Root Systems and Fractals: How Reliable are Calculations of Fractal Dimensions?

Fractal dimensions of the root systems of Betula populifoliaand Betula alleghaniensis grown at two levels of soil nutrientswere calculated from tracings of root systems (Fitter and Stickland,1992a) and from roots removed from the soil using a pin-board(Tatsumi, Yamauchi and Kono, 1989). The fractal dimensions obtainedfrom these two methods showed similar qualitative patterns betweenspecies and nutrient treatments, but were not significantlycorrelated with one another. These observations suggest thatcurrent methods used for estimating the fractal dimensions ofplant root systems are not yet reliable. It is suggested thatthe calculation of fractal dimensions needs to be carried outin three dimensions in order to appropriately quantify the fractaldimensions of plant root systems.Copyright 1994, 1999 AcademicPress Betula populifolia Marsh (gray birch), Betula alleghaniensis Britton (yellow birch), fractal dimension, root system     

Allocation,within and between organs,and the dynamics of root length changes in two birch species

Spatial and temporal dynamics of biomass allocation within and between organs were investigated in seedlings of two birch species of contrasting successional status. Seedlings of Betula alleghaniensis Britt (yellow birch) and B. populifolia Marsh (gray birch) were grown for 6 weeks at two nutrient levels in rectangular plexiglass containers to allow non-destructive estimates of root growth, production and loss. Leaf area and production were simultaneously monitored. Yellow birch responded more to nutrient level than gray birch in terms of total biomass, shoot biomass, leaf area and root length. Yellow birch also flexibly altered within-organ allocation (specific leaf area, specific root length and specific soil amount). In contrast, gray birch altered between-organ allocation patterns (root length:leaf area and soil amount:leaf area ratios) more than yellow birch in response to nutrient level. Yellow birch showed greater overall root density changes within a very compact root system, while gray birch showed localized root density changes as concentric bands of new root production spread through the soil. Species differ critically in their responses of standing root length and root production and loss rates to nutrient supply. Early successional species such as gray birch are hypothesized to exhibit higher plasticity in varied environments than later successional species such as yellow birch. Our results suggest that different patterns of allocation, within and between plant organs, do not necessarily follow the same trajectories. To characterize thoroughly the nature of functional flexibility through ontogeny, within- and between-organ patterns of allocation must be accounted for.     

Belowground positive and negative feedbacks on CO2 growth enhancement

In this paper we present a conceptual model of integrated plant-soil interactions which illustrates the importance of identifying the primary belowground feedbacks, both positive and negative, which can simultaneously affect plant growth responses to elevated CO₂. The primary negative feedbacks share the common feature of reducing the amount of nutrients available to plants. These negative feedbacks include increased litter C/N ratios, and therefore reduced mineralization rates, increased immobilization of available nutrients by a larger soil microbial pool, and increased storage of nutrients in plant biomass and detritus due to increases in net primary productivity (NPP). Most of the primary positive feedbacks share the common feature of being plant mediated feedbacks, the only exception being Zak et al.'s hypothesis that increased microbial biomass will be accompanied by increased mineralization rates. Plant nutrient uptake may be increased through alterations in root architecture, physiology, or mycorrhizal symbioses. Further, the increased C/N ratios of plant tissue mean that a given level of NPP can be achieved with a smaller supply of nitrogen.Identification of the net plant-soil feedbacks to enhanced productivity with elevated CO₂ are a critical first step for any ecosystem. It is necessary, however, that we first identify how universally applicable the results are from one study of one ecosystem before ecosystem models incorporate this information. The effect of elevated CO₂ on plant growth (including NPP, tissue quality, root architecture, mycorrhizal symbioses) can vary greatly for different species and environmental conditions. Therefore it is reasonable to expect that different ecosystems will show different patterns of interacting positive and negative feedbacks within the plant-soil system. This inter-ecosystem variability in the potential for long-term growth responses to rising CO₂ levels implies that we need to parameterize mechanistic models of the impact of elevated CO₂ on ecosystem productivity using a detailed understanding of each ecosystem of interest.     

Phylogenetic relationships within the class Anthozoa (phylum Cnidaria) based on nuclear 18S rDNA sequences

Taxonomic relationships within the corals and anemones (Phylum Cnidaria: Class Anthozoa) are based upon few morphological characters. The significance of any given character is debatable, and there is little fossil record available for deriving evolutionary relationships. We analyzed complete 18S ribosomal sequences to examine subclass-level and ordinal-level organization within the Anthozoa. We suggest that the Subclass Ceriantipatharia is not an evolutionarily relevant grouping. The Order Corallimorpharia appears paraphyletic and closely related to the Order Scleractinia. The 18S rRNA gene may be insufficient for establishing robust phylogenetic hypotheses concerning the specific relationships of the Corallimorpharia and the Ceriantharia and the branching sequence for the orders within the Hexacorallia. The 18S rRNA gene has sufficient phylogenetic signal, however, to distinguish among the major groupings within the Class Anthozoa, and we use this information to suggest relationships for the enigmatic taxa Dactylanthus and Dendrobrachia.     

