Resource availability and dimensionality result in ecology-dependent selection in bacteriophage spatial expansions

This study demonstrates that in bacteriophage spatial expansions, optimal fitness traits and competitive outcomes are not determined by standard isolation metrics but are instead driven by the complex interplay between resource availability, system dimensionality, and ecological context.

The Gist

The Big Idea: Why "Fastest" Doesn't Always Mean "Winner"

Imagine you are watching a race. Usually, we assume that the runner who runs the fastest in practice will win the actual race. In the world of viruses (specifically bacteriophages, which are viruses that eat bacteria), scientists have traditionally used two main ways to guess who the "fittest" virus is:

1. How many viruses can they make? (The crowd size).
2. How fast does their edge move? (The speed of the frontier).

This paper, by Hassan Alam and Diana Fusco, asks a simple but tricky question: If we know how fast a virus moves when it's alone, can we predict who will win when two different viruses race against each other?

The answer is a surprising "No."

The authors found that the rules of the game change completely depending on whether the viruses are alone, fighting each other, or racing in a 1D line versus a 2D sheet. It turns out that fitness is not a fixed number; it depends entirely on who your neighbors are and what the "terrain" looks like.

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The Analogy: The Zombie Apocalypse in a City

To understand this, let's imagine the bacteria are uninfected people in a city, and the phages are zombies.

1. The Solo Run (Isolation)

Imagine a zombie is released in an empty city.

• Metric A (Density): How many zombies can it create before running out of people?
• Metric B (Speed): How fast does the zombie horde spread across the map?

If you test two types of zombies (Zombie Type A and Zombie Type B) separately, you might find they both spread at the exact same speed (5 meters per minute) and create the same number of zombies. You would assume they are equally strong.

2. The Race (Competition)

Now, put Zombie Type A and Zombie Type B in the same city, starting from opposite sides. They race toward the middle.

The Shocking Discovery:
Even though they were equally fast when alone, one of them suddenly starts winning.

• Why? Because they are fighting over the same food (the uninfected people).
• The "Discreteness" Problem: The paper highlights a specific rule: A zombie needs a minimum number of other zombies nearby to successfully infect a person. If the group gets too small, the infection stops.
• When they race alone, the "front" of the zombie horde is thin, but there's plenty of food.
• When they race together, they crowd each other. The "front" gets messy. The virus that is slightly better at grabbing a victim first (even if it's slower overall) wins the race because it eats the food before the other one can get there.

The Result: The "fastest" solo runner often loses the head-to-head race because it wastes energy trying to infect people who are already being eaten by the other virus.

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The Twist: The Dimension of the World (1D vs. 2D)

This is where the paper gets really wild. The authors ran these simulations in two different "worlds":

• 1D (A Line): Like a zombie race down a single hallway.
• 2D (A Sheet): Like a zombie race spreading across a whole floor plan.

The "Rock-Paper-Scissors" Effect
In the 1D hallway, they found a weird pattern:

• Virus A beats Virus B.
• Virus B beats Virus C.
• But Virus C beats Virus A.

This is called Rock-Paper-Scissors dynamics. It means there is no single "best" virus. The winner depends entirely on who you are fighting. If you change the opponent, the winner changes.

The Dimension Flip
Here is the biggest surprise: The winner in the hallway (1D) is often the loser in the open room (2D).

• In the hallway (1D): The viruses are forced to compete directly. The one that is slightly better at "grabbing" the host first wins.
• In the open room (2D): The viruses can spread out sideways. The paper found that in 2D, the virus that was slower in isolation sometimes wins because the presence of the other virus actually helps it!
  • How? When the two viruses push against each other, they create a "traffic jam" at the front. This slows down the expansion. In this traffic jam, the virus that is better at surviving in crowded conditions (or has a specific trait) gets a boost. The "loser" in the 1D race suddenly becomes the "winner" in the 2D race.

The "Ecology-Dependent" Lesson

The authors call this "Ecology-Dependent Selection."

Think of it like a job interview:

• In a quiet office (Isolation): You might be the best candidate because you are fast and efficient.
• In a chaotic, noisy office (Competition): Your speed doesn't matter as much as your ability to navigate the chaos.
• In a different building (Different Dimension): The rules of the office change again. The person who was the best in the first office might be terrible in the second.

The Takeaway:
You cannot define a virus's "fitness" as a single number (like "Speed = 5"). Fitness is a relationship. It depends on:

1. Who you are fighting.
2. Where you are fighting (1D line or 2D space).
3. How you interact with the resources (bacteria).

Why Does This Matter?

This changes how scientists study evolution.

• Old way: "We found the fastest virus in a petri dish, so that's the one that will win in nature."
• New way: "We can't predict the winner just by looking at them alone. We have to simulate the whole ecosystem, because the winner changes based on the environment and the competition."

It's a reminder that in nature, context is everything. A trait that makes you a champion in one situation might make you a loser in another, and the "best" virus is simply the one that happens to be in the right place with the right neighbors.

Technical Summary

1. Problem Statement

The paper addresses a fundamental gap in evolutionary biology and virology: the lack of a universally applicable definition of bacteriophage fitness in spatially structured environments.

• Context: In well-mixed liquid cultures, fitness is often defined by growth rate or steady-state density. However, in spatial range expansions (e.g., plaque formation on bacterial lawns), fitness is context-dependent due to resource competition (susceptible host cells) and spatial constraints.
• The Challenge: Common metrics used to predict phage evolution in isolation—specifically steady-state phage density and plaque front expansion speed—have not been rigorously tested for their ability to predict the outcome of direct competitions between different phage strains.
• Core Question: Do fitness metrics derived from single-strain expansions in isolation reliably predict the winner in direct competitions, and does the dimensionality of the system (1D vs. 2D) alter these outcomes?

