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Phylogeny01:23

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Phylogeny is concerned with the evolutionary diversification of organisms or groups of organisms. A group of organisms with a name is called a taxon (singular). Taxa (plural) can span different levels of the evolutionary hierarchy. For instance, the group containing all birds is a taxon (comprising the class Aves), and the group of all species of daisies (the genus Bellis) is a taxon. Phylogenies can likewise include just one genus (i.e., depict species relationships) or span an entire kingdom.
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The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
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The rate of reaction is the change in the amount of a reactant or product per unit time. Reaction rates are therefore determined by measuring the time dependence of some property that can be related to reactant or product amounts. Rates of reactions that consume or produce gaseous substances, for example, are conveniently determined by measuring changes in volume or pressure.
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Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
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Related Rates01:18

Related Rates

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When two or more physical quantities are linked by a single relationship, a change in one variable necessarily affects the others. This interdependence forms the basis of related rates analysis, which examines how different quantities change with respect to time. A classic physical example is an expanding balloon, where the size of the balloon changes continuously as air is added.For a hot air balloon, the inflated envelope is commonly idealized as a perfect sphere to simplify mathematical...
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Speciation Rates01:07

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Updated: Feb 2, 2026

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding
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Phylogenies and Diversification Rates: Variance Cannot Be Ignored.

Daniel L Rabosky1

  • 1Museum of Zoology and Department of Ecology and Evolutionary Biology, Biological Sciences Building, 1105 North University Avenue, University of Michigan, Ann Arbor, MI 48109, USA.

Systematic Biology
|November 28, 2018
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Summary
This summary is machine-generated.

A new test for macroevolutionary models is flawed because it ignores sampling variation. Differences in evolutionary rate estimates are expected due to clade size, not model error. Biologists should account for variance in phylogenetic analyses.

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Area of Science:

  • Evolutionary Biology
  • Phylogenetics
  • Macroevolutionary Modeling

Background:

  • Hierarchical macroevolutionary models are used to study evolutionary rates.
  • A recent test in Evolution journal claims to assess model validity by comparing rate estimates at different phylogenetic levels.
  • This test was applied to BAMM software, which estimates evolutionary rates from phylogenetic trees.

Purpose of the Study:

  • To demonstrate that a proposed test for hierarchical macroevolutionary models is invalid.
  • To show that observed differences in rate estimates are due to sampling variation, not model flaws.
  • To highlight statistical and mathematical errors in the proposed testing framework.

Main Methods:

  • Analysis of rate estimates from BAMM software applied to phylogenies of varying sizes.
  • Statistical assessment of the impact of sampling variation on rate estimates.
  • Mathematical critique of the proposed testing framework's first principles.

Main Results:

  • Numerical differences in rate estimates between large clades and subclades are fully explained by sampling variation.
  • Variance in evolutionary rate estimates is inversely proportional to clade size, especially for small clades.
  • The proposed test relies on negative results stemming from low statistical power due to high variance.

Conclusions:

  • The proposed test for hierarchical macroevolutionary models is invalid due to a failure to account for sampling variation.
  • Differences in rate estimates do not necessarily indicate a flawed model, but can arise from statistical properties of small sample sizes.
  • Biologists should incorporate standard statistical practices, particularly accounting for variance, when estimating evolutionary parameters.