Evolutionary branching of male emergence timing: Trade-offs and variance asymmetry as drivers of dimorphism.

This study employs an adaptive dynamics model to demonstrate that trade-offs between emergence timing and competitiveness, combined with variance asymmetry between sexes, drive the evolutionary branching of male emergence timing into discrete dimorphic or multimorphic strategies, offering a theoretical explanation for the coexistence of early-small and late-large male morphs in insects.

The Gist

Imagine a bustling spring festival where thousands of butterflies and bees are trying to find a date. In this world, timing is everything. If you show up too early, there are no partners yet. If you show up too late, everyone else has already paired off.

For decades, scientists believed that all the males in a species would agree on one "perfect" time to show up—usually just a little bit before the females arrive. They thought nature would force everyone to converge on a single, optimal schedule.

But nature is messy. In the real world, scientists have noticed something weird: some males show up very early and are tiny, while others show up much later and are huge. They are like two different teams playing the same game with completely different strategies.

This paper asks: How does nature allow these two (or even more) different strategies to exist side-by-side without one of them dying out?

The authors built a mathematical "simulator" to figure this out. They found two main reasons why this split happens, using some fun analogies:

1. The "Fast Food vs. Slow Cook" Trade-off (The Trade-off Mechanism)

Imagine a race where the prize is a date.

• The Early Birds: These guys rush out of their cocoons early. They are small and weak, but they get there first. They find the "fresh" females who haven't met anyone else yet. It's like grabbing the last slice of pizza before the party gets crowded.
• The Late Bloomers: These guys stay in their cocoons longer. They grow big and muscular. By the time they emerge, the early birds have already done their business, but the Late Bloomers are so strong and competitive that they can win fights against other males to get the remaining females.

The Analogy: Think of it like a restaurant.

• Strategy A: Go to the restaurant at 5:00 PM. You get a table immediately, but the food is just okay (you're small).
• Strategy B: Wait until 8:00 PM. You have to wait in line, but by then, you've built up enough energy to order the best steak and win a food-eating contest.

The math shows that if the "growth" you get from waiting is really powerful (a steep curve), nature will split the population. You get a team of "Early, Small" guys and a team of "Late, Big" guys. Neither strategy beats the other; they just balance each other out.

2. The "Crowded Room" Effect (The Variance Asymmetry Mechanism)

This one is a bit more subtle. Imagine the females are arriving at a party over a long period (say, 10 days).

• The Scenario: The females arrive slowly and steadily. But the males? They are all very synchronized. They all burst out of their cocoons on the exact same day.
• The Problem: On that one specific day, the party is packed. There are 1,000 males fighting for 100 females. The competition is so fierce that the "average" guy has almost zero chance of getting a date.
• The Solution: Nature realizes that being "average" is a losing strategy.
  • The Early Males: They show up before the crowd. They find the few females who arrived early. No competition!
  • The Late Males: They show up after the crowd has left. They find the few females who arrived late. No competition!
  • The Middle Males: They get crushed in the middle.

The Analogy: Think of a popular concert.

• If everyone tries to get in at the exact same time, the line is impossible, and nobody gets in.
• But if some people sneak in 2 hours early (before the line forms) and others show up 2 hours late (after the line breaks), they both get in easily.
• The people who show up right when the line is longest? They go home empty-handed.

When the males are too synchronized (low variance) compared to the females (high variance), the "middle" strategy becomes a trap. Evolution pushes the males to the extremes, creating two distinct groups.

The Wild Card: The "Three-Team" Party

The most surprising finding is that if the males are extremely synchronized and the females are very spread out, the party doesn't just split into two teams. It can split into three, four, or even more groups!

Imagine the "crowded room" is so big that even the "Early" group gets too crowded. So, a third group evolves to show up super early. Then a fourth group shows up super late. The paper shows that under the right conditions, nature can create a whole lineup of different "shifts" of males, all coexisting.

Why Does This Matter?

This isn't just about butterflies. It explains how a single species can evolve into different "types" of individuals without splitting into two different species yet. It's a stepping stone toward speciation (becoming new species).

If the "Early" males only mate with "Early" females, and the "Late" males only mate with "Late" females, eventually they might stop recognizing each other as mates at all. This paper suggests that timing itself could be the first step in creating new species, driven by the simple logic of avoiding the crowd and finding the best deal.

In short: Nature loves options. Sometimes, being the first, the last, or the biggest is better than being the "average" middle. And when the competition gets too hot in the middle, evolution splits the team into distinct strategies to keep the game going.

Technical Summary

1. Problem Statement

Classical evolutionary models of protandry (where males emerge before females) predict a unimodal distribution of male emergence timing. These models suggest that natural selection drives all males toward a single optimal emergence time that balances the benefits of early mating opportunities against the costs of reduced survival or competitiveness.

However, empirical observations in various insects (e.g., butterflies like Fabriciana nerippe and bees like Amegilla dawsoni) reveal dimorphism: the coexistence of two distinct male strategies—early-emerging small males and late-emerging large males. Existing theoretical frameworks fail to explain how such discrete alternative reproductive strategies (dimorphism) evolve and are maintained within a single population. This study aims to identify the ecological and evolutionary mechanisms that drive the transition from a unimodal to a dimorphic (or polymorphic) male emergence distribution.

