Social patch foraging theory in an egalitarian group

Ahmed El Hady; Lisa Blum Moyse

REVIEW 6 major objections 6 minor 83 references

Social patch foraging theory in an egalitarian group

T0 review · 6 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper derives closed-form distributions for patch-leaving and patch occupancy in a large egalitarian foraging group, and shows each social information-sharing mechanism (reward, diffusive, counting, pulsatile) shifts group cohesion…

desk verdict A genuine, mostly honest extension of the two-agent stochastic foraging model to groups, with new coupling mechanisms and a useful analytic toolkit; the abstract oversells 'optimal strategies' and the coupled-equilibrium derivations need to be shown, but the core framework deserves refereeing. read the letter →

arxiv 2412.02381 v2 pith:6YSDOUEI submitted 2024-12-03 physics.bio-ph

Lisa Blum Moyse , Ahmed El Hady This is my paper · ORCID

classification physics.bio-ph MSC 92D5060J70

keywords socialforagingpatch-leavingdecisionsevidenceaccumulationdrift-diffusionmodelcollectivebehaviorinformationsharinggroupcohesionexploration-exploitationtrade-off

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper builds a stochastic, analytically tractable model of when individuals in a large egalitarian foraging group decide to leave a food patch. Each forager is treated as an evidence accumulator whose decision variable drifts with reward rate and social cues, and the model derives closed-form distributions for patch-leaving times and patch occupancy, plus equilibrium accuracy, a damping parameter for group cohesion, and mean residence time. Across two non-depleting patches and successive depleting patches, and across four information-sharing mechanisms (observing others' rewards, continuously sharing beliefs, counting group members, and pulses at departures or arrivals), the model predicts that each mechanism modulates cohesion, accuracy, and exploitation in a distinct, mostly monotone way. The framework is intended to be directly usable for designing social foraging experiments and for generating testable hypotheses, and it extends to hierarchical groups.

What carries the argument

The central object is the drift-diffusion decision variable $x_i(t)$ of each forager, which accumulates the difference between food rewards and a foraging cost plus social coupling terms and white noise, and triggers a patch departure when it hits a threshold $\theta$. The analytical engine is the quasi-continuous reward approximation, which replaces stochastic rewards by their average rate $p(T)$, giving a constant effective drift $\tilde{\alpha}_k = \alpha - p_k$ (or $\alpha - p_k(1+\kappa_r)$ with reward coupling) within each patch; departures then follow an inverse-Gaussian first-passage time $\Psi^k_\nu(t)$, and patch-switching dynamics are built from convolutions of these densities. This machinery yields the metrics used throughout: $P^k(t)$ (leaving probability), $Q^k(t)$ (occupancy), equilibrium values $Q^k_{\rm eq}$ and $P^k_{\rm eq}$ from flux balance, the damping parameter $\gamma$ quantifying cohesion, and the mean residence time $\bar{T}^k$ quantifying exploitation.

What would settle it

Simulate the same model with sparse, large-interval reward events (for example, $\Delta_r$ comparable to the mean residence time) and compare the simulated leaving-time distributions $P^k(t)$ and occupancy $Q^k(t)$ against equations (16)-(26) and (35)-(44); systematic deviation beyond Monte-Carlo error in a regime where $p(T)$ is no longer a good average would falsify the analytic derivations. A complementary empirical test would measure patch residence times in a group foraging on clumped, patchy food: the inverse-Gaussian-based predicted damping of oscillations should fail as reward events become rare.

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Extended reading notes

Core claim

The central claim is that a mechanistic evidence-accumulation model of patch leaving, generalized from one or two foragers to an arbitrarily large egalitarian group, remains analytically tractable and yields quantitative predictions for how social information changes collective foraging. Concretely, the leaving-time probability $P^k(t)$ and occupancy $Q^k(t)$ are given by infinite convolutions of inverse-Gaussian first-passage densities $\Psi^k_\nu(t)$, which in the quasi-continuous reward approximation reduce to closed-form expressions including the equilibrium accuracy $Q^k_{\rm eq}$, the equilibrium leaving probability $P^k_{\rm eq}$, the mean residence time $\bar{T}^k$, and the damping parameter $\gamma$ that measures cohesion. Applying these formulas and matching simulations, the paper shows that reward coupling and counting coupling increase accuracy and exploitation but reduce cohesion, diffusive coupling increases cohesion without changing accuracy or exploitation, and pulsatile coupling splits by direction: observing arrivals increases accuracy and exploitation, while observing departures reduces exploitation and can either raise or lower accuracy depending on whether normalization is by the whole group or by patch-local counts. The paper also finds that an individual long-term inference of which patch is best raises collective accuracy and residence time in the best patch.

