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How many more? Sample size determination in studies of morphological integration and evolvability

Grabowski, M and Porto, A (2016) How many more? Sample size determination in studies of morphological integration and evolvability. Methods in Ecology and Evolution, 8 (5). pp. 592-603. ISSN 2041-210X

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Abstract

1. The variational properties of living organisms are an important component of current evolutionary theory. As a consequence, researchers working on the field of multivariate evolution have increasingly used integration and evolvability statistics as a way of capturing the potentially complex patterns of trait association and their effects over evolutionary trajectories. Little attention has been paid, however, to the cascading effects that inaccurate estimates of trait covariance have on these widely used evolutionary statistics.
2. Here, we analyse the relationship between sampling effort and inaccuracy in evolvability and integration statistics calculated from 10‐trait matrices with varying patterns of covariation and magnitudes of integration. We then extrapolate our initial approach to different numbers of traits and different magnitudes of integration and estimate general equations relating the inaccuracy of the statistics of interest to sampling effort. We validate our equations using a data set of cranial traits and use them to make sample size recommendations.
3. Our results suggest that highly inaccurate estimates of evolvability and integration statistics resulting from small sample sizes are likely common in the literature, given the sampling effort necessary to properly estimate them. We also show that patterns of covariation have no effect on the sampling properties of these statistics, but overall magnitudes of integration interact with sample size and lead to varying degrees of bias, imprecision and inaccuracy.
4. Finally, we provide r functions that can be used to calculate recommended sample sizes or to simply estimate the level of inaccuracy that should be expected in these statistics, given a sampling design.

Item Type: Article
Additional Information: This is the peer reviewed version of the following article: Grabowski, M. and Porto, A. (2017), How many more? Sample size determination in studies of morphological integration and evolvability. Methods Ecol Evol, 8: 592-603. https://doi.org/10.1111/2041-210X.12674, which has been published in final form at https://dx.doi.org/10.1111/2041-210X.12674. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
Uncontrolled Keywords: 0502 Environmental Science and Management, 0602 Ecology, 0603 Evolutionary Biology
Subjects: G Geography. Anthropology. Recreation > GF Human ecology. Anthropogeography
Q Science > QH Natural history > QH301 Biology
Q Science > QM Human anatomy
Divisions: Biological & Environmental Sciences (new Sep 19)
Publisher: Wiley
Related URLs:
Date Deposited: 03 Feb 2021 11:50
Last Modified: 03 Feb 2021 12:00
DOI or Identification number: 10.1111/2041-210X.12674
URI: https://researchonline.ljmu.ac.uk/id/eprint/14394

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