Fractal geometry of bean root systems: correlations between spatial and fractal dimension

An obstacle to the study of root architecture is the difficulty of measuring and quantifying the three-dimensional configuration of roots in soil. The objective of this work was to determine if fractal geometry might be useful in estimating the three-dimensional complexity of root architecture from more accessible measurements. A set of results called projection theorems predict that the fractal dimension (FD) of a projection of a root system should be identical to the FD of roots in three-dimensional space (three-dimensional FD). To test this prediction we employed SimRoot, an explicit geometric simulation model of root growth derived from empirical measurements of common bean (Phaseolus vulgaris L.). We computed the three-dimensional FD, FD of horizontal plane intercepts (planar FD), FD of vertical line intercepts (linear FD), and FD of orthogonal projections onto planes (projected FD). Three-dimensional FD was found to differ from corresponding projected FD, suggesting that the analysis of roots grown in a narrow space or excavated and flattened prior to analysis is problematic. A log-linear relationship was found between FD of roots and spatial dimension. This log-linear relationship suggests that the three-dimensional FD of root systems may be accurately estimated from excavations and tracing of root intersections on exposed planes.     

Ethylene: a regulator of root architectural responses to soil phosphorus availability

The involvement of ethylene in root architectural responses to phosphorus availability was investigated in common bean ( Phaseolus vulgaris L.) plants grown with sufficient and deficient phosphorus. Although phosphorus deficiency reduced root mass and lateral root number, main root length was unchanged by phosphorus treatment. This resulted in decreased lateral root density in phosphorus-deficient plants. The possible involvement of ethylene in growth responses to phosphorus deficiency was investigated by inhibiting endogenous ethylene production with amino-ethoxyvinylglycine (AVG) and aerating the root system with various concentrations of ethylene. Phosphorus deficiency doubled the root-to-shoot ratio, an effect which was suppressed by AVG and partially restored by exogenous ethylene. AVG increased lateral root density in phosphorus- deficient plants but reduced it in phosphorus-sufficient plants. These responses could be reversed by exogenous ethylene, suggesting ethylene involvement in the regulation of main root extension and lateral root spacing. Phosphorus-deficient roots produced twice as much ethylene per g dry matter as phosphorus-sufficient roots. Enhanced ethylene production and altered ethylene sensitivity in phosphorus-deficient plants may be responsible for root responses to phosphorus deficiency.     

Fractal geometry of root systems: Field observations of contrasting genotypes of common bean (Phaseolus vulgaris L.) grown under different phosphorus regimes

Root growth and architecture are important for phosphorus acquisition due to the relative immobility of P in the soil. Fractal geometry is a potential new approach to the analysis of root architecture. Substantial genetic variation in root growth and architecture has been observed in common bean. Common bean (Phaseolus vulgaris L.) genotypes with contrasting root architecture were grown under moderate and low P conditions in a field experiment. Linear and planar fractal dimension were measured by tracing root intercepts with vertical planes. Linear fractal dimension increased over time in efficient genotypes, but remained fairly constant over time in inefficient genotypes. Planar fractal dimension increased over time for all genotypes, but was higher in efficient than inefficient genotypes at the end of the experiment. Planar fractal dimension of medium P plants was found to correlate with shoot P content indicating fractal dimension to be a possible indicator for root P uptake. The increasing fractal dimension over time indicates that fractal analysis is a sensitive measure of root branching intensity. A less destructive method for acquisition of data that allows for continuous analysis of fractal geometry and thereby screening for more P efficient genotypes in the field is suggested. This method will allow the researcher to conduct fractal analysis and still complete field trials with final yield evaluation.     

