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.     

Crown asymmetry in high latitude forests: disentangling the directional effects of tree competition and solar radiation

Light foraging by trees is a fundamental process shaping forest communities. In heterogeneous light environments this behavior is expressed as plasticity of tree growth and the development of structural asymmetries. We studied the relative influence of neighborhood structure and directional solar radiation on horizontal asymmetry of tree crowns in late‐successional high latitude (67–68°N) forests in northern Fennoscandia. We described crown asymmetries as crown vectors (i.e. horizontal vectors from stem center to crown center), which we obtained from canopy maps based on crown perimeter measurements in the field. To disentangle the influence of the two main determinants, inter‐tree competition and directionality of above‐canopy solar radiation at high latitudes, we applied circular statistical models, utilizing cylindrical distributions, to these data consisting of orientations and intensities of crown asymmetry. At the individual tree level, our model predicted crown asymmetry vectors from the current stand structure, and the predictions became better when the intensity of asymmetry (i.e. crown vector length) was higher. Competition was the main determinant of crown asymmetry for 2/3 of trees, and the model predictions improved when we incorporated the directionality of solar radiation. At the stand‐level, these asymmetries had resulted in a small increment of the projected canopy area and an increased regularity of spatial structure. Our circular statistical modelling approach provided a quantitative evaluation of the relative importance of directionality of solar radiation and neighborhood stand structure, showing how both of these factors play a role in formation of crown asymmetries in high latitude forests. This approach further demonstrated the applicability of circular statistical modeling in ecological studies where the response variable has both orientation and intensity.     

樟子松人工林树冠结构的分形分析

基于樟子松人工林7块固定标准地中的31株解析木的树冠体积和叶量,以幂函数关系(F=Av^(D/3))建立了预估树冠表面积的分形维数。同时根据生物量实测数据,建立预估叶量的生物模型Lw=0.180397D^3045903H^-1.67348。基于枝解析、树干解析数据,动态地预估了一年、二年、三年前的树冠体积,并结合树冠体积、叶量的这种幂函数关系可以动态地预估一年、二年、三年前树冠表面积的分形维数,从而反映出树冠结构的动态变化规律。为了了解不同分级样木的分维数变化情况,利用2003年调查的4块生物量标准地数据,根据单株树木各个枝条占据的空间体积与该枝条的带叶枝干重的关系,计算了各标准地不同分级样木树冠的分维数。为探讨单株样木树冠的分维数的计算提供了一种可行方法。树冠的分维数作为表征树冠的动态生长变化是一有用和可靠的指标。     

Branching tree model with fractal vascular resistance explains fractal perfusion heterogeneity

Perfusion heterogeneities in organs such as the heart obey a power law as a function of scale, a behavior termed "fractal." An explanation of why vascular systems produce such a specific perfusion pattern is still lacking. An intuitive branching tree model is presented that reveals how this behavior can be generated as a consequence of scale-independent branching asymmetry and fractal vessel resistance. Comparison of computer simulations to experimental data from the sheep heart shows that the values of the two free model parameters are realistic. Branching asymmetry within the model is defined by the relative tissue volume being fed by each branch. Vessel ordering for fractal analysis of morphology based on fed or drained tissue volumes is preferable to the commonly used Strahler system, which is shown to depend on branching asymmetry. Recently, noninvasive imaging techniques such as PET and MRI have been used to measure perfusion heterogeneity. The model allows a physiological interpretation of the measured fractal parameters, which could in turn be used to characterize vascular morphology and function.     

