The pipe model theory half a century on: a review

Advancing fine branch biomass estimation with lidar and structural models

BACKGROUND AND AIMS

Lidar is a promising tool for fast and accurate measurements of trees. There are several approaches to estimate above-ground woody biomass using lidar point clouds. One of the most widely used methods involves fitting geometric primitives (e.g. cylinders) to the point cloud, thereby reconstructing both the geometry and topology of the tree. However, current algorithms are not suited for accurate estimation of the volume of finer branches, because of the unreliable point dispersions from, for example, beam footprint compared to the structure diameter.

METHOD

We propose a new method that couples point cloud-based skeletonization and multi-linear statistical modelling based on structural data to make a model (structural model) that accurately estimates the above-ground woody biomass of trees from high-quality lidar point clouds, including finer branches. The structural model was tested at segment, axis and branch level, and compared to a cylinder fitting algorithm and to the pipe model theory.

KEY RESULTS

The model accurately predicted the biomass with 1.6 % normalized root mean square error (nRMSE) at the segment scale from a k-fold cross-validation. It also gave satisfactory results when scaled up to the branch level with a significantly lower error (13 % nRMSE) and bias (-5 %) compared to conventional cylinder fitting to the point cloud (nRMSE: 92 %, bias: 82 %), or using the pipe model theory (nRMSE: 31 %, bias: -27 %). The model was then applied to the whole-tree scale and showed that the sampled trees had more than 1.7 km of structures on average and that 96 % of that length was coming from the twigs (i.e. <5 cm diameter). Our results showed that neglecting twigs can lead to a significant underestimation of tree above-ground woody biomass (-21 %).

CONCLUSIONS

The structural model approach is an effective method that allows a more accurate estimation of the volumes of smaller branches from lidar point clouds. This method is versatile but requires manual measurements on branches for calibration. Nevertheless, once the model is calibrated, it can provide unbiased and large-scale estimations of tree structure volumes, making it an excellent choice for accurate 3D reconstruction of trees and estimating standing biomass.

Disentangling the effect of growth from development in size-related trait scaling relationships

In plant ecology, the terms growth and development are often used interchangeably. Yet these constitute two distinct processes. Plant architectural traits (e.g. number of successive forks) can estimate development stages. Here, we show the importance of including the effect of development stages to better understand size-related trait scaling relationships (i.e. between height and stem diameter). We focused on one common savanna woody species (Senegalia nigrescens) from the Greater Kruger Area, South Africa. We sampled 406 individuals that experience different exposure to herbivory, from which we collected four traits: plant height, basal stem diameter, number of successive forks (proxy for development stage), and resprouting. We analysed trait relationships (using standardized major axis regression) between height and stem diameter, accounting for the effect of ontogeny, exposure to herbivory, and resprouting. The number of successive forks affects the scaling relationship between height and stem diameter, with the slope and strength of the relationship declining in more developed individuals. Herbivory exposure and resprouting do not affect the overall height-diameter relationship. However, when height and stem diameter were regressed separately against number of successive forks, herbivory exposure and resprouting had an effect. For example, resprouting individuals allocate more biomass to both primary and secondary growth than non-resprouting plants in more disturbed conditions. We stress the need to include traits related to ontogeny so as to disentangle the effect of biomass allocation to primary and secondary growth from that of development in plant functional relationships.

Benefits of symbiotic ectomycorrhizal fungi to plant water relations depend on plant genotype in pinyon pine

Rhizosphere microbes, such as root-associated fungi, can improve plant access to soil resources, affecting plant health, productivity, and stress tolerance. While mycorrhizal associations are ubiquitous, plant-microbe interactions can be species specific. Here we show that the specificity of the effects of microbial symbionts on plant function can go beyond species level: colonization of roots by ectomycorrhizal fungi (EMF) of the genus Geopora has opposite effects on water uptake, and stomatal control of desiccation in drought tolerant and intolerant genotypes of pinyon pine (Pinus edulis Engelm.). These results demonstrate, for the first time, that microorganisms can have significant and opposite effects on important plant functional traits like stomatal control of desiccation that are associated with differential mortality and growth in nature. They also highlight that appropriate pairing of plant genotypes and microbial associates will be important for mitigating climate change impacts on vegetation.

Effect of strong wind on laminas and petioles of Farfugium japonicum (L.) Kitam. var. japonicum (Asteraceae)

Farfugium japonicum (L.) Kitam. var. japonicum grows mainly in the coastal areas of Japan. Meteorological recording data from natural habitats were used to investigate the factors associated with the laminas and petioles of radical leaves of F. japonicum var. japonicum to avoid or resist higher wind stress. Our morphological and mechanical results indicated that petiole length and petiole cross-sectional area had a weak correlation with wind speed and breaking strength, and the petiole second area moment of inertia did not differ significantly among populations. However, both lamina area and petiole length per petiole cross-sectional area decreased with increasing wind speed, indicating that F. japonicum var. japonicum resisted or avoided an increase in wind speed outdoors by reducing the lamina area and petiole length per petiole cross-sectional area without qualitative changes in their petioles. The results of this study indicated that densely distributed recording stations of the Automated Meteorological Data Acquisition System (AMeDAS) by the Japan Meteorological Agency can be used for environmental adaptation studies of plants in the field using nearby plant populations.

