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1.  Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry 
Background
Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers) or rotational symmetry (e.g. sea urchins and many flowers). So far, there is no general method for the shape analysis of these types of symmetry.
Results
We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis.
Conclusions
The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry.
doi:10.1186/1471-2148-11-280
PMCID: PMC3209460  PMID: 21958045
2.  Symmetrical crypsis and asymmetrical signalling in the cuttlefish Sepia officinalis 
The salience of bilateral symmetry to humans has led to the suggestion that camouflage may be enhanced in asymmetrical patterns. However, the importance of bilateral symmetry in visual signals (and overall morphology) may constrain the evolution of asymmetrical camouflage, resulting in the bilaterally symmetrical cryptic patterns that we see throughout the animal kingdom. This study investigates the cuttlefish (Sepia officinalis), which can control the degree of symmetry in its coloration. Ten juvenile S. officinalis were filmed in two behavioural contexts (cryptic and threatened) to test the prediction that cryptic patterns will be expressed more asymmetrically than an anti-predator signal known as the ‘deimatic display’. Cryptic body patterns, particularly those with a disruptive function, were found to exhibit a high degree of bilateral symmetry. By contrast, the components of the deimatic display were often expressed asymmetrically. These results are contrary to the predicted use of symmetry in defensive coloration, indicating that the role of symmetry in both crypsis and visual signalling is not as straightforward as previously suggested.
doi:10.1098/rspb.2005.3395
PMCID: PMC1560237  PMID: 16627281
symmetry; adaptive coloration; crypsis; cephalopod; Sepia officinalis; deimatic display
3.  Bipedalism in lizards: whole-body modelling reveals a possible spandrel. 
This paper illustrates how simple mechanical models based on morphological, ethological, ecological and phylogenetic data can add to discussions in evolutionary biology. Bipedal locomotion has evolved on numerous occasions in lizards. Traits that appear repeatedly in independent evolutionary lines are often considered adaptive, but the exact advantages of bipedal locomotion in lizards remain debated. Earlier claims that bipedalism would increase maximal running speed or would be energetically advantageous have been questioned. Here, we use 'whole body' mechanical modelling to provide an alternative solution to the riddle. The starting point is the intermittent running style combined with the need for a high manoeuvrability characterizing many small lizard species. Manoeuvrability benefits from a caudal shift of the centre of mass of the body (body-COM), because forces to change the heading and to align the body to this new heading do not conflict with each other. The caudally situated body-COM, however, might result in a lift of the front part of the body when accelerating (intermittent style), thus resulting in bipedal running bouts. Based on a momentum-impulse approach the effect of acceleration is quantified for a mechanical model, a virtual lizard (three segments) based on the morphometrics of Acanthodactylus erythrurus (a small lacertid lizard). Biologically relevant input (dimensions, inertial properties, step cycle information, etc.) results in an important lift of the front part of the body and observable distances passively covered bipedally as a consequence of the acceleration. In this way, no functional explanation of the phenomenon of lizard bipedalism is required and bipedalism can probably be considered non-adaptive in many cases. This does not exclude, however, some species that may have turned this consequence to their benefit. For instance, instantaneous manipulation of the position of the centre of the body-COM allows stable, persisting bipedal running. Once this was achieved, the bipedal spandrel could be exploited further.
doi:10.1098/rstb.2003.1342
PMCID: PMC1693243  PMID: 14561343
4.  Floral symmetry: pollinator-mediated stabilizing selection on flower size in bilateral species 
Pollinator-mediated stabilizing selection (PMSS) has been proposed as the driver of the evolutionary shift from radial to bilateral symmetry of flowers. Studies have shown that variation in flower size is lower in bilateral than in radial species, but whether bilateral flowers experience more stabilizing selection pressures by employing fewer, more specialized pollinators than radial flowers remains unclear. To test the PMSS hypothesis, we investigate plant–pollinator interactions from a whole community in an alpine meadow in Hengduan Mountains, China, to examine: (i) variance in flower size and level of ecological generalization (pollinator diversity calculated using functional groups) in 14 bilateral and 13 radial species and (ii) the role pollinator diversity played in explaining the difference of variance in flower size between bilateral and radial species. Our data showed that bilateral species had less variance in flower size and were visited by fewer pollinator groups. Pollinator diversity accounted for up to 40 per cent of the difference in variance in flower size between bilateral and radial species. The mediator effect of pollinator diversity on the relationship between floral symmetry and variance in flower size in the community is consistent with the PMSS hypothesis.
doi:10.1098/rspb.2009.1254
PMCID: PMC2825790  PMID: 19710062
bilateral and radial; variance in flower size; pollinator diversity; ecological specialization; pollinator-mediated stabilizing selection; mediator effect
5.  Hox, Wnt, and the evolution of the primary body axis: insights from the early-divergent phyla 
Biology Direct  2007;2:37.
