Effects of deleterious mutations on the fixation of chromosomal inversions on autosomes and sex chromosomes

Using individual-based simulations, this study demonstrates that while deleterious mutations generally reduce the fixation probability of chromosomal inversions on autosomes and sex chromosomes through mechanisms like Muller's ratchet, inversions can still occasionally fix if they carry a low mutation load or benefit from sheltering effects, potentially driving the evolution of recombination arrest.

The Gist

Imagine your genome (your genetic blueprint) as a massive, bustling library. Inside this library, there are millions of books (genes). Sometimes, a book gets a typo (a mutation). Most of the time, these typos are harmless, but some are "deleterious"—they make the book harder to read or useless.

Now, imagine a rare event where a whole chapter of the library gets physically flipped upside down and glued back in the wrong order. This is a chromosomal inversion.

For a long time, scientists thought these inversions were just accidents that usually caused trouble. But this paper asks a fascinating question: Can these "upside-down chapters" actually help a species survive and evolve, even if they carry some bad typos?

The authors, Denis Roze and Thomas Lenormand, used powerful computer simulations to watch thousands of these genetic libraries evolve over time. Here is what they found, broken down into simple concepts.

1. The "Lucky Break" (The Initial Advantage)

Imagine you are running a race. Most runners are carrying heavy backpacks filled with rocks (bad mutations). Suddenly, one runner appears with a backpack that is slightly lighter than average.

• The Analogy: When a new inversion happens, it grabs a random chunk of DNA. By pure luck, that chunk might have fewer "rocks" (bad mutations) than the average person in the population.
• The Result: This "lucky inversion" gets a head start. It spreads through the population because its carriers are slightly healthier.

2. The "Leaky Bucket" (The Problem)

Here is the catch: The backpack isn't sealed. New rocks (mutations) keep falling into it every generation.

• The Analogy: Even if the inversion starts with a light backpack, it eventually fills up with rocks again. The "lucky" advantage fades away as the inversion becomes common.
• The Result: Most inversions that start with a slight advantage eventually get weighed down and disappear.

3. The "Y-Chromosome Trap" (Muller's Ratchet)

The paper looks at two types of chromosomes: Autosomes (the standard pairs we have, like shoes) and Sex Chromosomes (like the Y chromosome in males, which has no partner to swap with).

• The Analogy: Imagine two groups of people trying to clean a messy room.
  • Group A (Autosomes): They can swap their dirty clothes with each other. If one person has a clean shirt, they can trade it. This helps them get rid of the dirt (mutations).
  • Group B (Y Chromosomes): They are stuck in a room with no one to trade with. They can't swap clothes.
• The Result: In the "No Trade" room (the Y chromosome), the dirt just piles up. This is called Muller's Ratchet. It's like a ratchet wrench that only turns one way: the room gets messier and messier, and there's no way to clean it. This makes it very hard for Y-linked inversions to survive.

4. The "Shelter" Effect (The Twist)

So, if the Y chromosome is a dirty trap, why do inversions ever stick there? The authors found a surprising loophole called the "Sheltering Effect."

• The Analogy: Imagine you have a very shy, dangerous monster (a bad mutation) that only attacks when it sees its own reflection (when it is "homozygous" or paired with another bad copy).
  • On Autosomes, the monster often meets its reflection and causes trouble.
  • On the Y Chromosome, the monster is always alone. It never sees its reflection because the Y chromosome never pairs up. The monster stays hidden in the shadows.
• The Result: If the bad mutations are "shy" (recessive), the Y chromosome acts like a shelter. It hides the monsters so they don't cause damage. This allows inversions on the Y chromosome to survive and spread, even if they carry some bad genes, provided those genes are very shy (recessive) and not too strong.

5. The "Inbreeding" Factor

The paper also looked at what happens when organisms mate with themselves or close relatives (inbreeding).

• The Analogy: Inbreeding is like forcing everyone to wear the same outfit. Usually, this is bad because it exposes all the hidden monsters. However, if an inversion captures a "mating type" (a rule that forces you to be different), it creates a special zone where the "shy monsters" stay hidden even in an inbred population.
• The Result: In some specific cases, inbreeding actually helps these inversions spread because it keeps the "shy monsters" hidden in the inversion, giving them a temporary advantage.

The Big Picture Conclusion

The authors conclude that while deleterious mutations generally act as a brake, slowing down the spread of inversions, they don't stop them completely.

