was important for the raw SRV (amplitude) but not for the SRV pattern, which might be important to consider when comparing intra-annual signals from multiple sites.     

Quartets MaxCut: a divide and conquer quartets algorithm

Accurate phylogenetic reconstruction methods are currently limited to a maximum of few dozens of taxa. Supertree methods construct a large tree over a large set of taxa, from a set of small trees over overlapping subsets of the complete taxa set. Hence, in order to construct the tree of life over a million and a half different species, the use of a supertree method over the product of accurate methods, is inevitable. Perhaps the simplest version of this task that is still widely applicable, yet quite challenging, is quartet-based reconstruction. This problem lies at the root of many tree reconstruction methods and theoretical as well as experimental results have been reported. Nevertheless, dealing with false, conflicting quartet trees remains problematic. In this paper, we describe an algorithm for constructing a tree from a set of input quartet trees even with a significant fraction of errors. We show empirically that conflicts in the inputs are handled satisfactorily and that it significantly outperforms and outraces the Matrix Representation with Parsimony (MRP) methods that have previously been most successful in dealing with supertrees. Our algorithm is based on a divide and conquer algorithm where our divide step uses a semidefinite programming (SDP) formulation of MaxCut. We remark that this builds on previous work of ours for piecing together trees from rooted triplet trees. The recursion for unrooted quartets, however, is more complicated in that even with completely consistent set of quartet trees the problem is NP-hard, as opposed to the problem for triples where there is a linear time algorithm. This complexity leads to several issues and some solutions of possible independent interest.     

May–June Maximum Temperature Reconstruction from Mean Earlywood Density in North Central China and Its Linkages to the Summer Monsoon Activities

Cores of Pinus tabulaformis from Tianshui were subjected to densitometric analysis to obtain mean earlywood density data. Climate response analysis indicates that May–June maximum temperature is the main factor limiting the mean earlywood density (EWD) of Chinese pine trees in the Shimen Mountains. Based on the EWD chronology, we have reconstructed May–June maximum temperature 1666 to 2008 for Tianshui, north central China. The reconstruction explains 40.1% of the actual temperature variance during the common period 1953–2008. The temperature reconstruction is representative of temperature conditions over a large area to the southeast and northwest of the sampling site. Preliminary analysis of links between large-scale climatic variation and the temperature reconstruction shows that there is a relationship between extremes in spring temperature and anomalous atmospheric circulation in the region. It is thus revealed that the mean earlywood density chronology of Pinus tabulaformis has enough potential to reconstruct the temperature variability further into the past.     

Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo

The rate at which a given site in a gene sequence alignment evolves over time may vary. This phenomenon--known as heterotachy--can bias or distort phylogenetic trees inferred from models of sequence evolution that assume rates of evolution are constant. Here, we describe a phylogenetic mixture model designed to accommodate heterotachy. The method sums the likelihood of the data at each site over more than one set of branch lengths on the same tree topology. A branch-length set that is best for one site may differ from the branch-length set that is best for some other site, thereby allowing different sites to have different rates of change throughout the tree. Because rate variation may not be present in all branches, we use a reversible-jump Markov chain Monte Carlo algorithm to identify those branches in which reliable amounts of heterotachy occur. We implement the method in combination with our 'pattern-heterogeneity' mixture model, applying it to simulated data and five published datasets. We find that complex evolutionary signals of heterotachy are routinely present over and above variation in the rate or pattern of evolution across sites, that the reversible-jump method requires far fewer parameters than conventional mixture models to describe it, and serves to identify the regions of the tree in which heterotachy is most pronounced. The reversible-jump procedure also removes the need for a posteriori tests of 'significance' such as the Akaike or Bayesian information criterion tests, or Bayes factors. Heterotachy has important consequences for the correct reconstruction of phylogenies as well as for tests of hypotheses that rely on accurate branch-length information. These include molecular clocks, analyses of tempo and mode of evolution, comparative studies and ancestral state reconstruction. The model is available from the authors' website, and can be used for the analysis of both nucleotide and morphological data.     

