Leaf phyllotaxis: Does it really affect light capture?

The intriguing mathematical properties of leaf phyllotaxis still attract scientific attention after centuries of research. Phyllotaxis, and in particular the divergence angle between successive leaves, have been frequently interpreted in terms of maximization of light capture, although certain model simulations of light capture by vertical shoots revealed minor effects of phyllotaxis in comparison with the effect of other morphological features of the plant. However, these simulations assumed a number of simplifications, did not take into account diffuse light, and were not based on real plants with their natural range of morphological variation. This study was aimed at filling these gaps by examining the influence on light harvesting of shoot architecture and divergence angle in four species with spiral phyllotaxis (Quercus ilex, Arbutus unedo, Heteromeles arbutifolia and Daphne gnidium) with a realistic 3-D model (Y-plant). A wide range of divergence angles (from 100° to 154°) was observed within each species, with 144° being the most frequent one. These different divergence angles rendered very different vertical projections of the shoot due to contrasting patterns of leaf overlap as seen from above, but they rendered indistinguishable light interception efficiencies (Ea). Setting the leaves with an opposite-decussate phyllotaxis led, however, to a 40–50% decrease of Ea. The interplay of internode length, leaf size and shape, and leaf elevation angle led to significant species differences in Ea. Thus, only particular phyllotaxis (e.g., decussate) might be functionally inefficient under certain combinations of the various morphological variables that influence light capture of a shoot. This revised version was published online in June 2006 with corrections to the Cover Date.     

The functional morphology of light capture and carbon gain in the Redwood forest understorey plant Adenocaulon bicolor Hook

1. A three-dimensional geometric simulation model of crown architecture was utilized to investigate the efficiency of light capture and its relationship to whole-plant CO₂ assimilation of Adenocaulon bicolor .
2. Positioning of the leaves by the combined effects of ontogenetic variations in petiole length and angle and leaf size, and the leaf divergence angles were shown to be effective in minimizing self shading. The efficiency of light absorption varied from 0·64 to 0·70 among individual plants that were sampled.
3. Plant to plant variation in simulated daily carbon gain was strongly influenced by variations in the direct and diffuse PFD received by the individual plants. When simulations were run for all plants under a single common light environment, the carbon gain was strongly dependent on the efficiencies of light absorption of the different plants.
4. Simulations in which petiole length was varied showed a non-linear dependence of light absorption efficiency on petiole length. When both petiole length and leaf size were varied in a way that maintained a constant biomass then an optimal petiole length that corresponded to the observed petiole length was apparent. The observed divergence angle between successive leaves also maximized light absorption efficiency as compared to greater or lesser angles, but increases in internode length had no significant effect.
5. The results of this study provide evidence for selection for an 'optimal design' of crown architecture in Adenocaulon bicolor that maximizes light capture.     

Properties of maximal spacing on a circle related to phyllotaxis and to the golden mean

A class of divergence angles φ_G of phyllotaxis is defined that distribute leaves about the stem of a plant in a more uniform manner than do nearby angles. A theorem of Swierczkowski concerning the intervals between adjacent points placed on a circle according to the divergence angle 137·5° is generalized to include the other angles encountered in phyllotaxis. These angles are characterized by having continued fraction expansions containing no intermediate fractions after a finite number of terms. This criterion is shown to be sufficient for uniform spacing of leaves.A morphogen concentration field established by the leaves acting as sources is determined principally by :he geometrical spacing of the leaves and hence by their divergence angle. It is shown that the mean square of such a concentration field, is a relative minimum if the leaves are positioned by means of one of the φ_G. Thornley's dynamic scheme for determining the phyllotaxis divergence angles by positioning a new leaf at the minimum of the concentration field of previously placed leaves is also shown to be related to the spacing properties of the φ_G.     