2. Methodology

The authors employed a computational approach using non-linear spatiotemporal reaction-diffusion equations to model phage-bacteria dynamics.

• Model System:

  • Phases: The infection cycle is modeled with two phases (eclipse and productive) to generate a hypoexponential distribution of lysis times, which is more biologically realistic than the exponential distributions used in many previous models.
  • Superinfection Exclusion: The model incorporates post-adsorption superinfection exclusion, where secondary phages adsorbing to an already infected cell cannot replicate and are lost.
  • Discreteness Threshold: A critical feature is the inclusion of a phage discreteness threshold ($\theta$). A Hill function $T(V)$ ensures that infection reaction terms are zero if phage density falls below a specific threshold (simulating the fact that a single lattice site cannot be infected by a fraction of a phage). This prevents unrealistic low-density dynamics.
  • Dimensions: Simulations were run in both 1D (linear expansion) and 2D (circular/plaque expansion) to compare outcomes.

• Fitness Definitions Tested:

  1. Steady-state maximum phage density at the plaque front.
  2. Steady-state plaque front expansion speed.

• Experimental Design:

  • The authors identified phage strains with identical fitness metrics in isolation (isofitness curves) but different underlying parameters (adsorption rate $\alpha$ and infection progression rate $\lambda$).
  • These strains were then pitted against each other in direct pairwise competitions in both 1D and 2D environments to observe which strain dominated.

3. Key Contributions

• Refutation of Isolation Metrics: The study demonstrates that fitness metrics measured in isolation (density or speed) are poor predictors of competitive outcomes in spatial expansions.
• Discovery of Non-Transitive (Rock-Paper-Scissors) Dynamics: The authors show that fitness is non-additive and non-transitive. If Strain A beats Strain B, and Strain B beats Strain C, it does not guarantee that Strain A beats Strain C. The outcome depends on the specific phenotypic makeup of the competing pair.
• Dimensionality Dependence: The paper establishes that the outcome of a competition can flip entirely when moving from 1D to 2D systems. A strain that wins in 1D may lose in 2D, even if their isolation metrics are identical.
• Ecology-Dependent Selection: The authors introduce the concept that optimal phage traits are not absolute but depend on the "ecological context" (i.e., the specific competitors present and the spatial dimension).

4. Key Results

A. Failure of Isolation Metrics in 1D

• Density vs. Speed: Two strains with the same steady-state density in isolation do not necessarily coexist; the one with a higher adsorption rate often wins. Similarly, strains with identical expansion speeds in isolation do not coexist; the winner depends on the specific trade-off between adsorption and lysis rates.
• Role of Discreteness: The failure of "expansion speed" to predict competition is directly linked to the phage discreteness threshold. In isolation, the expansion speed is determined by the very tip of the wave (low density, no competition). In competition, the shared resource constraint forces the "speed-determining" region to shift to higher densities where competition is fierce, altering the dynamics.

B. Dimensionality Flip (1D vs. 2D)

• 1D Outcome: In linear expansions, the competition outcome is determined by the specific interaction of adsorption rates and the resulting density profiles.
• 2D Outcome: In 2D, the dynamics are more complex. The authors observed that:
  • Transient Neutrality: Strains with equal isolation speeds often appear neutral at the interface for short timescales.
  • Long-Term Reversal: Over long timescales, the ordering of density profiles can reverse. A strain that initially lags (due to lower adsorption) may eventually overtake the leader.
  • The Flip: In specific pairwise competitions (e.g., Strains D, E, F), the winner in 1D was different from the winner in 2D. For example, Strain E was the most competitive in 1D but the least competitive in 2D.
• Mechanism: In 2D, the "bulging" of the front and the local variation in competitor proportions create a feedback loop where the presence of a competitor can actually enhance the local density of another strain (due to resource consumption patterns slowing the front), leading to counter-intuitive dominance.

C. Ecology-Dependent Fitness Landscapes

• The study reveals that isofitness curves (lines of equal fitness relative to a reference strain) are not universal. A strain that is neutral to a reference strain in a pairwise competition may not be neutral to a third strain.
• This leads to Rock-Paper-Scissors (RPS) dynamics, where the "fittest" trait changes depending on the population composition.

5. Significance

• Theoretical Impact: The paper challenges the standard practice of using single-strain expansion speeds as a proxy for evolutionary fitness in spatial models. It argues that fitness in spatially structured populations is an emergent property of the community, not just the individual.
• Experimental Implications: It suggests that evolutionary trajectories in phage experiments (and potentially other microbial systems) are highly sensitive to initial conditions and the specific mix of mutants present. Predicting evolution requires knowing the full "ecological" context, not just isolated traits.
• Broader Applicability: While focused on bacteriophages, the findings regarding resource consumption, replication trade-offs, and dimensionality effects likely apply to any population expanding in space while competing for shared, finite resources (e.g., cancer cell growth, invasive species, bacterial colonies).
• Modeling Insight: The inclusion of discreteness thresholds and hypoexponential lysis times proved essential for capturing these complex dynamics, highlighting the need for more biologically realistic parameters in reaction-diffusion models.

In conclusion, the paper demonstrates that fitness is not a fixed scalar value but a dynamic, ecology-dependent property heavily influenced by spatial dimensionality and the specific nature of resource competition.