Symmetry

Research

440 KiB

Open AccessArticle

Consistent Positive Co-Variation between Fluctuating Asymmetry and Sexual Trait Size: A Challenge to the Developmental Instability-Sexual Selection Hypothesis

by Michal Polak, Kassie J. Hooker and Frances Tyler

Symmetry 2015, 7(2), 976-993; https://doi.org/10.3390/sym7020976 - 3 Jun 2015

Cited by 6 | Viewed by 6233

Abstract

The developmental instability (DI)-sexual selection hypothesis proposes that large size and symmetry in secondary sexual traits are favored by sexual selection because they reveal genetic quality. A critical prediction of this hypothesis is that there should exist negative correlations between trait fluctuating asymmetry [...] Read more.

The developmental instability (DI)-sexual selection hypothesis proposes that large size and symmetry in secondary sexual traits are favored by sexual selection because they reveal genetic quality. A critical prediction of this hypothesis is that there should exist negative correlations between trait fluctuating asymmetry (FA) and size of condition dependent sexual traits; condition dependent traits should reveal an organism’s overall health and vigor, and be influenced by a multitude of genetic loci. Here, we tested for the predicted negative FA-size correlations in the male sex comb of Drosophila bipectinata. Among field-caught males from five widely separated geographic localities, FA-size correlations were consistently positive, despite evidence that sex comb size is condition dependent. After controlling for trait size, FA was significantly negatively correlated with body size within several populations, indicating that developmental instability in the comb may reveal individual genetic quality. We suggest the possibility that condition dependent traits in some cases tap into independent units of the genome (a restricted set of genes), rather than signaling overall genetic properties of the organism. There were pronounced among-population differences in both comb FA and size, and these traits were positively correlated across populations, recapitulating the within-population patterns. We conclude that the results are inconsistent with the DI-sexual selection hypothesis, and discuss potential reasons for positive FA-size co-variation in sexual traits. Full article

(This article belongs to the Special Issue Fluctuating Asymmetry)

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823 KiB

Open AccessArticle

Fluctuating and Directional Asymmetry of the Blue Mussel (Mytilus edulis): Improving Methods of Morphological Analysis to Explore Species Performance at the Northern Border of Its Range

by Dmitry Lajus, Marina Katolikova, Petr Strelkov and Herman Hummel

Symmetry 2015, 7(2), 488-514; https://doi.org/10.3390/sym7020488 - 29 Apr 2015

Cited by 12 | Viewed by 7993

Abstract

In this work we examined morphological variation at different levels to study performance and population structuring of the blue mussel Mytilus edulis. Our objectives were: (i) to develop an integrated technique for analyzing morphological variation in blue mussels and, based on this [...] Read more.

In this work we examined morphological variation at different levels to study performance and population structuring of the blue mussel Mytilus edulis. Our objectives were: (i) to develop an integrated technique for analyzing morphological variation in blue mussels and, based on this technique; (ii) to perform a morphometric description of mussels from the northern part of their range; and (iii) to verify the hypothesis that populations at the outer range of their distribution have reduced performance due to harsh climatic conditions. Means, directional asymmetry (i.e., systematic differences between left and right structures), fluctuating asymmetry (random deviations from perfect symmetry, a measure of developmental instability), factorial variation (difference between total variance and variance of fluctuating asymmetry, an indirect index of genotypic variation), and measurement error were examined for 14 bilateral characters of muscle scars on mussel shells. Also, we analyzed one non-bilateral character. For the first time directional asymmetry—approaching 13% of the right:left ratio—was described in blue mussels. Measurement error, often ignored in morphometric studies, contributed 26% of total variance. Accurately addressing these methodical challenges is key to further and improved ecological interpretations. Morphological differences were found between (i) samples from estuarine areas in the White and Pechora Seas and (ii) samples from Barents Sea areas with oceanic salinity. Samples from the first group exhibited lower fluctuating asymmetry, indicating higher developmental stability likely due to better feeding conditions and lower factorial variation, which may result from lower genotypic variation. Absence of correlation between fluctuating asymmetry and temperature suggests that low temperatures in the northern border of their range do not degrade the performance of adult blue mussels in this region. Full article

(This article belongs to the Special Issue Fluctuating Asymmetry)

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689 KiB

Open AccessArticle

Variation in Fractal Symmetry of Annual Growth in Aspen as an Indicator of Developmental Stability in Trees

by Jordan P. Sinclair, Daniel M. Kashian, John B. Bradford and D. Carl Freeman

Symmetry 2015, 7(2), 354-364; https://doi.org/10.3390/sym7020354 - 9 Apr 2015

Cited by 7 | Viewed by 5547

Abstract

Fractal symmetry is symmetry across scale. If one looks at a branch of a tree its branching pattern is reminiscent of the tree as a whole. Plants exhibit a number of different symmetries, including bilateral, rotational, translational, and fractal; deviations from each of [...] Read more.

