Simulating Genetic Entropy

"No standard population genetics model of the Wright-Fisher sort has 'fitnesses' whose effect depends only on their order.  The reason I hesitate to use Mendel's Accountant as a standard test of anything is that it seems to have a number of arbitrary properties that make it differ a lot from the standard models." — Joe Felsenstein¹

Nearly all quantitative creationist work on mutation accumulation runs through one program.  Nearly all criticism of that work is criticism of the program.  This article is about whether the program deserves it, what the alternatives do, and why the main article does not use any of them.

Mendel's Accountant

What it is

A forward-time population genetics simulator written by John Sanford, John Baumgardner, Wesley Brewer, Paul Gibson and Walter ReMine, published in Scalable Computing: Practice and Experience in 2007.²  It tracks every individual in a population, dividing each genome into linkage blocks that carry a running total of mutation effects, and follows those blocks through recombination for thousands of generations.

Its defaults, from its own manual: 10 non-neutral mutations per individual per generation, a beneficial-to-deleterious ratio of 1 in 10,000, a maximum beneficial effect of 0.01, heritability of fitness 0.2, 1,000 linkage blocks over 23 chromosomes, and 4 offspring per reproducing female.

What is right about it

The central design choice is sound, and the strongest evidence for that is who else made it.  The Masel lab at the University of Arizona — mainstream evolutionary theorists, publishing the current standard treatment of human mutation load — wrote their own simulator, MutationLoad, and describe it as breaking "genomes into discrete linkage blocks with numeric values summarizing combined mutation effects," with two recombination events per chromosome per meiosis.³

That is Mendel's core abstraction, arrived at independently by people with no interest in the creationist conclusion.  It is a legitimate technique for making whole-genome simulation tractable at high mutation rates.  Criticism of Mendel that treats its data structure as evidence of bad faith is criticism that lands on the Masel lab too.

What is wrong with it

Nobody outside the group uses it.  The 2007 paper has 23 citations.  About 13 are by the Mendel team or in creationist and intelligent-design venues.  Searching the remainder for a paper that actually uses Mendel to produce a result turns up none.  By contrast, SLiM has over 1,200 citations across its versions, simuPOP has 345, SFS_CODE has 231.  Claims in creationist literature that Mendel is "used and cited by other geneticists" do not survive checking the citing papers.

It has never been benchmarked against a mainstream simulator.  Not by its authors, and not by its critics.  The "fundamental flaws" claim against it exists in blog comments and a YouTube video, not in print.  That is a weakness on both sides: Sanford has no independent validation, and the critics have no published refutation.

Its selection scheme is not standard.  This is Felsenstein's objection above, and it is correct.  Mendel's "probability selection" multiplies each individual's fitness by a uniform random number and then applies a hard cutoff on the result.  The mapping from fitness to survival probability that comes out of that is neither proportional to fitness nor proportional to fitness rank.

The Barney Fife episode

The most interesting thing anyone has found in Mendel's selection algorithm was found by a creationist, arguing with a critic, on a creationist website.  It is worth recording in full because of how it ended.

In 2015 the critic Zachriel argued on Uncommon Descent that Mendel's selection was too weak, and ran a small simulation to show it — a population of 1,000 with a single novel mutation, checking how often the mutant survived one generation.  The illustration was that an unremarkable individual could be ranked first by Mendel's randomised sort: "Sure, 'time and chance happens to them all', but it is not usual for Barney Fife to get all the girls."

The author of this site's research notes, posting as JoeCoder, tested the opposite direction.  He built a small JavaScript page that put two individuals through Mendel's probability-selection formula a million times — Barney Fife with fitness 1.0 and Genghis Khan with fitness 1.1 — and counted.  Genghis won 20% more often, not 10%.⁴

Joe Felsenstein, a population geneticist and no friend of creationism, confirmed the finding:

"Exactly, and others here have tried to point this out too.  If the fitnesses stand in the ratio of 1.1 : 1.0 then Genghis Khan should be 10% more likely to survive.  But owing to (perhaps) the truncation you find him 20% more likely to survive.  The truncation part is not in standard population-genetic models."¹

A commenter named keiths worked out the algebra: the ratio of two uniform random variables makes the survival odds 0.5455 to 0.4545, which is 1.2 to 1, not 1.1 to 1.⁵

Three things follow, and creationists should be as interested in the third as in the first two.