A contact pressure model for semi-decussate and related phyllotaxis

Semi-decussate phyllotaxis, in which leaves arise singly and the divergence angles between successive pairs of leaves alternate between approximately 90° and approximately 180°, is accounted for by a contact pressure model. It is assumed that leaf primordia are initiated at a divergence angle close to the Fibonacci angle of 137·5°, that the primordia move under contact pressure, and that when a primordium first experiences contact pressure all other primordia are fixed. Extensions of the model account for: psuedodecussate phyllotaxis, where the leaves appear to arise in pairs; semi-tricussate and pseudo-tricussate phyllotaxis, where the leaves are arranged in, respectively, dissolved or apparent trimerous whorls; and phyllotaxis of the 1,3 series, where the divergence angle is about 100°. The compatibility of the model with current theories of Fibonacci phyllotaxis is discussed.     

What does optimization theory actually predict about crown profiles of photosynthetic capacity when models incorporate greater realism?

Measured profiles of photosynthetic capacity in plant crowns typically do not match those of average irradiance: the ratio of capacity to irradiance decreases as irradiance increases. This differs from optimal profiles inferred from simple models. To determine whether this could be explained by omission of physiological or physical details from such models, we performed a series of thought experiments using a new model that included more realism than previous models. We used ray‐tracing to simulate irradiance for 8000 leaves in a horizontally uniform canopy. For a subsample of 500 leaves, we simultaneously optimized both nitrogen allocation (among pools representing carboxylation, electron transport and light capture) and stomatal conductance using a transdermally explicit photosynthesis model. Few model features caused the capacity/irradiance ratio to vary systematically with irradiance. However, when leaf absorptance varied as needed to optimize distribution of light‐capture N, the capacity/irradiance ratio increased up through the crown – that is, opposite to the observed pattern. This tendency was counteracted by constraints on stomatal or mesophyll conductance, which caused chloroplastic CO₂ concentration to decline systematically with increasing irradiance. Our results suggest that height‐related constraints on stomatal conductance can help to reconcile observations with the hypothesis that photosynthetic N is allocated optimally.     

Phyllotactic pattern and stem cell fate are determined by the Arabidopsis homeobox gene BELLRINGER

Lateral organs in plants arise from the meristem in a stereotypical pattern known as phyllotaxy. Spiral patterns result from initiation of successive organs at a fixed angle of divergence but variable patterns of physical contact. Such patterns ultimately give rise to individual leaves and flowers at positions related to each other by consecutive terms in the mathematical series first described by Leonardo Fibonacci. We demonstrate that a BELL1 related homeodomain protein in Arabidopsis, BELLRINGER, maintains the spiral phyllotactic pattern. In the absence of BELLRINGER, the regular pattern of organ initiation is disturbed and lateral organs are initiated more frequently. BELLRINGER is also required for maintenance of stem cell fate in the absence of the regulatory genes SHOOT MERISTEMLESS and ASYMMETRIC LEAVES1. We propose a model whereby BELLRINGER coordinates the maintenance of stem cells with differentiation of daughter cells in stem cell lineages.     

Phyllotaxis

Phyllotaxis, the regular arrangement of leaves or flowers around a plant stem, is an example of developmental pattern formation and organogenesis. Phyllotaxis is characterized by the divergence angles between the organs, the most common angle being 137.5 degrees , the golden angle. The quantitative aspects of phyllotaxis have stimulated research at the interface between molecular biology, physics and mathematics. This review documents the rich history of different approaches and conflicting hypotheses, and then focuses on recent molecular work that establishes a novel patterning mechanism based on active transport of the plant hormone auxin. Finally, it shows how computer simulations can help to formulate quantitative models that in turn can be tested by experiment. The accumulation of ever increasing amounts of experimental data makes quantitative modeling of interest for many developmental systems.     

