Statistical Genomics Foundry
Paper
domain/gene-family-evolution

Han et al. 2013 — Estimating gene gain/loss rates in the presence of error using CAFE 3

1. Citation

Han MV, Thomas GWC, Lugo-Martinez J, Hahn MW. 2013. “Estimating Gene Gain and Loss Rates in the Presence of Error in Genome Assembly and Annotation Using CAFE 3.” Molecular Biology and Evolution 30(8):1987–1997. DOI 10.1093/molbev/mst100. PubMed 23709260. Article page: https://academic.oup.com/mbe/article/30/8/1987/1017616 Access date: 2026-07-03.

2. Access note (READ — boundary is load-bearing)

  • Not open access. Europe PMC / EBI reports isOpenAccess: "N", no PMCID, hasPDF: "N", and the only full-text link is DOI with availability: "Subscription required". No CC license.
  • Abstract — independently verified verbatim via the open PubMed record (PMID 23709260). Everything in §3 traces to that.
  • Body text (§5, §6, §9, most of §12) — retrieved only through WebFetch’s automated HTML→markdown conversion of the OUP article page, read by a small summarizing model; the raw article text was NOT directly inspected. No independent full-text host was reachable to cross-check (Europe PMC rendered only navigation; no PMC copy exists). Consequences: (a) quote wording is not preserved — §7 is own-words regardless; (b) the numerics below (λ, ε values, corrected/uncorrected estimates, per-clade error rates) carry residual retrieval uncertainty — they are internally consistent across repeated fetches of the same URL, but repeated fetches of one cached page are not independent corroboration. Treat body-text numbers as “reported by the retrieval, not raw-verified.” Re-check against the PDF if this note becomes load-bearing for a threshold.

3. Thesis (from the verified abstract)

Fragmented/incomplete genome assemblies produce annotation errors — especially in gene counts — that mislead gene-family duplication/loss inference and cause rates of gene-family evolution to be consistently overestimated; CAFE 3 models that error explicitly so gain/loss rates can be inferred accurately even from low-quality assemblies/annotations.

4. Problem & context

  • Sequencing yields large data but assemblies are “often fragmented and incomplete” (abstract).
  • Incomplete/error-filled assemblies → many annotation errors, notably in number of genes present.
  • Methods estimating gene duplication/loss are misled by such errors → gene-family evolution rates “consistently overestimated” (abstract). CAFE lineage: birth–death gene-family size modeling; this version (CAFE 3) adds the measurement-error layer.

5. Method / approach

(body-text — see §2 boundary)

  • Measurement-error layer at the tree leaves. The observed gene-family size (W) at a tip is treated as a noisy readout of the unobserved true size (X). The likelihood marginalizes over the true count X at each leaf instead of taking the observed count as truth.
  • Error matrix Θ. The measurement-error model is the set of probabilities P(W = w | X = x), arranged as a matrix Θ whose (i, j) entry is the probability of observing i when the true family size is j.
  • Simplifying assumption on Θ. Error probability depends only on the difference between observed and true count (w − x), not on the absolute/true size — reducing the number of parameters. A maximum offset (±D from truth) further caps parameters.
  • Error parameter ε. ε is the fraction of gene families (per species) whose observed size is miscounted. Retrieval-reported gloss: ε = 0.1 means ~90% of families observed = true, ~10% observed too large or too small, with the miscount being ±1 to ±3 genes per family per species. Error distributions may be symmetric (over- and under-counts equally likely) or asymmetric.
  • Global vs per-species. Both supported: one error distribution shared across all species, OR different (heterogeneous) error distributions specified per species.
  • How error enters the birth–death likelihood. CAFE 3 extends Felsenstein’s pruning algorithm. At internal nodes the conditional likelihood is weighted by birth–death transition probabilities; at leaf nodes the weighting is instead supplied by the error matrix Θ — i.e. sum over plausible true counts X at the tip, each weighted by P(W|X) from Θ, then prune upward as usual. The error layer is a substitution of the leaf-node weighting, not a change to the internal birth–death machinery.
  • How the error rate is ESTIMATED — three routes:
    1. External/known-truth comparison. Compare two versions of a genome (e.g. draft vs. reference); treat the better assembly as truth and compare the lesser to it → maximum-likelihood error matrix.
    2. Two error-prone versions. When no high-quality reference exists, compare two low-quality assemblies; reported as only slightly less accurate than comparison against a good reference.
    3. Grid search from the data alone (no external data). Fix an error model, find birth–death parameters maximizing the (pseudo)likelihood, repeat across a grid of ε values, and choose the error model that maximizes likelihood. Automated by the caferror.py script; the error model is applied in CAFE via the errormodel command/function with a specified error distribution.
  • Simulation/validation design. Simulated on a 12-species Drosophila phylogeny (supp. Fig. S1); family sizes drawn from the distribution of ~11,434 real Drosophila families. True rate λ = μ = 0.0012 (secondary runs at λ = 0.01 and 0.0001). Error levels ε ∈ {0.1, 0.4}, miscounts ±1 to ±3, symmetric and asymmetric variants. Number of replicates per condition: NOT SPECIFIED in retrieved text.