The subkingdom Bilateria encompasses the overwhelming majority of animals, including all but four early-branching phyla: Porifera, Ctenophora, Placozoa, and Cnidaria. On average, these early-branching phyla have fewer cell types, tissues, and organs, and are considered to be significantly less specialized along their primary body axis. As such, they present an attractive outgroup from which to investigate how evolutionary changes in the genetic toolkit may have contributed to the emergence of the complex animal body plans of the Bilateria. This review offers an up-to-date glimpse of genome-scale comparisons between bilaterians and these early-diverging taxa. Specifically, we examine these data in the context of how they may explain the evolutionary development of primary body axes and axial symmetry across the Metazoa. Next, we re-evaluate the validity and evolutionary genomic relevance of the zootype hypothesis, which defines an animal by a specific spatial pattern of gene expression. Finally, we extend the hypothesis that Wnt genes may be the earliest primary body axis patterning mechanism by suggesting that Hox genes were co-opted into this patterning network prior to the last common ancestor of cnidarians and bilaterians.
Reviewed by Pierre Pontarotti, Gáspár Jékely, and L Aravind. For the full reviews, please go to the Reviewers' comments section.
doi:10.1186/1745-6150-2-37
PMCID: PMC2222619  PMID: 18078518
6.  Evolutionary Trends in the Flowers of Asteridae: Is Polyandry an Alternative to Zygomorphy? 
Annals of Botany  2008;102(2):153-165.
Background and Aims
Floral symmetry presents two main states in angiosperms, actinomorphy (polysymmetry or radial symmetry) and zygomorphy (monosymmetry or bilateral symmetry). Transitions from actinomorphy to zygomorphy have occurred repeatedly among flowering plants, possibly in coadaptation with specialized pollinators. In this paper, the rules controlling the evolution of floral symmetry were investigated to determine in which architectural context zygomorphy can evolve.
Methods
Floral traits potentially associated with perianth symmetry shifts in Asteridae, one of the major clades of the core eudicots, were selected: namely the perianth merism, the presence and number of spurs, and the androecium organ number. The evolution of these characters was optimized on a composite tree. Correlations between symmetry and the other morphological traits were then examined using a phylogenetic comparative method.
Key Results
The analyses reveal that the evolution of floral symmetry in Asteridae is conditioned by both androecium organ number and perianth merism and that zygomorphy is a prerequisite to the emergence of spurs.
Conclusions
The statistically significant correlation between perianth zygomorphy and oligandry suggests that the evolution of floral symmetry could be canalized by developmental or spatial constraint. Interestingly, the evolution of polyandry in an actinomorphic context appears as an alternative evolutionary pathway to zygomorphy in Asteridae. These results may be interpreted either in terms of plant–pollinator adaptation or in terms of developmental or physical constraints. The results are discussed in relation to current knowledge about the molecular bases underlying floral symmetry.
doi:10.1093/aob/mcn082
PMCID: PMC2712368  PMID: 18511411
Floral symmetry; architectural constraints; Asteridae; comparative analysis; composite tree; correlated evolution; evolutionary scenario
7.  Spontaneous Symmetry Breaking in Interdependent Networked Game 
Scientific Reports  2014;4:4095.
