Source
Athreya, Czuppon & Gokhale (2025), LIT-1570, read in full in NOTE-1211 from the bioRxiv version 2. The sections “Independent evolution of obligacies and adhesions”, “The effect of within-collective mortality and reproduction”, “Collective growth rate and collective carrying capacity have different effects”, the conclusions, Figures 2–4, Table 2, and Supplementary Notes S3–S4.A.
What was actually shown
- Order of obligacy.
- With K_S > K_H and r_S > r_H, the symbiont’s obligacy reaches 1 first (Fig. 2). Swapping the parameters swaps the partners, and equal parameters give symmetric outcomes (Fig. S4).
- At Ω_S = 1, the host mutant’s R₀ is exactly 1 (Note S4.A), so host obligacy is neutral and neutral variation should accumulate.
- Within-collective demography (Fig. 3, Table 2, Eq. 7).
- With deaths only (d_H = d_S > 0), obligacy must start above a threshold, and then the host follows the symbiont to 1.
- With births only (b_H = b_S > 0), obligacy rises freely, and then the host falls to 0. There is then no equilibrium: the symbiont dies out while the collective grows without bound.
- Eq. 7 identifies b_S − d_S as the sign that decides.
- Carrying capacity (Fig. 4, Note S3.B). Traits leave (0,0) for
K_C = 50 or 500 but not 10, at either r_C = 1 or 40.
- The proposed sufficient condition is K_C > aK_HK_S/d, which is 40 at those parameters (checked in the reading).
- Moving a to 0.01 or 5 moved the outcome as predicted.
- Interpretation. The authors read the symbiont’s head start as the Red King effect: the faster-evolving partner concedes first when interests are aligned. Here the collective’s shared fate does the aligning, not a mutualism.
What could have failed: the faster partner could have been the one to keep its independence, or host dependence could have followed regardless of demography. In the model, neither happens.
What this does not say
- Not tested in any real symbiosis. No growth parameters, carrying capacities or within-collective rates are measured. The authors call measuring b and d “imperative”.
- Not for unequal or trait-dependent rates. Only b_H = b_S and d_H = d_S were simulated. The authors expect b_S − d_S to dominate, but have not tested it.
- Not that symbiont-first obligacy explains reduced symbiont genomes. The authors list Muller’s ratchet and “environment-induced redundancy” as other drivers, which they say depend on the symbiont living inside the host.
- Not a model of conflict. Interests are aligned by construction, and there is no within-collective selection. So it cannot speak to policing or to THEORY-141’s condition.
Note of 2026-10-30: narrowed
The old title said dependence “rises at all only if the collective’s carrying capacity is high enough”. The simulations show traits leaving (0,0) at K_C = 50 and 500 and not at 10, and the authors’ condition K_C > aK_HK_S/d is shown sufficient, not necessary (NOTE-1211, C3). Only b_H = b_S and d_H = d_S were simulated. Whether real symbioses bear out the model’s predictions is QUESTION-353.
Connections
- QUESTION-277. One-sided dependence (symbiont obligate, host free) and full mutual dependence are both outcomes of one model, decided by demography inside the collective. That gives the question a candidate variable for when a dependency becomes an individual.
- THEORY-443. The model’s transition criterion, full dependence plus full cohesion giving the pair a life cycle, is one operational version of Darwinian individuality for a partnership. Under it, most dependent symbioses stop short.
- THEORY-141. It describes a different mechanism of alignment. Here, shared reproduction and the Red King effect align interests, not policing. It does not compete with THEORY-141’s condition, because it models no conflict.
- CASE-173 and CASE-177. Aphid–Buchnera is the model’s mutually-obligate, vertical case. The model’s single-symbiont collectives cannot represent Hodgkinia’s splitting.