Light partitioning among species and species replacement in early successional grasslands

Abstract. We studied canopy structure, shoot architecture and light harvesting efficiencies of the species (photon flux captured per unit above‐ground plant mass) in a series of exclosures of different age (up to 4.5 yr) in originally heavily grazed grassland in N Japan.Vegetation height and Leaf Area Index (LAI) increased in the series and Zoysia japonica, the dominant in the beginning, was replaced by the much taller Miscanthus sinensis. We showed how this displacement in dominance can be explained by inherent constraints on the above‐ground architecture of these two species. In all stands light capture of plants increased with their above‐ground biomass but taller species were not necessarily more efficient in light harvesting. Some subordinate species grew disproportionally large leaf areas and persisted in the shady undergrowth. Some other species first grew taller and managed to stay in the better‐lit parts of the canopy, but ultimately failed to match the height growth of their neighbours in this early successional series. Their light harvesting efficiencies declined and this probably led to their exclusion. By contrast, species that maintained their position high in the canopy managed to persist in the vegetation despite their relatively low light harvesting efficiencies. In the tallest stands ‘later successional’ species had higher light harvesting efficiencies for the same plant height than ‘early successional’ species which was mostly the result of the greater area to mass ratio (specific leaf area, SLA) of their leaves. This shows how plant stature, plasticity in above‐ground biomass partitioning, and architectural constraints determine the ability of plants to efficiently capture light, which helps to explain species replacement in this early successional series.     

Modelling foliage characteristics in 3D tree crowns: influence on light interception and leaf irradiance

Because of the difficulty and time involved in making exhaustive measurements of the geometric parameters of large tree crowns, simplifying hypotheses are often used in 3D virtual plant modelling, but the effects on the radiation balance of each approximation are rarely assessed. Three hybrid walnut trees aged 7–9 years were digitized to analyse the effect of the crown geometric variables on light capture. The six studied variables were: (1) leaf area, (2) number of leaves per annual shoot, (3) position of leaves, (4) orientation of leaves, (5) leaflet inclination, and (6) lamina shape. For each variable, a sensitivity analysis compared a reference, based on observed values, with scenarios consisting of simplifying hypotheses. The total incident light intercepted during a bright day and the distributions of leaf irradiance were calculated using the Archimed radiative transfer model. Since some of the crown parameters were generated stochastically, the radiation simulations were repeated until results stabilised. Simplified models can be used to calculate with satisfactory results individual leaf area and number of leaves per shoot. Conversely, differentiating statistical distributions of individual leaf area between short and long shoots is more difficult and may generate errors up to 30%. Leaf clumping is a determining factor and requires correct grouping of leaves around the annual shoots bearing them. The effect of position of leaves along the shoot is less than 2%. Simple statistical distributions are adequate for representing leaf angle. Finally, the effect of specific leaf geometry is very important, but it can be approached using a limited number of representative leaf shapes.     

冠层部位对金叶女贞叶片结构的影响

金叶女贞是一种在园林绿化上广泛应用的彩叶植物,上层叶金黄色,下层叶深绿色。本文利用常规植物制片技术,研究了叶绿素缺少的金叶女贞上层金叶和下层绿叶的解剖结构。结果表明:(1)金叶女贞上层金叶和下层绿叶的上表皮无显著差异,但是下层绿叶的下表皮细胞较小,气孔密度较低;(2)下层绿叶的叶肉组织较薄,细胞较大,排列疏松;(3)在下层绿叶中叶绿体类囊体片层排列密集,叶肉组织内单位体积叶绿体数量较少;(4)冠层部位对光合色素的积累有明显影响。叶绿素缺少的金叶女贞叶片结构显著受到冠层部位的影响,光合色素的变化幅度较一般植物更大,不同冠层部位叶片叶色有明显差异,可以作为研究植物冠层部位对叶形态、结构和生理生化影响的好材料。     

Leaf investment and light partitioning among leaves of different genotypes of the clonal plant Potentilla reptans in a dense stand after 5 years of competition

Background and Aims

While within-species competition for light is generally found to be asymmetric – larger plants absorbing more than proportional amounts of light – between-species competition tends to be more symmetric. Here, the light capture was analysed in a 5-year-old competition experiment that started with ten genotypes of the clonal plant Potentilla reptans. The following hypotheses were tested: (a) if different genotypes would do better in different layers of the canopy, thereby promoting coexistence, and (b) if leaves and genotypes with higher total mass captured more than proportional amounts of light, possibly explaining the observed dominance of the abundant genotypes.