Spatial evolution game has traditionally assumed that players interact with direct neighbors on a single network, which is isolated and not influenced by other systems. However, this is not fully consistent with recent research identification that interactions between networks play a crucial rule for the outcome of evolutionary games taking place on them. In this work, we introduce the simple game model into the interdependent networks composed of two networks. By means of imitation dynamics, we display that when the interdependent factor α is smaller than a threshold value αC, the symmetry of cooperation can be guaranteed. Interestingly, as interdependent factor exceeds αC, spontaneous symmetry breaking of fraction of cooperators presents itself between different networks. With respect to the breakage of symmetry, it is induced by asynchronous expansion between heterogeneous strategy couples of both networks, which further enriches the content of spatial reciprocity. Moreover, our results can be well predicted by the strategy-couple pair approximation method.
doi:10.1038/srep04095
PMCID: PMC3924213  PMID: 24526076
8.  The metabolic and mechanical costs of step time asymmetry in walking 
Animals use both pendular and elastic mechanisms to minimize energy expenditure during terrestrial locomotion. Elastic gaits can be either bilaterally symmetric (e.g. run and trot) or asymmetric (e.g. skip, canter and gallop), yet only symmetric pendular gaits (e.g. walk) are observed in nature. Does minimizing metabolic and mechanical power constrain pendular gaits to temporal symmetry? We measured rates of metabolic energy expenditure and calculated mechanical power production while healthy humans walked symmetrically and asymmetrically at a range of step and stride times. We found that walking with a 42 per cent step time asymmetry required 80 per cent (2.5 W kg−1) more metabolic power than preferred symmetric gait. Positive mechanical power production increased by 64 per cent (approx. 0.24 W kg−1), paralleling the increases we observed in metabolic power. We found that when walking asymmetrically, subjects absorbed more power during double support than during symmetric walking and compensated by increasing power production during single support. Overall, we identify inherent metabolic and mechanical costs to gait asymmetry and find that symmetry is optimal in healthy human walking.
doi:10.1098/rspb.2012.2784
PMCID: PMC3574372  PMID: 23407831
symmetry; biomechanics; energetics; locomotion; limb work
9.  Left-right patterning in the C. elegans embryo 
The development of bilateral symmetry during the evolution of species probably 600 million years ago brought about several important innovations: It fostered efficient locomotion, streamlining and favored the development of a central nervous system through cephalization. However, to increase their functional capacities, many organisms exhibit chirality by breaking their superficial left-right (l-r) symmetry, which manifests in the lateralization of the nervous system or the l-r asymmetry of internal organs. In most bilateria, the mechanisms that maintain consistent l-r asymmetry throughout development are poorly understood. This review highlights insights into mechanisms that couple early embryonic l-r symmetry breaking to subsequent l-r patterning in the roundworm Caenorhabditis elegans. A recently identified strategy for l-r patterning in the early C. elegans embryo is discussed, the spatial separation of midline and anteroposterior axis, which relies on a rotational cellular rearrangement and non-canonical Wnt signaling. Evidence for a general relevance of rotational/torsional rearrangements during organismal l-r patterning and for non-canonical Wnt signaling/planar cell polarity as a common signaling mechanism to maintain l-r asymmetry is presented.
doi:10.4161/cib.4.1.14144
PMCID: PMC3073266  PMID: 21509174
left-right axis; symmetry breaking; embryonic development; Wnt signaling; planar cell polarity
10.  A moving topic: control and dynamics of animal locomotion 
Biology Letters  2010;6(3):387-388.
Animal locomotion arises from complex interactions among sensory systems, processing of sensory information into patterns of motor output, the musculo-skeletal dynamics that follow motor stimulation, and the interaction of appendages and body parts with the environment. These processes conspire to produce motions and forces that permit stunning manoeuvres with important ecological and evolutionary consequences. Thus, the habitats that animals may exploit, their ability to escape predators or attack prey, their capacity to manoeuvre and turn, or the use of their available energy all depend upon the processes that determine locomotion. Here, we summarize a series of 10 papers focused on this integrative research topic.
doi:10.1098/rsbl.2010.0294
PMCID: PMC2880073  PMID: 20410030
animal locomotion; sensory systems; motor control; biomechanics
11.  The Symmetry of Longevity 
We tested the hypothesis that relatively symmetrical flies live longer. Vein measurements on the left and right wings from the same individual were used to characterize bilateral symmetry in relationship to age-specific survival in defined cohorts. A longitudinal cohort study supported the hypothesis of a correlation between bilateral symmetry and longevity. For another type of experiment, wings were removed from females and males at approximately the beginning of adult life. Thus, there would be no effect of wings per se on adult survival. These wings were measured to characterize bilateral asymmetry, and the day of death of each dewinged individual was determined. Wing symmetry of females and males proved to be a statistically significant predictor of life span, especially for males.
