I · Explore the probabilities · Mutation load

Genetic entropy: does the genome decay?

Every generation adds new mutations. Most of those that matter are harmful, and many are too slight for selection to notice. Do they pile up until a species declines, as John Sanford argues under the name 'genetic entropy'? Or do selection, recombination and beneficial mutations hold the line?

In plain English

  1. Every child is born with a few dozen new spelling changes in their DNA. Most do nothing. Of the ones that do something, most do harm, usually very slight harm.
  2. Natural selection is the filter. People carrying more harmful changes have, on average, slightly fewer surviving children, so those changes tend to disappear.
  3. But the filter has a mesh size. In a population of N people, chance alone shifts gene frequencies about as much as a 1/2N difference in fitness. Changes weaker than that slip through as if they were invisible, and they can pile up.
  4. This page lets you run that process. You choose how many new mutations arrive, how harmful they are, how large the population is, whether there is sex and recombination, and whether low fitness actually kills (hard selection) or only reorders who has the most children (soft selection). Then watch what happens over thousands of generations. The formula panel shows what textbook population genetics predicts, so you can compare.
  5. The question at stake: are we looking at a slow, unstoppable decline (Sanford's "genetic entropy"), a stable balance (the usual textbook view), or a decline only in small or unusual populations? The answer depends on a few numbers that are still disputed, and the simulator shows you which ones.

Mostly harmful, mostly slight (the genetic-entropy assumptions). Every new mutation has some effect, nearly all are harmful, most of those are very slight (gamma shape 0.23), and beneficial ones are rare. Mutations below the drift barrier (s < 1/2N) slip past selection and pile up, so fitness keeps falling after the balance is reached. This is the core of Sanford's argument. The mutation rate is scaled down to 3 so a browser can keep up; raise it to see a heavier load.

The population

Real populations are far larger (humans: an effective size of about 10,000), but a browser can follow only a few thousand individuals. Smaller populations make drift stronger.

Reproduction
How selection works

The population stays the same size whatever its fitness. Fitter individuals simply leave more of the next generation. Most population-genetic models, and Lesecque et al. (2012), assume this.

Accidents, disease, luck: survival is multiplied by a random factor with this spread (log scale). It hides small genetic differences from selection.

New mutations

Humans: about 70 (Keightley 2012) to 100 (Sanford's lecture; Kong et al. 2012). What matters is how many of them affect fitness.

Harmful: 3 per person per generation. The mainstream view is that most of the genome is not under selection: Rands et al. (2014) estimate 8.2% is constrained, which with ~70 mutations gives roughly 2–6 harmful ones. Sanford argues nearly every mutation has some effect.

Poorly measured and disputed: from about 1 in a million (Sanford's figure) to about 1% in E. coli (Perfeito et al. 2007). The lowest setting means none.

How harmful are the harmful ones?

One copy costs about half this. Eyre-Walker et al. (2006) estimate an amino-acid change in humans costs 'a few percent' on average.

Below 1: most mutations very slight, a few severe. Eyre-Walker et al. (2006) fitted 0.23 to human data; Kim et al. (2017) found even more weakly harmful mutations.

Drift barrier at this population size: s < 1/2N = 0.001. Below it, harmful mutations behave almost as if neutral. 46% of harmful mutations fall below it (1.38 per person per generation).

Linkage

Mutations in the same block are always inherited together.

0.5: blocks are shuffled independently, as if each sat on its own chromosome. 0: whole genome copies are passed on intact.

Run

About 75,000 years at 25 years per generation.

What the formulas predict

Balance level, once selection catches up0.197mean fitness, e^−U for the mutations selection can see
Then, from fixations, per generation-0.0223%halves every 3,104 generations ≈ 77,588 years
Harmful mutations per person per generation, Uh3
…that selection can see (s ≥ 1/2N), Uvis1.62
…below the drift barrier, which accumulate almost freely1.38
Harmful mutations fixed per 1,000 generations710
Beneficial mutations fixed per 1,000 generations1.5
Children per woman needed at the balance level, 2e^Uvis10.1
  • Fitness here is relative to a genome with no mutations at all. Under relative selection a low number does not shrink the population; under absolute selection it does.
  • A balance of 0.197 would need 10.1 children per woman if this fitness were survival. This is the load paradox: the answer turns on whether selection is hard or soft (Kondrashov 1995; Lesecque et al. 2012).
  • The formulas treat every mutation independently, in a population large enough for deterministic selection on the visible ones. They ignore interference between linked mutations, so expect the simulation to fall somewhat faster.