Methods

In eight plots, 100 leaves were harvested at various depths in the canopy and their genotype determined to test for differences in leaf biomass allocation, leaf characteristics and the resulting light capture, calculated through a canopy model using the actual vertical light and leaf area profiles. Light capture was related to biomass to determine whether light competition between genotypes was asymmetric.

Key Results

All genotypes could reach the top of the canopy. The genotypes differed in morphology, but did not differ significantly in light capture per unit mass (Φ_mass) for leaves with the laminae placed at the same light levels. Light capture did increase disproportionately with leaf mass for all genotypes. However, the more abundant genotypes did not capture disproportionately more light relative to their mass than less-abundant genotypes.

Conclusions

Vertical niche differentiation in light acquisition does not appear to be a factor that could promote coexistence between these genotypes. Contrary to what is generally assumed, light competition among genetic individuals of the same species was size-symmetric, even if taller individual leaves did capture disproportionately more light. The observed shifts in genotype frequency cannot therefore be explained by asymmetric competition for light.Key words: Potentilla reptans, light, competition, symmetric, clonal, genotype, investment, petiole, canopy, allocation     

Expressions for the interpretation of circular intensity differential scattering of chiral aggregates

The derivation of compact expressions of the circular intensity differential scattering (CIDS) of chiral molecules is presented in the first Born approximation of the fields. The expressions derived are valid for a suspension of scattering chiral particles free to adopt any orientation in solution. The connection is established between the preferential scattering cross section for right- vs left-circularly polarized light for a given scattering angle and the geometrical parameters of the molecule. As observed experimentally, the equations predict that the circular differential scattering patterns must show as a function of the scattering angle a series of lobes of alternating sign. In between these lobes, zeros in the differential scattering cross section occur. For the case of two dipole moments arranged in chiral fashion, an expression is derived that shows how the relative arrangement of the dipoles and their separation relative to the wavelength of light control the number and the position of the zeros. A compact expression predicting the CIDS of a sample for very small angles of scattering is derived for a system of helices whose dimensions are small compared with the wavelength of light. Finally, the presence of CIDS in a sample is related to the appearance of anomalous signals in the CD spectrum of chiral systems. Expressions and computations of the magnitudes and sign of the anomalies are presented. The expressions obtained confirm the main features of the experimental CIDS patterns of chiral molecules previously published.     

On the design of closed recapture experiments

We propose a method to plan the number of occasions of recapture experiments for population size estimation. We do so by fixing the smallest number of capture occasions so that the expected length of the profile confidence interval is less than or equal to a fixed threshold. In some cases, we solve the optimization problem in closed form. For more complex models we use numerical optimization. We detail models assuming homogeneous, time‐varying, subject‐specific capture probabilities, behavioral response to capture, and combining behavioral response with subject‐specific effects. The principle we propose can be extended to plan any other model specification. We formally show the validity of the approach by proving distributional convergence. We illustrate with simulations and challenging examples in epidemiology and ecology. We report that in many cases adding as few as two sampling occasions may substantially reduce the length of confidence intervals.     

A hemiparasite in the forest understorey: photosynthetic performance and carbon balance of Melampyrum pratense

• Melampyrum pratense is an annual root‐hemiparasitic plant growing mostly in forest understorey, an environment with unstable light conditions. While photosynthetic responses of autotrophic plants to variable light conditions are in general well understood, light responses of root hemiparasites have not been investigated.
• We carried out gas exchange measurements (light response and photosynthetic induction curves) to assess the photosynthetic performance of M. pratense in spring and summer. These data and recorded light dynamics data were subsequently used to model carbon balance of the hemiparasite throughout the entire growth season.
• Summer leaves had significantly lower rates of saturated photosynthesis and dark respiration than spring leaves, a pattern expected to reflect the difference between sun‐ and shade‐adapted leaves. However, even the summer leaves of the hemiparasite exhibited a higher rate of light‐saturated photosynthesis than reported in non‐parasitic understorey herbs. This is likely related to its annual life history, rare among other understorey herbs. The carbon balance model considering photosynthetic induction still indicated insufficient autotrophic carbon gain for seed production in the summer months due to limited light availability and substantial carbon loss through dark respiration.
• The results point to potentially high importance of heterotrophic carbon acquisition in M. pratense, which could be of at least comparable importance as in other mixotrophic plants growing in forests – mistletoes and partial mycoheterotrophs. It is remarkable that despite apparent evolutionary pressure towards improved carbon acquisition from the host, M. pratense retains efficient photosynthesis and high transpiration rate, the ecophysiological traits typical of related root hemiparasites in the Orobanchaceae.