PMCID: PMC2611956  PMID: 16282553
12.  Inverse Symmetry in Complete Genomes and Whole-Genome Inverse Duplication 
PLoS ONE  2009;4(11):e7553.
The cause of symmetry is usually subtle, and its study often leads to a deeper understanding of the bearer of the symmetry. To gain insight into the dynamics driving the growth and evolution of genomes, we conducted a comprehensive study of textual symmetries in 786 complete chromosomes. We focused on symmetry based on our belief that, in spite of their extreme diversity, genomes must share common dynamical principles and mechanisms that drive their growth and evolution, and that the most robust footprints of such dynamics are symmetry related. We found that while complement and reverse symmetries are essentially absent in genomic sequences, inverse–complement plus reverse–symmetry is prevalent in complex patterns in most chromosomes, a vast majority of which have near maximum global inverse symmetry. We also discovered relations that can quantitatively account for the long observed but unexplained phenomenon of -mer skews in genomes. Our results suggest segmental and whole-genome inverse duplications are important mechanisms in genome growth and evolution, probably because they are efficient means by which the genome can exploit its double-stranded structure to enrich its code-inventory.
doi:10.1371/journal.pone.0007553
PMCID: PMC2771390  PMID: 19898631
13.  The constructal law of design and evolution in nature 
Constructal theory is the view that (i) the generation of images of design (pattern, rhythm) in nature is a phenomenon of physics and (ii) this phenomenon is covered by a principle (the constructal law): ‘for a finite-size flow system to persist in time (to live) it must evolve such that it provides greater and greater access to the currents that flow through it’. This law is about the necessity of design to occur, and about the time direction of the phenomenon: the tape of the design evolution ‘movie’ runs such that existing configurations are replaced by globally easier flowing configurations. The constructal law has two useful sides: the prediction of natural phenomena and the strategic engineering of novel architectures, based on the constructal law, i.e. not by mimicking nature. We show that the emergence of scaling laws in inanimate (geophysical) flow systems is the same phenomenon as the emergence of allometric laws in animate (biological) flow systems. Examples are lung design, animal locomotion, vegetation, river basins, turbulent flow structure, self-lubrication and natural multi-scale porous media. This article outlines the place of the constructal law as a self-standing law in physics, which covers all the ad hoc (and contradictory) statements of optimality such as minimum entropy generation, maximum entropy generation, minimum flow resistance, maximum flow resistance, minimum time, minimum weight, uniform maximum stresses and characteristic organ sizes. Nature is configured to flow and move as a conglomerate of ‘engine and brake’ designs.
doi:10.1098/rstb.2009.0302
PMCID: PMC2871904  PMID: 20368252
constructal; thermodynamics; animate design; inanimate design; technology evolution; human and machine species
14.  Unilateral and Bilateral Expression of a Quantitative Trait: Asymmetry and Symmetry in Coronal Craniosynostosis 
Bilateral symmetry in vertebrates is imperfect and mild asymmetries are found in normal growth and development. However, abnormal development is often characterized by strong asymmetries. Coronal craniosynostosis, defined here as consisting of premature suture closure and a characteristic skull shape, is a complex trait. The premature fusion of the coronal suture can occur unilaterally associated with skull asymmetry (anterior plagiocephaly) or bilaterally associated with a symmetric but brachycephalic skull. We investigated the relationship between coronal craniosynostosis and skull bilateral symmetry. Three-dimensional landmark coordinates were recorded on preoperative computed tomography images of children diagnosed with coronal nonsyndromic craniosynostosis (N = 40) and that of unaffected individuals (N = 20) and analyzed by geometric morphometrics. Our results showed that the fusion pattern of the coronal suture is similar across individuals and types of coronal craniosynostosis. Shape analysis showed that skulls of bilateral coronal craniosynostosis (BCS) and unaffected individuals display low degrees of asymmetry, whereas right and left unilateral coronal craniosynostosis (UCS) skulls are asymmetric and mirror images of one another. When premature fusion of the coronal suture (without taking into account cranial dysmorphology) is scored as a qualitative trait, the expected relationship between trait frequency and trait unilateral expression (i.e. negative correlation) is confirmed. Overall, we interpret our results as evidence that the same biological processes operate on the two sides in BCS skulls and on the affected side in UCS skulls, and that coronal craniosynostosis is a quantitative trait exhibiting a phenotypic continuum with BCS displaying more intense shape changes than UCS.