Load-bearing premise

All the analytical distributions are derived under the quasi-continuous reward approximation, which replaces stochastic rewards by their average rate within each patch; the paper itself states this approximation is not valid for time-spaced, noisy food intakes, so if real rewards are sparse and variable the closed-form formulas for $P^k(t)$, $Q^k(t)$, and the equilibrium values may fail.

Editorial extensions

If this is right

Observing others' rewards or counting group members will raise the fraction of foragers in the best patch and lengthen stays there, at the cost of less cohesive groups.
Continuous belief sharing (diffusive coupling) will make groups more cohesive as group size grows, while leaving accuracy and exploitation unchanged.
Pulsatile arrival information increases accuracy and exploitation; pulsatile departure information reduces exploitation and, depending on normalization, may reduce or increase accuracy.
Individual best-patch inference, even without social information, increases collective accuracy and time spent in the best patch.
The analytical formulas provide quantitative targets, such as $Q^k_{\rm eq}$ and $\gamma$, that experiments can fit to infer which social mechanism animals use.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural next step, not taken in the paper, would invert the machinery: given measured $P^k(t)$ or $\gamma$ from tracked animals, one could classify which coupling type (reward, diffusive, counting, pulsatile) the group uses, since the predicted signatures are distinct.
The model's cohesion-versus-accuracy trade-off suggests that under predation risk, groups should preferentially use diffusive or pulsatile information (which increase cohesion) rather than reward or counting information (which trade cohesion for accuracy); this is an editorial inference from the paper's discussion, not a paper claim.
Because the quasi-continuous reward approximation limits the analytical formulas to dense reward streams, a natural extension would be to derive analogous distributions for renewal reward processes, keeping the paper's conclusion that numerical simulations remain reliable when rewards are sparse.
In hierarchical groups, one could let coupling strengths depend on rank; the authors mention hierarchies as a future direction, and the same closed-form framework would need only parameter-dependent coupling terms.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's the short version: this paper takes the two-agent stochastic patch-foraging model from Bidari et al. and extends it to N agents with three genuinely new coupling mechanisms (reward observation, counting, arrival pulses), in two-patch and successive-patch environments. The non-interacting machinery—inverse-Gaussian leaving-time distributions, Laplace-transform convolutions for P^k(t), flux-balance Q^eq, and the gamma damping parameter—is cleanly derived and matches Monte Carlo. The perfectly-coupled limits (diffusive, and the kappa_d -> infinity pulsatile case) are also checked against simulation. That is real, useful work for collective-behavior modelers and experiment designers.

The soft spots, in rough order of importance.

First, the abstract says the authors 'analytically derive optimal agent strategies.' Nothing in the paper is an optimization. No cost function, no comparison of strategies against an optimum, no maximization of food intake or fitness. The paper derives distributions and qualitative effects of coupling strengths on cohesion, accuracy, and exploitation. That claim should be removed or rewritten.

Second, the equilibrium effective-drift equations for counting coupling (Eqs. 35-36) and finite pulsatile coupling (Eqs. 39-44) are stated as results of solving self-consistent systems, but the derivation is not shown, and the appendix does not cover them. The nonlinear system in Eq. 35 does not transparently reduce to the closed form in Eq. 36; a referee needs that step. This is a moderate gap for a paper whose selling point is analytic tractability, though the authors are explicit that full distributions for counting coupling are only simulated.

Third, the quasi-continuous reward approximation. The paper owns this limitation in Section IV.D, which counts for something. But the simulated regime is marginal: rewards arrive every ~1.7-2.5 s and mean sojourn times are ~6-8 s, so there are only a few reward events per sojourn. The analytic curves match the histograms anyway in the tested range, but no test shows whether Table IV's qualitative rankings survive under sparser or burstier reward schedules. For a framework aimed at designing experiments, that robustness question should be answered with a simulation sweep.

Minor: simulation figures have no error bars, and there is no code or data deposit. The self-citation of refs 35, 36, and 42 is not a problem—the N-agent extension and the new couplings are derived independently of those papers.