Estimating Stem Volume Using QuickBird Imagery and Allometric Relationships for Open Populus xiaohei Plantations

There has been a great deal of interest in studying the crown of trees using remote sensing data.In this study,crownwidth was extracted from high-resolution QuickBird images for open Populus xiaohei plantations.Regression modelsfor predicting the individual stem volumes of Populus xiaohei were established using extracted crown width,as well asestimated tree parameters(i.e.diameter at breast height[DBH]and tree height)as predictors.Our results indicated thatcrown width could be accurately extracted from QuickBird images using a multi-scale segmentation approach with a meanrelative error of 5.74%,especially for wide-spacing stands.Using either extracted crown width alone or with estimatedDBH and tree height can successfully estimate individual stem volume of Populus xiaohei with the R~2 value ranging from0.87 to 0.92 depending on different model forms.In particular,the two second-order polynomial models(model2 andmodel 6),based on QuickBird image-derived crown widths and estimated DBH and tree heights,respectively,were the bestat describing the relationship between stem volume and tree characteristics.     

Estimating Stem Volume Using QuickBird Imagery and Allometric Relationships for Open Populus xiaohei Plantations

There has been a great deal of interest in studying the crown of trees using remote sensing data. In this study, crown width was extracted from high-resolution QuickBird images for open Populus xiaohei plantations. Regression models for predicting the individual stem volumes of Populus xiaohei were established using extracted crown width, as well as estimated tree parameters （i.e. diameter at breast height [DBH] and tree height） as predictors. Our results indicated that crown width could be accurately extracted from QuickBird images using a multi-scale segmentation approach with a mean relative error of 5.74%, especially for wide-spacing stands. Using either extracted crown width alone or with estimated DBH and tree height can successfully estimate individual stem volume of Populus xiaohei with the R2 value ranging from 0.87 to 0.92 depending on different model forms. In particular, the two second-order polynomial models （model 2 and model 6）, based on QuickBird image-derived crown widths and estimated DBH and tree heights, respectively, were the best at describing the relationship between stem volume and tree characteristics.     

Evaluation of Ecotoxicity Effect Indicators for Use in LCIA (10+4 pp)

Goal, Scope and Background The paper describes different ecotoxicity effect indicator methods/approaches. The approaches cover three main groups, viz. PNEC approaches, PAF approaches and damage approaches. Ecotoxicity effect indicators used in life cycle impact assessment (LCIA) are typically modelled to the level of impact, indicating the potential impact on 'ecosystem health'. The few existing indicators, which are modelled all the way to damage, are poorly developed, and even though relevant alternatives from risk assessment exist (e.g. recovery time and mean extinction time), these are unfortunately at a very early stage of development, and only few attempts have been made to include them in LCIA. Methods The approaches are described and evaluated against a set of assessment criteria comprising compatibility with the methodological requirements of LCIA, environmental relevance, reproducibility, data demand, data availability, quantification of uncertainty, transparency and spatial differentiation. Results and Discussion The results of the evaluation of the two impact approaches (i.e. PNEC and PAF) show both pros and cons for each of them. The assessment factor-based PNEC approaches have a low data demand and use only the lowest data (e.g. lowest NOEC value). Because it is developed in tiered risk assessment, and hence makes use of conservative assessment factors, it is not optimal, in its present form, to use in the comparative framework of LCIA, where best estimates are sought. The PAF approaches have a higher data demand but use all data and can be based on effect data (PNEC is no-effect-based), thus making these approaches non-conservative and more suitable for LCIA. However, indiscriminate use of ecotoxicity data tends to make the PAF-approaches no more environmentally relevant than the assessment factor-based PNEC approaches. The PAF approaches, however, can at least in theory be linked to damage modelling. All the approaches for damage modelling which are included here have a high environmental relevance but very low data availability, apart from the 'media recovery-approach', which depends directly on the fate model. They are all at a very early stage of development. Conclusion Recommendations and Outlook. An analysis of the different PAF approaches shows that the crucial point is according to which principles and based on which data the hazardous concentration to 50% of the included species (i.e. HC50) is estimated. The ability to calculate many characterisation factors for ecotoxicity is important for this impact category to be included in LCIA in a proper way. However, the access to effect data for the relevant chemicals is typically limited. So, besides the coupling to damage modelling, the main challenge within the further development and improvement of ecotoxicity effect indicators is to find an optimal method to estimate HC50 based on little data.     

