Mutation, recombination and gene flow

Selection and drift sort existing variation, but they do not create it. Every allele that selection favours or drift fixes began as a mutation, and recombination shuffles mutations into new combinations on which selection can act. Gene flow moves alleles between populations, spreading adaptations and opposing local divergence. BIOL-201 explained the molecular kinds of mutation and their repair, and showed how mutation and selection reach a balance for harmful recessive alleles. This lesson asks evolutionary questions: how many mutations arise, what their effects on fitness are, why sex and recombination are so common despite their costs, and how gene flow and population structure shape variation across a species’ range.

How many mutations?

Mutation rates can now be measured directly by sequencing the genomes of parents and offspring. In humans, the rate of new single-base substitutions is about 1.2 × 10⁻⁸ per base per generation. With roughly 6 billion bases in a diploid genome, each child carries about 60 to 70 new point mutations not present in either parent, plus a few small insertions and deletions and occasional larger changes. Most come from the father, and the number rises with paternal age by about one or two extra mutations per year, because sperm-producing cells keep dividing throughout a man’s life. Rates differ among organisms: per base per generation, they are lower in bacteria and higher in many RNA viruses, which lack proofreading.

Interestingly, organisms with large genomes have lower per-base rates, so that the number of mutations per genome per generation varies much less than the per-base rate. Michael Lynch has proposed the drift-barrier hypothesis to explain this: selection pushes mutation rates down because most mutations are harmful, but in species with small effective sizes, drift prevents selection from refining the rate further. This is an example of how population-genetic forces shape even the machinery of heredity.

The distribution of fitness effects

Most new mutations that affect fitness are harmful, a smaller fraction are nearly neutral and a very small fraction are beneficial. The full spread of effects, the distribution of fitness effects (DFE), can be estimated from mutation-accumulation experiments, in which lines are kept so small that selection is almost powerless and mutations accumulate, and from patterns of polymorphism in genome data. In humans and fruit flies, estimates suggest that most new amino acid–changing mutations are deleterious, with a wide range from very mildly to strongly harmful. Mutations in non-coding DNA are mostly neutral or very slightly harmful.

import numpy as np
rng = np.random.default_rng(321)
# A gamma-distributed DFE for deleterious amino-acid mutations (shape 0.2; illustrative mean |s| = 0.01)
shape, mean_s = 0.2, 0.01
s = rng.gamma(shape, mean_s/shape, 200_000)          # selection coefficients (harm)
for Ne in (1_000, 10_000, 100_000):
    nearly_neutral = np.mean(Ne*s < 1)                # behave as effectively neutral
    strongly = np.mean(Ne*s > 100)
    print(f"Ne = {Ne:7,d}: effectively neutral {100*nearly_neutral:5.1f}%, "
          f"strongly selected {100*strongly:5.1f}%")

Ne =   1,000: effectively neutral  49.7%, strongly selected   1.2%
Ne =  10,000: effectively neutral  31.6%, strongly selected  23.5%
Ne = 100,000: effectively neutral  19.9%, strongly selected  50.3%

The same set of mutations behaves very differently depending on population size. In a population with an effective size of 1,000, a large share of these mutations are effectively neutral and can drift to high frequency; in a population of 100,000, most are strongly enough selected to be removed efficiently. This is the nearly neutral theory from lesson 3 applied to the whole distribution, and it helps explain why species with small effective sizes, including humans compared with fruit flies, carry relatively more slightly harmful variation.

Mutation accumulation and Muller’s ratchet

In a population that reproduces without recombination, such as an asexual organism, a mitochondrial genome or a non-recombining sex chromosome, harmful mutations can accumulate irreversibly. Hermann Muller pointed out in 1964 that the class of individuals carrying the fewest mutations can be lost by chance, and without recombination it can never be recreated except by an unlikely back mutation. Each such loss is a click of the ratchet, and the population’s fitness declines step by step.

import numpy as np
rng = np.random.default_rng(3213)

def ratchet(N=200, U=0.5, s=0.02, gens=2000, sex=False):
    k = np.zeros(N, int)                      # number of deleterious mutations per genome
    clicks, best = 0, 0
    for t in range(gens):
        w = (1 - s)**k
        parents = rng.choice(N, N, p=w/w.sum())
        if sex:                                # free recombination: offspring get a mix of two parents
            mates = rng.choice(N, N, p=w/w.sum())
            k = rng.binomial(k[parents] + k[mates], 0.5)
        else:
            k = k[parents]
        k = k + rng.poisson(U, N)
        if k.min() > best:
            clicks += k.min() - best; best = k.min()
    return clicks, k.mean()

for sex in (False, True):
    c, m = ratchet(sex=sex)
    print(f"{'sexual  ' if sex else 'asexual '} least-loaded class moved up {c:3d} times; mean load {m:6.1f}")

asexual  least-loaded class moved up 494 times; mean load  501.2
sexual   least-loaded class moved up  19 times; mean load   25.8

In the asexual population, the least-loaded class keeps being lost and the burden of mutations climbs steadily. With recombination, offspring with fewer mutations than either parent are produced each generation, so the best class is continually rebuilt and the ratchet is held in check. This is one reason why the human Y chromosome, which does not recombine over most of its length, has lost most of the genes it once shared with the X, and why mitochondrial genomes rely on special mechanisms, such as bottlenecks in egg cells, to purge harmful mutations.

