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.
In order to enable simulations of developing wind turbine array boundary layers with highly realistic inflow conditions a concurrent precursor method for Large Eddy Simulations is proposed. In this method we consider two domains simultaneously, i.e. in one domain a turbulent Atmospheric Boundary Layer (ABL) without wind turbines is simulated in order to generate the turbulent inflow conditions for a second domain in which the wind turbines are placed. The benefit of this approach is that a) it avoids the need for large databases in which the turbulent inflow conditions are stored and the correspondingly slow I/O operations and b) we are sure that the simulations are not negatively affected by statically swept fixed inflow fields or synthetic fields lacking the proper ABL coherent structures. Sample applications are presented, in which, in agreement with field data a strong decrease of the power output of downstream wind-turbines with respect to the first row of wind-turbines is observed for perfectly aligned inflow.
Developmental stability can be a sensitive indicator of the physiological state of individuals in natural populations. As such, it has potential as an indicator of stress, and is inexpensive and easily measured. Moreover, it can be estimated from museum specimens or from tree cores that span the time period of the disturbance. Thus, one can identify stressed populations and monitor their recovery. The most widely used measure of developmental stability is fluctuating asymmetry, the variance in random deviations from perfect bilateral symmetry. Fluctuating asymmetry is an outstanding measure of developmental stability because bilateral symmetry is an aspect of the individual that does not change during development (that is, a developmental invariant). We are therefore proposing three additional developmental invariants as new measures of developmental stability: phyllotaxy in plants, the equiangular spiral in snails, and the fractal dimension in both plants and animals. The arrangement of leaves on the stem of a plant is called phyllotaxis. In many plants, leaves or leaflets are arranged opposite one another on the stem or petiole. In plants with such an arrangement, we propose that deviation from an opposite arrangement be used as a measure of developmental stability. Many snails possess a self similar developmental invariance, the equiangular spiral. As the snail grows, the whorl of the shell increases at a constant rate. We propose that deviations from a perfect equiangular spiral be used as a measure of developmental stability. A fractal is an object that is invariant with regard to scaling. It appears the same at both high and low magnification. Fractals are common in living organisms, and represent a form of symmetry. The branching patterns of trees, blood vessels, and nerves are all fractals, as are skull sutures in vertebrates. Growth rings of trees and fish otoliths are fractals in time. In plants and other organisms, the fractal dimension of branching describes architectural complexity. For plants, the fractal dimension is the slope of the log of branch diameter or branch length regressed on the log of branch order. Assuming that the fractal dimension is indeed a developmental invariant, then the standard error of the regression can be used as the individual asymmetry measure. These measures allow one to assess the effects of stress on both natural and artificial populations, and to establish the history of stress within the impacted area. We present data from our own research on the effects of stress on the developmental stability of fish and plants.
Does endogenous or exogenous selection stabilize the big sagebrush (Artemisia tridentata) hybrid zone? After two years of study, our reciprocal transplant experiments showed significant genotype by environment interactions for a number of fitness components, including germination, growth, and reproduction. Hybrids were the most fit within the hybrid garden. In the parental gardens, the native parental taxon was more fit than either the alien parental or hybrids. These results are consistent with the bounded hybrid superiority model, which assumes exogenous selection, but are clearly at odds with the dynamic equilibrium model, which assumes endogenous selection and universal hybrid unfitness.
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