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Converting quadratic entropy to diversity: Both animals and alleles are diverse, but some are more diverse than others.

ABSTRACT: The use of diversity metrics has a long history in population ecology, while population genetic work has been dominated by variance-derived metrics instead, a technical gap that has slowed cross-communication between the fields. Interestingly, Rao's Quadratic Entropy (RQE), comparing elements for 'degrees of divergence', was originally developed for population ecology, but has recently been deployed for evolutionary studies. We here translate RQE into a continuous diversity analogue, and then construct a multiply nested diversity partition for alleles, individuals, populations, and species, each component of which exhibits the behavior of proper diversity metrics, and then translate these components into [0,1]-scaled form. We also deploy non-parametric statistical tests of the among-stratum components and novel tests of the homogeneity of within-stratum diversity components at any hierarchical level. We then illustrate this new analysis with eight nSSR loci and a pair of close Australian marsupial (Antechinus) congeners, using both 'different is different' and 'degree of difference' distance metrics. The total diversity in the collection is larger than that within either species, but most of the within-species diversity is resident within single populations. The combined A. agilis collection exhibits more diversity than does the combined A. stuartii collection, possibly attributable to localized differences in either local ecological disturbance regimes or differential levels of population isolation. Beyond exhibiting different allelic compositions, the two congeners are becoming more divergent for the arrays of allele sizes they possess.

SUBMITTER: Smouse PE

PROVIDER: S-EPMC5663342 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BACKGROUND:Genome-wide association studies (GWASs) have revealed relationships between over 57,000 genetic variants and diseases. However, unlike Mendelian diseases, complex diseases arise from the interplay of multiple genetic and environmental factors. Natural selection has led to a high tendency of risk alleles to be enriched in minor alleles in Mendelian diseases. Therefore, an allele that was previously advantageous or neutral may later become harmful, making it a risk allele. METHODS:Using data in the NHGRI-EBI Catalog and the VARIMED database, we investigated whether (1) GWASs more easily detect risk alleles and (2) facilitate evolutionary insights by comparing risk allele frequencies of different diseases. We conducted computer simulations of P-values for association tests when major and minor alleles were risk alleles. We compared the expected proportion of SNVs whose risk alleles were minor alleles with the observed proportion. RESULTS:Our statistical results revealed that risk alleles were enriched in minor alleles, especially for variants with low minor allele frequencies (MAFs <?0.1). Our computer simulations revealed that >?50% risk alleles were minor alleles because of the larger difference in the power of GWASs to differentiate between minor and major alleles, especially with low MAFs or when the number of controls exceeds the number of cases. However, the observed ratios between minor and major alleles in low MAFs (<?0.1) were much larger than the expected ratios of GWAS's power imbalance, especially for diseases whose average risk allele frequencies were low, such as myopia, sudden cardiac arrest, and systemic lupus erythematosus. CONCLUSIONS:Minor alleles are more likely to be risk alleles in the published GWASs on complex diseases. One reason is that minor alleles are more easily detected as risk alleles in GWASs. Even when correcting for the GWAS's power imbalance, minor alleles are more likely to be risk alleles, especially in some diseases whose average risk allele frequencies are low. These analyses serve as a starting point for future studies on quantifying the degree of negative natural selection in various complex diseases.

Project description:Numerical categories such as parity, i.e., being odd or even, have frequently been shown to influence how particular numbers are processed. Mathematically, number parity is defined categorically. So far, cognitive, and psychological accounts have followed the mathematical definition and defined parity as a categorical psychological representation as well. In this manuscript, we wish to test the alternative account that cognitively, parity is represented in a more gradual manner such that some numbers are represented as "more odd" or "more even" than other odd or even numbers, respectively. Specifically, parity processing might be influenced by more specific properties such as whether a number is a prime, a square number, a power of 2, part of a multiplication table, divisible by 4 or by 5, and many others. We suggest that these properties can influence the psychologically represented parity of a number, making it more or less prototypical for odd- or evenness. In the present study, we tested the influence of these numerical properties in a bimanual parity judgment task with auditorily presented two-digit numbers. Additionally, we further investigated the interaction of these numerical properties with linguistic factors in three language groups (English, German, and Polish). Results show significant effects on reaction times of the congruity of parity status between decade and unit digits, even if numerical magnitude and word frequency are controlled. We also observed other effects of the above specific numerical properties, such as multiplication attributes, which facilitated or interfered with the speed of parity judgment. Based on these effects of specific numerical properties we proposed and elaborated a parity continuum account. However, our cross-lingual study also suggests that parity representation and/or access seem to depend on the linguistic properties of the respective language or education and culture. Overall, the results suggest that the "perceived" parity is not the same as objective parity, and some numbers are more prototypical exemplars of their categories.

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Converting quadratic entropy to diversity: Both animals and alleles are diverse, but some are more diverse than others.

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