• The "Lucky" Ones: Occasionally, a "lucky" inversion with a light load of mutations gets fixed in the population.
• The Macro-Evolutionary Impact: Even though these events are rare, they are crucial. They are the spark that starts the process of sex chromosome evolution. Once an inversion locks a sex-determining gene (like "Male" or "Female") into a non-recombining block, it starts the long, slow process of the Y chromosome degenerating (getting messy) and evolving into the distinct sex chromosomes we see today.

In short: Nature is a game of chance. Sometimes, a genetic "glitch" (inversion) happens to carry a lighter load of errors than everyone else. Even though errors keep piling up, if that glitch happens on a chromosome that can "hide" its errors (like the Y chromosome), it can win the race and change the course of evolution forever.

Technical Summary

1. Problem Statement

Chromosomal inversions are a major driver of adaptation and speciation, often facilitating the evolution of sex chromosomes by suppressing recombination between sex-determining loci. A central question in evolutionary genetics is how deleterious mutations influence the probability that a new inversion will reach fixation in a population.

Previous theoretical work (e.g., Nei et al., 1967; Connallon and Olito, 2022) suggested that while "lucky" inversions (those initially carrying fewer deleterious mutations than the population average) may spread, this advantage erodes over time as new mutations accumulate, leading to an average fixation probability close to neutral. However, recent debates (Jay et al., 2022, 2025 vs. Olito and Charlesworth, 2023) have questioned whether Y-linked inversions (or those capturing sex-determining loci) enjoy a specific advantage due to the "sheltering effect" (recessive deleterious mutations remaining heterozygous and thus less harmful) versus the disadvantage of Muller's ratchet (accumulation of mutations due to lack of recombination).

This study aims to resolve these conflicts by using individual-based, multilocus simulations to quantify how deleterious mutations affect the fixation of inversions on autosomes versus sex chromosomes (Y-linked) and mating-type loci, considering factors like population size, dominance coefficients, and inbreeding.

2. Methodology

The authors developed individual-based, multilocus simulations in C++ to model a diploid population of size $N$ with discrete generations.

• Genetic Model:
  • Mutations: Deleterious mutations occur at rate $U$ per chromosome per generation. They have multiplicative fitness effects (no epistasis).
  • Fitness: $W = (1-sh)^{n_{He}} (1-s)^{n_{Ho}}$, where $s$ is the selection coefficient, $h$ is the dominance coefficient, and $n_{He}$ and $n_{Ho}$ are the counts of heterozygous and homozygous mutations.
  • Recombination: Crossovers follow a Poisson distribution. In heterokaryotypes (heterozygous for the inversion), recombination is suppressed within the inverted region.
• Scenarios Simulated:
  1. Autosomal Inversions: Standard Wright-Fisher population.
  2. Y-linked Inversions: Inversions capturing a dominant male-determining locus (XY system). These are permanently heterozygous and never recombine.
  3. Mating-Type Inversions: Inversions capturing a mating-type locus (e.g., in fungi), which are also permanently heterozygous.
  4. Inbreeding: Simulations included "standard" self-fertilization and automixis to test effects on mating-type inversions.
• Initialization: Populations evolved for 2,000–3,000 generations to reach mutation-selection balance before inversions were introduced.
• Metrics: The study estimated the relative fixation probability ($P^r_{fix}$), defined as the fixation probability of an inversion divided by that of a neutral mutation. $P^r_{fix} > 1$ indicates selective advantage; $P^r_{fix} < 1$ indicates disadvantage.

3. Key Contributions

• Resolution of the "Sheltering" Debate: The study clarifies the conditions under which the sheltering effect (masking recessive mutations) outweighs the cost of Muller's ratchet. It confirms that while Y-linked inversions generally have lower fixation probabilities than autosomes due to ratchet effects, they can exceed neutral expectations under specific conditions (very recessive mutations, small population sizes).
• Role of Muller's Ratchet: The authors demonstrate that Muller's ratchet significantly reduces the fixation probability of inversions, particularly for Y-linked inversions where recombination is absent even at high frequencies, and for rare autosomal inversions that remain heterozygous.
• Impact of Inbreeding: The paper provides novel insights into how selfing and automixis affect inversions linked to mating-type loci, revealing a trade-off between the masking advantage of enforced heterozygosity and the reduced efficiency of purging deleterious alleles.
• Parameter Sensitivity: The study systematically maps fixation probabilities against compound parameters like $N_{e}Uz$ (mutation load) and $N_{e}sh$ (selection strength relative to drift), showing that fixation depends heavily on the dominance coefficient ($h$) and the size of the inversion.

