Sexually antagonistic environments and the stability of environmental sex determination

This paper demonstrates that the specific functional form of sexually antagonistic environmental effects (Charnov-Bull effects) critically determines the evolutionary stability of environmental sex determination, influencing whether sex-biasing alleles invade to fixation or persist at intermediate frequencies to create mixed systems.

The Gist

The Big Picture: Nature's "Gender Switch"

Imagine a species of lizard or turtle where the sex of the baby isn't decided by a genetic coin flip (like having an X or Y chromosome). Instead, it's decided by the temperature of the nest.

• Hot nest? Baby becomes a boy.
• Cold nest? Baby becomes a girl.

Scientists call this Environmental Sex Determination (ESD). It's a clever system because it lets nature match the baby's gender to the environment where that gender will do the best. For example, maybe boys grow bigger and stronger in the heat, while girls survive better in the cold.

The Conflict: Nature vs. Nurture (Genetics)

For a long time, biologists thought this temperature system was unstable. They believed that "genetic" sex determination (where your DNA decides your sex, regardless of temperature) would eventually take over.

Why? Because of Sexual Antagonism.
Think of it like this: A specific gene might be great for a boy (making him a super-fast runner) but terrible for a girl (making her slow and easy prey). If a mutation arises that forces a baby to be a boy and carries that "super-runner" gene, it should spread like wildfire, turning the whole population into a genetic sex-determination system.

The New Discovery: It's Not That Simple

This paper argues that the old view is too simple. The authors say: "It depends on the shape of the relationship between temperature and success."

They call this relationship the "Charnov–Bull Effect." Think of it as a fitness landscape.

Analogy 1: The Slope vs. The Cliff

Imagine you are walking up a hill.

• Scenario A (The Gentle Slope): As you walk up, the view gets slightly better. If you take a wrong step (a genetic mutation that forces you to be a specific gender at the wrong temperature), you just stumble a little. You can recover. In this case, genetic mutations can easily invade and take over.
• Scenario B (The Cliff): Imagine the hill is flat, but then suddenly drops off a massive cliff. If you take a wrong step, you fall to your death.

The authors found that in many animals, the relationship between temperature and survival isn't a gentle slope; it's a cliff (or a sharp curve).

• If a "genetic" mutation tries to force a baby to be a boy in a temperature where girls actually do better, the baby might not just be slightly less fit—they might die.
• Because the "cost" of making the wrong choice is so high (the cliff), these genetic mutations get crushed before they can take over.

The "Mixed" System: The Best of Both Worlds

The most exciting part of the paper is what happens when the genetic mutation does try to invade but can't win completely.

Instead of the genetic system taking over 100% of the population, the two systems end up co-existing.

• The Analogy: Imagine a town where most people decide their children's gender based on the weather (ESD). But then, a few families start using a genetic rule (GSD).
• If the genetic rule is too aggressive (forcing a gender in the wrong weather), the family suffers.
• But if the genetic rule is just a little bit biased, it can survive alongside the weather rule.

This creates a "Mixed System." In these populations, some babies are born based on temperature, and others are born based on their genes. The paper shows that these mixed systems are actually very stable and common, especially when the "fitness landscape" has those sharp curves (non-linear effects).

Why This Matters: Climate Change

This isn't just theoretical math; it's crucial for the future.

• The Problem: Climate change is altering the temperature distribution. It's getting hotter, and the "weather" is changing.
• The Risk: If the temperature landscape changes, the "cliffs" might move. A system that was stable yesterday might become unstable tomorrow.
• The Takeaway: We can't just assume these animals will switch to genetic sex determination to save themselves. Whether they survive or switch depends entirely on the specific, complex shape of how temperature affects their survival.

Summary in One Sentence

This paper shows that environmental sex determination is more stable than we thought because the "cost" of getting the gender wrong in nature is often too high for genetic mutations to overcome, leading to a stable mix of both environmental and genetic sex determination rather than a total takeover by genes.

Technical Summary

1. Problem Statement

Environmental Sex Determination (ESD) is a system where an environmental cue (e.g., temperature) dictates the sex of an offspring. While ESD is theoretically advantageous because it allows each sex to develop in the environment where it has the highest fitness (known as Charnov–Bull effects), evolutionary theory often predicts that ESD is inherently unstable.

The prevailing view suggests that sexually antagonistic genetic variants (alleles beneficial to one sex but harmful to the other) linked to sex-determining mutations will inevitably drive transitions from ESD to Genetic Sex Determination (GSD). However, recent empirical evidence shows that many species exhibit "mixed" systems where both genetic and environmental factors influence sex determination, and transitions are not always unidirectional.

The Core Question: How does the precise functional form (shape) of Charnov–Bull effects (the relationship between environmental variables and sex-specific fitness) influence the stability of ESD systems against invasion by sex-biasing alleles, and under what conditions do these alleles lead to fixation (GSD) versus stable polymorphism (mixed systems)?

2. Methodology

The authors employ a theoretical population genetics framework to model the invasion and post-invasion dynamics of sex-biasing haplotypes in an ESD system.

