FakeProt

A stochastic simulator for synthetic protein families.

FakeProt is a stochastic simulator for generating synthetic protein families with known evolutionary histories. It produces multiple-sequence alignments, a gene tree, a species cladogram, ortholog-group assignments, ancestral sequences, and per-column physicochemical annotations. The intended use is methodological benchmarking: aligners, tree inference procedures, orthology pipelines, ancestral-sequence methods, and downstream comparative-genomics workflows can be tested against data for which the generating history is known.

Overview

Simulation studies in molecular evolution often require sequence families whose ground truth is explicit: the species tree, gene tree, duplication history, ortholog groups, ancestral states, and column-wise constraints should all be recoverable. FakeProt implements a discrete, event-driven generator for protein families. Starting from a single ancestral protein, the simulator repeatedly selects an extant species, optionally creates a paralog by gene duplication (Ohno, 1970), and then speciates the selected lineage into two daughter species. Sequence evolution along every gene-tree edge combines WAG-derived amino-acid substitution probabilities (Whelan & Goldman, 2001), gamma-distributed site-rate heterogeneity (Yang, 1994), a TKF92-compatible fragment indel model (Thorne, Kishino & Felsenstein, 1992), and probabilistic physicochemical constraints based on overlapping amino-acid property classes (Taylor, 1986). Insertions are represented as new alignment columns, while deletions are represented as gaps, so every emitted sequence remains in a common alignment.

FakeProt is not intended to be a fully calibrated biological model of protein evolution. Its substitution and indel components follow continuous-time formulations (WAG CTMC, TKF92), but the physicochemical constraint scheme and rate parameters are not estimated from empirical data. It is a transparent benchmark generator whose parameters control sequence-family size, root length, indel frequency, site-rate heterogeneity, and the target number of ortholog groups.

Installation

FakeProt requires Python 3.10 or later.

pip install .

For development:

pip install -e ".[dev]"

Quick Start

# 50 extant sequences, root length 200, three ortholog groups, fixed seed
fakeprot 50 200 -n 3 -r 42 -o my_family

The command above writes a set of FASTA, tree, CSV, and JSON files using my_family as the filename prefix.

Command-Line Interface

fakeprot SIZE LENGTH [options]

Argument	Meaning
SIZE	Minimum number of extant, leaf-level sequences to generate. The final number can exceed this value because one simulation step may add multiple leaves.
LENGTH	Root sequence length before lineage-specific insertions.

Option	Default	Meaning
-o, --out	fakeprot_out	Prefix for all output files.
-d, --mu	0.05	TKF91/92 deletion rate $\mu$ per unit branch length; per-edge intensity $\mu \cdot t$.
-i, --lam	0.001	TKF91/92 insertion rate $\lambda$ per unit branch length; per-edge intensity $\lambda \cdot t$.
--q	0.5	TKF92 fragment extension probability $q$; geometric run-length parameter. Mean run length $= 1/(1-q)$.
-n, --n-orthologs	1	Target number of ortholog-group anchors.
-a, --alpha	0.75	Shape parameter $\alpha$ for the gamma site-rate model. Scale is fixed to $1/\alpha$ so that the mean rate equals 1, following the standard convention introduced by Yang (1994).
-b, --branch-length	0.05	Expected substitutions per site on a branch of average rate. Controls overall sequence divergence; also scales the per-edge intensities $\mu \cdot t$ and $\lambda \cdot t$.
--dup-boost-factor	2.0	Branch-length multiplier applied to a boosted duplicate edge.
--dup-boost-decay	3.0	E-folding distance in speciation steps for the post-duplication rate burst. Set to 0 for a single-edge burst only.
--branch-cv	0.4	Coefficient of variation for per-branch stochastic rate noise (σ_log ≈ 0.39). Each speciation edge draws its length from a mean-preserving log-normal; 0 gives deterministic (equal-length) branches. Default chosen as the centre of the empirical range reported by Drummond et al. (2006).
-r, --seed	None	Random seed for reproducible simulations.
-f, --msa-format	fasta	Alignment format: fasta, clustal, nexus, phylip, or stockholm.
-t, --tree-format	newick	Tree format: newick, nexus, nexml, phyloxml, or cdao.

