arxiv: 2604.27520 · v1 · submitted 2026-04-30 · 🧬 q-bio.PE

Recognition: unknown

Incorporating the underuse problem in the tragedy of the commons

Shota Shibasaki , Wakaba Tateishi , Shuhei Fujii , Ryosuke Nakadai

Authors on Pith no claims yet

Pith reviewed 2026-05-07 09:03 UTC · model grok-4.3

classification 🧬 q-bio.PE

keywords tragedy of the commonsunderuseoveruseeco-evolutionary modeladaptive dynamicscommon-pool resourcesprovisioning benefitsevolutionary branching

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The pith

Both overuse and underuse of shared resources arise as natural evolutionary outcomes from the same process.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds an eco-evolutionary model of common-pool resource use that tracks how individual strategies change while altering resource levels. It incorporates both provisioning services that directly benefit users and non-provisioning services that affect the wider system. Analysis via adaptive dynamics reveals that the shape of the provisioning benefit function decides whether the population converges to a single intermediate strategy, overshoots into overuse, undershoots into underuse, or splits into branching strategies. This reframes the tragedy of the commons as a two-sided evolutionary problem rather than one limited to overexploitation.

Core claim

In the model, provisioning benefits that increase concavely produce a single continuously stable intermediate strategy that is also close to the social optimum when non-provisioning services are valued. When those benefits increase convexly, the same dynamics generate overuse, underuse, bistability between those extremes, or evolutionary branching, with the gap between the evolutionarily stable strategy and the social optimum widening as non-provisioning valuation changes. Analytical conditions for the number and stability of singular strategies are derived directly from the benefit functions.

What carries the argument

The shape of the provisioning benefit function (concave versus convex increasing) that governs how individual payoff changes with resource abundance in the adaptive-dynamics framework.

If this is right

Concave provisioning benefits produce a single continuously stable intermediate strategy.
Convex provisioning benefits allow overuse, underuse, bistability, and evolutionary branching as alternative outcomes.
The distance between the evolutionarily stable strategy and the socially optimal strategy increases with the relative valuation of non-provisioning services.
Common-pool resource problems must be treated as intrinsically two-sided evolutionary dilemmas rather than solely overuse problems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Management interventions could aim to alter the curvature of perceived provisioning benefits to shift outcomes away from both overuse and underuse.
The model supplies a baseline for adding spatial structure or stochasticity to test whether the reported qualitative patterns survive.
Similar benefit-shape logic may apply to other abandoned or degraded resources such as traditional agricultural terraces or urban green spaces.

Load-bearing premise

The shape of provisioning benefits can be cleanly classified as concave or convex, and adaptive dynamics without spatial structure or stochasticity captures the dominant evolutionary trajectory.

What would settle it

A field system with convex-increasing provisioning benefits in which observed resource-use strategies converge to a unique stable intermediate level rather than showing overuse, underuse, or branching would contradict the model's predicted outcomes.

read the original abstract

The tragedy of the commons has traditionally been framed as a problem of resource overuse driven by self-interested exploitation. In contrast, growing empirical evidence shows that insufficient use or abandonment of natural resources, known as underuse, can also lead to ecological degradation and loss of ecosystem services. Despite its relevance, underuse has rarely been examined within evolutionary theories of resource use. Here, we develop a simple eco-evolutionary model that integrates both provisioning and non-provisioning ecosystem services to analyze the evolution of resource-use strategies. Using adaptive dynamics, we investigate how individual resource use evolves while altering resource abundance. The model shows that overuse and underuse arise naturally as alternative evolutionary outcomes of the same underlying process, alongside intermediate use and evolutionary branching. We derive analytical conditions for the existence, number, and stability of evolutionarily singular strategies, and show that the qualitative evolutionary fate is primarily determined by the shape of provisioning benefits. Only when provisioning benefits increase in a concave manner does evolutionary dynamics converge to a unique intermediate strategy that is continuously stable. In contrast, convex increasing benefits generate a broader range of outcomes: overuse, underuse, bi-stability, and evolutionary branching. By explicitly comparing the continuously stable strategy with the socially optimal strategy, we further quantify how their deviations depend on the valuation of non-provisioning services. Our results provide a theoretical framework for viewing the common-pool resource dilemmas as intrinsically two-sided evolutionary problems, and offer a baseline for future studies exploring interventions to address overuse and underuse simultaneously.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper gives a clean adaptive-dynamics model in which overuse and underuse both emerge from the same evolutionary process, with the curvature of provisioning benefits deciding the outcome.

