On the eigenvalue distribution of genetic and phenotypic dispersion matrices: Evidence for a nonrandom organization of quantitative character variation

Wagner, Günter P.

doi:10.1007/bf00275224

Cited by 226 publications

(329 citation statements)

References 19 publications

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“…Within-floral correlations and especially correlations between floral and vegetative traits in plants are lower than 0.5, and holometabolous insects are much more highly integrated, with an average correlation of 0.84. Note that this higher correlation in holometabolous insects does not necessarily conflict with the results of Wagner [13], who showed lower integration in insects compared with mammals, as Wagner's comparison was made after removing the effects of overall size. It might be interesting to compare the patterns of integration after removing the effects of size in a large sample of plants and animals.…”

Section: Discussionmentioning

confidence: 53%

“…To make a strong case for functional integration in any set of traits, three lines of evidence are needed: (i) correlations among the traits are greater than the size-related background level of correlation (cf. [13]); (ii) there is correlational selection on the traits; and (iii) functional studies show how the traits work together in an integrated unit. For example, our work on wild radish flowers has provided these three lines of evidence for anther exsertion and the difference in lengths of the short and long stamens (see also [23]).…”

Section: Discussionmentioning

confidence: 99%

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Patterns of phenotypic correlations among morphological traits across plants and animals

Conner

Cooper

Rosa

et al. 2014

Phil. Trans. R. Soc. B

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Despite the long-standing interest of biologists in patterns of correlation and phenotypic integration, little attention has been paid to patterns of correlation across a broad phylogenetic spectrum. We report analyses of mean phenotypic correlations among a variety of linear measurements from a wide diversity of plants and animals, addressing questions about function, development, integration and modularity. These analyses suggest that vertebrates, hemimetabolous insects and vegetative traits in plants have similar mean correlations, around 0.5. Traits of holometabolous insects are much more highly correlated, with a mean correlation of 0.84; this may be due to developmental homeostasis caused by lower spatial and temporal environmental variance during complete metamorphosis. The lowest mean correlations were those between floral and vegetative traits, consistent with Berg's ideas about functional independence between these modules. Within trait groups, the lowest mean correlations were among vertebrate head traits and floral traits (0.38–0.39). The former may be due to independence between skull modules. While there is little evidence for floral integration overall, certain sets of functionally related floral traits are highly integrated. A case study of the latter is described from wild radish flowers.

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Section: Discussionmentioning

confidence: 53%

Section: Discussionmentioning

confidence: 99%

Patterns of phenotypic correlations among morphological traits across plants and animals

Conner

Cooper

Rosa

et al. 2014

Phil. Trans. R. Soc. B

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“…We refer to this assumption as "developmental integration" (although development may not be involved), because it refers to integration through the developmental function, in the sense of Wagner (1984Wagner ( , 1989 and Rice (2002Rice ( , 2004. It might be the most difficult assumption to evaluate.…”

Section: Practical Illustrationsmentioning

confidence: 99%

“…The random perturbation dx translates into dy ¼ fdy i g i2½1;:::;n ; via the developmental function: dy ¼ fðx þ dxÞ 2 fðxÞ: Assumption 3 (mild mutation effects) allows us to take a linear approximation of fð:Þ about the parent phenotype: dy B:dx; where B ¼ fb ij g i2½1;n;j2½1;p is an n 3 p matrix containing all the first derivatives of fð:Þ at the parent position x. We thus retrieve exactly Wagner's (1984Wagner's ( , 1989 linear developmental function, where the n p coefficients b ij in B describe how mutable traits x j integrate into optimized traits y i : I denote them "pathway coefficients," as they relate to functional pathways connecting phenotypes. Then, from assumptions 4-7, we can invoke a generalized central limit theorem (CLT).…”

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confidence: 99%

Fisher’s Geometrical Model Emerges as a Property of Complex Integrated Phenotypic Networks

