A stochastic model of tree architecture and biomass partitioning: application to Mongolian Scots pines

Background and Aims

Mongolian Scots pine (Pinus sylvestris var. mongolica) is one of the principal species used for windbreak and sand stabilization in arid and semi-arid areas in northern China. A model-assisted analysis of its canopy architectural development and functions is valuable for better understanding its behaviour and roles in fragile ecosystems. However, due to the intrinsic complexity and variability of trees, the parametric identification of such models is currently a major obstacle to their evaluation and their validation with respect to real data. The aim of this paper was to present the mathematical framework of a stochastic functional–structural model (GL2) and its parameterization for Mongolian Scots pines, taking into account inter-plant variability in terms of topological development and biomass partitioning.

Methods

In GL2, plant organogenesis is determined by the realization of random variables representing the behaviour of axillary or apical buds. The associated probabilities are calibrated for Mongolian Scots pines using experimental data including means and variances of the numbers of organs per plant in each order-based class. The functional part of the model relies on the principles of source–sink regulation and is parameterized by direct observations of living trees and the inversion method using measured data for organ mass and dimensions.

Key Results

The final calibration accuracy satisfies both organogenetic and morphogenetic processes. Our hypothesis for the number of organs following a binomial distribution is found to be consistent with the real data. Based on the calibrated parameters, stochastic simulations of the growth of Mongolian Scots pines in plantations are generated by the Monte Carlo method, allowing analysis of the inter-individual variability of the number of organs and biomass partitioning. Three-dimensional (3D) architectures of young Mongolian Scots pines were simulated for 4-, 6- and 8-year-old trees.

Conclusions

This work provides a new method for characterizing tree structures and biomass allocation that can be used to build a 3D virtual Mongolian Scots pine forest. The work paves the way for bridging the gap between a single-plant model and a stand model.     

Relationships between tree size, crown shape, gender segregation and sex allocation in Pinus halepensis, a Mediterranean pine tree

Background and Aims

Sex allocation has been studied mainly in small herbaceous plants but much less in monoecious wind-pollinated trees. The aim of this study was to explore changes in gender segregation and sex allocation by Pinus halepensis, a Mediterranean lowland pine tree, within tree crowns and between trees differing in their size or crown shape.

Methods

The production of new male and female cones and sex allocation of biomass, nitrogen and phosphorus were studied. The relationship between branch location, its reproductive status and proxies of branch vigour was also studied.

Key Results

Small trees produced only female cones, but, as trees grew, they produced both male and female cones. Female cones were produced mainly in the upper part of the crown, and male cones in its middle and lower parts. Lateral branch density was correlated with the number of male but not female cones; lateral branches were more dense in large than in small trees and even denser in hemispherical trees. Apical branches grew faster, were thicker and their phosphorus concentration was higher than in lateral shoots. Nitrogen concentration was higher in cone-bearing apical branches than in apical vegetative branches and in lateral branches with or without cones. Allocation to male relative to female function increased with tree size as predicted by sex allocation theory.

Conclusions

The adaptive values of sex allocation and gender segregation patterns in P. halepensis, in relation to its unique life history, are demonstrated and discussed. Small trees produce only female cones that have a higher probability of being pollinated than the probability of male cones pollinating; the female-first strategy enhances population spread. Hemispherical old trees are loaded with serotinous cones that supply enough seeds for post-fire germination; thus, allocation to males is more beneficial than to females.     

Modelling fruit-temperature dynamics within apple tree crowns using virtual plants

Background and Aims

Fruit temperature results from a complex system involving the climate, the tree architecture, the fruit location within the tree crown and the fruit thermal properties. Despite much theoretical and experimental evidence for large differences (up to 10 °C in sunny conditions) between fruit temperature and air temperature, fruit temperature is never used in horticultural studies. A way of modelling fruit-temperature dynamics from climate data is addressed in this work.