doi:10.1002/jezb.21449
PMCID: PMC3315613  PMID: 22532473
15.  Physical Model of Cellular Symmetry Breaking 
Cells can polarize in response to external signals, such as chemical gradients, cell–cell contacts, and electromagnetic fields. However, cells can also polarize in the absence of an external cue. For example, a motile cell, which initially has a more or less round shape, can lose its symmetry spontaneously even in a homogeneous environment and start moving in random directions. One of the principal determinants of cell polarity is the cortical actin network that underlies the plasma membrane. Tension in this network generated by myosin motors can be relaxed by rupture of the shell, leading to polarization. In this article, we discuss how simplified model systems can help us to understand the physics that underlie the mechanics of symmetry breaking.
Mechanical instabilities in animal cells can lead to symmetry breaking. Simplified experimental systems and models of cell polarization close to an instability threshold explains how.
doi:10.1101/cshperspect.a001909
PMCID: PMC2742081  PMID: 20066077
16.  Symmetry perception by poultry chicks and its implications for three-dimensional object recognition 
Bilateral symmetry is visually salient to diverse animals including birds, but whereas experimental studies typically use bilaterally symmetrical two-dimensional patterns that are viewed approximately fronto-parallel; in nature, animals observe three-dimensional objects from all angles. Many animals and plant structures have a plane of bilateral symmetry. Here, we first (experiment I) give evidence that young poultry chicks readily generalize bilateral symmetry as a feature of two-dimensional patterns in fronto-parallel view. We then test the ability of chicks to recognize symmetry in images that would be produced by the transformed view produced by a 40° horizontal combined with a 20° vertical rotation of a pattern on a spherical surface. Experiment II gives evidence that chicks trained to distinguish symmetrical from asymmetrical patterns treat rotated views of symmetrical ‘objects’ as symmetrical. Experiment III gives evidence that chicks trained to discriminate rotated views of symmetrical ‘objects’ from asymmetrical patterns generalize to novel symmetrical objects either in fronto-parallel or rotated view. These findings emphasize the importance of bilateral symmetry for three-dimensional object recognition and raise questions about the underlying mechanisms of symmetry perception.
doi:10.1098/rspb.2011.1486
PMCID: PMC3259931  PMID: 21920978
symmetry; vision; object recognition; domestic chick; categorization
17.  Evolution of a unique predatory feeding apparatus: functional anatomy, development and a genetic locus for jaw laterality in Lake Tanganyika scale-eating cichlids 
BMC Biology  2010;8:8.
Background
While bilaterality is a defining characteristic of triploblastic animals, several assemblages have managed to break this symmetry in order to exploit the adaptive peaks garnered through the lateralization of behaviour or morphology. One striking example of an evolved asymmetry in vertebrates comes from a group of scale-eating cichlid fishes from Lake Tanganyika. Members of the Perissodini tribe of cichlid fishes have evolved dental and craniofacial asymmetries in order to more effectively remove scales from the left or right flanks of prey. Here we examine the evolution and development of craniofacial morphology and laterality among Lake Tanganyika scale-eating cichlids.
Results
Using both geometric and traditional morphometric methods we found that the craniofacial evolution in the Perissodini involved discrete shifts in skeletal anatomy that reflect differences in habitat preference and predation strategies. Further, we show that the evolutionary history of the Perissodini is characterized by an accentuation of craniofacial laterality such that certain taxa show elaborate sided differences in craniofacial shape consistent with the sub-partitioning of function between sides of the head during attacks. Craniofacial laterality in the scale-eating specialist Perissodus microlepis was found to be evident early in development and exhibited a unimodal distribution, which is contrary to the adult condition where jaw laterality has been described as a discrete, bimodal antisymmetry. Finally, using linkage and association analyses we identified a conserved locus for jaw handedness that segregates among East African cichlids.
Conclusions
We suggest that, during the evolution of the Perissodini, selection has accentuated a latent, genetically determined handedness of the craniofacial skeleton, enabling the evolution of jaw asymmetries in order to increase predation success. Continued work on the developmental genetic basis of laterality in the Perissodini will facilitate a better understanding of the evolution of this unique group of fishes, as well as of left-right axis determination among vertebrates in general.
doi:10.1186/1741-7007-8-8
PMCID: PMC2828976  PMID: 20102595
18.  Parallel evolution of TCP and B-class genes in Commelinaceae flower bilateral symmetry 
EvoDevo  2012;3:6.