Why sex?

Sexual reproduction poses one of the deepest puzzles in evolution. An asexual female produces only daughters, each of which can reproduce, while a sexual female produces sons and daughters, and only the daughters bear offspring. All else being equal, an asexual lineage should grow twice as fast, the twofold cost of sex. Sex also breaks up favourable combinations of genes and requires finding a mate. Yet nearly all animals and plants reproduce sexually at least sometimes, and lineages that have abandoned sex entirely tend to be young twigs on the tree of life, suggesting that they usually go extinct.

The Red Queen hypothesis takes its name from the character in Lewis Carroll’s Through the Looking-Glass who must keep running to stay in the same place. Parasites evolve to exploit the commonest host genotypes, so hosts that produce variable offspring keep a step ahead. Studies of the New Zealand freshwater snail Potamopyrgus antipodarum, in which sexual and asexual forms live together, by Curtis Lively and colleagues found that sexual snails are more common where trematode parasites are abundant, and that asexual clones that become common are later attacked more heavily. Most biologists now think several advantages of sex act together, with their relative importance varying among organisms.

Recombination and the efficiency of selection

Recombination also matters within genomes. In regions of low recombination, selection at one site interferes with selection at linked sites, a phenomenon called Hill–Robertson interference. A beneficial mutation that arises on a chromosome carrying a harmful mutation may be dragged down with it, and a favoured allele that sweeps to fixation carries linked neutral variants with it, reducing diversity nearby (a selective sweep). Purifying selection against harmful mutations similarly removes linked neutral diversity (background selection). As a result, genetic diversity across the genome tracks the local recombination rate, a pattern seen in flies, humans and many other species and discussed further in BIOL-322.

Gene flow and population structure

Gene flow, or migration, is the movement of alleles between populations through dispersing individuals or gametes such as pollen. It makes populations more similar and opposes divergence caused by drift and local selection. A simple model, Wright’s island model, imagines many subpopulations of size N exchanging a fraction m of migrants each generation. At equilibrium between drift, which makes subpopulations differ, and migration, which homogenizes them, the fixation index F_ST, which measures the fraction of total genetic variation due to differences among subpopulations, is approximately 1/(4Nm + 1).

import numpy as np
rng = np.random.default_rng(3214)
# Island model: 20 demes of N = 50 diploids; migrants drawn from the global pool each generation
def fst_sim(N=50, m=0.01, demes=20, gens=1500):
    p = np.full(demes, 0.5)
    vals = []
    for t in range(gens):
        p = (1 - m)*p + m*p.mean()                 # migration
        p = rng.binomial(2*N, p) / (2*N)           # drift within each deme
        if t > 1000:
            pbar = p.mean()
            if 0 < pbar < 1: vals.append(p.var() / (pbar*(1 - pbar)))
    return np.mean(vals)

for m in (0.001, 0.005, 0.02, 0.1):
    Nm = 50*m
    print(f"m = {m:5.3f} (Nm = {Nm:4.2f}): simulated F_ST = {fst_sim(m=m):.3f}, island-model prediction {1/(4*Nm + 1):.3f}")

m = 0.001 (Nm = 0.05): simulated F_ST = 0.813, island-model prediction 0.833
m = 0.005 (Nm = 0.25): simulated F_ST = 0.438, island-model prediction 0.500
m = 0.020 (Nm = 1.00): simulated F_ST = 0.157, island-model prediction 0.200
m = 0.100 (Nm = 5.00): simulated F_ST = 0.049, island-model prediction 0.048

The simulations follow the predicted relationship: when Nm is well below 1, subpopulations drift apart; when it is several or more, they stay similar. Real populations depart from the island model because migration is usually between neighbours, producing isolation by distance, in which genetic differences increase with geographic distance. In humans, F_ST between continental groups is about 0.1 or a little higher, meaning that around 85 to 90 per cent of human genetic variation is found within any population rather than between them, a point that lesson 11 returns to.

Gene flow and local adaptation

When selection differs between habitats, gene flow can swamp local adaptation by importing alleles suited to elsewhere. Adaptation can persist only if selection is strong relative to migration, roughly when s exceeds m. A famous example is heavy-metal tolerance in grasses growing on mine waste in Britain: tolerant and non-tolerant populations stay distinct over distances of only a few metres because selection against non-tolerant plants on contaminated soil, and against tolerant plants on clean soil, is very strong. Gene flow can also spread adaptations. Insecticide resistance alleles in mosquitoes have spread across continents, and alleles introduced from one species to another by hybridization, adaptive introgression, have helped species adapt, as when modern humans acquired immune and high-altitude variants from archaic humans (lesson 11).

Gene flow can even move genes between distant branches of the tree of life. In bacteria, horizontal gene transfer by plasmids, viruses and uptake of free DNA is common, and it is the main way antibiotic resistance genes spread between species. Resistance plasmids carrying genes such as those for extended-spectrum β-lactamases or carbapenemases can move between Escherichia coli, Klebsiella and other bacteria within a patient’s gut. Horizontal transfer complicates the tree of life for microbes and is one reason why bacterial evolution can be so rapid.