Source
Athreya, Czuppon & Gokhale (2025), The American Naturalist 206(5): 435–451, LIT-1570, read in full in NOTE-1211 from the bioRxiv version 2 (2025-05-31), not the version of record. The section “Does mutual dependence evolve before or after reproductive cohesion?”, Figure 5, Supplementary Note S4.B–E, Table S1, Figures S11–S14, and Table 3 with its caption.
What was actually shown
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Model. Free-living growth is f_H = r_H(1 − Ω_H) and f_S = r_S(1 − Ω_S). Collective growth is f_C = r_C Ω_HΩ_Sα_Hα_S, and dissociation d = d₀(1 − α_Hα_S). The collective grows without a carrying capacity (the “exponential model”), which is valid while the traits are small.
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Analytically. The invasion criterion is exact and separable: f̃(1 − d̃/(a f̃_C)) > f(1 − d/(a f_C)). There is an optimization principle, no branching, and all four traits rise monotonically.
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By simulation (Figure 5). Both partners evolve Ωᵢ > αᵢ, and Ω_HΩ_S outruns α_Hα_S until the feasibility bound ends the trajectories. Figure S14 shows the bias persists with additive trait effects, symmetric or tenfold-asymmetric growth parameters, and higher d₀.
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The structural dependence (Note S4.E, Table S1). The appendix crosses two choices: free growth depending on (i) one’s own obligacy or (ii) both obligacies, and dissociation depending on (I) one adhesion or (II) both.
- i-II, the default: dependence-biased.
- ii-I: cohesion-biased.
- i-I and ii-II: no bias, the slight bias in i-I being “an artefact”.
The authors chose i-II “from biological considerations”.
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Against data (Table 3). Ten symbioses are classified qualitatively by dependence and transmission mode. The authors: “the available information does not allow us to confirm/refute the bias”.
What could have failed: under the default mapping, the simulations could have shown no bias. They do not. Under the alternative mapping, the result fails, as the authors report.
What this does not say
- Not that endosymbioses in nature are dependence-first. The authors draw that inference (“strongly suggests”), but it is conditional on the mapping and untested.
- Not about uncorrelated investment in a sense that decides the result. The traits have no genetic correlation in the model, but their functional effects are coupled by the mapping. That coupling is what produces the bias.
- Not about late evolution. The exponential model is trusted only early, and whether the bias “survives to later evolutionary times” is open.
- Not about any mechanism of dependence. Obligacy is a phenomenological trade-off. Gene loss, transfer and host control are not modelled.
Connections
- QUESTION-277. This bears on the order of D and R. It does not settle it: the order turns on how each partner’s traits act, which is an empirical question. It also corrects the question’s summary.
- LIT-1605. Frank (1996, unread) models host control of transmission. If the host can impose cohesion unilaterally, dissociation depends on one partner’s trait (mapping I). With free growth depending on one’s own obligacy that is the matched case i-I, and the dependence-first bias largely disappears. The inference is mine.