Talk:Minimum evolution

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This page is intended to help researchers and practitioners in phylogenetics to familiarize with one of the hardest topics in Computational Phylogenetics. Please help to improve this page, by introducing appropriately

1. Kidd and Sgaramella Zonta's Minimum Evolution Framework (Kidd, K.K., Sgaramella-Zonta, L.A., 1971. Phylogenetic analysis: Concepts and methods. American Journal of Human Genetics 23, 235–252).

2. Rzhetsky and Nei's Theoretical foundations of ME under the ordinary least-squares branch-length estimation model (Rzhetsky, A., Nei, M., 1993. Theoretical foundations of the mini- mum evolution method of phylogenetic inference. Molecular Biol- ogy and Evolution 10, 1073–1095)

3. Pauplin's Balanced Minimum Evolution (Pauplin, Y., 2000. Direct calculation of a tree length using a distance matrix. Journal of Molecular Evolution 51, 41–47).

4. Desper and Gascuel's theoretical foundation of BME (Desper, R., Gascuel, O., 2004. Theoretical foundations of the bal- anced minimum evolution method of phylogenetic inference and its relationship to the weighted least-squares tree fitting. Molecular Bi- ology and Evolution 21, 587–598)

5. Any other advanced in the field.

It is necessary also to connect this page to the one on the least-squares methods as well as on the Neighbor-Joining tree (which is a greedy heuristic for the BME).

Feel free to suggest further lines of improvements.

Content-free

So what's the method? It's not described in the article. Only meta-claims are given. 2001:171B:2274:2491:9847:3879:76DE:410E (talk) 09:46, 30 March 2021 (UTC)

It's a criterion with no concrete algorithm attached. The closest you've got is Minimum_evolution#Algorithmic_aspects. Artoria2e5 🌉 02:36, 18 November 2024 (UTC)

BME actually represents the convergence of the whole distance-based methods framework. It is a pity that this page is not further developed. ~2026-26607-50 (talk) 20:22, 2 May 2026 (UTC)

Substantive errors and misattributed citations

This article contains several substantive errors (not just typos), plus some misattributed citations. Listing them by severity so they can be discussed and fixed individually. Sources for the corrections are given where relevant.

Mathematical / conceptual errors

1. The FastME NNI formula is incorrect. The article gives $\Delta L=\delta _{AC}+\delta _{BD}-\delta _{AD}-\delta _{BC}$. Swapping subtrees B and C compares the current topology (A,B | C,D) with (A,C | B,D), so the length change must involve the current "parallel" pairs $\delta _{AB}$ and $\delta _{CD}$. Computing directly from Pauplin's weights gives $\Delta L={\tfrac {1}{4}}{\big [}(\delta _{AC}+\delta _{BD})-(\delta _{AB}+\delta _{CD}){\big ]}$. As written, the formula both omits the 1/4 factor and subtracts $\delta _{AD},\delta _{BC}$, which belong to the other resolution, not the starting topology. See Desper & Gascuel (2002).

1. The Maximum Likelihood time complexity is wrong. The comparison table lists ML as "O(N), this improves with larger datasets." Finding the ML tree is NP-hard (Roch 2006). Felsenstein's pruning evaluates a fixed tree in O(nm) (linear in taxa, per site), but the topology search is super-exponential. "Improves with larger datasets" is incorrect, and it contradicts the article's own Disadvantages section, which lists ML as the most computationally demanding method.

1. The Neighbor Joining description in the table is wrong. "Iteratively joins the shortest branch lengths" is incorrect. NJ joins the pair minimising the Q-criterion $Q_{ij}=(n-2)\,d_{ij}-\sum _{k}d_{ik}-\sum _{k}d_{jk}$, i.e. a rate-corrected distance, not simply the closest pair. This is precisely what distinguishes NJ from naive clustering / UPGMA. See Saitou & Nei (1987), Studier & Keppler (1988).

1. Maximum parsimony is mischaracterised. The text states it "uses Hamming distance branch lengths, was shown to be statistically inconsistent in 1978." Maximum parsimony is a character-based method that minimises the number of state changes; it does not fit branch lengths from Hamming distances. The 1978 date is correct (Felsenstein, "Cases in which parsimony or compatibility methods will be positively misleading"), but the distance/Hamming framing is not.

Misattributed or incorrect citations

1. The footnote for "Rzhetsky and Nei (1992)" actually points to Gascuel (1994), "A note on Sattath and Tversky's, Saitou and Nei's, and Studier and Keppler's algorithms…", a different work.

1. The DOI given for Kidd & Sgaramella-Zonta (1971) is 10.1126/science.155.3760.279, which is a Science DOI, not the American Journal of Human Genetics article.

1. The APX-hardness claim is not supported by its citation. The statement that BMEP is APX-hard, and "even harder to approximate," is sourced to Fiorini & Joret (2012) — but that work provides a polynomial-time approximation algorithm with proven guarantees (a positive result). Whether BMEP is actually established as APX-hard, and by which source, should be verified; the complexity of BMEP is treated by Kordi & Bansal (2015), already cited in this article.

1. The Denis & Gascuel consistency claim is overstated. "the Minimum Evolution principle is not consistent in WLS and GLS" is too categorical and conflicts with the (correct) statement elsewhere that BME is a WLS scheme and is consistent. Consistency depends on the variance structure / EDGE_LENGTHS property; BME is the balanced case that satisfies it. This should be qualified.

Minor issues

1. Several smaller points: "Looks for the most probable function" (ML) should read tree/hypothesis; "Saito and Nei" → "Saitou and Nei"; Edwards & Cavalli-Sforza (1964) is cited via a 1996 retrospective; "O(N³), can be improved using heuristics" for NJ is imprecise (improvements come from data structures and relaxed formulations, not heuristics); and NJ's statistical consistency is conflated with robustness to noise — the precise result is Atteson's theorem (1999): NJ recovers the true tree when the L∞ distance to a tree metric is below half the shortest internal edge.

~2026-34190-92 (talk) 11:06, 10 June 2026 (UTC)