Community‐level vs species‐specific approaches to model selection

A topic of particular current interest is community‐level approaches to species distribution modelling (SDM), i.e. approaches that simultaneously analyse distributional data for multiple species. Previous studies have looked at the advantages of community‐level approaches for parameter estimation, but not for model selection – the process of choosing which model (and in particular, which subset of environmental variables) to fit to data. We compared the predictive performance of models using the same modelling method (generalised linear models) but choosing the subset of variables to include in the model either simultaneously across all species (community‐level model selection) or separately for each species (species‐specific model selection). Our results across two large presence/absence tree community datasets were inconclusive as to whether there was an overall difference in predictive performance between models fitted via species‐specific vs community‐level model selection. However, we found some evidence that a community approach was best suited to modelling rare species, and its performance decayed with increasing prevalence. That is, when data were sparse there was more opportunity for gains from “borrowing strength” across species via a community‐level approach. Interestingly, we also found that the community‐level approach tended to work better when the model selection problem was more difficult, and more reliably detected “noise” variables that should be excluded from the model.     

Assessing canopy health of native eucalypt forests

Summary   The assessment of forest health is an essential part of the monitoring of ecological sustainability in managed native forests. In Australia, unfortunately, very limited quantitative information on forest health is actually obtained for management and reporting purposes. In this article, we summarize current approaches used in Australia to assess native forest health and some recent developments in the application of remotely acquired digital imagery for classifying canopy health. In a recent study examining Bell miner associated dieback (BMAD), high-resolution airborne imagery was successfully manipulated to present severity categories for BMAD affected canopy. The potential of remotely sensed imagery lies not in map production but in the statistical modelling capacity of this spatial information, particularly when added to climatic and terrain-based spatial data sets. There are several statistical approaches to modelling these spatial datasets and in this article, we discuss our approach to producing a preliminary BMAD model. The importance of ground-based assessments is also emphasized and we recommend tree crown condition as a key health attribute for the spatial modelling of forests. Although significant progress has been made in the application of remote sensing technologies, the structural complexity of native forests means that there are still technical issues that require resolving before this approach becomes operationally routine.     

Mathematical and computational approaches can complement experimental studies of host–pathogen interactions

In addition to traditional and novel experimental approaches to study host–pathogen interactions, mathematical and computer modelling have recently been applied to address open questions in this area. These modelling tools not only offer an additional avenue for exploring disease dynamics at multiple biological scales, but also complement and extend knowledge gained via experimental tools. In this review, we outline four examples where modelling has complemented current experimental techniques in a way that can or has already pushed our knowledge of host–pathogen dynamics forward. Two of the modelling approaches presented go hand in hand with articles in this issue exploring fluorescence resonance energy transfer and two-photon intravital microscopy. Two others explore virtual or ' in silico ' deletion and depletion as well as a new method to understand and guide studies in genetic epidemiology. In each of these examples, the complementary nature of modelling and experiment is discussed. We further note that multi-scale modelling may allow us to integrate information across length (molecular, cellular, tissue, organism, population) and time (e.g. seconds to lifetimes). In sum, when combined, these compatible approaches offer new opportunities for understanding host–pathogen interactions.     

Uncovering directional sensing: where are we headed?

We survey aspects of directional sensing, i.e. how a cell interprets differences in the external concentration of a chemoattractant to guide its motion, from the perspective of systems biology. We focus on questions that need to be addressed using a combination of modelling and experimental approaches. After briefly summarising the ideas underlying recent modelling efforts, we discuss a variety of experimental questions which are motivated by these models. Some of these questions focus on basic features of the chemotactic response, without involving much biochemistry, while others focus on filling some of the gaps in the biochemistry, which have been brought to light by the models. The emphasis is on systematic quantitative experiments that will unambiguously resolve many of these issues. Finally, we describe some current challenges for theoretical modelling and survey some of the theoretical tools and approaches employed to model the chemotaxis pathways.     

