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Lower Bounds on the Sample Complexity of Species Tree Estimation when Substitution Rates Vary Across Loci

biorxiv(2025)

University of Hawaii at Manoa

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Abstract
In this paper we analyze the effect of substitution rate heterogenity on the sample complexity of species tree estimation. We consider a model based on the multi-species coalescent (MSC), with the addition that gene trees exhibit random i.i.d. rates of substitution. Our first result is a lower bound on the number of loci needed to distinguish 2-leaf trees (i.e., pairwise distances) with high probability, when substitution rates satisfy a growth condition. In particular, we show that to distinguish two distances differing by length f with high probability, one requires O(f-2) loci, a significantly higher bound than the constant rate case. The second main result is a lower bound on the amount of data needed to reconstruct a 3-leaf species tree with high probability, when mutation rates are gamma distributed. In this case as well, we show that the number of gene trees must grow as O(f-2) . ### Competing Interest Statement The authors have declared no competing interest.
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