Methods

The model is based upon three-dimensional virtual representation of apple trees and links three-dimensional virtual trees with a physical-based fruit-temperature dynamical model. The overall model was assessed by comparing model outputs to field measures of fruit-temperature dynamics.

Key Results

The model was able to simulate both the temperature dynamics at fruit scale, i.e. fruit-temperature gradients and departure from air temperature, and at the tree scale, i.e. the within-tree-crown variability in fruit temperature (average root mean square error value over fruits was 1·43 °C).

Conclusions

This study shows that linking virtual plants with the modelling of the physical plant environment offers a relevant framework to address the modelling of fruit-temperature dynamics within a tree canopy. The proposed model offers opportunities for modelling effects of the within-crown architecture on fruit thermal responses in horticultural studies.     

Annual and spatial variation in shoot demography associated with masting in Betula grossa: comparison between mature trees and saplings

Backgrounds and Aims

Shoot demography affects the growth of the tree crown and the number of leaves on a tree. Masting may cause inter-annual and spatial variation in shoot demography of mature trees, which may in turn affect the resource budget of the tree. The aim of this study was to evaluate the effect of masting on the temporal and spatial variations in shoot demography of mature Betula grossa.

Methods

The shoot demography was analysed in the upper and lower parts of the tree crown in mature trees and saplings over 7 years. Mature trees and saplings were compared to differentiate the effect of masting from the effect of exogenous environment on shoot demography. The fate of different shoot types (reproductive, vegetative, short, long), shoot length and leaf area were investigated by monitoring and by retrospective survey using morphological markers on branches. The effects of year and branch position on demographic parameters were evaluated.

Key Results

Shoot increase rate, production of long shoots, bud mortality, length of long shoots and leaf area of a branch fluctuated periodically from year to year in mature trees over 7 years, in which two masting events occurred. Branches within a crown showed synchronized annual variation, and the extent of fluctuation was larger in the upper branches than the lower branches. Vegetative shoots varied in their bud differentiation each year and contributed to the dynamic shoot demography as much as did reproductive shoots, suggesting physiological integration in shoot demography through hormonal regulation and resource allocation.

Conclusions

Masting caused periodic annual variation in shoot demography of the mature trees and the effect was spatially variable within a tree crown. Since masting is a common phenomenon among tree species, annual variation in shoot demography and leaf area should be incorporated into resource allocation models of mature masting trees.     

Common allometric response of open-grown leader shoots to tree height in co-occurring deciduous broadleaved trees

Background and Aims

Morphology of crown shoots changes with tree height. The height of forest trees is usually correlated with the light environment and this makes it difficult to separate the effects of tree size and of light conditions on the morphological plasticity of crown shoots. This paper addresses the tree-height dependence of shoot traits under full-light conditions where a tree crown is not shaded by other crowns.

Methods

Focus is given to relationships between tree height and top-shoot traits, which include the shoot''s leaf-blades and non-leafy mass, its total leaf-blade area and the length and basal diameter of the shoot''s stem. We examine the allometric characteristics of open-grown current-year leader shoots at the tops of forest tree crowns up to 24 m high and quantify their responses to tree height in 13 co-occurring deciduous hardwood species in a cool-temperate forest in northern Japan.

Key Results

Dry mass allocated to leaf blades in a leader shoot increased with tree height in all 13 species. Specific leaf area decreased with tree height. Stem basal area was almost proportional to total leaf area in a leader shoot, where the proportionality constant did not depend on tree height, irrespective of species. Stem length for a given stem diameter decreased with tree height.

Conclusions

In the 13 species observed, height-dependent changes in allometry of leader shoots were convergent. This finding suggests that there is a common functional constraint in tree-height development. Under full-light conditions, leader shoots of tall trees naturally experience more severe water stress than those of short trees. We hypothesize that the height dependence of shoot allometry detected reflects an integrated response to height-associated water stress, which contributes to successful crown expansion and height gain.     