Generative Model

Notation

Let $A$ be the set of 20 canonical amino acids and let $\pi_a$ be the WAG equilibrium frequency of amino acid $a \in A$, and $s_{ab}$ the symmetric WAG exchangeability between $a$ and $b$ (Whelan & Goldman, 2001; values from PAML dat/wag.dat). The WAG rate matrix has off-diagonal entries $Q_{ab} = s_{ab},\pi_b$ ($a \neq b$), with diagonal set so rows sum to zero. FakeProt normalises these off-diagonal rates to obtain the row-stochastic Gillespie jump chain $W$:

$$W_{ab} = \frac{Q_{ab}}{\displaystyle\sum_{k \neq a} Q_{ak}} = \frac{s_{ab}\,\pi_b}{\displaystyle\sum_{k \neq a} s_{ak}\,\pi_k}, \qquad a \neq b,$$

where $W_{ab}$ is the conditional probability of proposing residue $b$ given that residue $a$ undergoes a change. The diagonal is zero by construction.

Let $C$ be the set of physicochemical classes used by the simulator. Each class $c \in C$ corresponds to a subset $A_c \subset A$; classes are allowed to overlap, following the Venn-diagram classification of amino-acid properties introduced by Taylor (1986). The class prior is proportional to the WAG background mass of its member residues:

$$\omega_c = \frac{\sum_{a \in A_c} \pi_a} {\sum_{d \in C} \sum_{a \in A_d} \pi_a}.$$

The conditional amino-acid distribution inside class $c$ is

$$P(X=a \mid c) = \frac{\pi_a 1[a \in A_c]}{\sum_{b \in A_c} \pi_b}.$$

Site-Rate Heterogeneity

Given root length $L$, FakeProt assigns a site-specific relative rate $r_i$ to every alignment site. The first site is fixed at $r_1 = 0$ to preserve the initial methionine. For the remaining $L - 1$ sites, rates are drawn independently from

$$r_{i} \;\sim\; \Gamma\!\left(\alpha,\,\frac{1}{\alpha}\right), \qquad i = 2,\ldots,L,$$

so the mean rate equals 1, following the standard phylogenetic convention (Yang, 1994). These rate values are then reordered by a local smoothing procedure (wave_shuffle). Each rate $r_i$ is first mapped to a normalised substitution probability

$$\hat{p}_i = \frac{1 - \exp(-t\,r_i)}{\max_j\bigl(1 - \exp(-t\,r_j)\bigr)},$$

so that all keys lie in $[0, 1]$ regardless of $t$. Starting from a random site, each next site is chosen from the remaining values with probability proportional to

$$\max\bigl(0,\; 1 - |\hat{p}_{\mathrm{previous}} - \hat{p}_{\mathrm{candidate}}|\bigr).$$

The original gamma-derived rates are returned in the order determined by this traversal, so the marginal rate distribution is unchanged. Using normalised substitution probabilities as sort keys ensures the kernel has full dynamic range for any $t$ and places comparisons in a scale where differences correspond directly to differences in evolutionary variability — encouraging neighboring sites to have similar mutability, an autocorrelation-along-sequence pattern motivated by hidden Markov models of rate variation (Felsenstein & Churchill, 1996; see also Yang, 1995).