沙冬青灌丛地的土壤颗粒大小分形维数空间变异性分析

通过土壤颗粒大小分形维数对土壤质地定量分析表明,土壤颗粒大小分形维数与沙粒含量（＞0.1mm）呈显著的线性负相关,与粘粉粒含量（＜0.05mm）呈显著的线性正相关关系（p＜0.0001）,沙粒和粘粉粒含量每增加1﹪,分形维数则降低或升高0.022个单位,沙粒增加导致分形维数的降低和粘粉粒增加导致分形维数升高幅度一致,所以土壤颗粒分形维数可以作为评价土地沙质荒漠化程度的定量指标之一.荒漠地带以沙冬青为优势种的沙生植被地段,地表土壤颗粒粗粒化和50～70cm土层土壤颗粒的细粒化,为该区有限降水的深层渗漏提供了基质,为沙冬青的存活提供了保障,一定程度上支持了一些专家提出的概念模型,验证了粗质土壤质地支持以灌木为主的群落的假说.但从空间变异性分析来看,荒漠区沙冬青群落因地表物质的吹蚀和堆积过程频繁以及灌丛沙堆发育程度引起的分枝形态差异,导致了土壤颗粒含量空间变异尺度并未集中在冠幅范围,并不支持灌丛在沙漠生态系统对降尘等细粒物质拦截所形成的＂沃岛＂作用.正是因为以沙冬青为优势种的沙生植被地段土壤颗粒组成的高度空间异质性,并且空间变异的范围并不局限于灌木冠幅范围和冠幅间的裸地,没有为其它植物种的入侵创造土壤基质条件,才使得沙冬青群落在该区稳定存在,为荒漠残遗植物种--沙冬青的迁地保护和干旱沙区植被恢复过程中合理地利用土壤资源,以避免营林失败等问题提供了理论依据.     

秦岭太白红杉种群空间分布格局动态及分形特征研究

采用相邻格子样方法采集数据,应用计盒维数和信息维数研究了太白红杉种群空间格局的分形特征,结果表明,太白红杉种群有较高的计盒维数(1.8087)和信息维数(1.7931),表明其对空间占据程度较高.用分布系数法和Morisita格局指数法检验格局类型,发现不同年龄组太白红杉种群均呈聚集分布.运用Greig-Smith的方法研究格局规模,发现太白红杉种群在128m²和512m²处聚集,不同年龄组在不同规模尺度聚集.以区组分布格局强度(PI)检测聚集强度,发现太白红杉种群格局强度随尺度变化程度较高,个体分布不均匀,随着年龄的增大,其聚集强度呈下降趋势.太白红杉种群的空间分布格局特征是其对严酷生境长期适应的结果.     

长江下游江心洲土壤颗粒特征及分形规律

研究了长江下游马鞍山段成长型江心洲洲头、洲中央和洲尾3个部位100cm深度范围内的土壤颗粒特征及分形规律。结果表明:江心洲土壤颗粒总体偏砂性,主要由粉粒、极细砂和细砂组成,颗粒最大粒径为350μm;在剖面上,3类颗粒的比例洲中央部位变化较小,洲头和洲尾变化较大;颗粒随深度的增加逐渐变粗;粉粒平均含量表现为洲中央>洲头>洲尾,分别为75.42%、43.58%和22.13%;土壤颗粒分形维数表现为洲中央>洲头>洲尾,分别为2.28、2.17和2.05,小于安徽省耕作表层土壤的分形维数平均值,与单位体积比表面积呈极显著正相关,与粘粒、粉粒含量极显著正相关,与极细砂、细砂极显著负相关。江心洲不同部位的土壤颗粒特征与江心洲的发育演变之间存在对应关系。     

Evaluation of self-similar features in time series of serum growth hormone and prolactin levels by fractal analysis: Effect of delayed sleep and complexity of diurnal variation

We assayed the diurnal concentrations of growth hormone (GH) and prolactin (PRL) in 6 healthy male volunteers to evaluate the self-similar features in the time series of each hormone on the basis of fractal theory and to determine the fractal dimension as an index of the complexity of the diurnal variation. In addition, we assessed the effects of a 6-hour delay in the sleep period on the complexity of the diurnal variaton of these hormones. There was a statistically significant fractal feature in the serum levels of GH both under the nocturnal-sleep and delayed-sleep conditions in all subjects. The time series of the serum PRL concentrations also showed a statistically significant fractal feature under the nocturnal-sleep and delayed-sleep conditions in all subjects. The fractal dimensions of the patterns of the GH or PRL levels were 1.879 and 1.929 or 1.754 and 1.785 under the nocturnal-sleep and delayed-sleep conditions, respectively. Two-way ANOVA revealed no significant difference in the fractal dimension between the two sleep conditions but did reveal a significant difference between the fractal dimensions of the GH and PRL levels. These results showed (1) that delayed sleep had no significant effect on the complexity of the diurnal pattern of these hormones, and (2) that the diurnal pattern of the GH levels was more complex than that of the PRL levels.     