6. Key claims / findings

(body-text — see §2 boundary; abstract-level items marked [abstract])

  • [abstract] Annotation errors “do lead to higher inferred rates of gene gain and loss,” but CAFE 3 “sufficiently accounts for these errors to provide accurate estimates.”
  • Uncorrected error inflates λ; correct error model restores it. With true λ = 0.0012:
    • ε = 0.1, no error model → λ̂ ≈ 0.00280; with the correct error model → λ̂ ≈ 0.00122.
    • ε = 0.4, no error model → λ̂ ≈ 0.00897; with the correct error model → λ̂ ≈ 0.00124. So uncorrected inflation grows with error level: ~2.3× at ε=0.1, ~7.5× at ε=0.4; correction returns estimates to within ~2% of truth.
  • Estimated real-data error rates. ε = 0.0277 (fungi), 0.0732 (mammals), 0.041 (Drosophila) — i.e. ~2.8%, ~7.3%, ~4.1% of families miscounted; reported as correlating with genome features such as repetitive-element content.
  • Two error-prone assemblies can estimate the error matrix “only very slightly less accurately” than a good-vs-poor comparison, so error estimation does not strictly require a high-quality reference.
  • Robustness: using an incorrect error model was also tested to gauge sensitivity (see §9).

7. Load-bearing statements — OWN-WORDS mode (restrictive/unknown license)

License posture: ”© The Author 2013. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution”; no Creative Commons or open license shown; EBI reports subscription required. → Restrictive. No verbatim prose reproduced. Functional strings (symbols, commands, numbers) are facts and kept verbatim.

  • Central claim (paraphrase of the abstract): because incomplete assemblies cause gene-count annotation errors, gene-duplication/loss methods are misled and rates of gene-family evolution are consistently overestimated; CAFE 3’s error model recovers accurate rates. (Operative term preserved: “overestimated.”) Verified against the open PubMed abstract.
  • Error-model definition (paraphrase): the measurement-error model specifies P(W = w | X = x), the probability of observing size w given true size x, arranged as matrix Θ with (i, j) = P(observe i | true is j); error depends on the difference w − x, not on x itself.
  • Likelihood integration (paraphrase): the leaf-node summation differs from the internal-node summation only in that the leaf probabilities come from the error matrix rather than the birth–death transition probabilities.
  • Functional strings (verbatim, license-exempt): symbols W (observed), X (true), Θ (error matrix), ε (error parameter/rate), λ (birth/gain rate), μ (death/loss rate); commands errormodel, script caferror.py; numbers λ=0.0012, λ̂ at ε=0.1 → 0.00280 / corrected 0.00122, λ̂ at ε=0.4 → 0.00897 / corrected 0.00124, ε = 0.0277 / 0.0732 / 0.041; miscount magnitude ±1 to ±3.

8. Stated scope, assumptions, limitations

(body-text — see §2 boundary)

  • Gene-family sizes in a genome assumed independent and identically distributed across families.
  • Error rate assumed to depend only on the difference (w − x), not on the true count x.
  • Error distribution assumed stationary — same across families and across phylogenetic time.
  • Errors modeled as symmetric or asymmetric offsets, capped at ±D from truth to limit parameters.
  • The error matrix is unknown a priori and must be estimated as extra parameters.