Root Sequence

The ancestral sequence begins with methionine:

$$X_1 = \mathrm{M}, \qquad c_1 = \text{With sulfur}, \qquad r_1 = 0.$$

For every other site $i$, FakeProt first decides whether the site has a physicochemical constraint using the same functional form as the substitution survival probability (see below), with $t$ acting as a tuning parameter for the proportion of constrained sites rather than as an actual edge length:

$$P(c_i \neq \varnothing) = \exp(-t\,r_i), \qquad P(c_i = \varnothing) = 1 - \exp(-t\,r_i).$$

If constrained, the class is drawn from $\text{Categorical}(\omega)$ and the amino acid is drawn from the class-conditional WAG background distribution (using the overlapping class scheme of Taylor, 1986). If unconstrained, the amino acid is drawn directly from the WAG background frequencies $\pi$.

Substitution Model Along an Edge

For each child sequence, FakeProt iterates through the parent sequence from left to right. At a non-gap site with parent residue $x_i$, site rate $r_i$, and constraint $c_i$, deletion is considered first:

$$P(\mathrm{delete}\ i) = 1 - \exp(-r_i\,\mu\,t),$$

where $\mu$ is --mu and $t$ is the per-edge branch length. This is the exact CTMC survival complement, consistent with the substitution formula below, and bounded in $[0, 1]$ for all $r_i$.

If the site is not deleted, the substitution probability is derived from the standard continuous-time Markov chain survival formula for a branch of length $t$ at site rate $r_i$:

$$P(\text{substitution at site } i) = 1 - \exp(-t\,r_i).$$

If there is no physicochemical constraint, the new residue is sampled using the WAG conditional substitution matrix $W$ (Whelan & Goldman, 2001):

$$P(X_i' = x_i) = \exp(-t\,r_i),$$ $$P(X_i' = a) = \bigl(1 - \exp(-t\,r_i)\bigr)\,W_{x_i a}, \qquad a \neq x_i.$$

If the site is constrained to physicochemical class $c_i$, the substitution proposal is restricted to residues in $A_{c_i}$. Let

$$T_{x_i,c_i} = \sum_{a \in A_{c_i}} W_{x_i a}.$$

(Since $W$ has zero diagonal entries, the sum implicitly excludes self-substitution even when $x_i \in A_{c_i}$.)

When $T_{x_i,c_i} > 0$, the constrained substitution distribution is

$$P(X_i' = x_i) = \exp(-t\,r_i),$$ $$P(X_i' = a) = \bigl(1 - \exp(-t\,r_i)\bigr)\,\frac{W_{x_i a}}{T_{x_i,c_i}}, \qquad a \in A_{c_i}.$$

If $T_{x_i,c_i} = 0$, the residue is retained. In all cases, gaps are treated as alignment characters and are carried forward unless explicitly filled by the gap process below.

Insertions, Deletions, and Gap Filling

Gaps in the final alignment arise from two distinct processes with separate per-branch Poisson intensities $\mu,t$ (deletion) and $\lambda,t$ (insertion), where $\mu$ (--mu) and $\lambda$ (--lam) are the TKF91/92 rate parameters.

Deletions accumulate along each lineage's path from the root. For a Yule (pure-birth) tree with $n$ leaves (Yule, 1925; Aldous, 2001) the expected leaf depth is $2(H_n - 1) \approx 2\ln n$, giving expected deletion gap fraction

$$f_d \;\approx\; \mu\,t\cdot 2\ln n.$$

Insertions in any one lineage create a new alignment column that appears as a gap in all other $n-1$ sequences. Each insertion event therefore has an $n$-fold amplifying effect on total gap cells. The expected insertion gap fraction is

$$f_i \;\approx\; \frac{4n\,\lambda\,t}{1 + 4n\,\lambda\,t}.$$

These formulas simplify to the above form because the gamma rates $r_i$ have mean 1 by construction (scale fixed to $1/\alpha$), so averaging over sites contributes a factor of 1.