半干旱矿区排土场苜蓿恢复过程中土壤颗粒分形的演变特征

种植苜蓿恢复模式在半干旱矿区植被恢复中占重要地位。为掌握其恢复过程中土壤颗粒分形的演变特征,选择恢复年限分别为2 a、4 a、6 a和10 a(M2、M4、M6和M10)的苜蓿种植地为研究对象,通过野外分层采样与室内测定,依据颗粒体积分形理论,研究了排土场苜蓿恢复过程中土壤颗粒分形的演变特征及与土壤特性的关系。结果表明:研究区土壤各粒径含量以砂粒为主,粉粒次之,粘粒最少;随着苜蓿恢复过程,粘粒与粉粒含量整体表现为先增加后下降的趋势,且在M4阶段达到最佳,砂粒反之。土壤分形维数变化在2.09—2.57,在苜蓿恢复过程中先增大后减小,在M4阶段达到最大。土壤分形维数与粘粒、粉粒具有极显著正相关性(P<0.01),与砂粒具有极显著负相关性(P<0.01);土壤分形维数与电导率呈极显著负相关关系(P<0.01),与pH值和速效钾含量呈显著负相关关系(P<0.05),与碱解氮含量呈显著正相关关系(P<0.05)。在半干旱矿区排土场采用苜蓿恢复模式,可用土壤分形维数表征土壤特性,应重视恢复年限的调控,适时进行适宜的利用与改造,确保矿区生态恢复的可持续性。     

Mineralization of nitrogen from15N labelled fungi,soil microbial biomass and roots and its uptake by barley plants

The effect of vesicular-arbuscular mycorrhizal fungi (VAM) on field bean and spring wheat dry matter production and on phosphorus, zinc, copper, iron and manganese uptake was determined under greenhouse conditions. Nutrient availability was varied by using different sizes of pots and by diluting the soil with sand. VAM increased plant dry matter production under all sets of growth conditions. VAM were found to directly increase the uptake of P, Zn, Cu and Fe by field beans and of P and Zn for wheat in both experiments. Increased uptake of the other nutrients measured was attributed to increased dry matter production or other factors. The effect of VAM decreased as the pot size holding the host plants decreased, but was not affected by the ratio of soil to sand if the pot size was kept constant. Nutrient uptake by beans as a proportion of total amount of nutrient present increased as the amount of nutrient decreased. Increase in root-soil contact and altered chemical equilibria are probable reasons for increased efficiency of nutrient uptake by beans as the level of available nutrient decreased. For wheat, which has a relatively fibrous root system, decreasing the nutrient availability had minimal effects on nutrient uptake in these experiments. Increases in total uptake of a particular nutrient resulting from inoculation with VAM are not necesarily indicative of a direct uptake of that nutrient by the VAM.     

Mediation of sterol-induced calmodulin synthesis in Phaseolus vulgaris roots by Ca2+ and its possible relationship to plant growth regulators

