Tree Spacing Research Articles

Experimental Study on Tree Shape Identification and Interaction Among Trees

Forests play a crucial role in mitigating global warming and maintaining climate balance, necessitating a comprehensive understanding of forest dynamics. However, many optical characteristics related to forests remain poorly understood, particularly models for determining forest parameters such as tree species, shape, and inter-tree distances. Although several models exist for estimating leaf area index and photosynthetically active radiation, fewer models address structural forest parameters. This research aims to develop a model using visible and near-infrared radiometer data from Earth observation satellites to estimate forest parameters, including tree species, shape, height, and spacing. Results show that as the distance between trees increases, the impact of multiple reflections decreases significantly. Elliptical tree shapes exhibit approximately three times higher multiple reflection effects compared to conical shapes, indicating potential for distinguishing tree shapes through radiometric data. For canopy shapes, shorter, thicker trees experience more significant reflection effects than taller, thinner trees, suggesting the feasibility of estimating tree height. Overall, the impact of multiple reflections ranges from a few to 10% of TOA radiance, necessitating its consideration when calculating forest reflectance to ensure accurate forest parameter retrieval from satellite observations.

Terraces in species tree inference from gene trees

A terrace in a phylogenetic tree space is a region where all trees contain the same set of subtrees, due to certain patterns of missing data among the taxa sampled, resulting in an identical optimality score for a given data set. This was first investigated in the context of phylogenetic tree estimation from sequence alignments using maximum likelihood (ML) and maximum parsimony (MP). It was later extended to the species tree inference problem from a collection of gene trees, where a set of equally optimal species trees was referred to as a “pseudo” species tree terrace which does not consider the topological proximity of the trees in terms of the induced subtrees resulting from certain patterns of missing data. In this study, we mathematically characterize species tree terraces and investigate the mathematical properties and conditions that lead multiple species trees to induce/display an identical set of locus-specific subtrees owing to missing data. We report that species tree terraces are agnostic to gene tree heterogeneity. Therefore, we introduce and characterize a special type of gene tree topology-aware terrace which we call “peak terrace”. Moreover, we empirically investigated various challenges and opportunities related to species tree terraces through extensive empirical studies using simulated and real biological data. We demonstrate the prevalence of species tree terraces and the resulting ambiguity created for tree search algorithms. Remarkably, our findings indicate that the identification of terraces could potentially lead to advances that enhance the accuracy of summary methods and provide reasonably accurate branch support.

Effects of Tree Spacing and Branch Configuration on Production, Fruit Quality, and Leaf Minerals of ‘Aztec Fuji’ Apple Trees in a Tatura Trellis System Over 5 Years

Tree spacing and branch architecture are critical for the productivity of high-density orchards. The influence of two tree spacings of 45.7 cm × 366 cm and 91.4 cm × 366 cm each with two branch architectures or configurations of shortened branch (ShBr) or overlapped branch (OverBr) on tree growth, yield components, fruit quality, and leaf mineral nutrients in an ‘Aztec Fuji’ apple (Malus domestica Borkh.) orchard with a 60-degree Tatura trellis (V) system was studied over 5 years. Trees planted with 91.4-cm spacing had a significantly greater trunk cross-sectional area (TCSA), higher number of fruit and greater yield per tree, and greater cumulative yield efficiency than those of trees planted with 45.7-cm spacing during 2012–16. Tree spacing did not significantly affect fruit weight and firmness at harvest or after storage. However, trees planted with 91.4-cm spacing always had higher fruit color, sunburn, fruit russet, and watercore at harvest and a higher soluble solids concentration but lower fruit bitter pit at harvest and after storage compared to those of trees with 45.7-cm spacing. These differences were often significant. Trees with 45.7-cm spacing had significantly higher leaf concentrations of potassium, iron, copper, and manganese and relatively higher leaf zinc than those of trees with 91.4-cm spacing. Trees trained according to ShBr architectures had a relatively larger TCSA than those of trees with an OverBr configuration every year. Branching architectures did not affect the number of fruits per tree, yield per tree, yield per hectare, yield efficiency, or biennial bearing index in any year. Trees with a ShBr architecture had significantly larger fruits than those with an OverBr system every year and over the 5 years. Trees with a ShBr architecture had higher average leaf fresh and dry weights and calcium concentration but a similar percentage of dry weight compared to those of trees with an OverBr architecture.