Cambial activity related to tree size in a mature silver-fir plantation

Background and Aims

Our knowledge about the influences of environmental factors on tree growth is principally based on the study of dominant trees. However, tree social status may influence intra-annual dynamics of growth, leading to differential responses to environmental conditions. The aim was to determine whether within-stand differences in stem diameters of trees belonging to different crown classes resulted from variations in the length of the growing period or in the rate of cell production.

Methods

Cambial activity was monitored weekly in 2006 for three crown classes in a 40-year-old silver-fir (Abies alba) plantation near Nancy (France). Timings, duration and rate of tracheid production were assessed from anatomical observations of the developing xylem.

Key Results

Cambial activity started earlier, stopped later and lasted longer in dominant trees than in intermediate and suppressed ones. The onset of cambial activity was estimated to have taken 3 weeks to spread to 90 % of the trees in the stand, while the cessation needed 6 weeks. Cambial activity was more intense in dominant trees than in intermediate and suppressed ones. It was estimated that about 75 % of tree-ring width variability was attributable to the rate of cell production and only 25 % to its duration. Moreover, growth duration was correlated to tree height, while growth rate was better correlated to crown area.

Conclusions

These results show that, in a closed conifer forest, stem diameter variations resulted principally from differences in the rate of xylem cell production rather than in its duration. Tree size interacts with environmental factors to control the timings, duration and rate of cambial activity through functional processes involving source–sink relationships principally, but also hormonal controls.     

Paternity analysis-based inference of pollen dispersal patterns, male fecundity variation, and influence of flowering tree density and general flowering magnitude in two dipterocarp species

Background and Aims

Knowledge of pollen dispersal patterns and variation of fecundity is essential to understanding plant evolutionary processes and to formulating strategies to conserve forest genetic resources. Nevertheless, the pollen dispersal pattern of dipterocarp, main canopy tree species in palaeo-tropical forest remains unclear, and flowering intensity variation in the field suggests heterogeneity of fecundity.

Methods

Pollen dispersal patterns and male fecundity variation of Shorea leprosula and Shorea parvifolia ssp. parvifolia on Peninsular Malaysian were investigated during two general flowering seasons (2001 and 2002), using a neighbourhood model modified by including terms accounting for variation in male fecundity among individual trees to express heterogeneity in flowering.

Key Results

The pollen dispersal patterns of the two dipterocarp species were affected by differences in conspecific tree flowering density, and reductions in conspecific tree flowering density led to an increased selfing rate. Active pollen dispersal and a larger number of effective paternal parents were observed for both species in the season of greater magnitude of general flowering (2002).

Conclusions

The magnitude of general flowering, male fecundity variation, and distance between pollen donors and mother trees should be taken into account when attempting to predict the effects of management practices on the self-fertilization and genetic structure of key tree species in tropical forest, and also the sustainability of possible management strategies, especially selective logging regimes.     

Centennial olive trees as a reservoir of genetic diversity

Background and Aims

Genetic characterization and phylogenetic analysis of the oldest trees could be a powerful tool both for germplasm collection and for understanding the earliest origins of clonally propagated fruit crops. The olive tree (Olea europaea L.) is a suitable model to study the origin of cultivars due to its long lifespan, resulting in the existence of both centennial and millennial trees across the Mediterranean Basin.

Methods

The genetic identity and diversity as well as the phylogenetic relationships among the oldest wild and cultivated olives of southern Spain were evaluated by analysing simple sequence repeat markers. Samples from both the canopy and the roots of each tree were analysed to distinguish which trees were self-rooted and which were grafted. The ancient olives were also put into chronological order to infer the antiquity of traditional olive cultivars.

Key Results

Only 9·6 % out of 104 a priori cultivated ancient genotypes matched current olive cultivars. The percentage of unidentified genotypes was higher among the oldest olives, which could be because they belong to ancient unknown cultivars or because of possible intra-cultivar variability. Comparing the observed patterns of genetic variation made it possible to distinguish which trees were grafted onto putative wild olives.