Allometry of the quasi-pipe (qPipe) model for estimating tree leaf area and tree leaf mass applied to plant functional types

The allometry of the pipe model quantifies the approximate proportionality between the tree leaf amount and the stem cross-sectional area at the crown base (A_CB). It is useful for estimating and modeling carbon fixation abilities of trees but requires climbing the tree and is thus unsuitable for large-scale studies. Here, we adopted a previously proposed allometry (hereafter the quasi-pipe (qPipe) model allometry) formulating the relationship between the tree leaf amount and a surrogate of A_CB, A_{CB_Est}, calculated from tree dimensions measurable from the ground. Using published/unpublished data for 962 trees of 159 species collected between tropical rainforests and boreal forests, we established pipe and qPipe model allometries for evergreen-conifer, deciduous-conifer, evergreen-broadleaf, and deciduous-broadleaf plant functional types (PFTs). For the leaf area per tree (LA), allometric lines on a log-log plane were almost identical among the four PFTs in both models, with slopes of ~ 1. For the leaf mass per tree (LM), however, the allometric lines separated among the four PFTs in both models and had slopes greater than 1, indicating that the proportionality assumed in the pipe model held for LA but not LM. The applicability of the qPipe model in estimating the stand-scale leaf amount was further examined.

A circuit analogy based girth growth model for living architecture design

Architecture with and from living trees (Baubotanik) is a promising approach to sustainable, climate-adapted construction. Shaping and grafting allows one to create resilient structures that combine the ecological performance and aesthetics of trees with the functions of buildings. In order to design and engineer such living structures, it is necessary to predict the growth of different tree segments, especially when trunks, branches or roots are bent and jointed into a complex inosculated network. To address this, we have developed a tool to forecast the relative girth growth of different segments in such structures based on topological skeletons, the pipe model theory and circuit analogy. We have validated our results with a set of (scaled) photographs of inosculated tree structures of the so-called 'Tree Circus', covering over 80 years of their growth. Our model has proven to predict the relative girth growth with sufficient accuracy for conceptual design purposes. So far, it does not allow the simulation of absolute growth in circumference over the course of time that is necessary to predict quantitative technical aspects, such as mechanical performance at a given time. We conclude by briefly outlining how this could be addressed in future research.

Conjoining Trees for the Provision of Living Architecture in Future Cities: A Long-Term Inosculation Study

Faced with the environmental challenges posed by climate change, architects are creating nature-based solutions for urban areas, such as transforming living trees into artificial architectural structures. In this study, we have analyzed stem pairs of five tree species conjoined for more than eight years by measuring the stem diameters below and above the resulting inosculation and by calculating the respective diameter ratio. Our statistical analyses reveal that Platanus × hispanica and Salix alba stems do not differ significantly in diameter below inosculation. However, in contrast to P. × hispanica, the diameters of the conjoined stems above inosculation differ significantly in S. alba. We provide a binary decision tree based on diameter comparisons above and below inosculation as a straightforward tool for identifying the likelihood of full inosculation with water exchange. Moreover, we have compared branch junctions and inosculations by means of anatomical analyses, micro-computed tomography, and 3D reconstructions showing similarities in the formation of common annual rings that increase the capacity for water exchange. Due to the highly irregular cell arrangement in the center of the inosculations, cells cannot be assigned clearly to either of the stems. In contrast, cells in the center of branch junctions can always be attributed to one of the branches.

Tracing plant source water dynamics during drought by continuous transpiration measurements: An in-situ stable isotope approach

The isotopic composition of xylem water (δ_X ) is of considerable interest for plant source water studies. In-situ monitored isotopic composition of transpired water (δ_T ) could provide a nondestructive proxy for δ_X -values. Using flow-through leaf chambers, we monitored 2-hourly δ_T -dynamics in two tropical plant species, one canopy-forming tree and one understory herbaceous species. In an enclosed rainforest (Biosphere 2), we observed δ_T -dynamics in response to an experimental severe drought, followed by a ² H deep-water pulse applied belowground before starting regular rain. We also sampled branches to obtain δ_X -values from cryogenic vacuum extraction (CVE). Daily flux-weighted δ¹⁸ O_T -values were a good proxy for δ¹⁸ O_X -values under well-watered and drought conditions that matched the rainforest's water source. Transpiration-derived δ¹⁸ O_X -values were mostly lower than CVE-derived values. Transpiration-derived δ² H_X -values were relatively high compared to source water and consistently higher than CVE-derived values during drought. Tracing the ² H deep-water pulse in real-time showed distinct water uptake and transport responses: a fast and strong contribution of deep water to canopy tree transpiration contrasting with a slow and limited contribution to understory species transpiration. Thus, the in-situ transpiration method is a promising tool to capture rapid dynamics in plant water uptake and use by both woody and nonwoody species.

Nitrogen deposition increases xylem hydraulic sensitivity but decreases stomatal sensitivity to water potential in two temperate deciduous tree species

Although the effects of nitrogen deposition on tree water relations are studied extensively, its impact on the relative sensitivities of stomatal and xylem hydraulic conductance to vapor pressure deficit and water potential is still poorly understood. This study investigated the effects of a 7-year N deposition treatment on the responses of leaf water relations and sensitivity of canopy stomatal conductance to vapor pressure deficit (VPD) and water potential, as well as the sensitivity of branch hydraulic conductance to water potential in a dominant tree species (Quercus wutaishanica) and an associated tree species (Acer mono) in a temperate forest. It was found that the N deposition increased stomatal sensitivity to VPD, decreased stomatal sensitivity to water potential, and increased the vulnerability of the hydraulic system to cavitation in both species. The standardized stomatal sensitivity to VPD, however, was not affected by the N deposition, indicating that the stomata maintained the ability to regulate the water balance under nitrogen deposition condition. Although the increased stomatal sensitivity to VPD could compensate the decreased stomatal sensitivity to water potential to some extent, the combined response would increase the percentage loss of hydraulic conductivity (PLC) when 50 % loss in stomatal conductance occurred, particularly in the dominant species Q. wutaishanica. The result indicates that N deposition would increase the risk of hydraulic failure in those species if the soil and/or air becomes drier under future climate change scenarios. The results of the study can have significant implications on the modelling of ecosystem vulnerability to drought under the scenario of atmospheric nitrogen deposition.