Variants of the James tree space

Variants of the James tree space

Gentrius: Generating Trees Compatible With a Set of Unrooted Subtrees and its Application to Phylogenetic Terraces.

For a set of binary unrooted subtrees generating all binary unrooted trees compatible with them, i.e. generating their stand, is one of the classical problems in phylogenetics. Here, we introduce Gentrius-an efficient algorithm to tackle this task. The algorithm has a direct application in practice. Namely, Gentrius generates phylogenetic terraces-topologically distinct, equally scoring trees due to missing data. Despite stand generation being computationally intractable, we showed on simulated and biological datasets that Gentrius generates stands with millions of trees in feasible time. We exemplify that depending on the distribution of missing data across species and loci and the inferred phylogeny, the number of equally optimal terrace trees varies tremendously. The strict consensus tree computed from them displays all the branches unaffected by the pattern of missing data. Thus, by solving the problem of stand generation, in practice Gentrius provides an important systematic assessment of phylogenetic trees inferred from incomplete data. Furthermore, Gentrius can aid theoretical research by fostering understanding of tree space structure imposed by missing data.

Эмоциональные коммуникации в детско-родительских отношениях и жизнеспособность будущей взрослой семьи

<p style="text-align: justify;"><strong>Objective</strong>. To analyze the contribution of the most immediate contextual influences (child-parent emotional communications) to the resilience of the adult family (using the samples from Belarus and Russia). <strong>Background. </strong>Understanding the role of emotional dysfunctions in parent-child relationships in the context of Russian and Belarusian cultures helps to identify the conditions for the resilience of a future adult family, which can become the basis for social family policy at the state level and improvement of the practice of psychological assistance to families. <br><strong>Study design. </strong>The study was conducted online using the snowball method. Multiple regression analysis was conducted to determine the impact of dysfunction in parental families, intensity of the negative events, age of respondents and number of children on family resilience. Children's experiences of adults are illustrated by the results of projective technique. <br><strong>Participants. </strong>The study involved 853 respondents (595 people from the Russian Federation, 258 from the Republic of Belarus) aged from 18 to 77 years (average age 36 ± 12 years, median = 36 years), 90,5% female. <br><strong>Measurements. </strong>Family resilience was assessed using Gusarova’s et al. “Family Resilience Assessment Scale” (FRAS-RII). Dysfunctions in parental families were determined according to Kholmogorova’s et al. “Family Emotional Communications” and the projective technique of Odintsova et al. “Space of Trees and Light.” The intensity of negative events in families was assessed on a scale from 1 to 10. <br><strong>Results. </strong>Dysfunctions in parental families make a significant contribution to the resilience of the future adult family (up to 20% of explained variance). Family perfectionism has a positive effect, and the elimination of emotions has a negative impact on the resilience of adult families in the context of two cultures. In Russian families of origin there is over-involvement, and in Belarusian families criticism negatively affects the resilience of respondent’s families. <br><strong>Conclusions. </strong>The critical atmosphere in parental families, the high intensity of adverse events in Belarusian families, and overprotection in the parental families of Russians contribute to a decrease in families’ resilience. The presence and number of children in a family contributes to the family resilience in both countries. Culture and traditions are a solid basis for the majority of Russians and Belarusians.</p>

An automated convergence diagnostic for phylogenetic MCMC analyses.