On the best evolutionary rate for phylogenetic analysis

The effect of the evolutionary rate of a gene on the accuracy of phylogeny reconstruction was examined by computer stimulation. The evolutionary rate is measured by the tree length, that is, the expected total number of nucleotide substitutions per site on the phylogeny. DNA sequence data were simulated using both fixed trees with specified branch lengths and random trees with branch lengths generated from a model of cladogenesis. The parsimony and likelihood methods were used for phylogeny reconstruction, and the proportion of correctly recovered branch partitions by each method was estimated. Phylogenetic methods including parsimony appear quite tolerant of multiple substitutions at the same site. The optimum levels of sequence divergence were even higher than upper limits previously suggested for saturation of substitutions, indicating that the problem of saturation may have been exaggerated. Instead, the lack of information at low levels of divergence should be seriously considered in evaluation of a gene's phylogenetic utility, especially when the gene sequence is short. The performance of parsimony, relative to that of likelihood, does not necessarily decrease with the increase of the evolutionary rate.     

Tree diversity,tree height and environmental harshness in eastern and western North America

Does variation in environmental harshness explain local and regional species diversity gradients? We hypothesise that for a given life form like trees, greater harshness leads to a smaller range of traits that are viable and thereby also to lower species diversity. On the basis of a strong dependence of maximum tree height on site productivity and other measures of site quality, we propose maximum tree height as an inverse measure of environmental harshness for trees. Our results show that tree species richness is strongly positively correlated with maximum tree height across multiple spatial scales in forests of both eastern and western North America. Maximum tree height co‐varied with species richness along gradients from benign to harsh environmental conditions, which supports the hypothesis that harshness may be a general mechanism limiting local diversity and explaining diversity gradients within a biogeographic region.     

Contrasting patterns of trait‐based community assembly in lianas and trees from temperate Australia

Trait variation in plant communities is thought to be constrained by two opposing community assembly processes operating at discrete spatial scales: habitat filtering and limiting similarity between coexisting species. Filtering processes cause convergence in ecological strategy as species are excluded from unsuitable sites, whilst limiting similarity leads to the divergence of trait values between co‐occurring species in order to alleviate competition for finite resources. Levels of alpha (within‐site) and beta (among‐site) trait variation can be indicative of the strength of these community assembly processes. We used trait‐gradient analysis to explicitly compare evidence of community assembly patterns in lianas (woody vines) and trees. These two growth forms exhibit striking differences in carbon capture and regeneration strategies, yet trait‐based mechanisms that maintain their coexistence remain understudied. Using data for four functional traits – leaf mass per area, leaf nitrogen content (N_mass), leaf area and seed mass – we partitioned interspecific trait variation in lianas and trees into alpha and beta components. Our three key findings were: 1) lianas and trees exhibit divergent patterns of trait‐based habitat filtering, due to differences in the relationship between leaf size and the other three traits examined (LMA, N_mass and seed mass), 2) on average, liana species possess smaller seeds, lower LMA and higher N_mass than do trees, but there was no clear difference in leaf area between the two growth forms, and 3) soil fertility was correlated with trait variation (leaf area, seed mass) at the site‐level in trees, but not in lianas. These results provide evidence that dominant growth forms can be filtered into the same habitat on the basis of different combinations of traits. Our findings have important implications for community assembly and co‐existence theory and for more pragmatic matters such as using trait‐based principles to inform community restoration.     