1. The bug is real and was confirmed by a hostile expert.
2. It runs the wrong way for creationism. If Mendel's selection is stronger than standard theory, Mendel understates mutation accumulation. Correcting it would make the decline faster, not slower. Zachriel, who was arguing that Mendel selects too weakly, dropped the exchange after saying the test looked "interesting and valid" and was never heard from on it again.
3. The finder later withdrew his own claim. A year afterwards, in a separate discussion, JoeCoder wrote: "I'm also no longer sure about the comment I made a year ago that selection in Mendel is 'TWICE as efficient as it should be.' It's possible I could be off by two somewhere due to haploid/diploid differences or something."⁶

That last sentence is the reason this episode is in the article.  A person who retracts his own point when he is no longer sure of it has earned some benefit of the doubt on the points he has not retracted.

The alternatives

SLiM (Haller & Messer) is what a working population geneticist reaches for.  Over 1,200 citations.  Its non-Wright-Fisher mode is the important one here: it models absolute fitness, individual survival and fecundity, with population size emerging from the model rather than being imposed.  That is exactly the framework in which "does the population actually go extinct?" is a well-posed question — and it is what Mendel, which holds population size fixed by construction, cannot properly ask.

fwdpy11 (Thornton) and SFS_CODE (Hernandez) are the other standard tools, both with arbitrary distributions of fitness effects and tree-sequence recording.  Ryan Hernandez, SFS_CODE's author, is a co-author on the Masel group's 2025 mutation-load paper.

MutationLoad (Masel lab) is the most relevant comparison, because it is the closest thing to Mendel written by people who conclude the opposite.  Linkage blocks with summed effects, two crossovers per chromosome, relative and absolute fitness, carrying capacity, epistasis.  Its published output includes the fixation counts the main article checks its arithmetic against.

Why Drift Lab exists

Not because the world needed another simulator.  Because the argument needed one nobody has to take on trust.

Drift Lab runs in the reader's browser.  The source is served as plain unminified JavaScript with a link on the page.  It grades itself, in front of you, against six results worked out on paper long before any of this was contentious:

The fourth and fifth are the ones that matter for trust.  A simulator rigged to produce decline could not reproduce a stable equilibrium on demand, and Drift Lab does: set every mutation to cost 1% and the decline stops dead, fitness parks at e^(−U), and nothing fixes for as long as you care to run it.

There are two kernels, not three, and the reason is worth stating.

Sites tracks allele frequencies at functional sites.  Every site is inherited independently — free recombination, no interference, no hitchhiking — and fitness is exactly the genome with no luck involved.  Both assumptions make selection more effective than it can possibly be in a real organism.  Set the site count to 10^8 and back mutation is negligible, which is the classical infinite-sites model; set it to 20,000 and the same code reaches a real equilibrium inside a run you can watch.  Those are not two models; they are one model at two settings, which is why they are one kernel.

Genomes tracks individuals: two copies of a genome divided into linkage blocks across chromosomes, crossovers at a genetic map length you set, environmental noise so that selection has to see through luck, finite fecundity, and a choice of selection schemes.  This is the same design as Mendel and MutationLoad, and its job is to check whether the Sites kernel's simplifications matter.

They do, and by less than expected:

Linkage at human map lengths costs almost nothing.  Removing recombination entirely triples the damage — which is Muller's ratchet in its original form, and the situation of mitochondrial DNA and the Y chromosome.

What a simulation cannot settle

None of these programs can tell you how much of the human genome is functional.  That is measured, not simulated, and it is the largest uncertainty in the subject.  Every simulator takes the deleterious mutation rate as an input, and every conclusion scales with it.

Nor can any of them settle the beneficial mutation rate, which is the parameter the mainstream answer depends on.  Hancock and Stern Cardinale's rebuttal to Basener and Sanford used a beneficial fraction of 1%; Basener and Sanford used 0.1%.  That is a tenfold difference in the one parameter the whole result turns on, and both sides chose the value that produced their answer.  The honest description is that the outcome is parameter-sensitive and the parameter has not been measured well.

A simulator's job is to tell you what follows from your assumptions.  Anyone who says it does more than that — in either direction — is selling something.

Sources