Correcting for finite spatial scales of self-similarity when calculating fractal dimensions of real-world structures

Fractal geometry is a potentially valuable tool for quantitatively characterizing complex structures. The fractal dimension (D) can be used as a simple, single index for summarizing properties of real and abstract structures in space and time. Applications in the fields of biology and ecology range from neurobiology to plant architecture, landscape structure, taxonomy and species diversity. However, methods to estimate the D have often been applied in an uncritical manner, violating assumptions about the nature of fractal structures. The most common error involves ignoring the fact that ideal, i.e. infinitely nested, fractal structures exhibit self-similarity over any range of scales. Unlike ideal fractals, real-world structures exhibit self-similarity only over a finite range of scales.Here we present a new technique for quantitatively determining the scales over which real-world structures show statistical self-similarity. The new technique uses a combination of curve-fitting and tests of curvilinearity of residuals to identify the largest range of contiguous scales that exhibit statistical self-similarity. Consequently, we estimate D only over the statistically identified region of self-similarity and introduce the finite scale- corrected dimension (FSCD). We demonstrate the use of this method in two steps. First, using mathematical fractal curves with known but variable spatial scales of self-similarity (achieved by varying the iteration level used for creating the curves), we demonstrate that our method can reliably quantify the spatial scales of self-similarity. This technique therefore allows accurate empirical quantification of theoretical Ds. Secondly, we apply the technique to digital images of the rhizome systems of goldenrod (Solidago altissima). The technique significantly reduced variations in estimated fractal dimensions arising from variations in the method of preparing digital images. Overall, the revised method has the potential to significantly improve repeatability and reliability for deriving fractal dimensions of real-world branching structures.     

Regenerating temperate forest mesocosms in elevated CO2: belowground growth and nitrogen cycling

The response of temperate forest ecosystems to elevated atmospheric CO₂ concentrations is important because these ecosystems represent a significant component of the global carbon cycle. Two important but not well understood processes which elevated CO₂ may substantially alter in these systems are regeneration and nitrogen cycling. If elevated CO₂ leads to changes in species composition in regenerating forest communities then the structure and function of these ecosystems may be affected. In most temperate forests, nitrogen appears to be a limiting nutrient. If elevated CO₂ leads to reductions in nitrogen cycling through increased sequestration of nitrogen in plant biomass or reductions in mineralization rates, long-term forest productivity may be constrained. To study these processes, we established mesocosms of regenerating forest communities in controlled environments maintained at either ambient (375 ppm) or elevated (700 ppm) CO₂ concentrations. Mesocosms were constructed from intact monoliths of organic forest soil. We maintained these mesocosms for 2 years without any external inputs of nitrogen and allowed the plants naturally present as seeds and rhizomes to regenerate. We used ¹⁵N pool dilution techniques to quantify nitrogen fluxes within the mesocosms at the end of the 2 years. Elevated atmospheric CO₂ concentration significantly affected a number of plant and soil processes in the experimental regenerating forest mesocosms. These changes included increases in total plant biomass production, plant C/N ratios, ectomycorrhizal colonization of tree fine roots, changes in tree fine root architecture, and decreases in plant NH₄ ⁺ uptake rates, gross NH₄ ⁺ mineralization rates, and gross NH₄ ⁺ consumption rates. In addition, there was a shift in the relative biomass contribution of the two dominant regenerating tree species; the proportion of total biomass contributed by white birch (Betula papyrifera) decreased and the proportion of total biomass contributed by yellow birch (B. alleghaniensis) increased. However, elevated CO₂ had no significant effect on the total amount of nitrogen in plant and soil microbial biomass. In this study we observed a suite of effects due to elevated CO₂, some of which could lead to increases in potential long term growth responses to elevated CO₂, other to decreases. The reduced plant NH₄ ⁺ uptake rates we observed are consistent with reduced NH₄ ⁺ availability due to reduced gross mineralization rates. Reduced NH₄ ⁺ mineralization rates are consistent with the increases in C/N ratios we observed for leaf and fine root material. Together, these data suggest the positive increases in plant root architectural parameters and mycorrhizal colonization may not be as important as the potential negative effects of reduced nitrogen availability through decreased decomposition rates in a future atmosphere with elevated CO₂. Received: 10 January 1997 / Accepted: 25 July 1997     

Modeling the belowground response of plants and soil biota to edaphic and climatic change—What can we expect to gain?