     

Tests of phenotypic and genetic concordance and their application to the conservation of Panamanian golden frogs (Anura, Bufonidae)

Evolutionarily significant units (ESUs) differ in the extent to which they capture, or even consider, adaptive variation, and most such designations are based solely on neutral genetic differences that may not capture variation relevant to species' adaptabilities to changing environmental conditions. While concordant patterns of divergence among data sets (i.e. neutral and potentially non-neutral characters) can strengthen ESU designations, determining whether such criteria are met for highly variable taxa is especially challenging. This study tests whether previously defined ESUs for endangered Panamanian golden frogs (Atelopus varius and Atelopus zeteki) exhibit concordant variation among multiple phenotypic traits and mitochondrial DNA sequences, and the extent to which such divergence corresponds to environmental differences. Multivariate analyses identify phenotypic and genetic differentiation consistent with proposed ESUs and support the status of A. varius and A. zeteki as separate species. Moreover, the significant association detected between ESU co-membership and genetic similarity, which remained strong after removing the effect of geographic distance, also indicates that genetic differences are not simply due to isolation by distance. Two phenotypic characters (body size and the extent of dorsal black patterning) that differ among ESUs also co-vary with environmental differences, suggesting that to the extent that these phenotypic differences are heritable, variation may be associated with adaptive divergence. Lastly, discriminant function analyses show that the frogs can be correctly assigned to ESUs based on simultaneous analysis of multiple characters. The study confirms the merit of conserving the previously proposed golden frog ESUs as well as demonstrates the utility and feasibility of combined analyses of ecological, morphological and genetic variation in evaluating ESUs, especially for highly variable taxa.     

Structural and functional variability within the canopyand its relevance for carbon gain and stress avoidance

The functional variability in leaf angle distribution within the canopy was analysed with respect to regulation of light interception and photoprotection. Leaf orientation strongly determined the maximum photochemical efficiency of PSII (F_v/F_m) during summer: horizontal leaves were highly photoinhibited whereas vertical leaf orientation protected the leaves from severe photoinhibition. The importance of leaf orientation within the canopy was analysed in two Mediterranean macchia species with distinct strategies for drought and photoinhibition avoidance during summer. The semi-deciduous species (Cistus monspeliensis) exhibited strong seasonal but minimal spatial variability in leaf orientation. Reversible structural regulation of light interception by vertical leaf orientation during summer protected the leaves from severe photoinhibition. The evergreen sclerophyll (Quercus coccifera) exhibited high spatial variability in leaf angle distribution throughout the year and was less susceptible to photoinhibition. The importance of both strategies for plant primary production was analysed with a three-dimensional canopy photoinhibition model (CANO-PI). Simulations indicated that high variability in leaf angle orientation in Q. coccifera resulted in whole-plant carbon gain during the summer, which was 94 % of the maximum rate achieved by theoretical homogeneous leaf orientations. The high spatial variability in leaf angle orientation may be an effective compromise between efficient light harvesting and avoidance of excessive radiation in evergreen plants and may optimize annual primary production. Whole plant photosynthesis was strongly reduced by water stress and photoinhibition in C. monspeliensis; however, the simulations indicated that growth-related structural regulation of light interception served as an important protection against photoinhibitory reduction in whole-plant carbon gain.     