Background
Flower bilateral symmetry (zygomorphy) has evolved multiple times independently across angiosperms and is correlated with increased pollinator specialization and speciation rates. Functional and expression analyses in distantly related core eudicots and monocots implicate independent recruitment of class II TCP genes in the evolution of flower bilateral symmetry. Furthermore, available evidence suggests that monocot flower bilateral symmetry might also have evolved through changes in B-class homeotic MADS-box gene function.
Methods
In order to test the non-exclusive hypotheses that changes in TCP and B-class gene developmental function underlie flower symmetry evolution in the monocot family Commelinaceae, we compared expression patterns of teosinte branched1 (TB1)-like, DEFICIENS (DEF)-like, and GLOBOSA (GLO)-like genes in morphologically distinct bilaterally symmetrical flowers of Commelina communis and Commelina dianthifolia, and radially symmetrical flowers of Tradescantia pallida.
Results
Expression data demonstrate that TB1-like genes are asymmetrically expressed in tepals of bilaterally symmetrical Commelina, but not radially symmetrical Tradescantia, flowers. Furthermore, DEF-like genes are expressed in showy inner tepals, staminodes and stamens of all three species, but not in the distinct outer tepal-like ventral inner tepals of C. communis.
Conclusions
Together with other studies, these data suggest parallel recruitment of TB1-like genes in the independent evolution of flower bilateral symmetry at early stages of Commelina flower development, and the later stage homeotic transformation of C. communis inner tepals into outer tepals through the loss of DEF-like gene expression.
doi:10.1186/2041-9139-3-6
PMCID: PMC3359255  PMID: 22394484
B class genes; Commelinaceae; CYCLOIDEA; homeotic change; monocots; tepals; teosinte branched1
19.  Facial attractiveness, symmetry and cues of good genes. 
Cues of phenotypic condition should be among those used by women in their choice of mates. One marker of better phenotypic condition is thought to be symmetrical bilateral body and facial features. However, it is not clear whether women use symmetry as the primary cue in assessing the phenotypic quality of potential mates or whether symmetry is correlated with other facial markers affecting physical attractiveness. Using photographs of men's faces, for which facial symmetry had been measured, we found a relationship between women's attractiveness ratings of these faces and symmetry, but the subjects could not rate facial symmetry accurately. Moreover, the relationship between facial attractiveness and symmetry was still observed, even when symmetry cues were removed by presenting only the left or right half of faces. These results suggest that attractive features other than symmetry can be used to assess phenotypic condition. We identified one such cue, facial masculinity (cheek-bone prominence and a relatively longer lower face), which was related to both symmetry and full- and half-face attractiveness.
PMCID: PMC1690211  PMID: 10535106
20.  The basis and significance of pre-patterning in mammals. 
The second polar body (Pb) provides an enduring marker of the animal pole of the zygote, thereby revealing that the axis of bilateral symmetry of the early blastocyst is aligned with the zygote's animal-vegetal axis. That this relationship is biologically significant appeared likely when subsequent studies showed that the equator of the blastocyst tended to correspond with the plane of first cleavage. However, this cleavage plane varies both with respect to the position of the second Pb and to the distribution of components of the fertilizing sperm that continue to mark the point where it entered the egg. It also maps too variably on the blastocyst to play a causal role in early patterning. The zygote has been found transiently to exhibit bilateral symmetry before regaining an essentially spherical shape prior to first cleavage. Marking experiments indicate that the plane of bilateral symmetry of the blastocyst is aligned with, and the plane of first cleavage is typically orthogonal to, the zygote's bilateral plane. The bilateral symmetry of the zygote bears no consistent relationship either to the point of sperm entry or to the distribution of the pronuclei, and may therefore be a manifestation of intrinsic organization of the egg. Finally, the two-cell blastomere inheriting the sperm entry point has not been found to differ consistently in fate from the one that does not.
doi:10.1098/rstb.2003.1322
PMCID: PMC1693237  PMID: 14511479
21.  Both Coordination and Symmetry of Arm Swing Are Reduced in Parkinson’s Disease 
Gait & posture  2011;35(3):373-377.