As atmospheric CO₂ concentrations continue to increase, so too will the emphasis placed on understanding the belowground response of plants to edaphic and climatic change. Controlled-exposure studies that address the significance of an increased supply of carbon to roots and soil biota, and the consequences of this to nutrient cycling will play a prominent role in this process. Models will also contribute to understanding the response of plants and ecosystems to changes in the earth's climate by incorporating experimental results into conceptual or quantitative frameworks from which potential feedbacks within the plant-soil system can be identified. Here we present five examples of how models can be used in this analysis and how they can contribute to the development of new hypotheses in the areas of root biology, soil biota, and ecosystem processes. Two examples illustrate the role of coarse and fine roots in nitrogen and phosphorus uptake from soils, the respiratory costs associated with this acquisition of nutrients, and the significance of root architecture in these relationships. Another example focuses on a conceptual model that has helped raise new ideas about the effects of elevated CO₂ on root and microbial biomass, and on nutrient dynamics in the rhizosphere. Difficulties associated with modeling the contribution of mycorrhizal fungi to whole-plant growth are also discussed. Finally, several broad-scale models are used to illustrate the importance of root turnover, litter decomposition, and nitrogen mineralization in determining an ecosystem's response to atmospheric CO₂ enrichment. We conclude that models are appropriate tools for use both in guiding existing studies and in identifying new hypotheses for future research. Development of models that address the complexities of belowground processes and their role in determining plant and ecosystem function within the context of rising CO₂ concentrations and associated climate change should be encouraged.     

Synthesis and opioid activities of stereoisomers and other D-amino acid analogs of methionine-enkephalin

A series of D-amino acid-substituted analogs of the opiate peptide, methionine⁵-enkephalin, were synthesized by solid-phase methods and tested for their abilities to inhibit electrically-evoked contractions of mouse vasa deferentia and to compete with tritiated enkephalin for opiate receptors on particulate fractions isolated from homogenates of rat brain. [D-Ala²]-enkephalin and [D-Ala²]-enkephalin amide were found to be the most potent peptides in both assay systems, being about 1000% active in the vas deferens bioassay and 120% and 150% active, respectively, in the stereospecific binding test relative to methionine⁵-enkephalin itself. In comparison, [D-Met⁵]-, [D-Tyr¹]-, [D-Leu²]-, [D-Phe²]-, [D-Ala³]-, and [D-Phe⁴]-enkephalin had not more than 10% activity. The stabilization of the β-bend conformation of methionine⁵-enkephalin by the substitution of D-alanine in position 2 of the peptide chain may contribute to the high activities of the [D-Ala²]-analogs.     

Size structure of populations within populations: leaf number and size in crowded and uncrowded Impatiens pallida individuals

Summary We compared the size distributions of leaves on naturally-occurring crowded and experimentally thinned uncrowded individuals of Impatiens pallida in southeastern Pennsylvania. Crowding decreased the number of leaves on individual plants and altered the distribution of leaf size. Crowded individuals had smaller leaves, but the size (length) inequality of the leaf population did not change. The relationships between the height of a plant and the mean and maximum length of its leaves were significantly different for crowded and uncrowded plants. There were weak positive relationships between height and total leaf area, and height and total number of leaves for uncrowded plants, whereas crowded plants showed tighter but curvilinear relationships between these variables. Our results point out the strengths and the limitations of viewing canopies as populations of modules.     

Multiple paternity is prevalent in Pacific ocean perch (Sebastes alutus) off the Oregon coast, and is correlated with female size and age

The need to rebuild Pacific ocean perch, Sebastes alutus, populations on the west coast of the United States has precipitated a need to better understand the life history characteristics of this rockfish species. One such characteristic is mating behavior, which has the potential to influence the amount of genetic diversity in a population. We documented and examined the frequency of multiple mating in Pacific ocean perch collected off the Oregon coast using five microsatellite loci. We found that 47 of 66 (71.2%) females examined had broods sired by multiple males. The mean number of sires per brood was 1.92 (SD = 0.76) and ranged from 1–4. Polyandrous females were significantly larger and had an older average age than monogamous females. Our results suggest that polyandrous behavior among female Pacific ocean perch off the coast of Oregon is prevalent, is related to female size and age, and should be preserved by maintaining a natural age structure in this population.