Conclusions

This study of ancient olives has been fruitful both for germplasm collection and for enlarging our knowledge about olive domestication. The findings suggest that grafting pre-existing wild olives with olive cultivars was linked to the beginnings of olive growing. Additionally, the low number of genotypes identified in current cultivars points out that the ancient olives from southern Spain constitute a priceless reservoir of genetic diversity.     

Reconstruction and analysis of a deciduous sapling using digital photographs or terrestrial-LiDAR technology

Background and Aims

To meet the increasing need for rapid and non-destructive extraction of canopy traits, two methods were used and compared with regard to their accuracy in estimatating 2-D and 3-D parameters of a hybrid poplar sapling.

Methods

The first method consisted of the analysis of high definition photographs in Tree Analyser (TA) software (PIAF-INRA/Kasetsart University). TA allowed the extraction of individual traits using a space carving approach. The second method utilized 3-D point clouds acquired from terrestrial light detection and ranging (T-LiDAR) scans. T-LiDAR scans were performed on trees without leaves to reconstruct the lignified structure of the sapling. From this skeleton, foliage was added using simple modelling rules extrapolated from field measurements. Validation of the estimated dimension and the accuracy of reconstruction was then achieved by comparison with an empirical data set.

Key Results

TA was found to be slightly less precise than T-LiDAR for estimating tree height, canopy height and mean canopy diameter, but for 2-D traits both methods were, however, fully satisfactory. TA tended to over-estimate total leaf area (error up to 50 %), but better estimates were obtained by reducing the size of the voxels used for calculations. In contrast, T-LiDAR estimated total leaf area with an error of <6 %. Finally, both methods led to an over-estimation of canopy volume. With respect to this trait, T-LiDAR (14·5 % deviation) greatly surpassed the accuracy of TA (up to 50 % deviation), even if the voxels used were reduced in size.

Conclusions

Taking into account their magnitude of data acquisition and analysis and their accuracy in trait estimations, both methods showed contrasting potential future uses. Specifically, T-LiDAR is a particularly promising tool for investigating the development of large perennial plants, by itself or in association with plant modelling.     

Influence of the exclusion distance among trees on gap fraction and foliage clumping index of forest plantations

Key message

A hypergeometric model is proposed explicitly instead of two previous stochastic models (the Poisson model and Neyman-A model) to describe the topological relationship of trees and the influence of the exclusion distance on gap fraction and clumping index of forest plantation canopies.

Abstract

Gap fraction (GF) and clumping index (CI) play key roles in plant light interception, and therefore they have strong impacts on plant growth and canopy radiative transfer processes. Trees are usually assumed to be randomly distributed in natural forests in many previous studies. However, few studies have shown how trees are distributed in forest plantations and how these distribution patterns affect GF and CI in these forests. In this paper, a simple and general distance factor defined as relative allowable shortest distance between centers of two adjacent crowns divided by the mean diameter of the crowns (RASD) is proposed to describe quantitatively the degree of mutual exclusion among trees in forest plantations of various tree distribution patterns. A hypergeometric model is proposed instead of two previous stochastic tree distribution models (the Poisson model and Neyman-A model) to describe the topological relationship of trees and the influences of the exclusion distance on the GF and CI of the forest plantation canopies. The results show that: (1) the hypergeometric model is more suitable than the Poisson model and Neyman-A model for describing the topological relationship of trees in forest plantations; (2) the exclusion distance has strong impacts on GF and CI: there are significant differences between the results of the hypergeometric model and the Poisson model. Larger RASD causes lower GF and larger CI. The simulations are verified by field measurements in four forest plantation stands. Similarly, impacts of RASD on GF and CI are also found for other two crown shapes (prolate and oblate ellipsoids).

     

Canopy structure of tropical and sub-tropical rain forests in relation to conifer dominance analysed with a portable LIDAR system

Background and Aims

Globally, conifer dominance is restricted to nutient-poor habitats in colder, drier or waterlogged environments, probably due to competition with angiosperms. Analysis of canopy structure is important for understanding the mechanism of plant coexistence in relation to competition for light. Most conifers are shade intolerant, and often have narrow, deep, conical crowns. In this study it is predicted that conifer-admixed forests have less distinct upper canopies and more undulating canopy surfaces than angiosperm-dominated forests.

