Autopolyploid establishment under gametophytic self-incompatibility: the impact of self-fertilization and pollen limitation

This theoretical study demonstrates that autotetraploid establishment in gametophytic self-incompatible populations is feasible through the evolution of self-compatibility, provided that selfing rates are sufficiently high to overcome minority cytotype exclusion, particularly under conditions of severe pollen limitation.

The Gist

The Big Picture: The "Double Trouble" Problem

Imagine a plant population as a bustling city of Diploids (people with two sets of chromosomes). Suddenly, a mutation happens, and a few new citizens are born with four sets of chromosomes. We call these Tetraploids.

In the world of plants, having extra chromosomes is usually a bad start. These new Tetraploids face a massive social barrier called Minority Cytotype Exclusion.

• The Analogy: Imagine a dance floor where everyone is looking for a partner with exactly two legs (Diploids). The new Tetraploids have four legs. If a Diploid tries to dance with a Tetraploid, the result is a "Triploid" (three legs), which is awkward, clumsy, and often can't dance at all (it's sterile).
• The Result: The Tetraploids are rare. They can't find partners like themselves, and they can't dance with the majority. They are destined to die out unless something changes.

The Secret Weapon: The "Self-Check" System

Most of these plants have a strict security system called Self-Incompatibility (SI).

• The Analogy: Think of the plant's pistil (female part) as a bouncer at a club. It has a list of "bad IDs" (S-alleles). If a pollen grain (male part) has an ID that matches the bouncer's list, the bouncer says, "No entry! You're too similar to us; we can't reproduce." This forces the plant to find a stranger (outcrossing) to reproduce.

Here is the twist: This specific paper looks at a type of security system called Gametophytic SI with Non-Self Recognition. It works like a toxin-antitoxin game.

• The Diploid Bouncer: Has two toxin keys. The pollen has one key. If the pollen's key matches the bouncer's toxin, the pollen is poisoned.
• The Tetraploid Bouncer: Because it has four sets of chromosomes, its pollen is "diploid" (it has two keys). Even if the bouncer has two toxins, the pollen has both antidotes.
• The Result: The security system breaks! The Tetraploid pollen can now bypass the bouncer and fertilize the plant with itself. The plant becomes Self-Compatible (SC).

The Experiment: Can Self-Sufficiency Save the Day?

The researchers asked: If these new Tetraploids can suddenly fertilize themselves, can they survive and take over the city, or do they still need help?

They ran computer simulations with two main scenarios:

Scenario 1: The "Empty Dance Floor" (High Pollen Limitation)

Imagine the city is very small, or the wind isn't blowing pollen around well. There are very few partners available.

• The Finding: The Tetraploids can only survive if they are extremely self-sufficient. They need to be able to fertilize themselves about 80% of the time.
• Why? If they rely on finding a partner, they will likely bump into a Diploid, create a sterile Triploid, and die out. They need to be so good at "self-dancing" that they don't need anyone else.

Scenario 2: The "Busy Dance Floor" (Low Pollen Limitation)

Imagine a big, crowded city where pollen is everywhere.

• The Finding: The Tetraploids have an easier time! They only need to be able to self-fertilize about 30% of the time to survive.
• Why? Because there are so many partners around, they have a better chance of finding another Tetraploid (a "four-legged" partner) to dance with, or they can occasionally rely on the "unreduced gametes" (accidental four-legged pollen) from the Diploids. They don't need to be 100% self-reliant; a little bit of self-sufficiency is enough to bridge the gap.

The Evolutionary Twist: Can They Learn to Self?

The researchers also asked: What if the Tetraploids don't start out self-fertilizing? Can they evolve to become self-fertilizing over time?

• The Bad News: If the mutation rate (the speed at which they can evolve new traits) is slow, they never make it. They get stuck in the "valley" of extinction before they can evolve the ability to self-fertilize.
• The Good News: If the mutation rate is high (they evolve fast), and the "dance floor" is busy (low pollen limitation), they can successfully evolve the habit of self-fertilization and take over the population.

The Aftermath: What Happens to the City?