The likelihood that a gappy column with $k$ gaps was caused by a deletion versus an insertion can be assessed via the subtree-size distribution of a Yule tree, which is approximately $P(\text{size}=s) \propto 1/s$ (Aldous, 2001):

$$\frac{P(\text{deletion} \mid k)}{P(\text{insertion} \mid k)} = \frac{\mu}{\lambda} \cdot \frac{n - k}{k}.$$

Columns with few gaps ($k \ll n/2$) are predominantly deletions; columns with many gaps ($k \gg n/2$) are predominantly insertions. The crossover is at $k = n,\mu/(\mu + \lambda)$.

The defaults are design choices tuned to produce realistic scaling behaviour rather than values read directly from any single empirical study:

$$\mu = 0.05, \qquad \lambda = 0.001, \qquad q = 0.5,$$

giving per-edge intensities $\mu,t$ and $\lambda,t$ at branch length $t$ (default 0.05). The deletion coefficient (5% of branch length) and insertion coefficient (0.1%) are not equal because each insertion in a single lineage creates a gap in every other sequence, amplifying its effect on total gap content by a factor of approximately $n$. As a result, gap content grows naturally with the number of sequences: deletion gaps accumulate as $O(\log n)$ (from tree depth) and insertion gaps as $O(n)$ (from the alignment-wide amplification). This matches the empirical observation, well known to practitioners working with large protein-family databases such as Pfam (Finn et al., 2006; Mistry et al., 2021), that larger and more diverged families are substantially gappier.

After each non-gap site — whether the site survives or is deleted — FakeProt may introduce an insertion fragment using the TKF92 birth/death model (Thorne, Kishino & Felsenstein, 1992). This is a fragment generalisation of TKF91 (Thorne, Kishino & Felsenstein, 1991) in which insertions arrive as geometric-length runs rather than single residues.

Let $\mu_i = r_i,\mu,t$ be the per-site death intensity and $r_{f,i} = r_i,\lambda,t,(1-q)$ the per-site fragment birth intensity, where $q$ (--q, default 0.5) is the fragment extension probability. The TKF92 probability that at least one fragment is inserted after site $i$ is

$$\beta_i = \frac{r_{f,i}\bigl(1 - \exp(-(\mu_i - r_{f,i}))\bigr)} {\mu_i - r_{f,i}\exp(-(\mu_i - r_{f,i}))},$$

with the limit $\beta_i = r_{f,i}/(1 + r_{f,i})$ when $\mu_i = r_{f,i}$. The process is subcritical (sequences do not grow without bound) whenever $r_{f,i} < \mu_i$, i.e. $\lambda,(1-q) < \mu$, which holds under all reasonable defaults. Given that a fragment starts, each additional residue is appended with probability $q$:

$$P(\text{extend by one more} \mid \text{already inserting}) = q.$$

This gives a geometrically distributed run length with mean $1/(1-q) = 2$. Crucially, the expected total residues inserted after a rate-1 site is $\beta \cdot 1/(1-q) \approx \lambda,t$, so --lam directly controls the per-unit-rate residue insertion intensity regardless of $q$.

Deletions do not suppress fragment birth: a deleted position can still birth a fragment (a "ghost lineage" in TKF terminology), consistent with the continuous-time formulation.

A geometric run-length distribution is a tractable approximation to the Zipfian (power-law) distribution empirically observed in real protein alignments, where the probability of a gap of length $L$ decreases approximately as $L^{-1.7}$ (Benner, Cohen & Gonnet, 1993; Chang & Benner, 2004).

Inserted residues are sampled from the WAG background distribution, assigned rate $1.0$, and assigned no physicochemical class. When an insertion creates a new alignment site, FakeProt inserts a gap in every previously generated row so that all sequences remain aligned.

Existing gap runs can also be filled in descendant lineages. The first position in a gap run is filled with the TKF92 probability $\beta_i$ (same formula as above, using the gap slot's own rate $r_i$); each subsequent position is filled with probability $q$, independently. Filling stops after the first failed attempt. Filled residues are sampled either from the WAG background distribution or, when the site has a physicochemical class, from the corresponding class-conditional distribution.