A comparison of statistical approaches for modelling fish species distributions

SUMMARY 1. The prediction of species distributions is of primary importance in ecology and conservation biology. Statistical models play an important role in this regard; however, researchers have little guidance when choosing between competing methodologies because few comparative studies have been conducted. 2. We provide a comprehensive comparison of traditional and alternative techniques for predicting species distributions using logistic regression analysis, linear discriminant analysis, classification trees and artificial neural networks to model: (1) the presence/absence of 27 fish species as a function of habitat conditions in 286 temperate lakes located in south‐central Ontario, Canada and (2) simulated data sets exhibiting deterministic, linear and non‐linear species response curves. 3. Detailed evaluation of model predictive power showed that approaches produced species models that differed in overall correct classification, specificity (i.e. ability to correctly predict species absence) and sensitivity (i.e. ability to correctly predict speciespresence) and in terms of which of the study lakes they correctly classified. Onaverage, neural networks outperformed the other modelling approaches, although all approaches predicted species presence/absence with moderate to excellent success. 4. Based on simulated non‐linear data, classification trees and neural networks greatly outperformed traditional approaches, whereas all approaches exhibited similar correct classification rates when modelling simulated linear data. 5. Detailed evaluation of model explanatory insight showed that the relative importance of the habitat variables in the species models varied among the approaches, where habitat variable importance was similar among approaches for some species and very different for others. 6. In general, differences in predictive power (both correct classification rate and identity of the lakes correctly classified) among the approaches corresponded with differences in habitat variable importance, suggesting that non‐linear modelling approaches (i.e. classification trees and neural networks) are better able to capture and model complex, non‐linear patterns found in ecological data. The results from the comparisons using simulated data further support this notion. 7. By employing parallel modelling approaches with the same set of data and focusing on comparing multiple metrics of predictive performance, researchers can begin to choose predictive models that not only provide the greatest predictive power, but also best fit the proposed application.     

LIGNUM: A Tree Model Based on Simple Structural Units

The model LIGNUM treats a tree as a collection of a large numberof simple units which correspond to the organs of the tree.The model describes the three dimensional structure of the treecrown and defines the growth in terms of the metabolism takingplace in these units. The activities of physiological processescan be explicitly related to the tree structures in which theyare taking place. The time step is 1 year. The crown of the model tree consists of tree segments, branchingpoints and buds. Each pair of tree segments is separated bya branching point. The buds produce new tree segments, branchingpoints and buds. The tree segments contain wood, bark and foliage.A model tree consisting of simple elements translates convenientlyto a list structure: the computer program implementing LIGNUMtreats the tree as a collection of lists. The annual growth of the tree is driven by available photosyntheticproducts after respiration losses are accounted for. The photosyntheticrate of foliage depends on the amount of light. The amount ofphotosynthates allocated to the growth of new tree segmentsis controlled by the light conditions and the amount of foliageon the mother tree segment. In principle, the biomass relationshipsof the tree parts follow the pipe model hypothesis. The orientationof new tree segments results from the application of constantbranching angles. LIGNUM has been parametrized for young Scotspine (Pinus sylvestrisL.) trees. However, the model is generic;with a change of parameter values and minor modifications itcan be applied to other species as well. Growth model; object-oriented modelling; tree architecture; branching structure; Pinus sylvestrisL.; developmental morphology and physiology; photosynthesis; respiration     

Intra‐specific variability and plasticity influence potential tree species distributions under climate change

