John H. Graham

Antisymmetry, directional asymmetry, and dynamic morphogenesis

Fluctuating asymmetry is the most commonly used measure of developmental instability. Some authors have claimed that antisymmetry and directional asymmetry may have a significant genetic basis, thereby rendering these forms of asymmetry useless for studies of developmental instability. Using a modified Rashevsky-Turing reaction-diffusion model of morphogenesis, we show that both antisymmetry and directional asymmetry can arise from symmetry-breaking phase transitions. Concentrations of morphogen on right and left sides can be induced to undergo transitions from phase-locked periodicity, to phase-lagged periodicity, to chaos, by simply changing the levels of feedback and inhibition in the model. The chaotic attractor has two basins of attraction-right sidedominance and left side dominance. With minor disturbance, a developmental trajectory settles into one basin or the other. With increasing disturbance, the trajectory can jump from basin to basin. The changes that lead to phase transitions and chaos are those expected to occur with either genetic change or stress. If we assume that the morphogen influences the behavior of cell populations, then a transition from phase-locked periodicity to chaos in the morphogen produces a corresponding transition from fluctuating asymmetry to antisymmetry in both morphogen concentrations and cell populations. Directional asymmetry is easily modeled by introducing a bias in the conditions of the simulation. We discuss the implications of this model for researchers using fluctuating asymmetry as an indicator of stress.

Fluctuating Asymmetry: Methods, Theory, and Applications

Fluctuating asymmetry consists of random deviations from perfect symmetry in populations of organisms. It is a measure of developmental noise, which reflects a population’s average state of adaptation and coadaptation. Moreover, it increases under both environmental and genetic stress, though responses are often inconsistent. Researchers base studies of fluctuating asymmetry upon deviations from bilateral, radial, rotational, dihedral, translational, helical, and fractal symmetries. Here, we review old and new methods of measuring fluctuating asymmetry, including measures of dispersion, landmark methods for shape asymmetry, and continuous symmetry measures. We also review the theory, developmental origins, and applications of fluctuating asymmetry, and attempt to explain conflicting results. In the process, we present examples from the literature, and from our own research at “Evolution Canyon” and elsewhere.

Developmental stability in plants: symmetries, stress and epigenesis

Plant developmental stability has received little attention in the past three or four decades. Here we review differences in plant and animal development, and discuss the advantages of using plants as experimental subjects in exploring developmental stability. We argue that any type of developmental invariant may be used to assess developmental stability and review the use of fluctuating asymmetry in studies of plant developmental stability. We also examine the use of deviations from translatory, radial, and self-symmetry as measures of developmental instability. The role of nonlinear dynamics and epigenesis in the production of the phenotype is also discussed.

Narrow hybrid zone between two subspecies of big sagebrush (Artemisia tridentata : Asteraceae) XII. Galls on sagebrush in a reciprocal transplant garden

Several species of gall-forming insects specialize on big sagebrush (Artemisia tridentata), a species that shows much clinal and subspecific variation throughout its geographic range. Two of those subspecies, basin big sagebrush (A. t. ssp. tridentata) and mountain big sagebrush (A. t. ssp. vaseyana), form a narrow hybrid zone at Salt Creek, Utah. Reciprocal transplant experiments have shown that the hybrid big sagebrush at Salt Creek are more fit than either parental subspecies, but only in the hybrid zone. Do genotype and environment influence the density and distribution of galls on big sagebrush? We counted galls on parental and hybrid big sagebrush in three reciprocal transplant gardens at Salt Creek. Gardens were in each of the two parental zones and in the hybrid zone. Transplanted seedlings came from five source populations: two parental and three hybrid populations. We identified seven kinds of gall-forming flies (Rhopalomyia midges and Eutreta fruitflies) that produced identifiable galls. Densities of galls varied among the three gardens and five source populations, and there was also a significant garden by source interaction in gall density. In general, variation in gall density among gardens (i.e., environments) was much greater than the variation among source populations (i.e., genotypes). Nevertheless, significant genotype-environment interactions were observed for five of the seven kinds of galls. Overall density of galls, mostly due to Rhopalomyia ampullaria, was greatest in the high-elevation (mountain) garden and least in the low-elevation (basin) garden. To the best of our knowledge, this is the first reciprocal transplant experiment addressing herbivore richness in a hybrid zone.