Assessing convergence of Markov chain Monte Carlo (MCMC) based analyses is crucial but challenging, especially so in high dimensional and complex spaces such as the space of phylogenetic trees (treespace). In practice, it is assumed that the target distribution is the unique stationary distribution of the MCMC and convergence is achieved when samples appear to be stationary. Here we leverage recent advances in computational geometry of the treespace and introduce a method that combines classical statistical techniques and algorithms with geometric properties of the treespace to automatically evaluate and assess practical convergence of phylogenetic MCMC analyses. Our method monitors convergence across multiple MCMC chains and achieves high accuracy in detecting both practical convergence and convergence issues within treespace. Furthermore, our approach is developed to allow for real-time evaluation during the MCMC algorithm run, eliminating any of the chain post-processing steps that are currently required. Our tool therefore improves reliability and efficiency of MCMC based phylogenetic inference methods and makes analyses easier to reproduce and compare. We demonstrate the efficacy of our diagnostic via a well-calibrated simulation study and provide examples of its performance on real data sets. Although our method performs well in practice, a significant part of the underlying treespace probability theory is still missing, which creates an excellent opportunity for future mathematical research in this area. The open source package for the phylogenetic inference framework BEAST2, called ASM, that implements these methods, making them accessible through a user-friendly GUI, is available from https://github.com/rbouckaert/asm/. The open source Python package, called tetres, that provides an interface for these methods enabling their applications beyond BEAST2 can be accessed at https://github.com/bioDS/tetres/.

Wasserstein Auto-Encoders of Merge Trees (and Persistence Diagrams).

This article presents a computational framework for the Wasserstein auto-encoding of merge trees (MT-WAE), a novel extension of the classical auto-encoder neural network architecture to the Wasserstein metric space of merge trees. In contrast to traditional auto-encoders which operate on vectorized data, our formulation explicitly manipulates merge trees on their associated metric space at each layer of the network, resulting in superior accuracy and interpretability. Our novel neural network approach can be interpreted as a non-linear generalization of previous linear attempts (Pont et al. 2023) at merge tree encoding. It also trivially extends to persistence diagrams. Extensive experiments on public ensembles demonstrate the efficiency of our algorithms, with MT-WAE computations in the orders of minutes on average. We show the utility of our contributions in two applications adapted from previous work on merge tree encoding (Pont et al. 2023). First, we apply MT-WAE to merge tree compression, by concisely representing them with their coordinates in the final layer of our auto-encoder. Second, we document an application to dimensionality reduction, by exploiting the latent space of our auto-encoder, for the visual analysis of ensemble data. We illustrate the versatility of our framework by introducing two penalty terms, to help preserve in the latent space both the Wasserstein distances between merge trees, as well as their clusters. In both applications, quantitative experiments assess the relevance of our framework. Finally, we provide a C++ implementation that can be used for reproducibility.

Identifiability of speciation times under the multispecies coalescent

The advent of rapid and inexpensive sequencing technologies has necessitated the development of computationally efficient methods for analyzing sequence data for many genes simultaneously in a phylogenetic framework. The coalescent process is the most commonly used model for linking the underlying genealogies of individual genes with the global species-level phylogeny, but inference under the coalescent model is computationally daunting in the typical inference frameworks (e.g., the likelihood and Bayesian frameworks) due to the dimensionality of the space of both gene trees and species trees. Here we consider estimation of the branch lengths in fixed species trees with three or four taxa, and show that these branch lengths are identifiable. We also show that for three and four taxa simple estimators for the branch lengths can be derived based on observed site pattern frequencies. Properties of these estimators, such as their asymptotic variances and large-sample distributions, are examined, and performance of the estimators is assessed using simulation. Finally, we use these estimators to develop a hypothesis test that can be used to delimit species under the coalescent model for three or four putative taxa.