Martin

2014

Genetics

126

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Models relating phenotype space to fitness (phenotype-fitness landscapes) have seen important developments recently. They can roughly be divided into mechanistic models (e.g., metabolic networks) and more heuristic models like Fisher's geometrical model. Each has its own drawbacks, but both yield testable predictions on how the context (genomic background or environment) affects the distribution of mutation effects on fitness and thus adaptation. Both have received some empirical validation. This article aims at bridging the gap between these approaches. A derivation of the Fisher model "from first principles" is proposed, where the basic assumptions emerge from a more general model, inspired by mechanistic networks. I start from a general phenotypic network relating unspecified phenotypic traits and fitness. A limited set of qualitative assumptions is then imposed, mostly corresponding to known features of phenotypic networks: a large set of traits is pleiotropically affected by mutations and determines a much smaller set of traits under optimizing selection. Otherwise, the model remains fairly general regarding the phenotypic processes involved or the distribution of mutation effects affecting the network. A statistical treatment and a local approximation close to a fitness optimum yield a landscape that is effectively the isotropic Fisher model or its extension with a single dominant phenotypic direction. The fit of the resulting alternative distributions is illustrated in an empirical data set. These results bear implications on the validity of Fisher's model's assumptions and on which features of mutation fitness effects may vary (or not) across genomic or environmental contexts.T HE distribution of the fitness effects (DFE) of random mutations is a central determinant of the evolutionary fate of a population, together with the rate of mutation. Obviously, it determines the rate of adaptation by de novo mutations, by setting the mutational input of fitness variance. Furthermore, by setting the distribution of fitness at mutation-selection balance, the DFE also determines the amount of standing variance in populations at equilibrium and their potential for future adaptation. The DFE is therefore central to evolutionary theory, for both adapting and equilibrium populations. There is, however, no widely accepted model that predicts the distribution of fitness effects of random mutations and how it is affected by various environmental or genetic contexts.Yet, predicting what happens under changed conditions is a minimum requirement for many applications of evolutionary theory. "Phenotype-fitness landscapes" provide a general tool for such inference: by defining changed conditions (genetic background or environment) as explicit alternative "positions" in the landscape, their effects can be handled quantitatively. "Mechanistic" landscapesOne such approach has seen considerable development in the past decade: models that explicitly describe the "direct" molecular effect of a mutation (on RNA secondary str...

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“…We calculated eigenvalues from principal component analyses of measured floral traits in each of the trait modules (spot traits, nonspot ray floret traits and disc floret traits) for all floral forms separately. We then calculated trait integration as the variance of the eigenvalues of the trait correlation matrices [INT ¼ V (l)] [32] in each trait module for all floral forms. To control for differences in sample size between the floral forms investigated and between trait modules, we subtracted the expected eigenvalue variance under the hypothesis of random covariation of traits [Exp(INT) ¼ (number traits 2 1)/N] from INT for each form to obtain the corrected INT values [32,33].…”

Section: (D) Assessing Trait Divergence Between Floral Formsmentioning

confidence: 99%

Floral trait variation and integration as a function of sexual deception inGorteria diffusa

Ellis

Jager

Mellers

et al. 2014

Phil. Trans. R. Soc. B

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Phenotypic integration, the coordinated covariance of suites of morphological traits, is critical for proper functioning of organisms. Angiosperm flowers are complex structures comprising suites of traits that function together to achieve effective pollen transfer. Floral integration could reflect shared genetic and developmental control of these traits, or could arise through pollinator-imposed stabilizing correlational selection on traits. We sought to expose mechanisms underlying floral trait integration in the sexually deceptive daisy, Gorteria diffusa , by testing the hypothesis that stabilizing selection imposed by male pollinators on floral traits involved in mimicry has resulted in tighter integration. To do this, we quantified patterns of floral trait variance and covariance in morphologically divergent G. diffusa floral forms representing a continuum in the levels of sexual deception. We show that integration of traits functioning in visual attraction of male pollinators increases with pollinator deception, and is stronger than integration of non-mimicry trait modules. Consistent patterns of within-population trait variance and covariance across floral forms suggest that integration has not been built by stabilizing correlational selection on genetically independent traits. Instead pollinator specialization has selected for tightened integration within modules of linked traits. Despite potentially strong constraint on morphological evolution imposed by developmental genetic linkages between traits, we demonstrate substantial divergence in traits across G. diffusa floral forms and show that divergence has often occurred without altering within-population patterns of trait correlations.

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On the eigenvalue distribution of genetic and phenotypic dispersion matrices: Evidence for a nonrandom organization of quantitative character variation

Cited by 226 publications

References 19 publications

Patterns of phenotypic correlations among morphological traits across plants and animals

Patterns of phenotypic correlations among morphological traits across plants and animals

Fisher’s Geometrical Model Emerges as a Property of Complex Integrated Phenotypic Networks

Floral trait variation and integration as a function of sexual deception inGorteria diffusa

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