• Model Setup:

  • Environment: A continuous environmental variable $t$ (e.g., temperature) distributed according to a density function $g(t)$.
  • Fitness Functions: Male and female viability ($V_m(t)$ and $V_f(t)$) are defined as functions of $t$. The authors explore both linear (monotonic) and nonlinear (e.g., logistic, U-shaped) fitness functions.
  • ESD Thresholds: The population possesses heritable thresholds ($\Theta$) that determine sex. An Evolutionarily Stable Strategy (ESS) threshold $\theta^*$ exists where the expected reproductive success of males and females is equal ($W_m = W_f$).
  • Invasion Model: The authors introduce a rare, sexually antagonistic haplotype ($H$) that:
    1. Biases the threshold: Shifts the developmental threshold by an amount $\delta$ (making the bearer more likely to develop as one sex).
    2. Confers direct fitness benefits: Has selection coefficients $s_m$ and $s_f$ (where $s_m > 0 > s_f$ or vice versa) representing sexually antagonistic effects.

• Analytical Approach:

  • Invasion Criteria: Deriving conditions under which the haplotype $H$ can invade a resident population fixed for the ESS threshold. This involves calculating the Charnov–Bull cost (fitness loss due to developing as the lower-fitness sex in a displaced temperature range) versus the sexual antagonism benefit.
  • Polymorphism Criteria: Determining if the resident haplotype ($h$) can re-invade a population fixed for $H$. If both can invade each other, the system reaches a stable polymorphism (mixed ESD-GSD).
  • Dynamics Simulation: Numerical simulations using a quantitative genetics approach (Breeder's equation) to model the co-evolution of the haplotype frequency and the "background" polygenic threshold value, accounting for sex-ratio distortion.

3. Key Contributions

1. Functional Form Sensitivity: The paper demonstrates that the stability of ESD is not just a function of the existence of Charnov–Bull effects, but critically depends on their mathematical shape (linearity vs. nonlinearity, single vs. double crossing).
2. Cost of Threshold Displacement: The authors formalize the "Charnov–Bull cost" as the area between male and female fitness curves over the temperature range where the mutant allele misassigns sex. They show this cost scales quadratically with the magnitude of the threshold shift ($\delta^2$) for small effects but accelerates non-linearly for large effects in nonlinear fitness landscapes.
3. Mechanism for Mixed Systems: The study provides a rigorous theoretical mechanism explaining how "mixed" ESD-GSD systems can persist. It shows that strong sex-biasing alleles often fail to reach fixation because the fitness costs of large threshold displacements in nonlinear environments prevent them from overcoming the sexual antagonism benefits.
4. Two-Threshold Systems: The authors analyze systems with two thresholds (e.g., males at intermediate temperatures, females at extremes), showing these are significantly more resistant to invasion by large-effect alleles than single-threshold systems due to the "wedge-shaped" fitness cost geometry.

4. Key Results

• Invasion vs. Fixation:

  • Small-effect alleles: In both linear and nonlinear Charnov–Bull scenarios, alleles with small threshold shifts can invade and often reach stable polymorphism. The outcome is relatively insensitive to the functional form of fitness.
  • Large-effect alleles: The outcome diverges sharply based on the fitness function shape.
    • Linear Fitness: Large-effect alleles can invade and potentially fix or reach high-frequency polymorphism.
    • Nonlinear Fitness (e.g., Logistic, U-shaped): The fitness cost of displacing the threshold increases rapidly (accelerates) as the shift magnitude grows. This creates a "barrier" where large-effect alleles cannot invade, or if they do, they are driven to intermediate frequencies rather than fixation.

• The "Mixed" System Outcome:

  • In nonlinear environments (specifically those with U-shaped female fitness and inverse-U shaped male fitness, as seen in the Jacky dragon), the parameter space allowing for long-term polymorphism is narrow.
  • Strong threshold-biasing alleles are less likely to invade these systems. If they do invade, they are more likely to be held at intermediate frequencies, resulting in a stable mixed ESD-GSD system where genetic and environmental cues coexist.

• Two-Threshold Systems:

  • Systems with two thresholds (females at extremes, males in the middle) exhibit "wedge-shaped" fitness costs. The cost of displacement is severe even for moderate shifts.
  • Consequently, these systems are highly resistant to the invasion of genetic sex determiners, explaining the phylogenetic persistence of two-threshold TSD in reptiles.

• Role of Environmental Distribution ($g(t)$):

  • The density of the environment matters. If the environment rarely occurs in the temperature range where the mutant allele causes a "wrong" sex assignment, the fitness cost is low, facilitating invasion. Climate change altering $g(t)$ could therefore destabilize or stabilize ESD systems.

5. Significance

• Re-evaluating ESD Stability: The paper challenges the dogma that ESD is inherently unstable and destined to be replaced by GSD. It argues that the complexity of the environmental-fitness relationship acts as a stabilizing force.
• Explaining Empirical Anomalies: The results provide a theoretical basis for the growing number of observed "mixed" systems in nature, where sex determination is neither purely genetic nor purely environmental.
• Climate Change Implications: Since the stability of ESD depends on the specific shape of fitness functions and the distribution of environmental variables, climate change (which alters $g(t)$) could unpredictably shift populations from stable ESD to mixed systems or GSD, or vice versa.
• Future Research Directions: The authors emphasize the urgent need for empirical studies to map the precise functional forms of Charnov–Bull effects in natural populations, as theoretical predictions vary wildly depending on whether these functions are linear or nonlinear.

In summary, the paper establishes that the nonlinearity of sex-specific fitness responses to environmental cues is a critical, often overlooked factor that can preserve Environmental Sex Determination against the invasion of genetic sex determiners, thereby maintaining evolutionary diversity in sex-determination systems.