The formulas used

w̄balance = e−Uvis   Haldane 1937; Muller 1950

ln w̄(t) ≈ −Σs ≥ 1/2N Uh·p(s)·[1 − (1 − s/2)t] + t·Δ

u(σ) = (1 − e−2σ) / (1 − e−4Nσ)   Kimura 1962, diploid, one copy changes fitness by σ

Δ = N·Ub·E[u(+σ)·2 ln(1 + σ)] − N·Uh·E[u(−σ)·2·(−ln(1 − σ))]

Uh, Ub
new harmful and beneficial mutations per person per generation
p(s)
the distribution of harmful effects (gamma, or a single value)
σ = s/2
what one copy costs (or adds): mutations are codominant and effects multiply
1/2N
the drift barrier: below it selection hardly sees a mutation
u
the chance a new mutation eventually spreads to everyone
Δ
long-run change in ln(mean fitness) per generation, as fixed mutations shift everyone alike

The first line is the classic mutation load: in a large population, mutations selection can see settle where they are removed as fast as they arrive, and the cost depends on the rate, not the effect size. The last line adds what drift does over the long run: mutations fix at Kimura's rate and shift everyone's fitness. The near-neutral argument (Ohta 1973; Kondrashov 1995) is that this term is negative and never stops.

Where the new harmful mutations fall

Red bars lie below the drift barrier, 1/2N = 0.001 for N = 500: selection hardly sees them, so they accumulate. Bars in ochre and ink lie above it and reach a balance. A larger population moves the barrier left, which is why population size matters so much here.

Simulation

Follow the population

Every individual and every mutation is simulated, generation by generation, from a population with no mutations at all. Seed ohta-1973: the same settings and seed give the same run.

Generation0
Individuals500
Mean fitness1
Harmful mutations per person0
…of which below the drift barrier0
Beneficial per person0
Change per generation, last third—
Formula, long run-0.0223%

Press Run. Fitness starts at 1 (no mutations). It first falls towards the balance level for the mutations selection can see, then follows the long-run trend.

Methodology and limitations

How this works, and what it leaves out

Method

  • Individuals. Each individual is diploid: two copies of a genome divided into B linkage blocks. Every generation, each new individual receives a Poisson-distributed number of new mutations (mean U), placed at random on one copy and one block. A mutation is neutral, beneficial, or harmful, in the proportions you set.
  • Effects. A harmful mutation's effect s is either fixed or drawn from a gamma distribution with your mean and shape (capped at 1). One copy multiplies fitness by 1 − s/2, so two copies cost about s (codominance). Beneficial effects are exponential with your mean, and multiply fitness by 1 + s/2 per copy. Fitness is the product over all mutations, relative to a genome with none.
  • Inheritance. Sexual: each child takes one gamete from each of two different parents. A gamete starts on a random copy and switches copy between neighbouring blocks with probability c, so c = 0.5 means blocks assort independently. Asexual: a child copies one parent. Mutations in one block are never separated from each other, as in Mendel's Accountant (Sanford et al. 2007).
  • Selection. Relative (soft): each generation N children are made, and each parent is drawn with probability proportional to its fitness times a random survival factor (log-normal, mean 1, spread as set). Absolute (hard): the population makes F/2 children per individual on average. Each child survives with probability equal to its fitness times the random factor (at most 1), and if more than K survive, K are kept at random. The population dies out if fewer than two remain.
  • Bookkeeping. Each block stores the summed log-fitness of its mutations and counts of five kinds: neutral; harmful below the drift barrier 1/2N; harmful between 1/2N and 1%; harmful above 1%; beneficial. Individual mutations are not tracked, so the simulator reports how many mutations people carry, not which have become fixed.
  • Formulas. The balance level e−U for visible mutations (Haldane 1937), approached as each copy is removed at rate s/2 (Kimura & Maruyama 1966). Long-run change from fixations at Kimura's (1962) diploid rate, as in Whitlock (2000). Both treat mutations as independent.
  • Checked against simulation. With strongly harmful mutations only (U = 1, s = 0.1) the simulation settled at 0.35–0.37, against the formula's 0.368. Fixation rates were exact for neutral mutations and within 0.7–1.5× of Kimura's rate when 2Ns was 1–5, where that rate is very sensitive to the effective population size. In the genetic-entropy scenario the simulation tracked the formula for about 1,000 generations, then fell faster (log-fitness about 28% lower by generation 3,000), because linked mutations interfere with one another's selection. With few blocks or a high mutation rate per block that interference dominates; the page warns when it applies.
  • Reproducibility. Seeded random numbers (xmur3 + sfc32), so the same settings and seed give the same run on any device. Runs entirely in your browser.