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.

Effects of lead and benzene on the developmental stability of Drosophila melanogaster

Fluctuating asymmetry has been proposed as a general and sensitive indicator of developmental instability. Although there have been many field studies of fluctuating asymmetry in populations exposed to toxic chemicals, there have been few laboratory studies. To test the hypothesis that stress from toxic chemicals causes an increase in fluctuating asymmetry, we exposed larval Drosophila melanogaster to six concentrations of lead and benzene in their food. Lead and benzene caused neither a significant reduction in the number of emerging adult flies, nor a significant difference in the average number of sternopleural bristles. Flies exposed to lead at 10mg kg-1 and benzene at 1000 mg kg-1, however, showed increased fluctuating asymmetry of sternopleural bristles. Higher concentrations (10,000 mg kg-1) of benzene caused a transition from fluctuating asymmetry to directional asymmetry. Flies exposed to benzene at 10,000 mg kg-1 also eclosed more than a day earlier than flies exposed to it at 0–1,000 mg kg-1.

Genomic coadaptation and developmental stability within introgressed populations of Enneacanthus gloriosus and E. obesus (Pisces, centrarchidae)

Using fluctuating bilateral asymmetry as a measure of developmental stability, we tested the hypothesis that genomic coadaptation mediates developmental stability in natural populations. Hybrid populations were more asymmetrical than populations of the parental species, and ranks of overall developmental instability were positively correlated with ranks of mean heterozygosity in these populations. The failure to find increased asymmetry in previous studies of natural hybrid populations (Jackson, 1973a, 1973b; Felley, 1980) suggests that such populations may have re‐evolved coadapted genomes. Increased asymmetry in hybrid Enneacanthus populations may reflect the youthfulness of these populations.

Within‐ and Among‐Individual Variation in Fluctuating Asymmetry of Leaves in the Fig (Ficus carica L.)

Plants are ideal organisms for studying genotypic and environmental influences on developmental stability. Because they may have numerous leaves, flowers, and stems, one can study variation in developmental stability in a single individual. Moreover, one often has sufficient degrees of freedom to test for differences in developmental stability among individuals. Nevertheless, within‐plant variation in developmental stability can be a potential problem. Leaf size and asymmetry in the common fig, Ficus carica, vary within a plant, depending on height (lower, middle, top) and position (inside, outside). Leaves from the outside top are the largest, and those from the inside bottom are the smallest. Outer leaves, which may experience greater stress from cold, heat, sunlight, and desiccation, are more asymmetrical than inner leaves. We also found significant differences in leaf asymmetry among plants.

Developmental stability and its applications in ecotoxicology

Developmental stability refers to the ability of a developing organism to produce a consistent phenotype in a given environment. It provides a simple, reliable method of detecting stressed populations and monitoring their recovery. The most common measure of developmental instability, fluctuating asymmetry, assesses minor deviations from perfect bilateral symmetry in traits that are normally symmetrical. Measures of developmental instability are based upon the concept of developmental invariance. The biotest approach consists of the simultaneous analysis of developmental instability (and related physiological instability) in a variety of species.

Detrended Correspondence Analysis of Dietary Data

Abstract Niche relationships of fishes can be inferred from dietary analysis. Individual fish and their prey can be ordered along an underlying continuum that has ecological relevance, The specific arrangement is a function of the predators behavior and the preys spatial distribution. This distribution of prey eaten by predators conforms to the underlying assumptions of detrended correspondence analysis. This multivariate technique, designed specifically for discrete data, uncovers underlying resource gradients in the dietary data. We used it to analyse dietary information collected from banded sunfish Enneacanthus obesus and bluespotted sunfish Enneacanthus gloriosus and compared then the results with analyses by discriminant analysis, factor analysis, and principal component analysis. Detrended correspondence analysis was as effective in discriminating among species on the basis of diet as discriminant analysis, and was much better than either factor analysis or principal component analysis in produci...