Methods

By using a ground-based, portable light detection and ranging (LIDAR) system, canopy structure was quantified for old-growth evergreen rainforests with varying dominance of conifers along altitudinal gradients (200–3100 m a.s.l.) on tropical and sub-tropical mountains (Mount Kinabalu, Malaysian Borneo and Yakushima Island, Japan) that have different conifer floras.

Key Results

Conifers dominated at higher elevations on both mountains (Podocarpaceae and Araucariaceae on Kinabalu and Cupressaceae and Pinaceae on Yakushima), but conifer dominance also varied with soil/substrate conditions on Kinabalu. Conifer dominance was associated with the existence of large-diameter conifers. Forests with higher conifer dominance showed a canopy height profile (CHP) more skewed towards the understorey on both Kinabalu and Yakushima. In contrast, angiosperm-dominated forests had a CHP skewed towards upper canopy, except for lowland dipterocarp forests and a sub-alpine scrub dominated by small-leaved Leptospermum recurvum (Myrtaceae) on Kinabalu. Forests with a less dense upper canopy had more undulating outer canopy surfaces. Mixed conifer–angiosperm forests on Yakushima and dipterocarp forests on Kinabalu showed similar canopy structures.

Conclusions

The results generally supported the prediction, suggesting that lower growth of angiosperm trees (except L. recurvum on Kinabalu) in cold and nutrient-poor environments results in a sparser upper canopy, which allows shade-intolerant conifers to co-occur with angiosperm trees either as emergents or as codominants in the open canopy.     

A functional-structural model for radiata pine (Pinus radiata) focusing on tree architecture and wood quality

Backgrounds and Aims

Functional–structural models are interesting tools to relate environmental and management conditions with forest growth. Their three-dimensional images can reveal important characteristics of wood used for industrial products. Like virtual laboratories, they can be used to evaluate relationships among species, sites and management, and to support silvicultural design and decision processes. Our aim was to develop a functional–structural model for radiata pine (Pinus radiata) given its economic importance in many countries.

Methods

The plant model uses the L-system language. The structure of the model is based on operational units, which obey particular rules, and execute photosynthesis, respiration and morphogenesis, according to their particular characteristics. Plant allometry is adhered to so that harmonic growth and plant development are achieved. Environmental signals for morphogenesis are used. Dynamic turnover guides the normal evolution of the tree. Monthly steps allow for detailed information of wood characteristics. The model is independent of traditional forest inventory relationships and is conceived as a mechanistic model. For model parameterization, three databases which generated new information relating to P. radiata were analysed and incorporated.

Key Results

Simulations under different and contrasting environmental and management conditions were run and statistically tested. The model was validated against forest inventory data for the same sites and times and against true crown architectural data. The performance of the model for 6-year-old trees was encouraging. Total height, diameter and lengths of growth units were adequately estimated. Branch diameters were slightly overestimated. Wood density values were not satisfactory, but the cyclical pattern and increase of growth rings were reasonably well modelled.

Conclusions

The model was able to reproduce the development and growth of the species based on mechanistic formulations. It may be valuable in assessing stand behaviour under different environmental and management conditions, assisting in decision-making with regard to management, and as a research tool to formulate hypothesis regarding forest tree growth and development.     

Water stress-induced xylem hydraulic failure is a causal factor of tree mortality in beech and poplar

Background and Aims

Extreme water stress episodes induce tree mortality, but the physiological mechanisms causing tree death are still poorly understood. This study tests the hypothesis that a potted tree''s ability to survive extreme monotonic water stress is determined by the cavitation resistance of its xylem tissue.

Methods

Two species were selected with contrasting cavitation resistance (beech and poplar), and potted juvenile trees were exposed to a range of water stresses, causing up to 100 % plant death.

