D.C. Freeman

Nonlinear growth dynamics and the origin of fluctuating asymmetry

The nonlinear, complex nature of biosynthesis magnifies the impacts of small, random perturbations on organism growth, leading to distortions in adaptive allometries and, in particular, to fluctuating asymmetry. These distortions can be partly checked by cell-cell and inter-body part feedback during growth and development, though the latter mechanism also may lead to complex patterns in right-left asymmetry. Stress can be expected to increase the degree to which random growth perturbations are magnified and may also result in disruption of the check mechanisms, thus exaggerating fluctuating asymmetry.The processes described not only provide one explanation for the existence of fluctuating asymmetry and its augmentation under stress, but suggest additional effects of stress as well. Specifically, stress is predicted to lead to decreased fractal dimension of bone sutures and branching structures in animals, and in increased dimension of growth trace patterns such as those found in mollusc shells and fish otoliths and scales.A basic yet broad primer on fractals and chaos is provided as background for the theoretical development in this manuscript.

Long-term effectiveness of translational manipulation for adhesive capsulitis.

Long term effects of glenohumeral joint translational (gliding) manipulation on range of motion, pain, and function in patients with adhesive capsulitis were studied. Thirty-one patients underwent brachial plexus block followed by translational manipulation of the glenohumeral joint. Changes in range of motion and pain were assessed before manipulation with the patient under anesthesia, immediately after manipulation with the patient still under anesthesia, at early followup (5.3 ± 3.2 weeks), and at long term followup (14.4 ± 7.3 months). Passive range of motion increased significantly for flexion, abduction, external rotation, and internal rotation. Significant decreases in visual analog pain scores between initial evaluation and the followup assessments also occurred. Furthermore, Wolfgangs criteria score increased significantly between initial evaluation and followup assessments. Translational manipulation provides a safe, effective treatment option for adhesive capsulitis.

Characterization of Branch Complexity by Fractal Analyses

The comparison between complexity in the sense of space occupancy (box‐counting fractal dimension Dc and information dimension DI) and heterogeneity in the sense of space distribution (average evenness index \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape

Fitting population models from field data

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Nonlinear dynamics and developmental instability

\end{document} and evenness variation coefficient JCV) were investigated in mathematical fractal objects and natural branch structures. In general, increased fractal dimension was paired with low heterogeneity. Comparisons between branch architecture in Anthyllis cytisoides under different slope exposure and grazing impact revealed that branches were more complex and more homogeneously distributed for plants on northern exposures than southern, while grazing had no impact during a wet year. Developmental instability was also investigated by the statistical noise of the allometric relation between internode length and node order. In conclusion, our study demonstrated that fractal dimension of branch structure can be used to analyze the structural organization of plants, especially if we consider not only fractal dimension but also shoot distribution within the canopy (lacunarity). These indexes together with developmental instability analyses are good indicators of growth responses to the environment.

Instability of development and fractal architecture in dryland plants as an index of grazing pressure

Abstract.Spatial heterogeneity, like species diversity, is an important ecosystem property. We examine the effects of land use on the diversity and spatial distribution of plants in five semi-arid communities of eastern Spain using non-linear methods to assess the spatialtemporal dynamics of plant populations. Specifically, we are interested in detecting long-term structural changes or drift in an ecosystem before it is too late to prevent irreversible degradation. Fractal analysis is used to characterize the complexity of plant spatial patterns and Information Theory indices are used to measure change in information flow with land use changes and soil substrate. We found that grazing favored diversity and heterogeneity of species distribution on the impoverished gypsum and saline substrate community, as opposed to the detrimental effect of grazing in the Alpha steppe community. Indeed, old-field succession after 30 years of abandonment showed a recovery of species diversity but not the spatial structure of the vegetation. Further, Information Fractal Dimension, representing the unpredictability of plant spatial patterns in the landscape, increased as we moved from a highly diverse to a less diverse community, revealing the change to a more scattered and homogeneous spatial plant distribution. The Information Fractal Dimension is a good estimator of ecosystem disturbance, independent of scale, and thus can be used to monitor ecosystem dynamics.

Estimating disturbance effects from military training using developmental instability and physiological measures of plant stress

Abstract The application of population and community ecology to solving real-world problems requires population and community dynamics models that reflect the myriad patterns of interaction among organisms and between the biotic and physical environments. Appropriate models are not hard to construct, but the experimental manipulations needed to evaluate their defining coefficients are often both time consuming and costly, and sometimes environmentally destructive, as well. In this paper we present an empirical approach for finding the coefficients of broadly inclusive models without the need for environmental manipulation, demonstrate the approach with both an animal and a plant example, and suggest possible applications. Software has been developed, and is available from the senior author, with a manual describing both field and analytic procedures.