Fractal symmetry is symmetry across scale. If one looks at a branch of a tree its branching pattern is reminiscent of the tree as a whole. Plants exhibit a number of different symmetries, including bilateral, rotational, translational, and fractal; deviations from each of these types has been associated with organisms developing in stressful environments. Here, we explore the utilization and meaning of fractal analysis on annual growth ring production in woody plants. Early detection of stress in plants is difficult and the compounding effects of multiple or severe stressors can lead to irreversible damage or death. Annual wood production was used to produce a time series for individuals from stands classified as either high vigor or low vigor (a general measure of health). As a measure of symmetry over time, the fractal dimension of each time series was determined and compared among vigor classes. We found that individuals obtained from low vigor sites had a significantly lower fractal dimension than those from high vigor sites. These results agree with patterns found in a variety of other organisms, and we argue that the reduced fractal dimension is related to a loss in system complexity of stressed individuals. Full article

(This article belongs to the Special Issue Fluctuating Asymmetry)

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562 KiB

Open AccessArticle

Variation in Measurement Error in Asymmetry Studies: A New Model, Simulations and Application

by Stefan Van Dongen

Symmetry 2015, 7(2), 284-293; https://doi.org/10.3390/sym7020284 - 24 Mar 2015

Cited by 7 | Viewed by 5346

Abstract

The importance of measurement error in studies of asymmetry has been acknowledged for a long time. It is now common practice to acquire independent repeated measurements of trait values and to estimate the degree of measurement error relative to the amount of asymmetry. [...] Read more.

The importance of measurement error in studies of asymmetry has been acknowledged for a long time. It is now common practice to acquire independent repeated measurements of trait values and to estimate the degree of measurement error relative to the amount of asymmetry. Methods also allow obtaining unbiased estimates of asymmetry, both at the population and individual level. One aspect that has been ignored is potential between-individual variation in measurement error. In this paper, I develop a new method to investigate this variation in measurement error and to generate unbiased estimates of individual asymmetries. Simulations show that variation in measurement error can indeed result in biased estimates of individual asymmetry and that the proposed method adequately provides unbiased estimates. The method is applied to two empirical datasets and shows that, at least in some traits, substantial variations in measurement occur. The limitations of the model are discussed. Full article

(This article belongs to the Special Issue Fluctuating Asymmetry)

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1427 KiB

Open AccessArticle

Fluctuating Asymmetry of Plant Leaves: Batch Processing with LAMINA and Continuous Symmetry Measures

by John H. Graham, Mattie J. Whitesell, Mark Fleming II, Hagit Hel-Or, Eviatar Nevo and Shmuel Raz

Symmetry 2015, 7(1), 255-268; https://doi.org/10.3390/sym7010255 - 13 Mar 2015

Cited by 17 | Viewed by 12119

Abstract

Unlike landmark methods for estimating object asymmetry, continuous symmetry measures (CSM) can be used to measure the symmetry distance (d_s) of inconsistent objects, such as plant leaves. Inconsistent objects have no homologous landmarks, no consistent topology, no quantitative consistency, and [...] Read more.

Unlike landmark methods for estimating object asymmetry, continuous symmetry measures (CSM) can be used to measure the symmetry distance (d_s) of inconsistent objects, such as plant leaves. Inconsistent objects have no homologous landmarks, no consistent topology, no quantitative consistency, and sometimes no matching points. When CSM is used in conjugation with LAMINA Leaf Shape Determination software, one can quickly and efficiently process a large number of scanned leaves. LAMINA automatically generates equally-spaced points around the perimeter of each leaf and the resulting x-y coordinates are normalized to average centroid size prior to estimating d_s using a fold, average, unfold algorithm. We estimated shape asymmetry of leaves of three species of flowering plants: Ligustrum sinense (Chinese Privet), Rubus cuneifolius (blackberry), and Perilla frutescens (Perilla), as well as individual leaves from a few species of oaks (Quercus) and maples (Acer). We found that 100 to 200 equally-spaced points worked well for all three of the main species. Measurement error accounted for a small proportion of the asymmetry variation. Nevertheless, measurement error was great enough to generate some negative size scaling after normalization to average centroid size. Full article

(This article belongs to the Special Issue Fluctuating Asymmetry)

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10569 KiB

Open AccessArticle

The Genetic Architecture of Fluctuating Asymmetry of Mandible Size and Shape in a Population of Mice: Another Look

by Larry J. Leamy, Christian Peter Klingenberg, Emma Sherratt, Jason B. Wolf and James M. Cheverud

Symmetry 2015, 7(1), 146-163; https://doi.org/10.3390/sym7010146 - 11 Feb 2015

Cited by 21 | Viewed by 7169

Abstract

Fluctuating asymmetry (FA), typically measured by variation in the differences between right and left sides of bilateral traits, is commonly used to assess developmental instability (DI) in populations. A previous quantitative trait locus (QTL) investigation using an F₂ intercross mouse population found [...] Read more.