Prediction of tree sapwood and heartwood profiles using pipe model and branch thinning theory

Estimates of tree heartwood and sapwood profiles are important in the pulp industry and for dynamic vegetation models, in which they determine tree biomechanical stability and hydraulic conductivity. Several phenomenological models of stem profiles have been developed for this purpose, based on assumptions on how tree crown and foliage distributions change over time. Here, we derive estimates of tree profiles by synthesizing a simple pipe model theory of plant form with a recently developed theory of branch thinning that from simple assumptions quantifies discarded branches and leaves. This allows us to develop a new trunk model of tree profiles from breast height up to the top of the tree. We postulate that leaves that are currently on the tree are connected by sapwood pipes, while pipes that previously connected discarded leaves or branches form the heartwood. By assuming that a fixed fraction of all pipes remain on the trunk after a branching event, as the trunk is traversed from the root system to the tips, this allows us to quantify trunk heartwood and sapwood profiles. We test the trunk model performance on empirical data from five tree species across three continents. We find that the trunk model accurately describes heartwood and sapwood profiles of all tested tree species (calibration; R2: 84-99%). Furthermore, once calibrated to a tree species, the trunk model predicts heartwood and sapwood profiles of conspecific trees in similar growing environments based only on the age and height of a tree (cross-validation/prediction; R2: 68-98%). The fewer and often contrasting parameters needed for the trunk model make it a potentially useful complementary tool for biologists and foresters.

The relationship between tree size and tree water-use: is competition for water size-symmetric or size-asymmetric?

Relationships between tree size and water use indicate how soil water is partitioned between differently sized individuals, and hence competition for water. These relationships are rarely examined, let alone whether there is consistency in shape across populations. Competition for water among plants is often assumed to be size-symmetric, i.e., exponents (b1) of power functions (water use ∝ biomassb1) equal to 1, with all sizes using the same amount of water proportionally to their size. We tested the hypothesis that b1 actually varies greatly, and based on allometric theory, that b1 is only centered around 1 when size is quantified as basal area or sapwood area (not diameter). We also examined whether b1 varies spatially and temporally in relation to stand structure (height and density) and climate. Tree water use ∝ sizeb1 power functions were fitted for 80 species and 103 sites using the global SAPFLUXNET database. The b1 were centered around 1 when tree size was given as basal area or sapwood area, but not as diameter. The 95% confidence intervals of b1 included the theoretical predictions for the scaling of plant vascular networks. b1 changed through time within a given stand for the species with the longest time series, such that larger trees gained an advantage during warmer and wetter conditions. Spatial comparisons across the entire dataset showed that b1 correlated only weakly (R2 < 12%) with stand structure or climate, suggesting that inter-specific variability in b1 and hence the symmetry of competition for water may be largely related to inter-specific differences in tree architecture or physiology rather than to climate or stand structure. In conclusion, size-symmetric competition for water (b1 ≈ 1) may only be assumed when size is quantified as basal area or sapwood area, and when describing a general pattern across forest types and species. There is substantial deviation in b1 between individual stands and species.

Relationships between trunk radial growth and fruit yield in apple and pear trees on size-controlling rootstocks

BACKGROUND AND AIMS

Understanding the mutual co-ordination of vegetative and reproductive growth is important in both agricultural and ecological settings. A competitive relationship between vegetative growth and fruiting is often highlighted, resulting in an apparent trade-off between structural growth and fruit production. However, our understanding of factors driving this relationship is limited.

METHODS

We used four scions grafted onto a series of size-controlling rootstocks to evaluate the relationships between the annual fruit yield and radial growth of trunks, branches and roots. To assess tree radial growth, we measured ring widths on extracted tree cores, which is an approach not frequently used in a horticultural setting.

KEY RESULTS

We found that the yield and radial growth were negatively related when plotted in absolute terms or as detrended and normalized indices. The relationship was stronger in low vigour trees, but only after the age-related trend was removed. In contrast, when trunk radial growth was expressed as basal area increment, the negative relationship disappeared, suggesting that the relationship between trunk radial growth and fruit yield might not be a true trade-off related to the competition between the two sinks. The effect of low yield was associated with increased secondary growth not only in trunks but also in branches and roots. In trunks, we observed that overcropping was associated with reduced secondary growth in a subsequent year, possibly due to the depletion of reserves.

CONCLUSIONS

Our results show that variation in annual fruit yield due to tree ageing, weather cueing and inherent alternate bearing behaviour is reflected in the magnitude of secondary growth of fruit trees. We found little support for the competition/architecture theory of rootstock-induced growth vigour control. More broadly, our study aimed at bridging the gap between forest ecology and horticulture.