4. Key Results

A. General Dynamics of Inversions

• "Lucky" Inversions: Inversions initially carrying fewer mutations than the population average are favored. However, this advantage is transient. As the inversion spreads, it reaches mutation-selection balance, and its marginal fitness declines.
• Average Fixation Probability: For most realistic parameter values (random mating, moderate selection), the average fixation probability of inversions is lower than neutral ($P^r_{fix} < 1$). This is because the probability of a new inversion being mutation-free decreases exponentially with its size, and Muller's ratchet further erodes fitness.

B. Autosomes vs. Y-Chromosomes

• Muller's Ratchet Dominance: In most regimes, Y-linked inversions have lower fixation probabilities than autosomal inversions. This is because Y-linked inversions never recombine, making them highly susceptible to Muller's ratchet even when common. Autosomal inversions can recombine when homozygous, allowing for the regeneration of mutation-free classes.
• The Sheltering Exception: Y-linked inversions can have a higher fixation probability than autosomes (and even exceed neutral expectations) only when:
  1. Deleterious mutations are very recessive ($h \approx 0$ or $h < 0.02$).
  2. Selection against them is weak (low $N_{e}sh$).
  3. The inversion is large.
  • Mechanism: Under these conditions, the "sheltering effect" allows Y-linked inversions to fix even if they initially carry deleterious mutations, because these mutations remain heterozygous and thus have a minimal fitness cost. In contrast, autosomal inversions would become homozygous as they spread, exposing the deleterious effects and causing elimination.
• Population Size Effect: The advantage of sheltering for Y-linked inversions is maximized at intermediate population sizes. In very large populations, the time to fixation is long enough for mutations to accumulate, negating the sheltering benefit.

C. Inversions Capturing Mating-Type Loci

• Random Mating: Results mirror Y-linked inversions (permanently heterozygous).
• Inbreeding (Selfing/Automixis):
  • Intermediate Selfing ($\sigma \approx 0.5$): Can increase fixation probability for inversions capturing mating-type loci if mutations are partially recessive ($h < 0.5$). The enforced heterozygosity of the inversion masks deleterious alleles that would otherwise become homozygous due to inbreeding.
  • Complete Selfing ($\sigma = 1$): Generally disadvantages inversions. While masking helps, the lack of recombination prevents the efficient purging of mutations. The equilibrium mutation load on the non-recombining inversion becomes higher than on the recombining background, leading to a net fitness disadvantage.

D. Comparison with Previous Models

• The results align with Connallon and Olito (2022) regarding the general erosion of fitness advantages.
• The study supports the Jay et al. (2025) observation that Y-linked inversions can fix with initial loads under specific conditions (very recessive mutations), but clarifies that this is not the general rule and depends heavily on $N_{e}sh$ and $h$.
• It refutes the idea that sheltering is a universal driver for sex chromosome evolution; it is a niche effect dependent on the distribution of fitness effects (DFE) and dominance.

5. Significance and Conclusion

• Evolution of Sex Chromosomes: The study suggests that while deleterious mutations generally hinder the fixation of inversions, the sheltering effect can facilitate the fixation of large inversions on Y/W chromosomes if mutations are highly recessive and selection is weak. However, this is likely not the sole driver of sex chromosome evolution; other mechanisms (e.g., sexual antagonism, gene silencing) are likely required to maintain recombination arrest long-term against the degenerative pressure of Muller's ratchet.
• Macroevolutionary Impact: Although the average fixation probability is low, the occasional fixation of a "lucky" inversion (or a sheltered one) can have significant macroevolutionary consequences, potentially initiating the stepwise expansion of non-recombining regions (evolutionary strata).
• Methodological Rigor: By using individual-based simulations rather than deterministic approximations, the authors successfully captured the stochastic effects of drift and Muller's ratchet, which are critical for understanding the fate of rare inversions in finite populations.

In summary, deleterious mutations act as a double-edged sword: they generally suppress the spread of inversions via Muller's ratchet and fitness erosion, but under specific conditions of high recessivity and weak selection, they can paradoxically promote the fixation of sex-linked inversions through the sheltering of deleterious alleles.