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arxiv: 1906.12050 · v1 · pith:ZZJGAEL3new · submitted 2019-06-28 · 🧮 math.DS

Adult sex ratio as an index for male strategy in primates

D. Rose , K. Hawkes , P.S. Kim This is my paper

Pith reviewed 2026-05-25 13:51 UTC · model grok-4.3

classification 🧮 math.DS
keywords adult sex ratiomale mating strategyprimatesODE modelguarding strategymultiple matinglife history parameterschimpanzees
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The pith

Adult sex ratio indexes whether primate males guard mates or mate multiply.

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

An ODE model with minimal age structure shows that the switch between multiple-mating and guarding strategies occurs along curves that align closely with constant adult sex ratio values when life history parameters vary but guarding effectiveness stays fixed. This alignment holds under changes in longevity and the age at which female fertility ends. The result supports using ASR as a predictor of dominant male strategy when some information on ecology and behavior is available. The model focuses on differences between chimpanzees and human hunter-gatherers.

Core claim

For fixed guarding effectiveness, the dominant strategy changes from multiple mating to guarding along a curve that aligns well with a contour of constant ASR as parameters such as longevity and age of female fertility end are varied. This confirms that ASR may serve as a useful index for predicting optimal male mating strategy given limited ecological and behavioral information.

What carries the argument

A minimal age-structured system of ordinary differential equations tracking fertile males and females under two competing male strategies: multiple mating versus searching then guarding.

If this is right

  • ASR is strongly influenced by life history parameters such as longevity.
  • Dominant strategy is affected most strongly by guarding effectiveness and moderately by some life history traits.
  • Strategy transition aligns with constant ASR contours under parameter variation.
  • ASR can predict male strategy with limited ecology and behavior information.

Where Pith is reading between the lines

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

  • Similar models could test ASR as an index in other species beyond primates.
  • Real-world data on ASR and observed strategies could validate the alignment.
  • Extensions with more age classes or spatial structure might refine the predictions.

Load-bearing premise

The minimal age structure ODE model with only two strategies captures the essential dynamics determining which mating strategy dominates.

What would settle it

Observations of primate populations with the same ASR but different longevity where the dominant male strategy differs from model predictions.

Figures

Figures reproduced from arXiv: 1906.12050 by D. Rose, K. Hawkes, P.S. Kim.

Figure 1
Figure 1. Figure 1: Illustration of our model, excluding removal due to death (adults at rate µ per head, young at rate δ per head) or retirement (adults only at rates τ for females and λ for males). Units of F G are pairs of individuals; if either partner dies or retires the remaining partner returns to the original group. Multiple-mating males will mate with receptive females and return immediately to search for another rec… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of paternity theft dynamics. Receptive females F may pair with either guarding G or multiple-mating M males; females who have mated with a male of either type produce offspring at rate ρ, but a proportion of pair-bonded females produce offspring fathered by multiple maters. opposed to necessarily having current dependents), and even if they retire or die, we assume that any juveniles already b… view at source ↗
Figure 3
Figure 3. Figure 3: Block diagram of the age structure model governed by Equations (2), with juveniles denoted by C and adults by A. Juvenile death rate, adult death rate and maturation rate are represented by δ, µ and γ respectively. ages determine the average longevities, but we are interested in what strategy (or balance of strategies) might be chosen by populations with given longevities. Dividing the population into fert… view at source ↗
Figure 4
Figure 4. Figure 4: A typical example of S(t) (solid curve) governed by the dynamics of equations (2). The dotted curve shows A(t), indicating the demographic breakdown of individuals of age t, split between juveniles and adults. The grey shaded region indicates juveniles: initially all individuals are juveniles, who decrease in proportion of surviving population exponentially as age t → ∞ according to exp(−(δ + γ)t) (through… view at source ↗
Figure 5
Figure 5. Figure 5: Contour plots in the Lt1-plane (longevity–age female fertility ends) of equilibrium values of ASR (numbered contours in red) and dominant strategy (yellow/green regions) as outcomes of numerically integrating equations (1). Initial fraction of males guarding 0.5, male retirement age t2 = 60, adult male relative mortality risk k = 1.0, with proportion surviving until maturity s0 = 1/2, mean birth rate ρ = 1… view at source ↗
Figure 6
Figure 6. Figure 6: Results of simulations as in [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Results of simulations as in [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Results of simulations as in [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Contour plots similar to subplots of Figures 5-8, showing the effect of different initial population structures when paternity theft is in effect (g = 0.1). Left 9a, initial fraction of adult population multiple￾mating R0 = 0.1; right 9b, initial fraction of adult male multiple-mating R0 = 0.9. Observe that when more multiple-mating males are initially present (right) the yellow area corresponding to multi… view at source ↗
read the original abstract

The adult sex ratio (ASR) is defined as the number of fertile males divided by the number of fertile females in a population. We build an ODE model with minimal age structure, in which males compete for paternities using either a multiple-mating or searching-then-guarding strategy, to investigate the value of ASR as an index for predicting which strategy males will adopt, with a focus in our investigation on the differences of strategy choice between chimpanzees Pan troglodytes and human hunter-gatherers Homo sapiens. Parameters in the model characterise aspects of life history and behaviour, and determine both dominant strategy and the ASR when the population is at or near equilibrium. Sensitivity analysis on the model parameters informs us that ASR is strongly influenced by parameters characterising life history, while dominant strategy is affected most strongly by the effectiveness of guarding (average length of time a guarded pair persists, and resistance to paternity theft) and moderately by some life history traits. For fixed effectiveness of guarding and other parameters, dominant strategy tends to change from multiple mating to guarding along a curve that aligns well with a contour of constant ASR, under variation of parameters such as longevity and age female fertility ends. This confirms the hypothesis that ASR may be a useful index for predicting the optimal male mating strategy, provided we have some limited information about ecology and behaviour.