Biomass Partitioning, Carbon Storage, and Pea (Pisum sativum L.) Crop Production under a Grewia optiva-Based Agroforestry System in the Mid-Hills of the Northwestern Himalayas

A well-designed tree-based culture provides multiple benefits, aiding in achieving sustainable development goals (SDGs), especially SDG1 (no poverty), SDG2 (zero hunger), SDG13 (climate action), and SDG15 (life on land). A split-plot field experiment near Solan, Himachal Pradesh, tested the following Grewia optiva tree spacings as main plots: S1 10 m × 1 m, S2 10 m × 2 m, S3 10 m × 3 m, and sole cropping (S0—Open) of pea (Pisum sativum L.). Pea cultivation included the following six fertilizer treatments as subplots: control (no application), farmyard manure (FYM), vermicompost (VC), Jeevamrut, FYM + VC, and the recommended dose of fertilizers (RDFs), each replicated three times. The results indicated that the leaves, branches, total biomass, carbon density, and carbon sequestration rate of G. optiva alleys at 10 m × 1 m were greater than those at the other spacings. However, peas intercropped at 10 m × 3 m produced the highest yield (5.72 t ha−1). Compared with monocropping, G. optiva-based agroforestry significantly improved soil properties. Among fertilizers, FYM had the highest yield (6.04 t ha−1) and improved soil health. The most lucrative practice was the use of peas under a 10 m × 1 m spacing with FYM, with economic gains of 2046.1 USD ha−1. This study suggests integrating pea intercropping with G. optiva at broader spacing (10 m × 3 m) and using FYM for optimal carbon sequestration, soil health, and economic returns, and this approach is recommended for the region’s agroecosystems.

Urban Canyon Design with Aspect Ratio and Street Tree Placement for Enhanced Thermal Comfort: A Comprehensive Thermal Comfort Assessment Accounting for Gender and Age in Seoul, Republic of Korea

Rapid urbanization and increased human activity have negatively impacted the microclimate of cities, leading to unfavorable conditions for human thermal comfort, particularly in outdoor spaces. Thermal comfort can be improved through various means, such as adjusting the height of urban buildings, the aspect ratio of road widths, and the placement of street trees. This study employed the ENVI-met software V5.5.1 to simulate the microclimate based on aspect ratio (H/W = 1.5) and street tree spacing (6 m) similar to actual conditions with different aspect ratios (H/W = 0.5, 1.0, and 2.0) and street tree spacing (2 m) in Seoul, Republic of Korea. Thermal comfort was assessed through a comprehensive predicted mean vote (PMV) evaluation, considering the gender (male and female) and age (8, 35, and 80 years) of residents in the target area, to determine the optimal urban canyon scenario. The results of the study indicated that the height of the building and the percentage of trees had a significant impact on the temperature and PMV results. When comparing PMV results, women have higher thermal vulnerability than men, and based on age, older adults have higher thermal vulnerability. The aspect ratio of 1.5 and tree spacing of 2 m resulted in the lowest temperature of 35.91 °C at 12:00 p.m. at 0° wind direction and 36.09 °C at 90° wind direction, lower than the actual input value of 36.9 °C. The PMV values were also under the same conditions, with an average PMV by gender of 3.87 at 0° and 4.21 at 90° and an average PMV by age of 3.86 at 0° and 4.19 at 90°. This finding is significant because it can inform the development of planned cities that prioritize urban thermal comfort during summer. This can be achieved through the strategic design of urban canyons and incorporation of street trees in both new and existing cities.

The genus Cortinarius should not (yet) be split

The genus Cortinarius (Agaricales, Basidiomycota) is one of the most species-rich fungal genera, with thousands of species reported. Cortinarius species are important ectomycorrhizal fungi and form associations with many vascular plants globally. Until recently Cortinarius was the single genus of the family Cortinariaceae, despite several attempts to provide a workable, lower-rank hierarchical structure based on subgenera and sections. The first phylogenomic study for this group elevated the old genus Cortinarius to family level and the family was split into ten genera, of which seven were described as new. Here, by careful re-examination of the recently published phylogenomic dataset, we detected extensive gene-tree/species-tree conflicts using both concatenation and multispecies coalescent approaches. Our analyses demonstrate that the Cortinarius phylogeny remains unresolved and the resulting phylogenomic hypotheses suffer from very short and unsupported branches in the backbone. We can confirm monophyly of only four out of ten suggested new genera, leaving uncertain the relationships between each other and the general branching order. Thorough exploration of the tree space demonstrated that the topology on which Cortinarius revised classification relies on does not represent the best phylogenetic hypothesis and should not be used as constrained topology to include additional species. For this reason, we argue that based on available evidence the genus Cortinarius should not (yet) be split. Moreover, considering that phylogenetic uncertainty translates to taxonomic uncertainty, we advise for careful evaluation of phylogenomic datasets before proposing radical taxonomic and nomenclatural changes.