A support vector machine based test for incongruence between sets of trees in tree space

ABSTRACT: BACKGROUND: The increased use of multi-locus data sets for phylogenetic reconstruction has increased the need to determine whether a set of gene trees significantly deviate from the phylogenetic patterns of other genes. Such unusual gene trees may have been influenced by other evolutionary processes such as selection, gene duplication, or horizontal gene transfer. RESULTS: Motivated by this problem we propose a nonparametric goodness-of-fit test for two empirical distributions of gene trees, and we developed the software GeneOut to estimate a p-value for the test. Our approach maps trees into a multi-dimensional vector space and then applies support vector machines (SVMs) to measure the separation between two sets of pre-defined trees. We use a permutation test to assess the significance of the SVM separation. To demonstrate the performance of GeneOut, we applied it to the comparison of gene trees simulated within different species trees across a range of species tree depths. Applied directly to sets of simulated gene trees with large sample sizes, GeneOut was able to detect very small differences between two set of gene trees generated under different species trees. Our statistical test can also include tree reconstruction into its test framework through a variety of phylogenetic optimality criteria. When applied to DNA sequence data simulated from different sets of gene trees, results in the form of receiver operating characteristic (ROC) curves indicated that GeneOut performed well in the detection of differences between sets of trees with different distributions in a multi-dimensional space. Furthermore, it controlled false positive and false negative rates very well, indicating a high degree of accuracy. CONCLUSIONS: The non-parametric nature of our statistical test provides fast and efficient analyses, and makes it an applicable test for any scenario where evolutionary or other factors can lead to trees with different multi-dimensional distributions. The software GeneOut is freely available under the GNU public license.     

Not so different after all: a comparison of methods for detecting amino acid sites under selection

We consider three approaches for estimating the rates of nonsynonymous and synonymous changes at each site in a sequence alignment in order to identify sites under positive or negative selection: (1) a suite of fast likelihood-based "counting methods" that employ either a single most likely ancestral reconstruction, weighting across all possible ancestral reconstructions, or sampling from ancestral reconstructions; (2) a random effects likelihood (REL) approach, which models variation in nonsynonymous and synonymous rates across sites according to a predefined distribution, with the selection pressure at an individual site inferred using an empirical Bayes approach; and (3) a fixed effects likelihood (FEL) method that directly estimates nonsynonymous and synonymous substitution rates at each site. All three methods incorporate flexible models of nucleotide substitution bias and variation in both nonsynonymous and synonymous substitution rates across sites, facilitating the comparison between the methods. We demonstrate that the results obtained using these approaches show broad agreement in levels of Type I and Type II error and in estimates of substitution rates. Counting methods are well suited for large alignments, for which there is high power to detect positive and negative selection, but appear to underestimate the substitution rate. A REL approach, which is more computationally intensive than counting methods, has higher power than counting methods to detect selection in data sets of intermediate size but may suffer from higher rates of false positives for small data sets. A FEL approach appears to capture the pattern of rate variation better than counting methods or random effects models, does not suffer from as many false positives as random effects models for data sets comprising few sequences, and can be efficiently parallelized. Our results suggest that previously reported differences between results obtained by counting methods and random effects models arise due to a combination of the conservative nature of counting-based methods, the failure of current random effects models to allow for variation in synonymous substitution rates, and the naive application of random effects models to extremely sparse data sets. We demonstrate our methods on sequence data from the human immunodeficiency virus type 1 env and pol genes and simulated alignments.     

EFFECTS OF POPULATION STRUCTURE AND CONE PRODUCTION ON OUTCROSSING RATES IN ENGELMANN SPRUCE AND SUBALPINE FIR

Variation in the mating systems of Engelmann spruce and subalpine fir was examined in two adjacent subpopulations in the Colorado Front Range. Multilocus outcrossing rates were estimated from analysis of allozyme variation in embryo and megagametophyte tissue. The overall multilocus outcrossing rate of 0.93 for spruce was significantly higher than the outcrossing rate of 0.89 for fir. Outcrossing rates varied from 0.73 to 0.97 for spruce and from 0.65 to 0.94 for fir when trees of each species were grouped according to age, size, spatial distribution, maternal heterozygosity, cone production, and year of sampling. In both spruce and fir, trees with higher levels of male-cone production and/or more clumped spatial distribution had lower outcrossing rates. Temporal variation in outcrossing rates within subpopulations, examined only in spruce, was less than variation between subpopulations. Male-cone production was significantly correlated with tree size, and regression analyses revealed that the highest outcrossing rates are expected on trees that are medium to large in size, rather than the largest trees in the forest. The results show that, while there is some temporal variation, patterns of male cone production and spatial distribution of individuals are the most important factors influencing outcrossing levels in these wind-pollinated forest trees.     