When the Tetraploids successfully invade and take over:

1. Genetic Diversity Drops: Because they are mating with themselves, the city becomes less diverse. It's like a family reunion where everyone looks the same.
2. The "Bad Genes" Get Purged: Self-fertilization exposes bad genetic mutations. The plants that survive are the ones that have successfully "cleaned out" their bad genes.
3. The Security System Fades: The strict "bouncer" system (Self-Incompatibility) weakens because the plants are mostly mating with themselves anyway.

The Bottom Line

This paper tells us that polyploidy (doubling chromosomes) isn't just a genetic accident; it's a "get out of jail free" card for self-fertilization.

In plants with this specific type of security system, becoming a Tetraploid automatically unlocks the ability to self-fertilize. This is a powerful survival tool. However, it only works if the environment helps them out:

• If the environment is harsh (hard to find pollen), they need to be super self-reliant.
• If the environment is generous (lots of pollen), they just need to be moderately self-reliant.

It's a story of how a genetic glitch (extra chromosomes) accidentally broke the rules, allowing a new type of plant to survive by learning to rely on itself.

Technical Summary

1. Problem Statement

The establishment of neo-polyploids (specifically autotetraploids) within diploid populations is hindered by Minority Cytotype Exclusion (MCE). Because tetraploids are initially rare, they struggle to find compatible mates; crosses between diploids and tetraploids produce sterile or non-viable triploids.

While self-fertilization (selfing) is often hypothesized to aid polyploid establishment by providing reproductive assurance, the specific mechanisms under Gametophytic Self-Incompatibility (GSI) with collaborative non-self-recognition are not fully understood. In this specific GSI system (common in Solanaceae), whole-genome duplication (polyploidy) mechanistically disrupts the SI reaction, automatically rendering heterozygous tetraploids Self-Compatible (SC) without requiring the loss or mutation of specific S-alleles.

The study addresses two main questions:

1. Under what conditions (specifically regarding selfing rates and pollen limitation) can these automatically SC tetraploids invade and establish in a diploid population?
2. How does the evolution of selfing rates (fixed vs. evolving) influence this establishment?

2. Methodology

The authors employed a multi-faceted theoretical approach combining analytical modeling and individual-based simulations.

A. Models Used

1. Neutral Model (Analytical & Simulation):

   • Assumptions: No fitness differences between ploidy levels; no S-locus genotypes tracked. All diploids are obligate outcrossers (SI); all tetraploids are SC.
   • Mechanism: Tetraploids arise via unreduced gametes ($p_u$). Reproduction requires gametes of the same ploidy level (diploid $\times$ diploid or tetraploid $\times$ tetraploid).
   • Goal: Derive analytical thresholds for tetraploid invasion based on selfing rates ($s$) and unreduced gamete probability ($p_u$).

2. GSI Model (Simulation):

   • Assumptions: Tracks S-locus genotypes and fitness via a quantitative genetic model.
   • Mechanism: Implements a collaborative non-self-recognition system (toxin-antitoxin).
     • Diploids: Haploid pollen lacks the antitoxin for its own S-allele $\rightarrow$ SI.
     • Tetraploids: Diploid pollen carries a full set of antitoxins (unless fully homozygous) $\rightarrow$ SC.
   • Pollen Limitation Scenarios: Simulated by limiting the number of pollen grains an ovule receives before rejection (1 attempt = high limitation; 20 attempts = low limitation).
   • Selfing Rate Dynamics: Tested two scenarios:
     • Fixed: Selfing rate ($s$) is constant for all tetraploids.
     • Evolving: Selfing rate is a quantitative trait subject to mutation ($U_{SR}$) and selection.

B. Parameters

• Population Size ($N_{pop}$): 1,000.
• Unreduced Gamete Rate ($p_u$): 0.05 (default).
• Mutation Rates: $U_{SI}$ (S-locus), $U$ (fitness loci), $U_{SR}$ (selfing rate).
• Inbreeding Depression: Calculated as $ID = 1 - (W_s / W_{oc})$.