Aim To assess the effect of local adaptation and phenotypic plasticity on the potential distribution of species under future climate changes. Trees may be adapted to specific climatic conditions; however, species range predictions have classically been assessed by species distribution models (SDMs) that do not account for intra‐specific genetic variability and phenotypic plasticity, because SDMs rely on the assumption that species respond homogeneously to climate change across their range, i.e. a species is equally adapted throughout its range, and all species are equally plastic. These assumptions could cause SDMs to exaggerate or underestimate species at risk under future climate change. Location The Iberian Peninsula. Methods Species distributions are predicted by integrating experimental data and modelling techniques. We incorporate plasticity and local adaptation into a SDM by calibrating models of tree survivorship with adaptive traits in provenance trials. Phenotypic plasticity was incorporated by calibrating our model with a climatic index that provides a measure of the differences between sites and provenances. Results We present a new modelling approach that is easy to implement and makes use of existing tree provenance trials to predict species distribution models under global warming. Our results indicate that the incorporation of intra‐population genetic diversity and phenotypic plasticity in SDMs significantly altered their outcome. In comparing species range predictions, the decrease in area occupancy under global warming conditions is smaller when considering our survival–adaptation model than that predicted by a ‘classical SDM’ calibrated with presence–absence data. These differences in survivorship are due to both local adaptation and plasticity. Differences due to the use of experimental data in the model calibration are also expressed in our results: we incorporate a null model that uses survival data from all provenances together. This model always predicts less reduction in area occupancy for both species than the SDM calibrated with presence–absence. Main conclusions We reaffirm the importance of considering adaptive traits when predicting species distributions and avoiding the use of occurrence data as a predictive variable. In light of these recommendations, we advise that existing predictions of future species distributions and their component populations must be reconsidered.     

Reprint of: Tree-tree interactions and crown complementarity: the role of functional diversity and branch traits for canopy packing

Previous studies have shown that tree species richness increases forest productivity by allowing for greater spatial complementarity of tree crowns (crown complementarity), which in turn results in more densely packed canopies. However, the mechanisms driving crown complementarity in tree species mixtures remain unclear. Here, we take advantage of a high-resolution, three-dimensional terrestrial laser scanning approach in the context of a large-scale biodiversity-ecosystem functioning experiment in subtropical China (BEF-China) to quantify the extent to which functional dissimilarity and divergences in branch traits between neighbouring trees affect crown complementarity at the scale of tree species pairs (i.e., two adjacent trees). Overall, we found no support that functional dissimilarity (divergence in morphological flexibility, specific leaf area and wood density) promotes crown complementarity. However, we show that the effects of functional dissimilarity (the plasticity of the outer crown structure) on crown complementarity vary in their magnitude and importance depending on branch trait divergences. Firstly, crown complementarity tended to be highest for tree species pairs that strongly differed in their functional traits, but were similar in branch density. In contrast, heterospecific pairs with a low functional trait divergence benefitted the most from a large difference in branch density compared with pairs characterised by a large functional dissimilarity. Secondly, the positive effects of increasing divergence in branching intensity (the plasticity of the inner crown structure) on crown complementarity became most important at low levels of functional dissimilarity, i.e. when species pairs were similar in their branch packing and vice versa. This suggests that species mixing allows trees to occupy canopy space more efficiently mainly due to phenotypic changes associated with crown morphology and branch plasticity. Our findings highlight the importance of considering outer and inner crown structures (e.g. branching architecture) to deepen our understanding of tree-tree interactions in mixed-species communities.     

Tree-tree interactions and crown complementarity: The role of functional diversity and branch traits for canopy packing

Previous studies have shown that tree species richness increases forest productivity by allowing for greater spatial complementarity of tree crowns (crown complementarity), which in turn results in more densely packed canopies. However, the mechanisms driving crown complementarity in tree species mixtures remain unclear. Here, we take advantage of a high-resolution, three-dimensional terrestrial laser scanning approach in the context of a large-scale biodiversity-ecosystem functioning experiment in subtropical China (BEF-China) to quantify the extent to which functional dissimilarity and divergences in branch traits between neighbouring trees affect crown complementarity at the scale of tree species pairs (i.e., two adjacent trees). Overall, we found no support that functional dissimilarity (divergence in morphological flexibility, specific leaf area and wood density) promotes crown complementarity. However, we show that the effects of functional dissimilarity (the plasticity of the outer crown structure) on crown complementarity vary in their magnitude and importance depending on branch trait divergences. Firstly, crown complementarity tended to be highest for tree species pairs that strongly differed in their functional traits, but were similar in branch density. In contrast, heterospecific pairs with a low functional trait divergence benefitted the most from a large difference in branch density compared with pairs characterised by a large functional dissimilarity. Secondly, the positive effects of increasing divergence in branching intensity (the plasticity of the inner crown structure) on crown complementarity became most important at low levels of functional dissimilarity, i.e. when species pairs were similar in their branch packing and vice versa. This suggests that species mixing allows trees to occupy canopy space more efficiently mainly due to phenotypic changes associated with crown morphology and branch plasticity. Our findings highlight the importance of considering outer and inner crown structures (e.g. branching architecture) to deepen our understanding of tree-tree interactions in mixed-species communities.     