Key Results

The lethal dose of water stress, defined as the xylem pressure inducing 50 % mortality, differed sharply across species (1·75 and 4·5 MPa in poplar and beech, respectively). However, the relationships between tree mortality and the degree of cavitation in the stems were similar, with mortality occurring suddenly when >90 % cavitation had occurred.

Conclusions

Overall, the results suggest that cavitation resistance is a causal factor of tree mortality under extreme drought conditions.     

Identifying ontogenetic, environmental and individual components of forest tree growth

Background and Aims

This study aimed to identify and characterize the ontogenetic, environmental and individual components of forest tree growth. In the proposed approach, the tree growth data typically correspond to the retrospective measurement of annual shoot characteristics (e.g. length) along the trunk.

Methods

Dedicated statistical models (semi-Markov switching linear mixed models) were applied to data sets of Corsican pine and sessile oak. In the semi-Markov switching linear mixed models estimated from these data sets, the underlying semi-Markov chain represents both the succession of growth phases and their lengths, while the linear mixed models represent both the influence of climatic factors and the inter-individual heterogeneity within each growth phase.

Key Results

On the basis of these integrative statistical models, it is shown that growth phases are not only defined by average growth level but also by growth fluctuation amplitudes in response to climatic factors and inter-individual heterogeneity and that the individual tree status within the population may change between phases. Species plasticity affected the response to climatic factors while tree origin, sampling strategy and silvicultural interventions impacted inter-individual heterogeneity.

Conclusions

The transposition of the proposed integrative statistical modelling approach to cambial growth in relation to climatic factors and the study of the relationship between apical growth and cambial growth constitute the next steps in this research.     

Growth and posture control strategies in Fagus sylvatica and Acer pseudoplatanus saplings in response to canopy disturbance

Background and Aims

Forest tree saplings that grow in the understorey undergo frequent changes in their light environment to which they must adapt to ensure their survival and growth. Crown architecture, which plays a critical role in light capture and mechanical stability, is a major component of sapling adaptation to canopy disturbance. Shade-adapted saplings typically have plagiotropic stems and branches. After canopy opening, they need to develop more erect shoots in order to exploit the new light conditions. The objective of this study was to test whether changes in sapling stem inclination occur after canopy opening, and to analyse the morphological changes associated with stem reorientation.

Methods

A 4-year canopy-opening field experiment with naturally regenerated Fagus sylvatica and Acer pseudoplatanus saplings was conducted. The appearance of new stem axes, stem basal diameter and inclination along the stem were recorded every year after canopy opening.

Key Results

Both species showed considerable stem reorientation resulting primarily from uprighting (more erect) shoot movements in Fagus, and from uprighting movements, shoot elongation and formation of relay shoots in Acer. In both species, the magnitude of shoot uprighting movements was primarily related to initial stem inclination. Both the basal part and the apical part of the stem contributed to uprighting movements. Stem movements did not appear to be limited by stem size or by stem growth.

Conclusions

Stem uprighting movements in shade-adapted Fagus and Acer saplings following canopy disturbance were considerable and rapid, suggesting that stem reorientation processes play a significant role in the growth strategy of the species.     

Post-pruning shoot growth increases fruit abscission and reduces stem carbohydrates and yield in macadamia

Background and Aims

There is good evidence for deciduous trees that competition for carbohydrates from shoot growth accentuates early fruit abscission and reduces yield but the effect for evergreen trees is not well defined. Here, whole-tree tip-pruning at anthesis is used to examine the effect of post-pruning shoot development on fruit abscission in the evergreen subtropical tree macadamia (Macadamia integrifolia, M. integrifolia × tetraphylla). Partial-tree tip-pruning is also used to test the localization of the effect.

