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Correlation between Shapley values of rooted phylogenetic trees under the beta-splitting model
Michael Fuchs1, Ariel R Paningbatan2
1Department of Mathematical Sciences, National Chengchi University, Taipei, 116, Taiwan. mfuchs@nccu.edu.tw.
Journal of Mathematical Biology
|October 2, 2019
Summary
This study proves that the unrooted Shapley value strongly correlates with the fair proportion index in random phylogenetic trees. This theoretical result supports using these methods for ranking biodiversity data preservation.
Area of Science:
- Phylogenetics
- Biodiversity Informatics
- Computational Biology
Background:
- Shapley value variations are used to rank biodiversity data for conservation decisions.
- The rooted and unrooted Shapley values have been compared to the computationally simpler fair proportion index.
- Previous work showed the rooted Shapley value equals the fair proportion index and the unrooted Shapley value is strongly correlated.
Purpose of the Study:
- To provide a theoretical proof for the strong correlation between the unrooted Shapley value and the fair proportion index.
- To analyze the behavior of this correlation in random phylogenetic trees under the [Formula: see text]-splitting model.
Main Methods:
- Theoretical proof using mathematical derivations.
- Analysis of random phylogenetic trees generated by the [Formula: see text]-splitting model.
- Calculation of correlation coefficients.
Main Results:
- The correlation coefficient between the unrooted Shapley value and the fair proportion index tends to one for all [Formula: see text] with [Formula: see text] in the [Formula: see text]-splitting model.
- Data suggests the convergence rate of this correlation degrades as [Formula: see text] approaches [Formula: see text].
Conclusions:
- The theoretical findings strongly support the observed high correlation between the unrooted Shapley value and the fair proportion index.
- This validates the use of the fair proportion index as an efficient proxy for the unrooted Shapley value in phylogenetic biodiversity ranking.
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