Limitations

  • Scale. A few thousand individuals and at most 200 blocks, where humans have an effective size of about 10,000, a census size in the billions, and recombination down to the scale of kilobases. Small N moves the drift barrier up, so the browser exaggerates drift compared with a large population at the same U. Coarse blocks exaggerate interference.
  • Starting point. Every run begins with a genome free of mutations, so fitness first drops towards the balance level. That early drop is the load being established, not evidence of ongoing decay. Only the long-run trend speaks to genetic entropy.
  • Left out: dominance other than codominance (a lethal mutation in two copies costs 75% here, not 100%); epistasis, including the synergistic kind proposed as a way out of the load paradox; back-mutation; compensatory mutations that depend on genetic background; population structure, migration and changing environments; separate sexes and sexual selection; mutation rates that vary with parental age; insertions, deletions and duplications.
  • Beneficial mutations never run out and can raise fitness without limit. That is generous to persistence. In models with an optimum (Poon & Otto 2000) gains are bounded but compensation is easier.
  • Fitness is a number in a model. What "mean fitness 0.2" means for a real species depends on whether selection is hard or soft, which this page lets you switch but cannot settle.
  • What it cannot answer: the actual human distribution of effects below 10−4, the fraction of the genome that is functional, or the true rate of beneficial mutations. Those are measurements. The simulator shows how much the answer depends on them.
Evidence and debate

Weighing the evidence

Addresses: Biological evolutionThe origin of biological information

01 What is observed?

  • EstablishedEach person carries about 70 new mutations not present in either parent (Keightley's estimate; Kong et al. measured about 1.2 × 10⁻⁸ per nucleotide). How many of them affect fitness is much less certain. (Keightley 2012; Kong et al. 2012)
  • EstablishedOf mutations that change fitness, most are harmful. Their effects span many orders of magnitude, with a long tail of very slight effects. (Eyre-Walker & Keightley 2007)
  • Active researchFor amino-acid changes in humans, a gamma distribution with shape 0.23 fits the data: more than half reduce fitness by between 0.1% and 10%, and fewer than 15% are strongly harmful. Larger samples suggest even more are only weakly harmful (|s| < 0.001). (Eyre-Walker et al. 2006; Kim et al. 2017)
  • EstablishedLines kept through single-individual bottlenecks, which nearly switches off selection, steadily lose fitness in many organisms. (Halligan & Keightley 2009)
  • EstablishedMuller's ratchet has been seen directly in asexual lineages: an RNA virus, and Salmonella, in which 1% of 444 bottlenecked lineages had visibly lost fitness after 1,700 generations. Endosymbiotic bacteria, which live asexually in small populations, show the accelerated sequence change it predicts. (Chao 1990; Andersson & Hughes 1996; Moran 1996)
  • EstablishedToo many mutations can kill a population. A 9.7-fold rise in mutation rate caused by the drug ribavirin cut poliovirus infectivity by 99.3% in a single round of infection. (Crotty et al. 2001)
  • EstablishedDegradation can be reversed. Mutationally degraded C. elegans lines returned to full mean fitness in fewer than 80 generations once kept in large populations, partly through compensatory mutations. (Estes & Lynch 2003)
  • Active researchThe human H1N1 influenza lineage accumulated about 1,400 point mutations between 1918 and its disappearance in 2009, while its mortality rate fell. Carter and Sanford read this as genetic attenuation. A common alternative, here in the Lab's own words, is that rising immunity and better medicine lowered mortality. (Carter & Sanford 2012)