read the letter

The main point is that the authors treat underuse as an evolutionary outcome on equal footing with overuse. They build a simple eco-evolutionary model that includes both provisioning and non-provisioning services, then use adaptive dynamics to track how individual resource-use strategies change resource levels. The central result is that concave increasing benefits produce a single continuously stable intermediate strategy, while convex benefits allow overuse, underuse, bi-stability, and branching. They also give analytical conditions for the number and stability of singular strategies and show how the gap between the evolutionary outcome and the social optimum grows with the weight placed on non-provisioning services. That comparison is useful and not automatic in this literature. The work is new in pulling underuse into an evolutionary framework for common-pool resources; most prior models focused only on overuse. The derivations appear self-contained and the logic is straightforward, which makes the claims easy to follow. The model is deliberately minimal, so the qualitative regimes stand out clearly. The main limitation is that the qualitative fate depends on classifying the benefit function as concave or convex. Real provisioning benefits may not fall neatly into one category, and the paper does not explore intermediate or non-monotonic shapes. Adaptive dynamics also assumes gradual change in large populations, so spatial structure or demographic stochasticity could alter the picture. These are standard modeling choices rather than fatal gaps, but they limit how far the results travel without further checks. The paper is for readers who already work with adaptive dynamics or evolutionary models of resource use. Someone looking for a baseline theoretical unification of the two-sided tragedy of the commons will find the conditions and the social-optimum comparison worth reading. It is coherent on its own terms and the claims are stated precisely enough to be checked. I would send it for peer review, with the usual request that the authors supply the full functional forms and stability calculations in the supplement so referees can verify the derivations directly.

Referee Report

0 major / 2 minor

Summary. The paper develops a simple eco-evolutionary model integrating provisioning and non-provisioning ecosystem services to study the evolution of resource-use strategies under adaptive dynamics. It claims that overuse and underuse arise as alternative evolutionary outcomes of the same process, with analytical conditions derived for the existence, number, and stability of evolutionarily singular strategies. The qualitative outcome is determined primarily by the curvature of provisioning benefits: concave increasing benefits yield a unique continuously stable intermediate strategy, while convex increasing benefits produce overuse, underuse, bi-stability, and evolutionary branching. The continuously stable strategy is compared to the socially optimal strategy, with deviations quantified in terms of the valuation of non-provisioning services.

Significance. If the analytical derivations and stability results hold, the work is significant for providing a unified theoretical framework that treats overuse and underuse as symmetric outcomes of eco-evolutionary feedback in common-pool resources. The explicit derivation of conditions for singular strategies, the role of benefit curvature, and the comparison to the social optimum supply a baseline for future modeling and intervention studies. Credit is due for the analytical approach and for embedding both provisioning and non-provisioning services in the fitness function.

minor comments (2)

The abstract states that analytical conditions are derived for singular strategies, but a compact summary table listing the conditions for existence, stability, and branching under concave versus convex benefits would improve accessibility.
The section comparing the continuously stable strategy to the social optimum would benefit from an explicit statement of how the deviation metric is defined and whether it remains robust when the non-provisioning service valuation is varied continuously rather than at discrete points.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and accurate summary of our manuscript, as well as for recommending minor revision. The referee correctly identifies the core contribution: an eco-evolutionary model showing that overuse and underuse emerge as alternative outcomes depending on the curvature of provisioning benefits, with analytical conditions for singular strategies and comparison to the social optimum. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper constructs an eco-evolutionary model with explicit benefit functions (provisioning and non-provisioning services) and applies standard adaptive dynamics to derive analytical conditions on the number, location, and stability of singular strategies. These conditions are obtained by direct differentiation and stability analysis of the invasion fitness function with respect to the curvature parameter (concave vs. convex increasing benefits), which is an exogenous modeling choice varied across cases rather than fitted or defined from the output. No step reduces by construction to its own inputs, no self-citation supplies a load-bearing uniqueness theorem, and the comparison of the CSS to the social optimum follows immediately from the same payoff structure without renaming or smuggling prior results. The qualitative regimes (overuse, underuse, branching) emerge as distinct mathematical outcomes of the same equations under different functional assumptions.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions from evolutionary ecology and specific functional forms for benefits; no new entities are introduced.

free parameters (1)

shape parameter for provisioning benefits (concave vs convex)
The distinction between concave and convex increasing benefits is central to determining whether outcomes are unique intermediate, overuse, underuse, or branching.

axioms (2)

domain assumption Adaptive dynamics framework accurately captures long-term evolution of resource-use strategies while resource abundance changes
Invoked to investigate how individual resource use evolves and to derive conditions for singular strategies.
domain assumption Fitness depends additively on provisioning and non-provisioning ecosystem services
Integrated in the model to analyze evolution of use strategies and compare to social optimum.

pith-pipeline@v0.9.0 · 5579 in / 1544 out tokens · 54736 ms · 2026-05-07T09:03:45.378940+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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write newline

" write newline "" before.all 'output.state := FUNCTION string.to.integer 't := t text.length 'k := #1 'char.num := t char.num #1 substring 's := s is.num s "." = or char.num k = not and char.num #1 + 'char.num := while char.num #1 - 'char.num := t #1 char.num substring FUNCTION find.integer 't := #0 'int := int not t empty not and t #1 #1 substring 's :=...