Fluctuating asymmetry (FA), typically measured by variation in the differences between right and left sides of bilateral traits, is commonly used to assess developmental instability (DI) in populations. A previous quantitative trait locus (QTL) investigation using an F₂ intercross mouse population found little evidence of individual loci affecting FA in mandible size, but an abundance of epistatic interactions between loci. Here we extend this work by testing whether these patterns replicate in an F₃ population derived from the same intercross. Using a large number of molecular markers genotyped in over 1200 mice, we uncovered significant interactions between loci (QTLs) affecting FA in mandible size (and shape). Epistasis contributed roughly 20% of the variation in FASIZE and 19% of the variation in FASHAPE at the 0.0001 probability level alone, and was comparable to that previously estimated for the F₂ mice, and much greater than that generated from the few single-locus QTLs affecting the mandible FA traits. The positions of the single-locus and epistatic QTLs for FA that we discovered suggested that logical candidate genes for DI are those controlling size or shape in the traits themselves, and that they may be interacting with genes for heat shock proteins. Full article

(This article belongs to the Special Issue Fluctuating Asymmetry)

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Review

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87264 KiB

Open AccessReview

Analyzing Fluctuating Asymmetry with Geometric Morphometrics: Concepts, Methods, and Applications

by Christian Peter Klingenberg

Symmetry 2015, 7(2), 843-934; https://doi.org/10.3390/sym7020843 - 2 Jun 2015

Cited by 329 | Viewed by 39194

Abstract

Approximately two decades after the first pioneering analyses, the study of shape asymmetry with the methods of geometric morphometrics has matured and is a burgeoning field. New technology for data collection and new methods and software for analysis are widely available and have [...] Read more.

Approximately two decades after the first pioneering analyses, the study of shape asymmetry with the methods of geometric morphometrics has matured and is a burgeoning field. New technology for data collection and new methods and software for analysis are widely available and have led to numerous applications in plants and animals, including humans. This review summarizes the concepts and morphometric methods for studying asymmetry of shape and size. After a summary of mathematical and biological concepts of symmetry and asymmetry, a section follows that explains the methods of geometric morphometrics and how they can be used to analyze asymmetry of biological structures. Geometric morphometric analyses not only tell how much asymmetry there is, but also provide information about the patterns of covariation in the structure under study. Such patterns of covariation in fluctuating asymmetry can provide valuable insight about the developmental basis of morphological integration, and have become important tools for evolutionary developmental biology. The genetic basis of fluctuating asymmetry has been studied from empirical and theoretical viewpoints, but serious challenges remain in this area. There are many promising areas for further research that are only little explored at present. Full article

(This article belongs to the Special Issue Fluctuating Asymmetry)

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Other

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377 KiB

Open AccessBrief Report

A New Fluctuating Asymmetry Index, or the Solution for the Scaling Effect?

by Cino Pertoldi and Torsten Nygaard Kristensen

Symmetry 2015, 7(2), 327-335; https://doi.org/10.3390/sym7020327 - 1 Apr 2015

Cited by 9 | Viewed by 5682

Abstract

Two principal methods are commonly employed for the estimation of developmental instability at the population level. Some studies use variances of morphological traits (σ²_p), while others use fluctuating asymmetry (FA). In both cases, differences in the degree of developmental instability [...] Read more.

Two principal methods are commonly employed for the estimation of developmental instability at the population level. Some studies use variances of morphological traits (σ²_p), while others use fluctuating asymmetry (FA). In both cases, differences in the degree of developmental instability can be tested with an F-test, which is the most common way to compare variances. However, the variance is expected to scale proportionally to the square of the mean as there is a tendency in biological data for σ²_p to scale proportionally to the square of the mean ( ): σ²_p = Z ^ξ, where ξ is the scaling exponent, which is expected to be two for pure statistical reasons, is the mean of the trait and Z is a measure of individual-level variability. Because of this scaling effect, the fluctuating asymmetry will be affected, FA is estimated as the variance between the right and the left sides of a trait (σ²_r_{− l} = σ²_r + σ²_l − 2rσ_rσ_l), where σ²_r and σ²_l are the variances of the right and the left trait values, respectively. In this paper, we propose a novel method that allows an exact correction of the scaling effect, which will enable a proper comparison of the degree of fluctuating asymmetry for a trait. The problem of the scaling of the FA with the trait size is quite crucial if FA is to be considered an indicator of fitness or an indicator of environmental or genetic stress, as different stresses or fitness levels are typically accompanied by a change of the traits’ . Full article

(This article belongs to the Special Issue Fluctuating Asymmetry)

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