Pluripotency in the light of the developmental hourglass

The hourglass model of development postulates divergence in early and late embryo development bridged by a period of developmental constraint at mid‐embryogenesis. Recently, molecular support for the hourglass model of development has accumulated, with the emphasis on studies using zebrafish and Drosophila species. Across mammals, the hourglass model and specifically divergence in early development has thus far received little attention. Divergence in mammalian pre‐implantation development is particularly interesting because of its potential impact on derivation of pluripotent embryonic stem cells. Here, we review recent findings that support the hourglass model of development. We provide striking examples of variation in key events in mammalian peri‐implantation development and their potential consequences for pluripotency of embryonic stem cell lines, including mechanisms of cell signalling and differentiation, gene regulatory networks, X‐chromosome inactivation, and epigenetic regulation. The variation in these processes indicates divergence in early mammalian development as was postulated by the hourglass model of development. We discuss the naive and primed states of pluripotency in light of this developmental divergence and their implications for human pluripotent stem cell states.     

南丹金线兰的植物形态和显微鉴定

采用生药学显微鉴定方法研究南丹金线兰(Anoectochilus nandanensis)的原植物形态、组织构造及粉末显微特征。南丹金线兰叶片呈卵形或卵状披针形,具金红色叶脉,花不倒置;唇瓣白色,呈Y字形,前部明显扩大并2裂,裂片狭长圆形,中部收狭,其两侧呈向下的细齿状或角片状,两侧白色细齿各4～5条。显微结构中,根、茎横切面中皮层明显,具草酸钙针晶、粘液细胞等;叶横切面上表皮细胞形状为乳突状突起。粉末中可见草酸钙针晶和导管。这些特征可为南丹金线兰的生药鉴别和资源开发利用提供参考依据。     

Changes in crown development patterns and current-year shoot structure with light environment and tree height in Fagus crenata (Fagaceae)

The relative effects of light and tree height on the architecture of leader crowns (i.e., the leading section of the main trunk, 100 cm in length) and current-year shoots for a canopy species, Fagus crenata, occupying both the ridge top and the valley bottom in a cool-temperate forest in Japan were investigated. For leader crowns, the number of current-year shoots and leaves increased with increasing tree height, whereas the mean length of current-year shoots increased with increasing relative photon flux density (PFD). The leader crown area decreased, and the depth and leaf area index of leader crowns increased, with increasing relative PFD. The mass of current-year shoots increased with relative PFD. However, this total mass was allocated differently between stems and leaves depending on tree height, such that the relative allocation to stems increased with increasing tree height. Furthermore, stem structures within current-year shoots also changed with height, such that taller trees produced thicker and shorter stems of the same volume. In contrast, leaf structure and leaf biomass allocations changed with relative PFD. Specific leaf area decreased with increasing relative PFD. In addition, leaf number increased more rapidly with increasing individual leaf mass for trees exposed to greater relative PFD. Consequently, the total leaf area supported by a stem of a given diameter decreased with increasing tree height and relative PFD. Thus, the architecture of leader crowns and current-year shoots were related differently to light and tree height, which are considered important for efficient light capture and the growth of small and tall trees in different environments.     

A model‐driven approach towards rational microbial bioprocess optimization

Due to sustainability concerns, bio‐based production capitalizing on microbes as cell factories is in demand to synthesize valuable products. Nevertheless, the nonhomogenous variations of the extracellular environment in bioprocesses often challenge the biomass growth and the bioproduction yield. To enable a more rational bioprocess optimization, we have established a model‐driven approach that systematically integrates experiments with modeling, executed from flask to bioreactor scale, and using ferulic acid to vanillin bioconversion as a case study. The impacts of mass transfer and aeration on the biomass growth and bioproduction performances were examined using minimal small‐scale experiments. An integrated model coupling the cell factory kinetics with the three‐dimensional computational hydrodynamics of bioreactor was developed to better capture the spatiotemporal distributions of bioproduction. Full‐factorial predictions were then performed to identify the desired operating conditions. A bioconversion yield of 94% was achieved, which is one of the highest for recombinant Escherichia coli using ferulic acid as the precursor.