Methods

In the first experiment (2005/2006), all branches on trees were tip-pruned at anthesis, some trees were allowed to re-shoot (R treatment) and shoots were removed from others (NR treatment). Fruit set and stem total non-structural carbohydrates (TNSC) over time, and yield were measured. In the second experiment (2006/2007), upper branches of trees were tip-pruned at anthesis, some trees were allowed to re-shoot (R) and shoots were removed from others (NR). Fruit set and yield were measured separately for upper (pruned) and lower (unpruned) branches.

Key Results

In the first experiment, R trees set far fewer fruit and had lower yield than NR trees. TNSC fell and rose in all treatments but the decline in R trees occurred earlier than in NR trees and coincided with early shoot growth and the increase in fruit abscission relative to the other treatments. In the second experiment, fruit abscission on upper branches of R trees increased relative to the other treatments but there was little difference in fruit abscission between treatments on lower branches.

Conclusions

This study is the first to demonstrate an increase in fruit abscission in an evergreen tree in response to pruning. The effect appeared to be related to competition for carbohydrates between post-pruning shoot growth and fruit development and was local, with shoot growth on pruned branches having no effect on fruit abscission on unpruned branches.     

Characterization of three-dimensional spatial aggregation and association patterns of brown rot symptoms within intensively mapped sour cherry trees

Background and Aims

Characterization of spatial patterns of plant disease can provide insights into important epidemiological processes such as sources of inoculum, mechanisms of dissemination, and reproductive strategies of the pathogen population. Whilst two-dimensional patterns of disease (among plants within fields) have been studied extensively, there is limited information on three-dimensional patterns within individual plant canopies. Reported here are the detailed mapping of different symptom types of brown rot (caused by Monilinia laxa) in individual sour cherry tree (Prunus cerasus) canopies, and the application of spatial statistics to the resulting data points to determine patterns of symptom aggregation and association.

Methods

A magnetic digitizer was utilized to create detailed three-dimensional maps of three symptom types (blossom blight, shoot blight and twig canker) in eight sour cherry tree canopies during the green fruit stage of development. The resulting point patterns were analysed for aggregation (within a given symptom type) and pairwise association (between symptom types) using a three-dimensional extension of nearest-neighbour analysis.

Key Results

Symptoms of M. laxa infection were generally aggregated within the canopy volume, but there was no consistent pattern for one symptom type to be more or less aggregated than the other. Analysis of spatial association among symptom types indicated that previous year''s twig cankers may play an important role in influencing the spatial pattern of current year''s symptoms. This observation provides quantitative support for the epidemiological role of twig cankers as sources of primary inoculum within the tree.

Conclusions

Presented here is a new approach to quantify spatial patterns of plant disease in complex fruit tree canopies using point pattern analysis. This work provides a framework for quantitative analysis of three-dimensional spatial patterns within the finite tree canopy, applicable to many fields of research.     

Branch transpiration of pine and spruce scaled to tree and canopy using needle biomass distributions

Branch water exchange and total tree water uptake were measured in a mixed Norway spruce and Scots pine stand in central Sweden during the 1995 and 1996 growing seasons. Branch transpiration was scaled to canopy level on the basis of a branch conductance model, using vertical needle-area distributions obtained by destructive sampling. Comparison with total tree water uptake scaled to canopy level showed agreement within 10%, for periods when the canopy was not affected by climatically induced stress. Comparison of scaled fluxes on individual trees showed that measurements of transpiration at branch level provide information on the direct response of transpiration to variations in weather, and furthermore that the time-lag between transpiration and tree water uptake was as much as 3 h. The vertical needle-area distribution of Scots pine was similar to that found by other authors. Needle-area distribution on Norway spruce, which has not been described before, showed that it has its largest needle area at the top of the crown. Specific needle area varied considerably both within trees and between trees. For spruce, mean specific needle area (±SD) varied from 2.4±0.5 mm² mg^–1 at the top of the crown to 7.1±1.9 mm² mg^–1 at the base. Corresponding figures for Scots pine were 3.4±2.0 and 9.1±2.1. Received: 5 March 1999 / Accepted: 17 March 2000