Scaling the leaf length-times-width equation to predict total leaf area of shoots

BACKGROUND AND AIMS

An individual plant consists of different-sized shoots, each of which consists of different-sized leaves. To predict plant-level physiological responses from the responses of individual leaves, modelling this within-shoot leaf size variation is necessary. Within-plant leaf trait variation has been well investigated in canopy photosynthesis models but less so in plant allometry. Therefore, integration of these two different approaches is needed.

METHODS

We focused on an established leaf-level relationship that the area of an individual leaf lamina is proportional to the product of its length and width. The geometric interpretation of this equation is that different-sized leaf laminas from a single species share the same basic form. Based on this shared basic form, we synthesized a new length-times-width equation predicting total shoot leaf area from the collective dimensions of leaves that comprise a shoot. Furthermore, we showed that several previously established empirical relationships, including the allometric relationships between total shoot leaf area, maximum individual leaf length within the shoot and total leaf number of the shoot, can be unified under the same geometric argument. We tested the model predictions using five species, all of which have simple leaves, selected from diverse taxa (Magnoliids, monocots and eudicots) and from different growth forms (trees, erect herbs and rosette herbs).

KEY RESULTS

For all five species, the length-times-width equation explained within-species variation of total leaf area of a shoot with high accuracy (R2 > 0.994). These strong relationships existed despite leaf dimensions scaling very differently between species. We also found good support for all derived predictions from the model (R2 > 0.85).

CONCLUSIONS

Our model can be incorporated to improve previous models of allometry that do not consider within-shoot size variation of individual leaves, providing a cross-scale linkage between individual leaf-size variation and shoot-size variation.

Divergence of hydraulic traits among tropical forest trees across topographic and vertical environment gradients in Borneo

Fine-scale topographic-edaphic gradients are common in tropical forests and drive species spatial turnover and marked changes in forest structure and function. We evaluate how hydraulic traits of tropical tree species relate to vertical and horizontal spatial niche specialization along such a gradient. Along a topographic-edaphic gradient with uniform climate in Borneo, we measured six key hydraulic traits in 156 individuals of differing heights in 13 species of Dipterocarpaceae. We investigated how hydraulic traits relate to habitat, tree height and their interaction on this gradient. Embolism resistance increased in trees on sandy soils but did not vary with tree height. By contrast, water transport capacity increased on sandier soils and with increasing tree height. Habitat and height only interact for hydraulic efficiency, with slope for height changing from positive to negative from the clay-rich to the sandier soil. Habitat type influenced trait-trait relationships for all traits except wood density. Our data reveal that variation in the hydraulic traits of dipterocarps is driven by a combination of topographic-edaphic conditions, tree height and taxonomic identity. Our work indicates that hydraulic traits play a significant role in shaping forest structure across topographic-edaphic and vertical gradients and may contribute to niche specialization among dipterocarp species.

Forest disturbances and climate constrain carbon allocation dynamics in trees

Forest disturbances such as drought, fire, and logging affect the forest carbon dynamics and the terrestrial carbon sink. Forest mortality after disturbances creates uncertainties that need to be accounted for to understand forest dynamics and their associated C-sink. We combined data from permanent resampling plots and biomass oriented dendroecological plots to estimate time series of annual woody biomass growth (ABI) in several forests. ABI time series were used to benchmark a vegetation model to analyze dynamics in forest productivity and carbon allocation forced by environmental variability. The model implements source and sink limitations explicitly by dynamically constraining carbon allocation of assimilated photosynthates as a function of temperature and moisture. Bias in tree-ring reconstructed ABI increased back in time from data collection and with increasing disturbance intensity. ABI bias ranged from zero, in open stands without recorded mortality, to over 100% in stands with major disturbances such as thinning or snowstorms. Stand leaf area was still lower than in control plots decades after heavy thinning. Disturbances, species life-history strategy and climatic variability affected carbon-partitioning patterns in trees. Resprouting broadleaves reached maximum biomass growth at earlier ages than nonresprouting conifers. Environmental variability and leaf area explained much variability in woody biomass allocation. Effects of stand competition on C-allocation were mediated by changes in stand leaf area except after major disturbances. Divergence between tree-ring estimated and simulated ABI were caused by unaccounted changes in allocation or misrepresentation of some functional process independently of the model calibration approach. Higher disturbance intensity produced greater modifications of the C-allocation pattern, increasing error in reconstructed biomass dynamics. Legacy effects from disturbances decreased model performance and reduce the potential use of ABI as a proxy to net primary productivity. Trait-based dynamics of C-allocation in response to environmental variability need to be refined in vegetation models.

Experimental evidence for logarithmic fractal structure of botanical trees

The area-preserving rule for botanical trees by Leonardo da Vinci is discussed in terms of a very specific fractal structure, a logarithmic fractal. We use a method of the numerical Fourier analysis to distinguish the logarithmic fractal properties of the two-dimensional objects and apply it to study the branching system of real trees through its projection on the two-dimensional space, i.e., using their photographs. For different species of trees (birch and oak) we observe the Q^{-2} decay of the spectral intensity characterizing the branching structure that is associated with the logarithmic fractal structure in two-dimensional space. The experiments dealing with the side view of the tree should complement the area preserving Leonardo's rule with one applying to the product of diameter d and length l of the k branches: d_{i}l_{i}=kd_{i+1}l_{i+1}. If both rules are valid, then the branch's length of the next generation is sqrt[k] times shorter than previous one: l_{i}=sqrt[k]l_{i+1}. Moreover, the volume (mass) of all branches of the next generation is a factor of d_{i}/d_{i+1} smaller than previous one. We conclude that a tree as a three-dimensional object is not a logarithmic fractal, although its projection onto a two-dimensional plane is. Consequently, the life of a tree flows according to the laws of conservation of area in two-dimensional space, as if the tree were a two-dimensional object.