Species, Gene Trees, and Orthology

FakeProt maintains two directed graphs during simulation: a species tree and a sequence/gene tree. The species tree contains extant and ancestral species nodes. The gene tree contains ancestral, duplicated, and extant sequence nodes. The orthology and paralogy terminology used throughout follows the definitions introduced by Fitch (1970) and the modern formulation reviewed by Koonin (2005): orthologs descend from a common ancestor via speciation, while paralogs descend via gene duplication.

At each simulation step:

1. One extant species is selected uniformly at random.
2. A gene duplication may occur inside that species.
3. The selected species is split into two daughter species.
4. Each paralog in the selected species independently evolves into one child sequence in each daughter species.

The process stops when the number of extant sequence leaves is at least SIZE.

Gene Duplication

Let $K$ be the requested number of ortholog groups, $m$ the current number of ortholog anchors, and $s$ the number of extant species. If $m < K$, duplication is attempted with probability

$$P(\mathrm{duplication}) = 2^{-(K-m)/s}.$$

When a duplication occurs, one paralog in the selected species is copied and mutated. The new copy becomes an ortholog-group anchor. Its rate profile is redrawn using a perturbed shape parameter

$$\alpha' \sim N(\alpha, 1) \mid \alpha' \geq 1,$$

with scale fixed to $1/\alpha'$ as usual (Yang, 1994). The rank order of the parent rates is preserved: sites that were slow or fast in the parent remain relatively slow or fast in the duplicate, but the numerical rate scale may shift.

For duplicated sequences, physicochemical constraints may also be relaxed or changed. Let $t_e$ denote the branch length of the creation edge — equal to $t$ × dup_boost_factor for a boosted duplication, and $t$ otherwise. Let $r_i'$ be the duplicate's redrawn site rate at position $i$. If a parent site has class $c$, the duplicate first retains any constraint with probability $\exp(-t_e,r_i')$. Conditional on retaining a constraint, the class is preserved with probability $\exp(-t_e,r_i')$ or changed according to a class-level transition matrix $M$ derived by averaging WAG probabilities between the residues in each pair of physicochemical classes:

$$P(c_i' = c \mid c_i' \neq \varnothing, c_i=c) = \exp(-t_e\,r_i'),$$ $$P(c_i' = d \mid c_i' \neq \varnothing, c_i=c) = \bigl(1 - \exp(-t_e\,r_i')\bigr)\,M_{cd}, \qquad d \neq c.$$

If the retained or newly chosen class does not contain the current residue, FakeProt resamples the residue using the WAG probabilities restricted to the new class. Sites with no parent constraint ($c_i = \varnothing$) may also acquire a new class during duplication, sampled from the background prior $\text{Categorical}(\omega)$ with the same probability $\exp(-t_e,r_i')$; if the current residue is not a member of the newly assigned class, it is likewise resampled.

Each duplication modulates the new copy's divergence rate. The duplicate's creation edge and its downstream lineage carry an elevated branch-length multiplier that decays exponentially with each subsequent speciation event:

$$m(d) = 1 + (\texttt{dup\_boost\_factor} - 1) \exp\!\Bigl(-\tfrac{d}{\texttt{dup\_boost\_decay}}\Bigr),$$

where $d$ is the number of speciation steps separating the edge from the duplication node. At $d = 0$ (the duplicate's creation edge) the multiplier equals dup_boost_factor (default 2.0). At $d =$ dup_boost_decay (default 3.0) it has decayed by $1/e$. Setting --dup-boost-decay 0 restricts the boost to the duplicate's creation edge only. This models the transient rate asymmetry between paralogs observed in the period immediately following duplication (Ohno, 1970; Conant & Wagner, 2003; Lynch & Conery, 2000; Kellis et al., 2004). The boost is directly visible in the output gene tree: edges in the duplicate's subtree carry their elevated generative branch length, decaying toward the global rate with each subsequent speciation event.