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.

Referee Report

1 major / 2 minor

Summary. The paper constructs a minimal age-structured ODE model with two male mating strategies (multiple mating vs. searching-then-guarding) whose equilibria determine both the dominant strategy and the adult sex ratio (ASR). Sensitivity analysis on life-history and behavioral parameters shows that ASR is primarily driven by longevity and female fertility schedules while strategy choice is most sensitive to guarding effectiveness. For fixed guarding effectiveness, the boundary between dominant strategies traces a curve that closely follows a level set of constant ASR when longevity and the age at which female fertility ends are varied. This is presented as evidence that ASR can serve as a useful index for predicting male strategy in primates such as chimpanzees and humans, conditional on limited ecological information.

Significance. If the reported alignment is shown to be robust rather than an algebraic consequence of the chosen state space, the result would supply a simple, observable proxy (ASR) for predicting shifts in male mating tactics across primate populations. The minimal ODE formulation is a deliberate strength that keeps the model tractable and falsifiable. No machine-checked proofs or open code are mentioned, but the parameter-sensitivity approach itself is a positive feature that could be extended.

major comments (1)
  1. [sensitivity analysis / results] Abstract and sensitivity-analysis results: the claim that strategy transition 'aligns well with a contour of constant ASR' under variation of longevity and terminal female fertility age (guarding effectiveness held fixed) is load-bearing for the central hypothesis. Because ASR is an algebraic function of precisely the life-history rates being varied and strategy payoffs depend on the same rates, the alignment could be an artifact of the two-strategy, coarse-age ODE; the manuscript does not report an invasion analysis, a comparison with additional age classes, or a spatial extension that would test whether the contour coincidence survives.
minor comments (2)
  1. [model description] Notation for the two male strategies and the age-partition variables should be introduced with explicit symbols in the model section rather than only in the text.
  2. [methods] The manuscript would benefit from a table listing all free parameters, their baseline values, and the ranges used in the sensitivity sweeps.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and for highlighting the central claim of our work. We respond to the major comment below, clarifying the intended scope of the minimal model.

read point-by-point responses

  1. Referee: [sensitivity analysis / results] Abstract and sensitivity-analysis results: the claim that strategy transition 'aligns well with a contour of constant ASR' under variation of longevity and terminal female fertility age (guarding effectiveness held fixed) is load-bearing for the central hypothesis. Because ASR is an algebraic function of precisely the life-history rates being varied and strategy payoffs depend on the same rates, the alignment could be an artifact of the two-strategy, coarse-age ODE; the manuscript does not report an invasion analysis, a comparison with additional age classes, or a spatial extension that would test whether the contour coincidence survives.

    Authors: The alignment is demonstrated within the deliberately minimal two-strategy, coarse-age ODE framework, where life-history parameters are varied while holding guarding effectiveness fixed. Although ASR is algebraically determined by the life-history rates, the strategy equilibrium is determined by the behavioral payoffs (which depend on guarding parameters and the resulting population frequencies). The sensitivity analysis shows that, for fixed guarding effectiveness, the switch in dominant strategy occurs along a curve that closely tracks a level set of constant ASR. This is offered as evidence that ASR can serve as a useful observable proxy under limited ecological information, not as a claim of robustness outside the model class. We did not perform invasion analysis, add age classes, or introduce spatial structure because the model is formulated as a minimal ODE system chosen for tractability and falsifiability; such extensions would require reformulating the model as individual-based or spatially explicit. We therefore view the reported contour coincidence as a feature of the chosen state space rather than an unintended algebraic artifact, but we acknowledge that testing the pattern in richer models would be a natural next step. revision: no

Circularity Check

0 steps flagged

No circularity: strategy-ASR alignment reported as emergent from independent parameter variation in ODE equilibria

full rationale

The paper constructs a minimal age-structured ODE tracking two male strategies and computes equilibria for ASR and dominant strategy as functions of life-history and behavioral parameters. The reported alignment is obtained by holding guarding effectiveness fixed while varying longevity and terminal female fertility age, then observing that the strategy transition surface intersects constant-ASR contours. This is presented as a numerical/model outcome rather than a definitional identity, fitted input renamed as prediction, or result justified solely by self-citation. No equations or steps are shown that reduce the alignment to an algebraic tautology or to a parameter fit by construction. The derivation therefore remains self-contained against the model's own state variables and rates.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on the parameters characterising life history and behaviour in the ODE model, the assumption that the two strategies are exhaustive, and the results of the sensitivity analysis showing alignment with constant ASR; no independent empirical validation or external benchmarks are mentioned.

free parameters (3)
  • effectiveness of guarding
    Includes average length of time a guarded pair persists and resistance to paternity theft; strongly affects which strategy is dominant.
  • longevity
    Life history parameter varied to show that strategy change aligns with constant ASR contour.
  • age female fertility ends
    Life history parameter used in the sensitivity analysis demonstrating the ASR alignment.
axioms (2)
  • domain assumption An ODE model with minimal age structure adequately captures the population dynamics determining dominant male mating strategy and equilibrium ASR.
    Invoked as the foundation for building the model and performing sensitivity analysis.
  • domain assumption Males adopt exclusively either the multiple-mating or the searching-then-guarding strategy.
    The two strategies are the only options modeled to determine which is dominant at equilibrium.

pith-pipeline@v0.9.0 · 5764 in / 1550 out tokens · 51018 ms · 2026-05-25T13:51:47.469666+00:00 · methodology

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Reference graph

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