Effects of Stem Density on Crown Architecture of Scots Pine Trees

Trees adapt to their growing conditions by regulating the sizes of their parts and their relationships. For example, removal or death of adjacent trees increases the growing space and the amount of light received by the remaining trees enabling their crowns to expand. Knowledge about the effects of silvicultural practices on crown size and shape and also about the quality of branches affecting the shape of a crown is, however, still limited. Thus, the aim was to study the crown structure of individual Scots pine trees in forest stands with varying stem densities due to past forest management practices. Furthermore, we wanted to understand how crown and stem attributes and also tree growth affect stem area at the height of maximum crown diameter (SAHMC), which could be used as a proxy for tree growth potential. We used terrestrial laser scanning (TLS) to generate attributes characterizing crown size and shape. The results showed that increasing stem density decreased Scots pine crown size. TLS provided more detailed attributes for crown characterization compared with traditional field measurements. Furthermore, decreasing stem density increased SAHMC, and strong relationships (Spearman's correlations > 0.5) were found between SAHMC and crown and stem size and also stem growth. Thus, this study provided quantitative and more comprehensive characterization of Scots pine crowns and their growth potential. The combination of a traditional growth and yield study design and 3D characterization of crown architecture and growth potential can open up new research possibilities.

Fruit tree crop models: an update

Functional structural plant models of tree crops are useful tools that were introduced more than two decades ago. They can represent the growth and development of a plant through the in silico simulation of the 3D architecture in connection with physiological processes. In tree crops, physiological processes such as photosynthesis, carbon allocation and growth are usually integrated into these models, although other functions such as water and nutrient uptake are often disregarded. The implementation of the 3D architecture involves different techniques such as L-system frameworks, pipe model concepts and Markovian models to simulate branching processes, bud fates and elongation of stems based on the production of metamers. The simulation of root architecture is still a challenge for researchers due to a limited amount of information and experimental issues in dealing with roots, because root development is not based on the production of metamers. This review aims to focus on functional-structural models of fruit tree crops, highlighting their physiological components. The potential and limits of these tools are reviewed to point out the topics that still need more attention.

The shaping of plant axes and crowns through tropisms and elasticity: an example of morphogenetic plasticity beyond the shoot apical meristem

Shoot morphogenetic plasticity is crucial to the adaptation of plants to their fluctuating environments. Major insights into shoot morphogenesis have been compiled studying meristems, especially the shoot apical meristem (SAM), through a methodological effort in multiscale systems biology and biophysics. However, morphogenesis at the SAM is robust to environmental changes. Plasticity emerges later on during post-SAM development. The purpose of this review is to show that multiscale systems biology and biophysics is insightful for the shaping of the whole plant as well. More specifically, we review the shaping of axes and crowns through tropisms and elasticity, combining the recent advances in morphogenetic control using physical cues and by genes. We focus mostly on land angiosperms, but with growth habits ranging from small herbs to big trees. We show that generic (universal) morphogenetic processes have been identified, revealing feedforward and feedback effects of global shape on the local morphogenetic process. In parallel, major advances have been made in the analysis of the major genes involved in shaping axes and crowns, revealing conserved genic networks among angiosperms. Then, we show that these two approaches are now starting to converge, revealing exciting perspectives.

Identifying Developmental Patterns in Structured Plant Phenotyping Data

Technological breakthroughs concerning both sensors and robotized plant phenotyping platforms have totally renewed the plant phenotyping paradigm in the last two decades. This has impacted both the nature and the throughput of data with the availability of data at high-throughput from the tissular to the whole plant scale. Sensor outputs often take the form of 2D or 3D images or time series of such images from which traits are extracted while organ shapes, shoot or root system architectures can be deduced. Despite this change of paradigm, many phenotyping studies often ignore the structure of the plant and therefore loose the information conveyed by the temporal and spatial patterns emerging from this structure. The developmental patterns of plants often take the form of succession of well-differentiated phases, stages or zones depending on the temporal, spatial or topological indexing of data. This entails the use of hierarchical statistical models for their identification.The objective here is to show potential approaches for analyzing structured plant phenotyping data using state-of-the-art methods combining probabilistic modeling, statistical inference and pattern recognition. This approach is illustrated using five different examples at various scales that combine temporal and topological index parameters, and development and growth variables obtained using prospective or retrospective measurements.

Integrating terrestrial laser scanning with functional-structural plant models to investigate ecological and evolutionary processes of forest communities

BACKGROUND

Woody plants (trees and shrubs) play an important role in terrestrial ecosystems, but their size and longevity make them difficult subjects for traditional experiments. In the last 20 years functional-structural plant models (FSPMs) have evolved: they consider the interplay between plant modular structure, the immediate environment and internal functioning. However, computational constraints and data deficiency have long been limiting factors in a broader application of FSPMs, particularly at the scale of forest communities. Recently, terrestrial laser scanning (TLS), has emerged as an invaluable tool for capturing the 3-D structure of forest communities, thus opening up exciting opportunities to explore and predict forest dynamics with FSPMs.