Speciation

Speciation replaces one extant species by two daughter species. Every paralog in the parent species gives rise to one independently mutated copy in each daughter. Thus a speciation event branches both the species tree and, for every inherited paralog, the gene tree.

Ortholog Groups

Ortholog groups are defined by anchor nodes (Fitch, 1970; Koonin, 2005): the root sequence and every successful duplication copy. A leaf belongs to anchor $a_j$ if it descends from $a_j$ without crossing another ortholog anchor:

$$OG_j = \{\ell : a_j \rightsquigarrow \ell \ \mathrm{and\ no\ other\ anchor\ lies\ on\ the\ path}\}.$$

This definition ensures that every extant sequence is assigned to exactly one ortholog group in the emitted CSV file.

Branch Lengths

Gene-tree edge weights are the generative branch-length values recorded at the time of evolution. For each speciation edge the realised length is drawn independently from a log-normal with mean $t$ (or $t \cdot m(d)$ inside a boosted duplicate's subtree) and coefficient of variation --branch-cv; with --branch-cv 0 every edge uses the mean exactly. Because these values are stored during simulation rather than derived from the alignment after the fact, they constitute true ground-truth branch lengths for the simulated family. The species cladogram is emitted without branch lengths.

Outputs

For output prefix PREFIX, FakeProt writes:

File	Contents
PREFIX_all_sequences.<msa-format>	All generated sequences, including ancestral and internal sequence nodes.
PREFIX_current_sequences.<msa-format>	Extant leaf sequences only.
PREFIX_gene_tree.<tree-format>	Gene tree with generative (ground-truth) branch lengths.
PREFIX_species_cladogram.<tree-format>	Species cladogram without branch lengths.
PREFIX_ortholog_groups.json	Mapping from extant sequence identifiers to ortholog-group labels ({"sp1_seq1": "OG_A", ...}).
PREFIX_OG_A.<msa-format>, PREFIX_OG_B.<msa-format>, ...	Per-ortholog-group alignments, emitted when --n-orthologs > 1.
PREFIX_physicochemical_groups.json	Per-column amino-acid frequencies and physicochemical class annotations for each ortholog group.
PREFIX_run_info.json	Version, timestamp, parameters, and random seed for reproducibility.

Implementation Notes

Sequences are stored in three aligned NumPy arrays: amino-acid/gap codes, site-rate values, and physicochemical-class codes. Insertions are handled by adding columns to the global alignment store and filling earlier rows with gap sentinels. This makes output generation straightforward because every internal and extant sequence is already represented in a shared alignment.

Trees and traversal operations are implemented with NetworkX. Sequence and tree serialization use Biopython, and tabular outputs use pandas.

Assumptions and Limitations

FakeProt is a benchmark simulator rather than an inference-calibrated biological model. In particular:

1. Physicochemical classes overlap (Taylor, 1986), so class priors are normalized over class masses rather than over a partition of amino acids.
2. The requested number of ortholog groups is a target, not a hard guarantee; if too few duplication opportunities occur before the leaf target is reached, the simulator emits a warning.
3. The requested size is a lower bound because one speciation event can add more than one sequence leaf.

These design choices make the simulator easy to inspect and useful for controlled benchmarking, but they should be considered when interpreting results as biological evolutionary histories.

Running Tests

pip install -e ".[dev]"
pytest

Citation

If you use this simulator in your research, please cite the original software and the associated publication (if any). The original module was developed by Lucas Carrijo de Oliveira (lucas@ebi.ac.uk). For now, you may reference the repository directly:

Lucas C. de Oliveira. FakeProt. 2018–2026.
https://github.com/lucas-ebi/fakeprot

A formal publication is in preparation; check the repository for updates.

Substitution Model

Whelan, S. and Goldman, N. (2001). A general empirical model of protein evolution derived from multiple protein families using a maximum-likelihood approach. Molecular Biology and Evolution, 18(5), 691–699.