Objective
A recent study reporting significantly reduced symmetry in arm swing amplitude in early Parkinson’s disease (PD), as measured during single strides in a gait laboratory, led to this investigation of arm swing symmetry and coordination over many strides using wearable accelerometers in PD.
Methods
Forearm accelerations were recorded while eight early PD subjects and eight Controls performed eight-minute walking trials. Arm swing asymmetry (ASA), maximal cross-correlation (MXC), and instantaneous relative phase (IRP) of bilateral arm swing were compared between PD and Controls. Correlations between arm swing measurements (ASA and MXC) and Unified PD Rating Scale (UPDRS) scores were estimated.
Results
PD subjects demonstrated significantly higher ASA (p = 0.002) and lower MXC (p < 0.001) than Controls. The IRP probability distribution for PD was significantly different than Controls (p < 0.001), with an angular standard deviation of 67.2° for PD and 50.6° for Controls. Among PD subjects, ASA was significantly correlated with the UPDRS score for the limbs (R2 = 0.58, p = 0.049), whereas MXC was significantly correlated with the tremor subscore of the limbs (R2 = 0.64, p = 0.031).
Discussion
The study confirms previously reported higher arm swing asymmetry in PD but also shows there is significantly lower MXC and greater IRP variability, suggesting that reduction in bilateral arm coordination may contribute to clinically observed asymmetry in PD. The differential correlation of clinical measures of motor disability with measurements of arm swing during gait is intriguing and deserves further investigation.
doi:10.1016/j.gaitpost.2011.10.180
PMCID: PMC3297736  PMID: 22098825
Parkinson’s disease, Arm swing asymmetry; Maximum cross correlation; Relative Phase; Synchronization; Gait; Accelerometers
22.  The predation costs of symmetrical cryptic coloration 
In psychological studies of visual perception, symmetry is accepted as a potent cue in visual search for cryptic objects, yet its importance for non-human animals has been assumed rather than tested. Furthermore, while the salience of bilateral symmetry has been established in laboratory-based search tasks using human subjects, its role in more natural settings, closer to those for which such perceptual mechanisms evolved, has not, to our knowledge, been investigated previously. That said, the salience of symmetry in visual search has a plausible adaptive rationale, because biologically important objects, such as prey, predators or conspecifics, usually have a plane of symmetry that is not present in their surroundings. We tested the conspicuousness to avian predators of cryptic artificial, moth-like targets, with or without bilateral symmetry in background-matching coloration, against oak trees in the field. In two independent experiments, symmetrical targets were predated at a higher rate than otherwise identical asymmetrical targets. There was a small, but significant, fitness cost to symmetry in camouflage patterns. Given that birds are the most commonly invoked predators shaping the evolution of defensive coloration in insects, this raises the question of why bilateral asymmetry is not more common in cryptic insects.
doi:10.1098/rspb.2005.3438
PMCID: PMC1560277  PMID: 16720401
defensive coloration; bilateral symmetry; bird vision; predation risk; visual search
23.  Laws of Conservation as Related to Brain Growth, Aging, and Evolution: Symmetry of the Minicolumn 
Development, aging, and evolution offer different time scales regarding possible anatomical transformations of the brain. This article expands on the perspective that the cerebral cortex exhibits a modular architecture with invariant properties in regards to these time scales. These properties arise from morphometric relations of the ontogenetic minicolumn as expressed in Noether’s first theorem, i.e., that for each continuous symmetry there is a conserved quantity. Whenever minicolumnar symmetry is disturbed by either developmental or aging processes the principle of least action limits the scope of morphometric alterations. Alternatively, local and global divergences from these laws apply to acquired processes when the system is no longer isolated from its environment. The underlying precepts to these physical laws can be expressed in terms of mathematical equations that are conservative of quantity. Invariant properties of the brain include the rotational symmetry of minicolumns, a scaling proportion or “even expansion” between pyramidal cells and core minicolumnar size, and the translation of neuronal elements from the main axis of the minicolumn. It is our belief that a significant portion of the architectural complexity of the cerebral cortex, its response to injury, and its evolutionary transformation, can all be captured by a small set of basic physical laws dictated by the symmetry of minicolumns. The putative preservations of parameters related to the symmetry of the minicolumn suggest that the development and final organization of the cortex follows a deterministic process.