9. Failure modes / invalidity patterns

  • Ignoring error → systematic overestimation of gain/loss rates (the paper’s core warning); the inflation scales with the true error level (~2.3× at ε=0.1, ~7.5× at ε=0.4 in simulation).
  • Too many free error parameters → non-convergence. Estimating the error matrix from external data with more than four parameters was reported to fail to converge — a practical detector/limit on error-model complexity.
  • Wrong error model (mis-specified ε/distribution) was tested; using an incorrect error model when inferring rates degrades accuracy relative to the correct model (magnitude of degradation: NOT captured precisely in retrieved text).
  • Assumption violations that would invalidate correction: error that depends on true family size, non-stationary error across lineages/time, or correlated (non-i.i.d.) family sizes — all excluded by the stated assumptions, so real data breaking them is an unmodeled-error risk. [summarizer-inferred that these are the invalidation triggers; the paper states the assumptions but the retrieved text does not enumerate them as failure conditions.]

10. What the source does NOT address (from what was retrievable)

  • The abstract cites “several other novel features” of CAFE 3 but the retrieved text did not enumerate them; whether separate λ/μ, per-family p-values / significance, Viterbi reconstruction, or special handling of large/fast families are framed as new here is NOT established from what was read. (Do not backfill from CAFE5/CAFE manuals.)
  • Number of simulation replicates per condition not stated in retrieved text.
  • No explicit numeric threshold “ε above which correction is mandatory” was found (see §12).

11. Open questions / ambiguities

  • Exact minimum ε at which uncorrected inflation becomes practically material — the paper shows inflation at ε=0.1 and 0.4 but (in retrieved text) sets no cutoff.
  • Precise accuracy penalty of a mis-specified error model (only qualitatively established).
  • Whether “several other novel features” materially change outputs vs. the parent CAFE (De Bie 2006).

12. Guidance answers

  • Central overestimation claim + magnitude: YES. Abstract (verified): errors “do lead to higher inferred rates of gene gain and loss,” rates “consistently overestimated.” Magnitude (body, retrieval-dependent): true λ=0.0012 inflates to ~0.00280 at ε=0.1 and ~0.00897 at ε=0.4 without correction (~2.3× and ~7.5×); correction restores ~0.00122 / ~0.00124.
  • Error model — what ε represents: ε = fraction of gene families per species whose observed size is miscounted (miscount ±1 to ±3 genes); formally the model is the matrix Θ of P(observe w | true x), depending only on w − x. Symbol: ε (rate) / Θ (matrix).
  • Global vs per-species: BOTH — a single shared error distribution, or heterogeneous per-species distributions.
  • How ε is estimated: three routes — (1) compare draft vs. reference genome (better = truth), ML-estimate the matrix; (2) compare two low-quality assemblies (only slightly less accurate); (3) no external data → grid search over ε maximizing the (pseudo)likelihood, automated by caferror.py, applied via the errormodel command.
  • How error enters the likelihood: Felsenstein pruning with leaf-node weighting replaced by the error matrix Θ — marginalize over true count X at each tip, weighting by P(W|X), then prune upward; internal nodes still use birth–death transition probabilities.
  • What CAFE 3 adds beyond the error model: abstract says “several other novel features” but the retrieved text did not enumerate them; separate λ/μ mentioned as possible but not clearly flagged as new-in-v3 in what was read. NOT fully answered — access boundary (§2).
  • Validation design/numbers: 12-species Drosophila tree; families from ~11,434 real families; true λ=μ=0.0012 (also 0.01, 0.0001); ε∈{0.1,0.4}, ±1–3, symmetric/asymmetric; corrected estimates recover truth (see §6). Replicate count NOT specified.
  • Threshold for when correction is needed: the paper gives NO explicit ε cutoff in retrieved text; it demonstrates material inflation already at ε=0.1. Report as: no stated threshold.
  • Own caveats/limitations: i.i.d. families; error depends on w−x not x; stationary error; matrix must be estimated; >4 external-data parameters did not converge (§8, §9).
  • Must-quote items: under restrictive license, rendered as own-words paraphrases in §7 (the overestimation sentence and the error-model definition), with the operative term “overestimated” and functional symbols preserved verbatim.