SCOPE

The potential synergies between TLS-derived data and FSPMs have yet to be fully explored. Here, we summarize recent developments in FSPM and TLS research, with a specific focus on woody plants. We then evaluate the emerging opportunities for applying FSPMs in an ecological and evolutionary context, in light of TLS-derived data, with particular consideration of the challenges posed by scaling up from individual trees to whole forests. Finally, we propose guidelines for incorporating TLS data into the FSPM workflow to encourage overlap of practice amongst researchers.

CONCLUSIONS

We conclude that TLS is a feasible tool to help shift FSPMs from an individual-level modelling technique to a community-level one. The ability to scan multiple trees, of multiple species, in a short amount of time, is paramount to gathering the detailed structural information required for parameterizing FSPMs for forest communities. Conventional techniques, such as repeated manual forest surveys, have their limitations in explaining the driving mechanisms behind observed patterns in 3-D forest structure and dynamics. Therefore, other techniques are valuable to explore how forests might respond to environmental change. A robust synthesis between TLS and FSPMs provides the opportunity to virtually explore the spatial and temporal dynamics of forest communities.

Forest structure drives changes in light heterogeneity during tropical secondary forest succession

Light is a key resource for tree performance and hence, tree species partition spatial and temporal gradients in light availability. Although light distribution drives tree performance and species replacement during secondary forest succession, we yet lack understanding how light distribution changes with tropical forest development.This study aims to evaluate how changes in forest structure lead to changes in vertical and horizontal light heterogeneity during tropical forest succession.We described successional patterns in light using a chronosequence approach in which we compared 14 Mexican secondary forest stands that differ in age (8-32 years) since agricultural abandonment. For each stand, we measured vertical light profiles in 16 grid cells, and structural parameters (diameter at breast height, height and crown dimensions) for each tree.During succession, we found a rapid increase in stand size (basal area, crown area and length) and stand differentiation (i.e. a gradual leaf distribution along the forest profile), which leads to fast changes in light conditions and more light heterogeneity. The inflection points of the vertical light gradient (i.e. the absolute height at which 50% relative light intensity is attained) rapidly moved towards higher heights in the first 20 years, indicating that larger amounts of light are intercepted by canopy trees. Light attenuation rate (i.e. the rate of light extinction) decreased during succession due to slower accumulation of the crown area with height. Understorey light intensity and heterogeneity slightly decreased during succession because of an increase in crown size and a decrease in lateral gap frequency. Understorey relative light intensity was 1.56% at 32 years after abandonment.Synthesis. During succession, light conditions changed linearly, which should lead to a continuous and constant replacement of species. Especially in later successional stages, stronger vertical light gradients can limit the regeneration of light-demanding pioneer species and increase the proportion of shade-tolerant late-successional species under the canopy. These changes in light conditions were largely driven by the successional changes in forest structure, as basal area strongly determined the height where most light is absorbed, whereas crown area, and to a lesser extent crown length, determined light distribution.

Measuring the Contribution of Leaves to the Structural Complexity of Urban Tree Crowns with Terrestrial Laser Scanning

Trees have a fractal-like branching architecture that determines their structural complexity. We used terrestrial laser scanning technology to study the role of foliage in the structural complexity of urban trees. Forty-five trees of three deciduous species, Gleditsia triacanthos, Quercus macrocarpa, Metasequoia glyptostroboides, were sampled on the Michigan State University campus. We studied their structural complexity by calculating the box-dimension (Db) metric from point clouds generated for the trees using terrestrial laser scanning, during the leaf-on and -off conditions. Furthermore, we artificially defoliated the leaf-on point clouds by applying an algorithm that separates the foliage from the woody material of the trees, and then recalculated the Db metric. The Db of the leaf-on tree point clouds was significantly greater than the Db of the leaf-off point clouds across all species. Additionally, the leaf removal algorithm introduced bias to the estimation of the leaf-removed Db of the G. triacanthos and M. glyptostroboides trees. The index capturing the contribution of leaves to the structural complexity of the study trees (the ratio of the Db of the leaf-on point clouds divided by the Db of the leaf-off point clouds minus one), was negatively correlated with branch surface area and different metrics of the length of paths through the branch network of the trees, indicating that the contribution of leaves decreases as branch network complexity increases. Underestimation of the Db of the G. triacanthos trees, after the artificial leaf removal, was related to maximum branch order. These results enhance our understanding of tree structural complexity by disentangling the contribution of leaves from that of the woody structures. The study also highlighted important methodological considerations for studying tree structure, with and without leaves, from laser-derived point clouds.

Conductivity of the phloem in mango (Mangifera indica L.)

Mango (Mangifera indica L., Anacardiaceae), the fifth most consumed fruit worldwide, is one of the most important fruit crops in tropical regions, but its vascular anatomy is quite unexplored. Previous studies examined the xylem structure in the stems of mango, but the anatomy of the phloem has remained elusive, leaving the long-distance transport of photoassimilates understudied. We combined fluorescence and electron microscopy to evaluate the structure of the phloem tissue in the tapering branches of mango trees, and used this information to describe the hydraulic conductivity of its sieve tube elements following current models of fluid transport in trees. We revealed that the anatomy of the phloem changes from current year branches, where it was protected by pericyclic fibres, to older ones, where the lack of fibres was concomitant with laticiferous canals embedded in the phloem tissue. Callose was present in the sieve plates, but also in the walls of the phloem sieve cells, making them discernible from other phloem cells. A scaling geometry of the sieve tube elements-including the number of sieve areas and the pore size across tapering branches-resulted in an exponential conductivity towards the base of the tree. These evaluations in mango fit with previous measurements of the phloem architecture in the stems of forest trees, suggesting that, despite agronomic management, the phloem sieve cells scale with the tapering branches. The pipe model theory applied to the continuous tubing system of the phloem appears as a good approach to understand the hydraulic transport of photoassimilates in fruit trees.