Bias and error in using survey records for ponderosa pine landscape restoration

Aim Public land survey records are commonly used to reconstruct historical forest structure over large landscapes. Reconstruction studies have been criticized for using absolute measures of forest attributes, such as density and basal area, because of potential selection bias by surveyors and unknown measurement error. Current methods to identify bias are based upon statistical techniques whose assumptions may be violated for survey data. Our goals were to identify and directly estimate common sources of bias and error, and to test the accuracy of statistical methods to identify them. Location Forests in the western USA: Mogollon Plateau, Arizona; Blue Mountains, Oregon; Front Range, Colorado. Methods We quantified both selection bias and measurement error for survey data in three ponderosa pine landscapes by directly comparing measurements of bearing trees in survey notes with remeasurements of bearing trees at survey corners (384 corners and 812 trees evaluated). Results Selection bias was low in all areas and there was little variability among surveyors. Surveyors selected the closest tree to the corner 95% to 98% of the time, and hence bias may have limited impacts on reconstruction studies. Bourdo’s methods were able to successfully detect presence or absence of bias most of the time, but do not measure the rate of bias. Recording and omission errors were common but highly variable among surveyors. Measurements for bearing trees made by surveyors were generally accurate. Most bearings were less than 5° in error and most distances were within 5% of our remeasurements. Many, but not all, surveyors in the western USA probably estimated diameter of bearing trees at stump height (0.3 m). These estimates deviated from reconstructed diameters by a mean absolute error of 7.0 to 10.6 cm. Main conclusions Direct comparison of survey data at relocated corners is the only method that can determine if bias and error are meaningful. Data from relocated trees show that biased selection of trees is not likely to be an important source of error. Many surveyor errors would have no impact on reconstruction studies, but omission errors have the potential to have a large impact on results. We suggest how to reduce potential errors through data screening.     

Monoterpene variation mediated attack preference evolution of the bark beetle Dendroctonus valens

Several studies suggest that some bark beetle like to attack large trees. The invasive red turpentine beetle (RTB), Dendroctonus valens LeConte, one of the most destructive forest pests in China, is known to exhibit this behavior. Our previous study demonstrated that RTBs preferred to attack large-diameter trees (diameter at breast height, DBH ≥30 cm) over small-diameter trees (DBH ≤10 cm) in the field. In the current study, we studied the attacking behavior and the underlying mechanisms in the laboratory. Behavioral assays showed that RTBs preferred the bark of large-DBH trees and had a higher attack rate on the bolts of these trees. Y-tube assays showed that RTBs preferred the volatiles released by large-DBH trees to those released by small-DBH trees. Subsequent analysis revealed that both large- and small-DBH trees had the same composition of monoterpenes, but the concentration of each component differed; thus it appeared that the concentrations acted as cues for RTBs to locate the right-sized host which was confirmed by further behavioral assays. Moreover, large-DBH pine trees provided more spacious habitat and contained more nutrients, such as nitrogen, than did small-DBH pine trees, which benefited RTBs' fecundity and larval development. RTBs seem to have evolved mechanisms to locate those large hosts that will allow them to maximize their fitness. Monoterpene variation mediated attack preference implies the potential for the management of RTB.     