Strategies for falcata (Falcataria falcata (L.) Greuter and R.Rankin) farmers to mitigate gall rust severity across elevations

The extent of gall rust severity in Falcata plantations across various elevations and locations in the country is insufficiently documented, posing challenges for developing an integrated disease management strategy. This study aimed to assess the conditions favorable for gall rust severity in Falcata plantations at different elevations in Mindanao. Our survey revealed that gall rust severity is significantly higher at elevations exceeding 400 m above sea level (asl), with potential yield losses estimated between 23% and 52% of the total log volume per hectare. Factors contributing to increased severity, regardless of elevation, include low stand density (<1000 trees/ha), extended distances from natural vegetation (>1000 m), low understorey species diversity, and low average temperatures (<24°C). These factors interact significantly with elevation, as higher severity was observed in plantations with greater understorey vegetation diversity and elevated temperatures (>24°C), particularly at elevations over 600 m (asl). Based on our findings, it is recommended to avoid planting Falcata in areas with elevations exceeding 400 m (asl). However, if planting at higher elevations is unavoidable, adequate tree spacing (3 m x 3 m or 3 m x 4 m) should be maintained to achieve a moderate stand density (1000-1500 trees/ha). This practice can help regulate air circulation within the plantation, mitigate pathogen spread, and control understory vegetation growth and temperature impacts. Additionally, establishing and maintaining native vegetation or forest within 1000 m around Falcata plantations is advisable to create a protective buffer zone, thereby reducing gall rust severity.

Interference Effect of Tree Spacing on Natural Volatile Organic Compound Concentrations Measured Using Passive Samplers

Research highlights: The increasing rates of mental health disorders during the COVID-19 pandemic have popularized the notion of access to natural environments as a solution, leading to a surge in demand for urban green spaces. The concentration of natural volatile organic compounds (NVOCs) in forests, resulting from plant metabolism, plays a crucial role in forest-based healing and ecosystem health. Background and objectives: This study aimed to investigate how tree spacing influences NVOC concentrations within forest ecosystems using passive samplers, thereby enhancing the understanding of optimal forest management practices to promote human health benefits. Methods: We employed passive samplers to investigate tree spacing effects on NVOC concentrations. We placed passive samplers among trees in the study area to measure NVOC concentrations in individual trees and analyzed the relationship between NVOC concentration and tree spacing and structure. Results: A multiple regression analysis using distance decay models showed that a tree spacing of 2.7–3 m had a significant impact on NVOC concentrations. These findings provide a better understanding of how tree structure, tree spacing, and microclimate within the forest influence NVOC concentration. Conclusion: These findings have important implications for forest management and the design of forest landscapes to promote human health and well-being by considering the spatial distribution of NVOC concentrations.

Estimating the mean in the space of ranked phylogenetic trees.

