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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.
developmental stability, ecotoxicology, equiangular spiral, fluctuating asymmetry, fractal, phenodeviant, phyllotaxis, risk assessment, rescaled range analysis, time series
Population Biologist, Berry College, Mount Berry, GA
Population Biologist, Wayne State University, Detroit, MI
Ecologist, U.S. Fish & Wildlife Service, Seattle, WA