Defoliation-induced tree growth declines are jointly limited by carbon source and sink activities

Defoliation resulting from herbivory, storm, drought, and frost may seriously impair tree growth and forest production. However, a comprehensive evaluation of defoliation impacts on tree carbon (C) assimilation and growth has not been conducted. We performed a meta-analysis of a dataset that included 1562 observations of 40 tree species from 50 studies worldwide, and evaluated defoliation impacts on photosynthetic capacity, C allocation, and tree growth. Our results showed that the reduced tree-level leaf area by defoliation outweighed the enhanced leaf-level photosynthesis, leading to a net reduction in tree C assimilation that was accompanied with decreases in nonstructural carbohydrates (NSCs) concentrations. The negative effects of defoliation on leaf NSCs decreased over time, but leaf production increased following defoliation, suggesting a shift in the C allocation towards shoots over roots. Defoliation intensity negatively affected tree growth, but post-defoliated recovery time did oppositely. The structure equation modelling showed that defoliation reduced tree growth mainly by indirectly reducing C assimilation (r = -0.4), and minorly by direct negative effect of defoliation intensity (r = -0.28) and positive effect of post-defoliated time (r = 0.33). These findings suggest that tree growth declines caused by defoliation are co-limited by C-source and sink activities, which provide a physiological basis of tree growth that is of significance in tree growth modelling and forest management under global changes.

Internal trophic pressure, a regulator of plant development? Insights from a stochastic functional-structural plant growth model applied to Coffea trees

BACKGROUND AND AIMS

Using internal trophic pressure as a regulating variable to model the complex interaction loops between organogenesis, production of assimilates and partitioning in functional-structural models of plant growth has attracted increasing interest in recent years. However, this approach is hampered by the fact that internal trophic pressure is a non-measurable quantity that can be assessed only through model parametric estimation, for which the methodology is not straightforward, especially when the model is stochastic.

METHODS

A stochastic GreenLab model of plant growth (called 'GL4') is developed with a feedback effect of internal trophic competition, represented by the ratio of biomass supply to demand (Q/D), on organogenesis. A methodology for its parameter estimation is presented and applied to a dataset of 15 two-year-old Coffea canephora trees. Based on the fitting results, variations in Q/D are reconstructed and analysed in relation to the estimated variations in organogenesis parameters.

KEY RESULTS

Our stochastic retroactive model was able to simulate realistically the progressive set-up of young plant architecture and the branch pruning effect. Parameter estimation using real data for Coffea trees provided access to the internal trophic dynamics. These dynamics correlated with the organogenesis probabilities during the establishment phase.

CONCLUSIONS

The model can satisfactorily reproduce the measured data, thus opening up promising avenues for further applying this original procedure to other experimental data. The framework developed can serve as a model-based toolkit to reconstruct the hidden internal trophic dynamics of plant growth.

Two decades of functional-structural plant modelling: now addressing fundamental questions in systems biology and predictive ecology

BACKGROUND

Functional-structural plant models (FSPMs) explore and integrate relationships between a plant's structure and processes that underlie its growth and development. In the last 20 years, scientists interested in functional-structural plant modelling have expanded greatly the range of topics covered and now handle dynamical models of growth and development occurring from the microscopic scale, and involving cell division in plant meristems, to the macroscopic scales of whole plants and plant communities.

SCOPE

The FSPM approach occupies a central position in plant science; it is at the crossroads of fundamental questions in systems biology and predictive ecology. This special issue of Annals of Botany features selected papers on critical areas covered by FSPMs and examples of comprehensive models that are used to solve theoretical and applied questions, ranging from developmental biology to plant phenotyping and management of plants for agronomic purposes. Altogether, they offer an opportunity to assess the progress, gaps and bottlenecks along the research path originally foreseen for FSPMs two decades ago. This review also allows discussion of current challenges of FSPMs regarding (1) integration of multidisciplinary knowledge, (2) methods for handling complex models, (3) standards to achieve interoperability and greater genericity and (4) understanding of plant functioning across scales.

CONCLUSIONS

This approach has demonstrated considerable progress, but has yet to reach its full potential in terms of integration and heuristic knowledge production. The research agenda of functional-structural plant modellers in the coming years should place a greater emphasis on explaining robust emergent patterns, and on the causes of possible deviation from it. Modelling such patterns could indeed fuel both generic integration across scales and transdisciplinary transfer. In particular, it could be beneficial to emergent fields of research such as model-assisted phenotyping and predictive ecology in managed ecosystems.

V-Mango: a functional-structural model of mango tree growth, development and fruit production

BACKGROUND AND AIMS

Mango (Mangifera indica L.) is the fifth most widely produced fruit in the world. Its cultivation, mainly in tropical and sub-tropical regions, raises a number of issues such as the irregular fruit production across years, phenological asynchronisms that lead to long periods of pest and disease susceptibility, and the heterogeneity of fruit quality and maturity at harvest. To address these issues, we developed an integrative functional-structural plant model that synthesizes knowledge about the vegetative and reproductive development of the mango tree and opens up the possible simulation of cultivation practices.