Reconstructing evolutionary histories of biological entities, such as genes, cells, organisms, populations, and species, from phenotypic and molecular sequencing data is central to many biological, palaeontological, and biomedical disciplines. Typically, due to uncertainties and incompleteness in data, the true evolutionary history (phylogeny) is challenging to estimate. Statistical modelling approaches address this problem by introducing and studying probability distributions over all possible evolutionary histories, but can also introduce uncertainties due to misspecification. In practice, computational methods are deployed to learn those distributions typically by sampling them. This approach, however, is fundamentally challenging as it requires designing and implementing various statistical methods over a space of phylogenetic trees (or treespace). Although the problem of developing statistics over a treespace has received substantial attention in the literature and numerous breakthroughs have been made, it remains largely unsolved. The challenge of solving this problem is 2-fold: a treespace has nontrivial often counter-intuitive geometry implying that much of classical Euclidean statistics does not immediately apply; many parametrizations of treespace with promising statistical properties are computationally hard, so they cannot be used in data analyses. As a result, there is no single conventional method for estimating even the most fundamental statistics over any treespace, such as mean and variance, and various heuristics are used in practice. Despite the existence of numerous tree summary methods to approximate means of probability distributions over a treespace based on its geometry, and the theoretical promise of this idea, none of the attempts resulted in a practical method for summarizing tree samples. In this paper, we present a tree summary method along with useful properties of our chosen treespace while focusing on its impact on phylogenetic analyses of real datasets. We perform an extensive benchmark study and demonstrate that our method outperforms currently most popular methods with respect to a number of important 'quality' statistics. Further, we apply our method to three empirical datasets ranging from cancer evolution to linguistics and find novel insights into corresponding evolutionary problems in all of them. We hence conclude that this treespace is a promising candidate to serve as a foundation for developing statistics over phylogenetic trees analytically, as well as new computational tools for evolutionary data analyses. An implementation is available at https://github.com/bioDS/Centroid-Code.

Where is the heat threat in a city? Different perspectives on people-oriented and remote sensing methods: The case of Prague

Extreme heat in urban areas has a severe impact on urban populations worldwide. In light of the threats posed by climate change, it is clear that more holistic and people-oriented approaches to reducing heat stress in urban areas are needed. From this perspective we aim to identify and compare thermal hotspots and places with favourable thermal conditions, based on three different methods – thermal walk, participatory-based cognitive mapping, and remote sensing in a Central European city. Although major hotspots in large low-rise development zones were identified by all three methods, the overall agreement between on-site thermal sensation votes, cognitive maps and surface temperatures is low. In the urban canyon of compact mid-rise and open mid-rise development, the thermal walk method proved to be useful in the identification of the specific (parts of) streets and public spaces where citizens can expect thermal discomfort and experience heat stress, e.g. crossroads, arterial streets with a lack of greenery, north facing unshaded parts of streets, and streets with inappropriate tree spacing. Cognitive maps on an urban neighbourhood scale are not specific enough on a street level; however, as a supplementary method they can help identify discrepancies between on-site sensations and thermal conditions. For further research on effective and cost-efficient urban heat mitigation, we suggest combining thermal walks with numerical model simulations.

Integrated effect of aspect ratio and tree spacing on pedestrian thermal comfort of street canyon.

Increasing heat stress in urban environments due to climate change has a significant adverse impact on human work and daily life. Street canyons as the main component of the underlying surface of the city and the main place of residents' activities, a comprehensive understanding of street morphology and tree planting practices can help to improve thermal comfort. Based on survey data and field experiments, this study designed 30 scenarios and employed ENVI-met model (version 5.0.3) to quantify the effect of street aspect ratio (H/W: H is building height and W is street width) and tree spacing (TS) on pedestrian thermal comfort in two differently oriented streets (north-south and east-west) in Taiyuan, China. Results showed that H/W ratio and TS significantly influenced the street thermal comfort mainly owing to shading. H/W ratio played a pivotal role in reducing mean radiant temperature (Tmrt) and physiological equivalent temperature (PET), and was negatively correlated with Tmrt and PET. Compared to no-tree scenarios, street trees significantly improved thermal comfort (mean reductions of Tmrt and PET were 12.74℃ and 5.66℃, respectively), and PET and Tmrt were significantly negatively correlated with TS. The improvement effect of street trees on Tmrt and PET in east-west oriented street was better than north-south oriented street. H/W = 1.0 and TS = 6m appeared as the proposed combination to mitigate the summer thermal comfort in the temperate monsoon climate zone. These quantitative results provide new insights into renewal and design strategies for future urban planning.