Cerulean Warblers in the Ozark region: habitat selection,breeding biology,survival, and space use

Cerulean Warblers (Setophaga cerulea) are a species with declining populations that exhibit regional variation in habitat selection and demographic rates. The Ozark region of the south‐central United States likely provides important habitat for Cerulean Warblers, but little is known about their breeding biology in that region. We studied Cerulean Warblers in riparian forests of the Ozarks of Arkansas from 2018 to 2020. We assessed multi‐scale habitat selection for vegetative and topographic features, documented their breeding biology, estimated within‐season and annual apparent survival, and estimated territory sizes. We found that Cerulean Warblers selected riparian habitat characterized by large‐diameter trees across all spatial scales. Contrary to the results of previous studies, males appeared to avoid white oaks (Quercus spp., Section Quercus) at the territory scale, but this avoidance may reflect an underlying preference for riparian habitat. Our logistic‐exposure estimate of nest survival (0.32; 85% confidence interval: 0.21–0.46) was similar to the median of estimates reported in previous studies. Our results indicate that maintaining riparian forests with large trees is important to provide suitable habitat for Cerulean Warblers in the Ozark region. Because of similarities in habitat selection among regions, some management practices from other populations, including retaining large trees and promoting a heterogeneous canopy structure, may be useful for managing for Cerulean Warblers in riparian areas of the Ozarks. However, selection for topography and tree species by Cerulean Warblers in our study also suggests that region‐specific management strategies will be beneficial. Finally, our demographic rate estimates for this population should prove valuable in future full‐annual‐cycle population modeling efforts.     

Response of young<Emphasis Type="Italic"> Tsuga heterophylla</Emphasis> to deer browsing: developing tools to assess deer impact on forest dynamics

We used dendroecology to describe and understand the consequences of deer browsing on regenerating western hemlock (Tsuga heterophylla). We compared tree shape, growth rate, height and age at four different sites in Haida Gwaii (British Columbia, Canada) that had trees representative of the range of deer impact on trees: (1) trees showing no sign of browsing, (2) escaped trees which were still browsed below the browse line and (3) stunted and heavily browsed trees. Repeated and intense browsing resulted in the small size, compact heavily ramified shape of stunted trees and in the short compact and ramified lower branches of escaped trees. These contrasted with the shape of non-browsed trees, a shape that was also found in escaped trees above the browse line. Before release, all browsed trees experienced stagnation in growth characterised by narrow rings (0.3 mm/year) and a small annual height increment (2.5 cm/year). At release, growth rate increased and stabilised: rings were wider (1.3 mm/year) and annual height increments were greater (10.5 cm/year). Non-browsed trees had a mean ring-width of 1.3 mm/year and an annual height increment of 22 cm/year. Delay in tree recruitment caused by deer varied from site to site. It had been about 15 years for the escaped trees and is estimated at 30–40 years for the stunted trees. Spatial variation in deer impact may reflect spatial variation of browsing pressure resulting from local differences in the availability of preferred forage or to differences in tree chemical defences/nutritional values.     

REVERSIBILITY IN EVOLUTION: A MAXIMUM LIKELIHOOD APPROACH TO CHARACTER GAIN/LOSS BIAS IN PHYLOGENIES

Statistical methods are used to test the hypothesis that rate of gain is equal to rate of loss for a single character on a cladogram. Ancestral character states are used as input for maximum likelihood (ML) rate estimation. Two markovian models of character evolution are considered: one has equality of rate across branches; the other permits variation in rate according to predetermined weights for branches. ML estimates are derived for both models, and their properties in large and small trees are investigated. Bias and error are significant in small trees. Error is greatest for characters in which rate of gain is low, and is greater for the loss estimate than for the gain estimate. Likelihood ratio (LR) tests of the null hypothesis of equality of gain/loss rate are derived, and their properties investigated. The distribution of -2 log LR is close to χ² with 1 df with as few as 32 taxa. However, the power of the test is low unless the character is evolving rapidly. Methods for increasing power are examined, including selection of rapidly evolving subsets of characters, and pooling across characters. A goodness of fit test is presented to determine if pooling is justified. An example using published restriction site data on the Asteraceae demonstrates significant deviation from the null model in the direction predicted on the basis of the molecular biology of restriction enzyme site recognition, but only for one large subset of the data in which pooling is warranted.     

