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The Concept of Within-Pair Concordance

Quantifying the Similarity of Monozygotic and Dizygotic Co-Twins

The concept of within-pair concordance is used to describe the similarity between monozygotic (mz) and dizygotic (dz) co-twins with respect to a set of variables ("traits"), preferably in a quantitative way. This concept is a special form of a more general approach to quantifying between-subject and within-subject similarity for a given set of features, for example, when addressing the question of "familiality" of psychopathology syndrome scores within families, or when comparing the intra-individual stability of brainwave patterns over time with the inter-individual differences in the general population. Unlike correlation analysis, where the comparison of a feature derived from all first-born co-twins with the same feature derived from all second-born co-twins of the sample under investigation yields a single correlation coefficient, the concordance approach evaluates the similarity for each twin pair separately, thus yielding a distribution of similarity measures.

Distributions of Quantiative Traits

Quantitative similarity measures are under most circumstances normally distributed and sample-independent. By contrast, qualitative measures often lack reproducibility because they require the definition of "tresholds" for the underlying categories which may be, to some extent, arbitrary. This is particularly true for the yes-no dichotomie of the concordant/discordant models. Figure 2 shows the within-pair concordances in mz and dz twins for the quantitative traits "finger ridge count", "body height", "shoe size", "body weight", and "brain-wave patterns" [Lykken and Stassen: data of 1,300 dizygotic and 1,434 monozygotic twin pairs]. Mean values and variances are strongly correlated (the higher the mean value the smaller the variance. All means values display a mz:dz ratio of 2:1 independent of the observed magnitude.

Norm of Reaction — From Genotype to Phenotype

Genes code for proteins or RNA (“gene products”) —which may interact among each other or with their immediate environment within the cells in a variety of ways— and influence the observable phenotypes ("traits of interest") only after a cascade of intermediate steps. In consequence, empirically derived genotype-phenotype correlations are typically weak, while the amount of phenotypic variance explainable through a single genomic locus is generally modest, often tiny, in the range of a few percent. Close genotype-phenotype correspondences with an approximate one-to-one mapping are rare. The cascade of intermediate steps leading from a particular gene to its corresponding phenotype gives rise to modulations and modifications through endogenous and exogenous factors, particularly in cases where the gene under investigation is part of a self regulating system encompassing a number of genes rather than a single gene. The modulations and modifications induced by endogenous and exogenous factors lead to variations in the observed phenotypes which are almost always normally distributed ("norm of reaction") with well-defined means and standard deviations for ethnically homogeneous populations.

concordance
Fig. 2: Within-pair concordances in mz and dz twins for the quantitative traits "finger ridge count", "body height", "shoe size", "body weight", and "brain-wave patterns". The distributions are approximately normal with means ranging between 0.99 (finger ridge count) and 0.65 (body weight). Mean values and variances are strongly correlated (the higher the mean value the smaller the variance. All means values display a mz:dz ratio of 2:1 independent of magnitude [Lykken and Stassen: data of 1,300 dizygotic and 1,434 monozygotic twin pairs].
Please note: No more than 55% of mz and 15% of dz co-twins are concordant for schizophrenia, thus displaying highly significant deviations from the expected mz:dz ratio of 2:1 for genetically additive traits. This deviation indicates the existence of strong non-linearities.

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