2. Methodology

The authors employed an Adaptive Dynamics (AD) framework to model the long-term evolutionary dynamics of male emergence timing.

• Model Assumptions:
  • Generations do not overlap.
  • Emergence timing is a genetically determined trait following a normal distribution.
  • Females mate only once immediately upon emergence; males can mate multiple times.
  • Total population size and sex ratio are constant.
  • Male mortality is constant.
• Key Variables:
  • $\tau$: Mean emergence timing of males (the evolving trait).
  • $\sigma_m, \sigma_f$: Standard deviations (variances) of male and female emergence distributions, respectively.
  • $f(t)$: A sigmoidal competitiveness function linking emergence time to body size/mating success.
• Analytical Approach:
  • Invasion Fitness ($W$): Calculated as the expected lifetime number of matings for a rare mutant male with trait $\tau'$ in a resident population with trait $\tau$.
  • Singular Strategy ($\tau^*$): Found by solving the fitness gradient $D(\tau) = 0$.
  • Stability Analysis:
    • Convergence Stability: Determines if the population evolves toward $\tau^*$.
    • Evolutionary Stability (ESS): Determines if $\tau^*$ resists invasion by nearby mutants.
    • Evolutionary Branching: Occurs if a singular strategy is convergence stable but not evolutionarily stable (disruptive selection), leading to the divergence of the population into distinct clusters.
  • Validation: Results were verified using Individual-Based Simulations (IBS) over 10,000 generations.

3. Key Contributions

The study introduces two distinct mechanisms that can drive evolutionary branching in male emergence timing, challenging the assumption that protandry must be unimodal:

1. Trade-off Mechanism: A nonlinear trade-off between emergence timing and male competitiveness (body size).
2. Variance Asymmetry Mechanism: Differences in the variance of emergence timing between sexes, specifically when male emergence is more synchronized (lower variance) than female emergence.

4. Key Results

A. Evolutionary Outcomes under Different Conditions

• Neutral Condition: When there is no trade-off and variances are equal ($\sigma_m = \sigma_f$), the population converges to a single, stable, unimodal emergence time (protandry).
• Trade-off Condition:
  • When the relationship between development time and competitiveness is highly nonlinear (steep sigmoid), evolutionary branching occurs.
  • Result: The population splits into two clusters: Early males (smaller, high mating success due to virgin female availability) and Late males (larger, high mating success due to superior competitive ability).
  • Parameter Dependence: Branching is most likely when the steepness ($k$) of the competitiveness function is high and the inflection point ($s$) is intermediate.
• Different-Variance Condition:
  • Branching occurs when the variance of male emergence ($\sigma_m$) is significantly smaller than that of females ($\sigma_f$).
  • Mechanism: High synchronization of males creates intense scramble competition at the peak of female emergence. This depletes the "resource" (virgin females) for intermediate phenotypes, creating a fitness valley. Selection favors phenotypes at the tails (very early or very late), driving disruptive selection.
  • Result: The population splits into early and late morphs. Notably, the early-emerging morph is consistently smaller in frequency than the late-emerging morph due to the temporal constraint of the pre-peak window.

B. Multiple Branching

• Under the variance asymmetry mechanism, if male variance is extremely low relative to female variance, multiple branching events can occur.
• Result: The population can evolve into three or more distinct phenotypic clusters (e.g., very early, intermediate, and very late), rather than just a simple dimorphism.

C. Parameter Sensitivity

• Mortality ($\mu$): Higher adult male mortality facilitates polymorphism, as it reduces temporal overlap among competitors, effectively partitioning the mating season into more distinct niches.
• Competitiveness Shape: The sigmoidal shape of the competitiveness function is crucial; linear or exponential functions (used in older models) failed to produce branching.

5. Significance and Implications

• Theoretical Resolution: The study resolves the discrepancy between classical unimodal predictions and empirical dimorphic observations by identifying specific ecological conditions (nonlinear trade-offs and variance asymmetry) that generate disruptive selection.
• Testable Predictions:
  • Trade-off Mechanism: Predicts a strong positive correlation between emergence timing and body size/competitiveness. (Consistent with observations in Fabriciana nerippe and Amegilla dawsoni).
  • Variance Mechanism: Predicts that male emergence variance should be significantly lower than female variance, with minimal body size differences between morphs.
• Broader Evolutionary Context:
  • The findings link the evolution of protandry to the broader phenomenon of Alternative Reproductive Strategies (ARS).
  • The model suggests that multiple branching can generate complex polymorphisms (3+ strategies), expanding the understanding of how discrete morphs arise.
  • Speciation Potential: The temporal segregation of mating strategies could act as a "magic trait," potentially leading to allochronic reproductive isolation and incipient speciation if female emergence timing is heritable.
• Future Directions: The authors suggest extending the model to allow the evolution of variance itself and incorporating condition-dependent tactics, which are common in nature but not captured in this genetic polymorphism model.

In summary, this paper provides a robust mathematical foundation for understanding how discrete male reproductive strategies evolve in seasonal breeders, demonstrating that both physiological trade-offs and statistical properties of emergence distributions can drive the evolution of dimorphism and polymorphism.