Post 3 — The Maths of Misaligned Incentives: Modeling the Evolution of Bad Science

In the first two posts, we discussed a striking proposition: modern scientific practices evolve under natural selection. Labs that publish more quickly have higher “fitness,” and traits that boost publication rates — even if they weaken the reliability of findings — spread across generations of scientists.

But how do we formalize such a claim?

Smaldino & McElreath didn’t simply rely on anecdotes or intuition. They constructed mathematical and computational models to test how scientific cultures evolve under different incentives. The results were stark:

When productivity (number of publications) is rewarded over accuracy, scientific rigor inevitably declines.

This decline isn’t slow. It’s rapid, predictable, and difficult to avoid without deliberate counter-selection.

In this post, we explore:

• the core structure of their model,

• how “lab traits” are encoded mathematically,

• how selection pressure is simulated,

• why low methodological rigor outcompetes high rigor,

• and how these results mirror real-world science.

We’ll also use examples from population genetics, epidemiology, and cultural evolution to illustrate why the model behaves the way it does.

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1. Why Model Science at All?

Science is complicated. Labs vary enormously:

• Some are huge industrial-scale operations.

• Others are tiny one-person groups.

• Some fields can run 200 experiments per year.

• Others take 2 years for a single dataset.

So why did the authors model scientific evolution using simplified assumptions?

Because models clarify causality.

Real scientific cultures are messy — but the underlying logic of incentives is simple. By stripping away the noise, the model reveals a core truth:

Even with well-intentioned scientists, a system that rewards quantity will select for low-quality methods.

This is the same reason evolutionary biologists model complex ecosystems using simple genetic or ecological equations: clarity emerges from abstraction.

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2. The Core Entities of the Model: Labs, Traits, and Fitness

The model treats labs as the evolving unit — not individual scientists.

Each lab is defined by three key traits:

1. Effort (E)
   How much methodological rigor the lab applies (large samples, careful controls, slow pace).
   Higher effort → lower false positives but fewer studies per year.

2. Power (W)
   The statistical power of research produced by the lab.
   Higher power → more true discoveries, but more expensive studies.

3. Replication Rate (R)
   How often the lab attempts to replicate existing findings.

Each trait comes with a cost:

• Higher power → fewer total studies

• Higher effort → even fewer studies

• Higher replication → fewer original publications

Meanwhile, the scientific environment rewards total publication count, not accuracy.

That reward system is encoded into a fitness function.

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3. Fitness = Publication Count × Reward Structure

A lab’s fitness in the model is determined by:

• the number of studies it runs,

• the probability each study yields a publishable result,

• the reward associated with each result
  (original positive > replication > null results).

Crucial point:

Positive results almost always produce higher rewards than nulls, regardless of truth.

Thus, labs face pressure to:

• increase throughput,

• maximize positive outcomes,

• minimize time spent on replications,

• avoid costly, high-effort research.

The fitness function creates a landscape where low effort and low power produce evolutionary advantages.

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4. How Do Labs “Reproduce”?

Just as organisms with more offspring spread their genes, labs with high fitness:

• train more students,

• place more postdocs in new positions,

• expand into new subfields,

• receive more grant money,

• split or spawn new labs.

In the simulation, “offspring” labs inherit their parent’s traits with slight mutations. This mirrors real-world mentorship:

A student leaves the lab carrying its habits — sample size norms, statistical techniques, even its attitudes toward novelty vs. rigor.

Over generations, labs that publish more (even unreliably) produce more academic descendants.
High-rigor labs produce fewer.

Thus, traits that maximize publication count spread.

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5. The Model’s Heart: The Trade-Off Between Power and Productivity

Scientific studies have costs.

A high-power study (e.g., N = 200) provides robust statistical inference.
But it is expensive.

A low-power study (e.g., N = 10) is cheap and fast.

In the model:

• Low power = many studies per year.

• Many studies = more chances at positive results.

• Positive results = more publications.

• More publications = higher evolutionary fitness.

The logic is evolutionary dynamite.

Mathematically, the expected number of publishable results for a lab is:

Expected Positives = Number of Studies × P(Significant Result)

But P(Significant Result) includes:

• true positives (depends on power & reality)

• false positives (depends on effort & statistical standards)

This means:

Low power increases false positives → increasing publication output → increasing fitness.