Site-Rate Heterogeneity and Rate Autocorrelation

Yang, Z. (1994). Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: approximate methods. Journal of Molecular Evolution, 39(3), 306–314.

Felsenstein, J. and Churchill, G. A. (1996). A Hidden Markov Model approach to variation among sites in rate of evolution. Molecular Biology and Evolution, 13(1), 93–104.

Yang, Z. (1995). A space-time process model for the evolution of DNA sequences. Genetics, 139(2), 993–1005.

Physicochemical Amino-Acid Classes

Taylor, W. R. (1986). The classification of amino acid conservation. Journal of Theoretical Biology, 119(2), 205–218.

Indel Processes and Gap Length Distributions

Thorne, J. L., Kishino, H. and Felsenstein, J. (1991). An evolutionary model for maximum likelihood alignment of DNA sequences. Journal of Molecular Evolution, 33(2), 114–124.

Thorne, J. L., Kishino, H. and Felsenstein, J. (1992). Inching toward reality: an improved likelihood model of sequence evolution. Journal of Molecular Evolution, 35(1), 3–16.

Benner, S. A., Cohen, M. A. and Gonnet, G. H. (1993). Empirical and structural models for insertions and deletions in the divergent evolution of proteins. Journal of Molecular Biology, 229(4), 1065–1082.

Chang, M. S. S. and Benner, S. A. (2004). Empirical analysis of protein insertions and deletions determining parameters for the correct placement of gaps in protein sequence alignments. Journal of Molecular Biology, 341(2), 617–631.

Yule (Pure-Birth) Trees and Their Statistics

Yule, G. U. (1925). A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, F.R.S. Philosophical Transactions of the Royal Society of London, Series B, 213, 21–87.

Aldous, D. J. (2001). Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today. Statistical Science, 16(1), 23–34.

Orthology and Paralogy

Fitch, W. M. (1970). Distinguishing homologous from analogous proteins. Systematic Zoology, 19(2), 99–113.

Koonin, E. V. (2005). Orthologs, paralogs, and evolutionary genomics. Annual Review of Genetics, 39, 309–338.

Branch-Length Rate Variation

Drummond, A. J., Ho, S. Y. W., Phillips, M. J. and Rambaut, A. (2006). Relaxed phylogenetics and dating with confidence. PLoS Biology, 4(5), e88.

Gene Duplication and Post-Duplication Rate Asymmetry

Ohno, S. (1970). Evolution by Gene Duplication. Springer-Verlag, Berlin.

Conant, G. C. and Wagner, A. (2003). Asymmetric sequence divergence of duplicate genes. Genome Research, 13(9), 2052–2058.

Lynch, M. and Conery, J. S. (2000). The evolutionary fate and consequences of duplicate genes. Science, 290(5494), 1151–1155.

Kellis, M., Birren, B. W. and Lander, E. S. (2004). Proof and evolutionary analysis of ancient genome duplication in the yeast Saccharomyces cerevisiae. Nature, 428(6983), 617–624.

Protein-Family Database

Finn, R. D., Mistry, J., Schuster-Böckler, B., Griffiths-Jones, S., Hollich, V., Lassmann, T., Moxon, S., Marshall, M., Khanna, A., Durbin, R. et al. (2006). Pfam: clans, web tools and services. Nucleic Acids Research, 34, D247–D251.

Mistry, J., Chuguransky, S., Williams, L., Qureshi, M., Salazar, G. A., Sonnhammer, E. L. L., Tosatto, S. C. E., Paladin, L., Raj, S., Richardson, L. J., Finn, R. D. and Bateman, A. (2021). Pfam: the protein families database in 2021. Nucleic Acids Research, 49(D1), D412–D419.

License

GNU General Public License v3.0 or later. See LICENSE.

Copyright (C) 2018 Lucas Carrijo de Oliveira.