METHODS

We designed a model of architectural development in order to precisely characterize the intricate developmental processes of the mango tree. The appearance of botanical entities was decomposed into elementary stochastic events describing occurrence, intensity and timing of development. These events were determined by structural (position and fate of botanical entities) and temporal (appearance dates) factors. Daily growth and development of growth units and inflorescences were modelled using empirical distributions and thermal time. Fruit growth was determined using an ecophysiological model that simulated carbon- and water-related processes at the fruiting branch scale.

KEY RESULTS

The model simulates the dynamics of the population of growth units, inflorescences and fruits at the tree scale during a growing cycle. Modelling the effects of structural and temporal factors makes it possible to simulate satisfactorily the complex interplays between vegetative and reproductive development. The model allowed the characterization of the susceptibility of mango tree to pests and the investigatation of the influence of tree architecture on fruit growth.

CONCLUSIONS

This integrative functional-structural model simulates mango tree vegetative and reproductive development over successive growing cycles, allowing a precise characterization of tree phenology and fruit growth and production. The next step is to integrate the effects of cultivation practices, such as pruning, into the model.

Carboniferous plant physiology breaks the mold

How plants have shaped Earth surface feedbacks over geologic time is a key question in botanical and geological inquiry. Recent work has suggested that biomes during the Carboniferous Period contained plants with extraordinary physiological capacity to shape their environment, contradicting the previously dominant view that plants only began to actively moderate the Earth's surface with the rise of angiosperms during the Mesozoic Era. A recently published Viewpoint disputes this recent work, thus here, we document in detail, the mechanistic underpinnings of our modeling and illustrate the extraordinary ecophysiological nature of Carboniferous plants.

Testing the benefits of early vessel evolution

This article comments on: Trueba S, Delzon S, Isnard S, and Lens F. 2019. Similar hydraulic efficiency and safety across vesselless angiosperms and vessel-bearing species with scalariform perforation plates. Journal of Experimental Botany 70, 3227–3240.

Ramification has little impact on shoot hydraulic efficiency in the sexually dimorphic genus Leucadendron (Proteaceae)

Despite the diversity of branching architectures in plants, the impact of this morphological variation on hydraulic efficiency has been poorly studied. Branch junctions are commonly thought to be points of high hydraulic resistance, but adjustments in leaf area or xylem conduit abundance or dimensions could compensate for the additional hydraulic resistance of nodal junctions at the level of the entire shoot. Here we used the sexually dimorphic genus Leucadendron (Proteaceae) to test whether variation in branch ramification impacts shoot hydraulic efficiency. We found that branch ramification was related to leaf traits via Corner’s rules such that more highly ramified shoots had smaller leaves, but that branch ramification had little consistent impact on shoot hydraulic efficiency, whether measured on a leaf area or stem cross-sectional area basis. These results suggest that the presumed increase in resistance associated with branching nodes can be compensated by other adjustments at the shoot level (e.g. leaf area adjustments, increased ramification to add additional branches in parallel rather than in series) that maintain hydraulic efficiency at the level of the entire shoot. Despite large morphological differences between males and females in the genus Leucadendron, which are due to differences in pollination and reproduction between the sexes, the physiological differences between males and females are minimal.

Evolution of Plant Architecture, Functional Diversification and Divergent Evolution in the Genus Atractocarpus (Rubiaceae) for New Caledonia

The diversification of ecological roles and related adaptations in closely related species within a lineage is one of the most important processes linking plant evolution and ecology. Plant architecture offers a robust framework to study these processes as it can highlight how plant structure influences plant diversification and ecological strategies. We investigated a case of gradual evolution of branching architecture in Atractocarpus spp. (Rubiaceae), forming a monophyletic group in New Caledonia that has diversified rapidly, predominantly in rainforest understory habitats. We used a transdisciplinary approach to depict architectural variations and revealed multiple evolutionary transitions from a branched (Stone's architectural model) to a monocaulous habit (Corner's architectural model), which involved the functional reduction of branches into inflorescences. We propose an integrative functional index that assesses branching incidence on functional traits influencing both assimilation and exploration functions. We showed that architectural transitions correlate with ecologically important functional traits. Variation in ecologically important traits among closely relatives, as supported by the architectural analysis, is suggestive of intense competition that favored divergence among locally coexisting species. We propose that Pleistocene climatic fluctuations causing expansion and contraction of rainforest could also have offered ecological opportunities for colonizers in addition to the process of divergent evolution.

Computational botany: advancing plant science through functional–structural plant modelling

The need to integrate the ever-expanding body of knowledge in the plant sciences has led to the development of sophisticated modelling approaches. This special issue focuses on functional–structural plant (FSP) models, which are the result of cross-fertilization between the domains of plant science, computer science and mathematics. FSP models simulate growth and morphology of individual plants that interact with their environment, from which complex plant community properties emerge. FSP models can be used for a broad range of research questions across disciplines related to plant science. This special issue presents the latest developments in FSP modelling, including the novel incorporation of plant ecophysiological concepts and the application of FSP models to address new scientific questions. Additionally, it illustrates the breadth of model evaluation approaches that are performed. FSP modelling is a very active domain of plant research which brings together a wide range of scientific disciplines. It offers the opportunity to address questions in complex plant systems that cannot be addressed by empirical approaches alone, including questions on fundamental concepts related to plant development such as regulation of morphogenesis, as well as on applied concepts such as the relationship between crop performance and plant competition for resources.