This is the central paradox of modern science:

• Low-power labs produce less reliable results,
  but

• Low-power labs produce more publishable results.

Thus low power is selected for.

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6. Replication in the Model: A Weak Immune System

The model incorporates replication attempts. But there are incentives against replication:

• Replications earn less prestige.

• Replications of null results rarely get published.

• Labs conducting replications lose precious time.

Mathematically, replications have:

• lower reward,

• lower impact,

• higher cost.

Thus in the simulation:

• Replication rates evolve downward.

• Fields drift toward poor self-correction.

Even when replication is present, it cannot overcome the selection pressure toward low power unless the rewards for replication are radically increased.

This reflects real-world patterns:

• Replications are rare in psychology, biology, and ecology.

• Journals routinely reject replications.

• Funding agencies rarely support them.

Replication becomes evolutionarily disadvantageous.

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7. The Model’s Results: Decline Is Inevitable Under Current Incentives

After many generations in the simulation, labs evolve toward:

Low effort

(minimal methodological rigor)

Low power

(maximal throughput)

Low replication

(minimal time spent correcting errors)

This is not just one possible outcome. It is the stable outcome of the system.

The authors show that:

• Even if all labs begin as high-quality, high-effort, high-power groups…

• Evolutionary pressure rapidly degrades methods.

• The average false-positive rate skyrockets.

• Replication does not save the system.

• High-quality labs go extinct (outcompeted by low-quality ones).

This reflects reality across many fields where:

• underpowered studies dominate,

• novelty outruns replication,

• flashy claims outnumber reliable findings.

The model formalizes what many scientists intuitively observe.

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8. Real-World Parallels: Why the Model Matches Reality

(a) Population Genetics Parallel

Low-power labs resemble advantageous alleles:

• They reproduce more,

• Their “offspring” spread,

• They take over the population.

High-power labs resemble disadvantageous alleles:

• They reproduce less,

• They gradually disappear.

(b) Epidemiology Parallel

False positives behave like infectious agents:

• They spread rapidly,

• Transmission is easy,

• Labs are susceptible hosts.

Replication is like an immune response:

• Slow,

• Underfunded,

• Often neutralized by social pressures.

(c) Cultural Evolution Parallel

Just as religious rituals or political ideologies spread when they confer social benefits, bad scientific methods spread when they confer career benefits.

The parallels are mathematically and conceptually tight.

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9. Why Good Intentions Do Not Change the Outcome

A key contribution of the paper is dispelling a myth:

Bad science is not the result of bad intentions.

Even if every scientist:

• wants to uncover truth,

• values rigor,

• disapproves of p-hacking,

…the system pushes them toward:

• cutting corners,

• reducing sample sizes,

• publishing prematurely,

• avoiding replications.

This is why the authors emphasize:

“Good science will not survive unless good scientists are rewarded for doing good work.”

The mechanism is evolutionary, not ethical.

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10. When Does Good Science Win? Rare but Possible

The authors simulated strong reforms:

• high rewards for replication,

• penalties for false positives,

• mandatory methodological standards.

Under these artificial conditions, high-effort, high-power labs flourish.

This reflects real-world domains like:

• particle physics (high standardization)

• genomics (large collaborative consortia)

• mathematics (proof-based verification)

These fields have strict norms that counterbalance productivity incentives.

The lesson is optimistic:

If we change the incentive landscape, evolution will favor good science.

But until then, decline is inevitable.

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11. Conclusion: The Mathematics Make It Clear — Incentives Shape Evolution

Smaldino & McElreath’s model shows that:

• Publication incentives are misaligned with truth-seeking.

• Natural selection acts on labs based on those incentives.

• Low rigor and low power spread through academic “lineages.”

• Replication is too weak to stop this trend.

• Only structural reforms can reverse the decline.

This is evolutionary theory applied not to organisms, but to epistemic culture.

The model is not meant to be a perfect mirror of science, but a lens to reveal its hidden structure. And it reveals something stark: we have built an evolutionary environment that selects against good science.

In the next post, we examine a critical question:

Why do bad methods spread faster than good ones — even when scientists know they’re bad?

This will take us deeper into incentives, lab sociology, and the dynamics of statistical shortcuts.