Vitamin D₃ and stigmasterol have been previously shown to stimulate growth, Ca²⁺ fluxes and calmodulin synthesis in Phaseolus vulgaris roots. In this study, these sterols (10⁻⁹ M ) were shown to accelerate the incorporation of [³H]-thymidine into DNA in Phaseolus vulgaris (L. cv. Contraancha) root apices, similarly to a mixture of the mitogenic plant growth factors 2,4-dichlorophenoxyacetic acid and kinetin (4.6 μ M each). The effects of stigmasterol were blocked by flufenazine, a calmodulin antagonist. Analogously to stigmasterol, the plant hormones stimulated calmodulin synthesis as shown by double labeling of root proteins with [¹⁴C]-leucine and [³H]-leucine, respectively, followed by their separation on sodium dodecyl sulfate-po-lyacrylamide gels and a calmodulin affinity column, immunoblot analysis and cyclic AMP phosphodiesterase activation assays. The stimulation of root calmodulin formation by stigmasterol was abolished in the absence of Ca²⁺ in the incubation medium and was mimicked by the Ca²⁺ ionophore A–23187. The results suggest that the sterols, like plant mitogenic hormones, promote DNA synthesis, and that these compounds stimulate calmodulin synthesis as a consequence of their mitogenic activity. ^Ca2+ appears to mediate the action of the sterols.     

Resistance of Common Bean (Phaseolus vulgaris) to Bacterial Wilt Caused by Curtobacterium flaccumfaciens pv. flaccumfaciens

Bacterial wilt caused by Curtobacterium flaccumfaciens pv. flaccumfaciens is an important new disease of common bean (Phaseolus vulgaris) in western Canada. Both yellow and orange variants of the pathogen were found in the region. A controlled environment study was conducted to assess 124 common bean cultivars and lines from eight market classes for resistance to the yellow and orange variants of the pathogen, using the hilum injury/seed inoculation method. Results of the screening tests showed significant (P < 0.05) differences in resistance to bacterial wilt among the cultivars or lines. The great northern line L02E317, the great northern cultivar Resolute and pinto lines L02B662 and 999S‐2A, were highly resistant to both variants of the pathogen, with disease severity indices of 0 on a rating scale of 0 (no wilt symptoms) to 5 (dead seedling). Resistant cultivars or lines were found among black, great northern, pink, pinto, small red and Flor de Mayo bean market classes. The study concludes that new bacterial wilt‐resistant germplasm exists among Canadian bean cultivars and lines, and constitutes a valuable resource for breeding common beans for resistance to both yellow and orange variants of C. flaccumfaciens pv. flaccumfaciens.     

Measurement and modelling of photosynthetic response of pearl millet to soil phosphorus addition

There have been no studies of the effects of soil P deficiency on pearl millet (Pennisetum glaucum (L.) R. Br.) photosynthesis, despite the fact that P deficiency is the major constraint to pearl millet production in most regions of West Africa. Because current photosynthesis-based crop simulation models do not explicitly take into account P deficiency effects on leaf photosynthesis, they cannot predict millet growth without extensive calibration. We studied the effects of soil addition on leaf P content, photosynthetic rate (A), and whole-plant dry matter production (DM) of non-water-stressed, 28 d pearl millet plants grown in pots containing 6.00 kg of a P-deficient soil. As soil P addition increased from 0 to 155.2 mg P kg^–1 soil, leaf P content increased from 0.65 to 7.0 g kg^–1. Both A and DM had maximal values near 51.7 mg P kg^–1 soil, which corresponded to a leaf P content of 3.2 g kg^–1. Within this range of soil P addition, the slope of A plotted against stomatal conductance (g_s) tripled, and mean leaf internal CO₂ concentration ([CO₂]_i) decreased from 260 to 92 L L^–1, thus indicating that P deficiency limited A through metabolic dysfunction rather than stomatal regulation. Light response curves of A, which changed markedly with P leaf content, were modelled as a single substrate, Michaelis-Menten reaction, using quantum flux as the substrate for each level of soil P addition. An Eadie-Hofstee plot of light response data revealed that both K_M, which is mathematically equivalent to quantum efficiency, and V_max, which is the light-saturated rate of photosynthesis, increased sharply from leaf P contents of 0.6 to 3 g kg^–1, with peak values between 4 and 5 g P kg^–1. Polynomial equations relating K_M and V_max, to leaf P content offered a simple and attractive way of modelling photosynthetic light response for plants of different P status, but this approach is somewhat complicated by the decrease of leaf P content with ontogeny.