doi:10.3389/fnana.2011.00066
PMCID: PMC3245969  PMID: 22207838
cerebral cortex; neocortex; minicolumns; symmetry
24.  Visual signalling by asymmetry: a review of perceptual processes. 
Individual levels of asymmetry in traits that display fluctuating asymmetry could be used as visual signals of phenotypic (and perhaps genotypic) quality, as asymmetry can often be negatively related to fitness parameters. There are some data to support this hypothesis but the experimental protocols employed have commonly resulted in asymmetries far larger than those observed in nature. To date, there has been little consideration of the ability of animals to accurately discriminate small asymmetries (of the magnitude observed in the wild) from perfect symmetry. This is key to assessing the plausibility of the asymmetry-signalling hypothesis. Here, I review the perceptual processes that may lead to the discrimination of asymmetry and discuss a number of ecologically relevant factors that may influence asymmetry signalling. These include: signal orientation, distance of trait elements from the axis of symmetry, trait complexity, trait contrast and colour, and the behaviour of both signaller and receiver. I also discuss the evolution of symmetry preferences and make suggestions as to where researchers should focus attention to examine the generality of asymmetry-signalling theory. In highly developmentally stable signalling systems the magnitude of asymmetry may be too small to be detected accurately and reliably, hence asymmetry signalling is unlikely to have evolved in these situations.
PMCID: PMC1692659  PMID: 10515000
25.  Gait in adolescent idiopathic scoliosis: kinematics and electromyographic analysis 
European Spine Journal  2009;18(4):512-521.
Adolescent idiopathic scoliosis (AIS) is a progressive growth disease that affects spinal anatomy, mobility, and left-right trunk symmetry. Consequently, AIS can modify human locomotion. Very few studies have investigated a simple activity like walking in a cohort of well-defined untreated patients with scoliosis. The first goal of this study is to evaluate the effects of scoliosis and scoliosis severity on kinematic and electromyographic (EMG) gait variables compared to an able-bodied population. The second goal is to look for any asymmetry in these parameters during walking. Thirteen healthy girls and 41 females with untreated AIS, with left thoracolumbar or lumbar primary structural curves were assessed. AIS patients were divided into three clinical subgroups (group 1 < 20°, group 2 between 20 and 40°, and group 3 > 40°). Gait analysis included synchronous bilateral kinematic and EMG measurements. The subjects walked on a treadmill at 4 km/h (comfortable speed). The tridimensional (3D) shoulder, pelvis, and lower limb motions were measured using 22 reflective markers tracked by four infrared cameras. The EMG timing activity was measured using bipolar surface electrodes on quadratus lumborum, erector spinae, gluteus medius, rectus femoris, semitendinosus, tibialis anterior, and gastrocnemius muscles. Statistical comparisons (ANOVA) were performed across groups and sides for kinematic and EMG parameters. The step length was reduced in AIS compared to normal subjects (7% less). Frontal shoulder, pelvis, and hip motion and transversal hip motion were reduced in scoliosis patients (respectively, 21, 27, 28, and 22% less). The EMG recording during walking showed that the quadratus lumborum, erector spinae, gluteus medius, and semitendinosus muscles contracted during a longer part of the stride in scoliotic patients (46% of the stride) compared with normal subjects (35% of the stride). There was no significant difference between scoliosis groups 1, 2, and 3 for any of the kinematic and EMG parameters, meaning that severe scoliosis was not associated with increased differences in gait parameters compared to mild scoliosis. Scoliosis was not associated with any kinematic or EMG left–right asymmetry. In conclusion, scoliosis patients showed significant but slight modifications in gait, even in cases of mild scoliosis. With the naked eye, one could not see any difference from controls, but with powerful gait analysis technology, the pelvic frontal motion (right–left tilting) was reduced, as was the motion in the hips and shoulder. Surprisingly, no asymmetry was noted but the spine seemed dynamically stiffened by the longer contraction time of major spinal and pelvic muscles. Further studies are needed to evaluate the origin and consequences of these observations.
doi:10.1007/s00586-009-0899-7
PMCID: PMC2899459  PMID: 19224255
Scoliosis; Gait; Asymmetry; Electromyography

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