Two Geometrical Models of Branching of Botanical Trees

A botanical tree may be regarded as a system of axes which developby repeated bifurcation. A complicated tree can be describedby a few parameters of bifurcation which determine the geometryof the bifurcation process. A bifurcation model (H-model) haspreviously been proposed and shown to be useful for comparisonwith trees which have branch complexes which approach a horizontalplane (e.g. Terminalia). Another bifurcation model (P-model)is now proposed which is appropriate to branching systems inwhich successive branch planes are perpendicular to each other(e.g. Cameraria and Tabernaemontana of the Apocynaceae). Bymodification of the P-model to take into account a geotropiceffect, a more realistic branching model for one kind of treespecies is produced. The relationship among these geometricalmodels of branching is discussed and illustrated with computersimulations. computer simulations, tree crown geometry, branching patterns, bifurcation models, Terminalia, Cameraria latifolia, Tabernaemontana, sp     

Infection dynamics of endemic malaria in a wild bird population: parasite species-dependent drivers of spatial and temporal variation in transmission rates

1.?Investigating the ecological context in which host-parasite interactions occur and the roles of biotic and abiotic factors in forcing infection dynamics is essential to understanding disease transmission, spread and maintenance. 2.?Despite their prominence as model host-pathogen systems, the relative influence of environmental heterogeneity and host characteristics in influencing the infection dynamics of avian blood parasites has rarely been assessed in the wild, particularly at a within-population scale. 3.?We used a novel multievent modelling framework (an extension of multistate mark-recapture modelling) that allows for uncertainty in disease state, to estimate transmission parameters and assess variation in the infection dynamics of avian malaria in a large, longitudinally sampled data set of breeding blue tits infected with two divergent species of Plasmodium parasites. 4.?We found striking temporal and spatial heterogeneity in the disease incidence rate and the likelihood of recovery within this single population and demonstrate marked differences in the relative influence of environmental and host factors in forcing the infection dynamics of the two Plasmodium species. 5.?Proximity to a permanent water source greatly influenced the transmission rates of P.?circumflexum, but not of P.?relictum, suggesting that these parasites are transmitted by different vectors. 6.?Host characteristics (age/sex) were found to influence infection rates but not recovery rates, and their influence on infection rates was also dependent on parasite species: P.?relictum infection rates varied with host age, whilst P.?circumflexum infection rates varied with host sex. 7.?Our analyses reveal that transmission of endemic avian malaria is a result of complex interactions between biotic and abiotic components that can operate on small spatial scales and demonstrate that knowledge of the drivers of spatial and temporal heterogeneity in disease transmission will be crucial for developing accurate epidemiological models and a thorough understanding of the evolutionary implications of pathogens.     

The mathematical modelling of cell kinetics in corneal epithelial wound healing

This paper considers the comparison of experimental spatial and temporal data of mitotic rates measured during corneal epithelial wound healing (CEWH) of a rat model with the predictions of a computer modelling framework. We begin by briefly showing that previous models, used in the study of corneal epithelial wound healing speeds, are inadequate for the study of cell kinetics. We proceed to formulate a new modelling framework more suited to such a study. This framework is simulated in its simplest form, and the results from this motivate a new realisation of the modelling framework, including a caricature of age structuring. Finally, a model with a simple representation of juxtacrine signalling is considered. The final model captures many, though not all, of the trends of the experimental data. This paper thus lays a foundation for the modelling of the cell kinetics of corneal epithelial wound healing, and yields valuable insight regarding the important mechanisms a model should consider in order to reproduce the observed experimental trends.