There has been tremendous recent interest in developmental stability, which is an individual’s ability to produce a consistent phenotype in a given environment (Zakharov 1989). The primary reason for this interest is that many evolutionary biologists view developmental stability as an easily measured surrogate for fitness. But developmental processes are complex, dynamical, and nonlinear. Consequently, one should not expect a developmental system to respond to stress in a simple linear fashion. A theory of developmental stability must be rooted in the theory of nonlinear dynamics (Graham et al. 2003, 2010).
Phenotypic variation among individuals can be partitioned into three components, that are caused by genetic variation, environmental variation, and gene-environment interactions (Kozhara 1989, Lajus 1991, Lajus et al. 2003). The environmental component can be further subdivided into macro- and micro-environmental variation, maternal effects, and random developmental processes. The random developmental processes that contribute to phenotypic variation may be estimated by measuring deviations from perfect bilateral symmetry. Such random deviations are called fluctuating asymmetry. They arise from two sources: (1) developmental noise (at both molecular and cellular levels) and (2) the inherent nonlinearity of complex developmental processes, which give rise to morphogenetic oscillations, and perhaps chaos or near chaos (Emlen et al. 1993, Freeman et al. 1993, Graham et al. 1993).
Developmental noise represents variation arising inside the system (i.e. embryo) from perturbations that originate outside the system (i.e. environment). Deterministic chaos, on the other hand, arises entirely from within the system (i.e. it is part of the norm of reaction), but is often indistinguishable from developmental noise. Because such variation is part of the norm of reaction, it can be generated by either genetic or environmental variation (Graham et al. 1993).
A theory of developmental stability must account for observed transitions from fluctuating asymmetry to either directional asymmetry or antisymmetry. Directional asymmetry (i.e., handedness, or laterality) occurs when most individuals are either left or right dominant. Antisymmetry occurs when most individuals are asymmetric, but it is random which side is dominant. The transitions between fluctuating asymmetry and directional asymmetry or antisymmetry can be easily modeled via the Rashevsky-Turing Reaction Diffusion Equations (Graham et al. 1993). But such phase transitions are a general property of complex dynamical systems (Nicolis and Prigogine 1989). Thus, stress, which influences the feedback term in the model, should lead to both symmetry breaking (Graham et al. 1993) and increased developmental noise (Emlen et al. 1993). Antisymmetry then involves a phase transition leading to the breaking of bilateral symmetry (Graham et al. 2003). Directional asymmetry, which also involves a breaking of bilateral symmetry, occurs when there is a slight developmental bias for one side. The slight initial bias is ultimately amplified into a large consistent difference (i.e., directional asymmetry).
Fluctuating asymmetry, directional asymmetry, and antisymmetry are dynamically interrelated, and so it is important to estimate all three components of asymmetry. In particular, fluctuating asymmetry may be estimated from directionally asymmetric traits if the additive genetic component for directional asymmetry is nil (Graham et al 1998). The fluctuating asymmetry variance is simply the residual variance in a major-axis regression of one side on the other (say left on right). In some cases, it may even be possible to estimate the fluctuating asymmetry component of an antisymmetric trait, such as the claws of male fiddler crabs.
Developmental trajectories for male and female fiddler crabs, Uca urvillei. Females are open circles; right-dominant males are closed circles; left dominant males are open squares. From Graham et al. (1998)
The theory presented here can be extended to include the concepts of canalization and plasticity. Canalization is an individual’s ability to produce a consistent phenotype under different environmental and genetic conditions, while plasticity is its converse. Plasticity is usually adaptive, but such adaptive plasticity cannot be explained by neo-Darwinian theory, because the adaptation occurs within the life-span of an individual. Emlen et al. (1998) show that adaptive plasticity is an unavoidable emergent property of complex organisms. This adaptation involves selection for the most energy-efficient physiological and developmental states, or attractors.
In conclusion, a well-defined theory of developmental stability may lead to a better understanding of bilateral asymmetry in multicellular organisms.
References
Emlen, J. M., D. C. Freeman, and J. H. Graham. 1993. Nonlinear growth dynamics and the origin of fluctuating asymmetry. Genetica 89: 77-96.
Emlen, J. M., D. C. Freeman, A. Mills, J. H. Graham. 1998. How organisms do the right thing: the attractor hypothesis. Chaos 8: 717-726. (pdf)
Freeman, D. C., J. H. Graham, and J. M. Emlen. 1993. Developmental stability in plants: symmetries, stress and epigenesis. Genetica 89: 97-119
Graham, J. H., J. M. Emlen, and D. C. Freeman. 2003. Nonlinear dynamics and developmental instability. Pages 35-50 In: M. Polak (editor) Developmental Instability: Causes and Consequences. Oxford University Press, New York.
Graham, J. H., J. M. Emlen, D. C. Freeman, L. J. Leamy, and J. A. Kieser. 1998. Directional asymmetry and the measurement of developmental instability. Biological Journal of the Linnean Society 64: 1-16.
Graham, J. H., D. C. Freeman, and J. M. Emlen. 1993. Antisymmetry, directional asymmetry, and dynamic morphogenesis. Genetica 89: 121-137.
Graham, J. H., S. Raz, E. Nevo. 2010. Fluctuating asymmetry: methods, theory, and applications. Symmetry 2: 466-540.
Kozhara, A. V. 1989. On the ratio of components of phenotypic variances of bilateral characters in populations of some fishes. Genetika 25: 1508-1513. (in Russian)
Lajus, D. L. 1991. Analysis of fluctuating asymmetry as a method of population study of the White Sea herring. Proceedings of the Zoological Institute (Leningrad) 235: 113-121. (in Russian)
Lajus, D. L., J. H. Graham, and A. V. Kozhara. 2003. Developmental instability and the stochastic component of total phenotypic variance. Pages 343-363 In: M. Polak (editor) Developmental instability: causes and consequences. Oxford University Press, New York.
Nicolis, G. and I. Prigogine. 1989. Understanding Complexity. Freeman, New York.
Zakharov, V. M. 1989. Future prospects for population phenogenetics. Soviet Scientific Reviews F. Physiology and General Biology 4: 1-79.
Last Updated 10 August 2015