Imprint of the Atlantic multidecadal oscillation on tree-ring widths in northeastern Asia since 1568

We present a new tree-ring reconstruction of the Atlantic Multidecadal Oscillation (AMO) spanning 1568-2007 CE from northeast Asia. Comparison of the instrumental AMO index, an existing tree-ring based AMO reconstruction, and this new record show strongly similar annual to multidecadal patterns of variation over the last 440 years. Warm phases of the AMO are related to increases in growth of Scots pine trees and moisture availability in northeast China and central eastern Siberia. Multi-tape method (MTM) and cross-wavelet analyses indicate that robust multidecadal (～64-128 years) variability is present throughout the new proxy record. Our results have important implications concerning the influence of North Atlantic sea surface temperatures on East Asian climate, and provide support for the possibility of an AMO signature on global multidecadal climate variability.     

Effects of natural and simulated herbivory on spine lengths of Acacia drepanolobium in Kenya

We present experimental evidence supporting the hypothesis that increased spine length in acacia species is a defense induced by herbivory. Acacia drepanolobium is the dominant tree over large areas of East Africa. Each individual tree is occupied by one of four ant species at our study site. Using two types of electric fences, we have effectively controlled herbivory by megaherbivores (elephants and giraffes) and other large mammalian herbivores at a field site in Laikipia, Kenya since 1995. Mean spine lengths of new spines on trees occupied by the most abundant ant species (presumed to be a defensive mutualist) have shown a slow and steady decline over the first five years of the experiment on branches protected from these herbivores. This reduction has been 35–40%, or approximately half of the reduction in spine length that we anticipate will eventually occur, based on trees that have been protected from herbivory for many years. In contrast, trees occupied by a resident ant species that systematically prunes shoots have shown no reduction in spine length associated with herbivore exclusion treatments. Experimental pruning of shoots similar to that carried out by this ant species resulted in longer spines on seedlings in a greenhouse setting. Simulated large mammal browsing in the field rapidly (re-)induced greater spine lengths on trees that had been protected from large mammals for five years. The slow relaxation of spine length in the absence of herbivory, contrasted with its rapid induction after simulated browsing, suggests that there is a difference in the reliability of these two signals. Spine length responses to herbivory were extremely local (limited to individual branches). These branch-specific responses are consistent with the hypothesis that induced defense in this system evolved in the context of within-tree spatial variation in herbivore pressure, in particular variation in branch height.     

Chloroplast DNA variation in a hyperdiverse tropical tree community

• We investigate chloroplast DNA variation in a hyperdiverse community of tropical rainforest trees in French Guiana, focusing on patterns of intraspecific and interspecific variation. We test whether a species genetic diversity is higher when it has congeners in the community with which it can exchange genes and if shared haplotypes are more frequent in genetically diverse species, as expected in the presence of introgression.
• We sampled a total of 1,681 individual trees from 472 species corresponding to 198 genera and sequenced them at a noncoding chloroplast DNA fragment.
• Polymorphism was more frequent in species that have congeneric species in the study site than in those without congeners (30% vs. 12%). Moreover, more chloroplast haplotypes were shared with congeners in polymorphic species than in monomorphic ones (44% vs. 28%).
• Despite large heterogeneities caused by genus‐specific behaviors in patterns of hybridization, these results suggest that the higher polymorphism in the presence of congeners is caused by local introgression rather than by incomplete lineage sorting. Our findings suggest that introgression has the potential to drive intraspecific genetic diversity in species‐rich tropical forests.

     

On the impossibility of reconstructing ancestral data and phylogenies.

We prove that it is impossible to reconstruct ancestral data at the root of "deep" phylogenetic trees with high mutation rates. Moreover, we prove that it is impossible to reconstruct the topology of "deep" trees with high mutation rates from a number of characters smaller than a low-degree polynomial in the number of leaves. Our impossibility results hold for all reconstruction methods. The proofs apply tools from information theory and percolation theory.