02 What does evolutionary theory propose?

  • EstablishedMutations that selection can see reach a balance at which they are removed as fast as they arrive. With multiplicative effects, mean fitness settles near e^−U, whatever the size of each effect. (Haldane 1937; Muller 1950; Kimura & Maruyama 1966)
  • EstablishedSex and recombination break up linked mutations, which stops Muller's ratchet and lets selection act on each mutation separately. (Muller 1964; Felsenstein 1974; Kondrashov 1988)
  • Active researchA high load need not shrink a population if selection acts on relative fitness (soft selection), or if mutations interact so that selection removes several at once. On this view a deleterious rate of about 2.2 per generation is tolerable. (Wallace 1975; Keightley 2012; Lesecque et al. 2012; Agrawal & Whitlock 2012)
  • Active researchBeneficial and compensatory mutations can offset the slow fixation of slightly harmful ones. Above a critical effective size, likely a few hundred, populations hold their fitness on average. (Whitlock 2000; Poon & Otto 2000)
  • EstablishedSmall populations are genuinely at risk. Drift fixes harmful mutations, fewer offspring survive, numbers fall, and drift grows stronger: a mutational meltdown. (Gabriel et al. 1993; Lynch et al. 1995; Lynch et al. 1995)
  • Active researchSome mainstream geneticists also expect decline in modern humans, because medicine and small families relax selection, possibly measurably within a few generations. (Lynch 2016)

03 What are the unresolved questions and criticisms?

  • Active researchSanford argues that most mutations are slightly harmful, that selection cannot see them (especially when survival is noisy), and that the human genome is therefore degenerating. He bases this on simulations with Mendel's Accountant. Most population geneticists dispute the premises and the conclusion. (Sanford 2005; Sanford et al. 2007; Gibson et al. 2013)
  • Active researchKondrashov identified a 'dangerous range' of effects, between 1/genome size and 1/4Nₑ, in which mutations accumulate almost freely yet together could carry a large load. He called the resulting paradox real and proposed soft selection or synergistic epistasis as possible ways out. (Kondrashov 1995)
  • Active researchHow much of the genome is functional? About 8.2% of the human genome shows evidence of constraint. If that is right, most new mutations are neutral. If, as Sanford argues, nearly all of the genome matters, the harmful rate is far higher. (Rands et al. 2014)
  • Active researchThe weakest effects, the ones that matter most here, are the hardest to measure. Estimates of the distribution's tail depend on demographic models and sample size. (Kim et al. 2017; Eyre-Walker & Keightley 2007)
  • Active researchIs selection in real populations mostly hard or mostly soft? The answer decides whether a low 'mean fitness' number means fewer survivors or just a different ranking. (Wallace 1975; Agrawal & Whitlock 2012)
  • Active researchHow common are beneficial mutations, and do they keep pace? Estimates range from about 1 in a million (the figure in Sanford's lecture) to about 1 in 100 (from beneficial mutation rates measured in E. coli). (Perfeito et al. 2007; Lee et al. 2012)
  • Active researchBasener and Sanford argue that, once mutations are included, Fisher's fundamental theorem does not guarantee that fitness rises. (Basener & Sanford 2018)
  • Active researchLoad estimates across human populations with very different histories are similar, which constrains how fast recent changes alter load. (Simons et al. 2014)

04 What evidence would help distinguish competing explanations?

  • Standardised, multigenerational measurements of fitness-related human traits, as Lynch (2016) calls for.
  • Long mutation-accumulation and recovery experiments in large sexual populations, run for thousands of generations, that measure absolute fitness and not only growth rate relative to an ancestor.
  • Direct estimates of how many harmful mutations have effects below 10⁻⁴, from very large samples.
  • Time series of mutation load from ancient DNA within one lineage.
  • Fitness assays, not only sequence counts, along the H1N1 lineage and other long-studied viral lineages.
  • Whether species with long-term small populations (island endemics, endosymbionts) show the predicted decline, and how fast.

Established Measured or observed repeatedly; not in serious dispute.Active research An open research question, or a claim that specialists still dispute.Speculative A proposed explanation that has not yet been tested directly.

Your conclusions

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References

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