Tropical Logistic Regression Model on Space of Phylogenetic Trees

Classification of gene trees is an important task both in the analysis of multi-locus phylogenetic data, and assessment of the convergence of Markov Chain Monte Carlo (MCMC) analyses used in Bayesian phylogenetic tree reconstruction. The logistic regression model is one of the most popular classification models in statistical learning, thanks to its computational speed and interpretability. However, it is not appropriate to directly apply the standard logistic regression model to a set of phylogenetic trees, as the space of phylogenetic trees is non-Euclidean and thus contradicts the standard assumptions on covariates. It is well-known in tropical geometry and phylogenetics that the space of phylogenetic trees is a tropical linear space in terms of the max-plus algebra. Therefore, in this paper, we propose an analogue approach of the logistic regression model in the setting of tropical geometry. Our proposed method outperforms classical logistic regression in terms of Area under the ROC Curve in numerical examples, including with data generated by the multi-species coalescent model. Theoretical properties such as statistical consistency have been proved and generalization error rates have been derived. Finally, our classification algorithm is proposed as an MCMC convergence criterion for Mr Bayes. Unlike the convergence metric used by Mr Bayes which is only dependent on tree topologies, our method is sensitive to branch lengths and therefore provides a more robust metric for convergence. In a test case, it is illustrated that the tropical logistic regression can differentiate between two independently run MCMC chains, even when the standard metric cannot.

Adaptación de leguminosas arbóreas en un sistema silvopastoril para ovinos en clima templado

The objective was to evaluate, over a one-year period, the survival, production, and nutritional value of forage from tree legumes as well as grasses and weeds in a silvopastoral system. A mixed protein bank was established, consisting of two plots: in the first plot, planting orientation was East to West, and in the second, North to South. The planted tree species were leguminous: pata de vaca (Bauhinia forficata), albizia (Albizia lebbeck), leucaena (Leucaena leucocephala), and palo dulce (Eysenhardtia polystachya). Three planting densities were used, with tree spacings of 70x70, 90x90, and 110x110 cm. Survival was assessed visually and manually by identifying the species and recording their condition as either alive (1) or dead (0). A three-way classification model with an unequal number of repetitions was used, employing the Generalized Linear Models procedure of the statistical analysis system under a fixed effects model. The nutritional value of thetree legumes ranged from 11% to 18% protein. Differences (p ≤ 0.05) were observed between treatments and orientation regarding height. There was a significant effect (p ≤ 0.05) of treatment, orientation, period, and species on foliage production. Differences (p ≤ 0.05) were found in species survival, with albizia (Albizia lebbeck) being notable. The period also significantly influenced (p ≤ 0.05) tree survival. It is concluded that the survival rate of forage tree legume species determines their capacity to establish silvopastoral systems in a subhumid temperate climate in mixed protein bank arrangements

Phylo2Vec: a vector representation for binary trees

Abstract Binary phylogenetic trees inferred from biological data are central to understanding the shared history among evolutionary units. However, inferring the placement of latent nodes in a tree is computationally expensive. State-of-the-art methods rely on carefully designed heuristics for tree search, using different data structures for easy manipulation (e.g., classes in object-oriented programming languages) and readable representation of trees (e.g., Newick-format strings). Here, we present Phylo2Vec, a parsimonious encoding for phylogenetic trees that serves as a unified approach for both manipulating and representing phylogenetic trees. Phylo2Vec maps any binary tree with n leaves to a unique integer vector of length n − 1. The advantages of Phylo2Vec are fourfold: i) fast tree sampling, (ii) compressed tree representation compared to a Newick string, iii) quick and unambiguous verification if two binary trees are identical topologically, and iv) systematic ability to traverse tree space in very large or small jumps. As a proof of concept, we use Phylo2Vec for maximum likelihood inference on five real-world datasets and show that a simple hill-climbing-based optimisation scheme can efficiently traverse the vastness of tree space from a random to an optimal tree.