3. Key Contributions

• Mechanistic Clarification: Confirms that in GSI with non-self-recognition, polyploidy causes an automatic shift to SC due to the dosage of S-alleles in diploid pollen, distinct from systems requiring non-functional S-allele mutations.
• Pollen Limitation Interaction: Demonstrates that the degree of pollen limitation is a critical determinant for tetraploid establishment, interacting non-linearly with selfing rates.
• Evolutionary Constraints: Shows that the evolution of selfing rates is highly constrained by mutation rates and pollen availability, challenging the assumption that selfing always evolves rapidly to rescue polyploids in harsh environments.

4. Key Results

A. Neutral Model Results

• Threshold Selfing Rate: Tetraploid invasion is only possible if the selfing rate ($s$) exceeds a critical threshold ($s_t$).
• Dependence on $p_u$: The threshold $s_t$ is inversely related to the rate of unreduced gamete production.
  • For realistic $p_u = 0.05$, $s_t \approx 0.8$. Tetraploids cannot invade if selfing is below 80%.
  • Higher $p_u$ lowers the required selfing threshold.

B. GSI Model Results (Fixed Selfing Rates)

• High Pollen Limitation (1 attempt): Tetraploid invasion occurs only when selfing rates are very high ($s > 0.8$). This mirrors the neutral model results.
• Low Pollen Limitation (20 attempts): The threshold for invasion drops significantly. Tetraploids can invade with selfing rates as low as $s > 0.3$, and occasionally even at $s = 0.1$ or $0.2$.
  • Reasoning: Under low limitation, tetraploids can successfully outcross with diploids producing unreduced gametes or other tetraploids, reducing their reliance on selfing to overcome MCE.
• Genetic Consequences: Successful invasion leads to:
  • Reduced S-allele diversity (loss of rare alleles).
  • Increased homozygosity at the S-locus.
  • Decreased inbreeding depression (due to purging of deleterious alleles).
  • No significant fitness difference between established tetraploids and diploids.

C. GSI Model Results (Evolving Selfing Rates)

• Mutation Rate Dependency: The evolution of selfing is highly sensitive to the mutation rate ($U_{SR}$).
  • Realistic $U_{SR}$ ($10^{-5}$): Tetraploids never invade. The mutation rate is too slow to generate individuals with high enough selfing rates to overcome MCE before they are lost to drift.
  • High $U_{SR}$ ($10^{-3}$ to $10^{-1}$): Tetraploids invade under low pollen limitation but fail under high pollen limitation.
• Counter-Intuitive Finding: Contrary to the "reproductive assurance" hypothesis (which suggests selfing evolves faster in stressful/pollen-limited environments), tetraploid establishment via evolving selfing is more likely in low pollen limitation scenarios. In high limitation, the population size bottleneck prevents the accumulation of high-selfing mutants fast enough to rescue the lineage.

5. Significance and Implications

• Resolution of MCE: The study proves that autotetraploid establishment is possible through the evolution of selfing alone, without needing extrinsic fitness advantages or the introduction of non-functional S-alleles, provided specific ecological (pollen limitation) and genetic (mutation rates) conditions are met.
• Ecological Context: The results suggest that the evolution of self-compatibility in polyploids is more likely to succeed in stable, large populations (low pollen limitation) where outcrossing is still viable, rather than in colonization events (high pollen limitation) where the "rescue" effect of selfing is insufficient without pre-existing high selfing rates.
• Empirical Predictions:
  • Polyploid species with GSI non-self-recognition should show high selfing rates ($>0.8$) if they established in pollen-limited environments, or moderate rates ($>0.3$) if established in resource-rich environments.
  • Populations of established polyploids should exhibit reduced S-allele diversity compared to their diploid ancestors.
  • The "evolutionary rescue" of polyploids via the evolution of selfing is unlikely to happen rapidly in small, isolated populations unless mutation rates are unusually high.

In summary, the paper provides a rigorous theoretical framework showing that while the mechanistic breakdown of SI in polyploids facilitates selfing, the ecological context (pollen limitation) and genetic parameters (mutation rates) strictly dictate whether this mechanism leads to successful polyploid establishment.