The reader is right to be conditional rather than enthusiastic. The central framework holds up, the limitations are acknowledged in the text, and the gaps are repairable. I would send this to peer review, with the abstract claim and the missing derivations as the main revision requests. Worth a careful referee.

Referee Report

6 major / 6 minor

Summary. This paper extends a drift-diffusion evidence-accumulation model of patch-leaving decisions to groups of N egalitarian foragers. It considers three environments (single patch, two non-depleting patches, and successive depleting patches) and four social information mechanisms (reward, diffusive, counting, and pulsatile coupling). Under a quasi-continuous reward approximation, the authors derive closed-form expressions for leaving-time distributions, occupancy fractions, equilibrium accuracy, a damping parameter for cohesion, and mean residence times, and they compare these predictions with forward Euler simulations. The paper's main output is a qualitative classification, summarized in Table IV, of how environmental, individual, and social parameters affect cohesion, accuracy, and exploitation.

Significance. If the results hold, this is a useful analytically tractable bridge between individual stochastic decision rules and collective foraging metrics, extending earlier two-agent work to arbitrary group size and several new interaction channels. The paper's strengths include the absence of any parameter fitting to data, direct comparison of analytical curves to forward simulations, and falsifiable qualitative predictions that could guide experimental design. Its central limitation is that the quantitative and, potentially, qualitative conclusions rest on the quasi-continuous reward approximation and on several equilibrium equations that are not derived and contain algebraic errors.

major comments (6)

[III.A, IV.D, Table IV] All analytical distributions replace the stochastic reward process by its mean rate and treat the effective drift as constant within each patch (Eqs. 10-17, 31, 35, 39, 43). The authors state in Section IV.D that these computations are not possible for time-spaced, noisy food intakes, but no sensitivity analysis is provided for sparser or burstier rewards: every simulation uses a single value Delta_r = 0.01 s. Consequently the domain of validity of the quantitative predictions, and even the qualitative monotonicity rankings in Table IV, is not established outside that narrow regime. Please add simulations with larger or heterogeneous reward intervals and report whether the Table IV rankings survive.
[III.B.1, Eq. (26)] Equation (26) is algebraically inconsistent with Eq. (25). Using Q^k_eq = 1/(1 + alpha_k/alpha_k' - 2 alpha_k T_tr/theta) and T^k = -theta/alpha_k gives P^k_eq = Q^k_eq/T^k = alpha_k / [(-theta)(1 + alpha_k/alpha_k') + 2 alpha_k T_tr], not the expression printed, which has a factor (1 + alpha_k/alpha_k') in the numerator. As written, Eq. (26) violates the flux-balance identity P^0_eq = P^1_eq that the Fig. 2 caption explicitly invokes; for p0=0.4, p1=0.6, theta=-5, T_tr=0 it gives 0.392 and 0.229 for the two patches. Please correct Eq. (26) and regenerate the affected theoretical curves.
[III.B.3.d, Eq. (38)] For perfect pulsatile coupling the group leaves at the first of N independent first-passage times, so the density should be N * Psi(T) * Omega(T)^(N-1), not Psi(T) * Omega(T)^(N-1). The expression in Eq. (38) integrates to 1/N and is therefore not a normalized leaving-time density; this affects the analytical P^k(t) and Q^k(t) used for the kappa_d -> infinity pulsatile case in Figs. 5 and 6.
[III.B.2, Eq. (30)] The admissibility interval for y_b given in Eq. (30) is empty for the simulation parameters used throughout the paper. With alpha = 1.25, p0 = 0.4, p1 = 0.6, the upper bound is p1/[2(alpha-p1)] = 0.462 and the lower bound is (2 alpha - p0)/[2(alpha-p0)] = 1.235, so the stated condition cannot be satisfied, yet Fig. 3 uses y_b = 0.8. The lower bound appears to involve the wrong expression (probably p0 rather than 2 alpha - p0), and the inequality direction should be re-examined. Please state the correct condition and reconcile it with the value y_b = 0.8 used in the figure.
[III.B.3.c-d, Eqs. (35)-(44)] The equilibrium equations for counting and pulsatile coupling are stated without derivation and are internally inconsistent. For example, setting kappa_d = 0 in Eq. (39) gives the linear relation alpha_k_eq = alpha - p_k + kappa_a, but the quadratic solution in Eqs. (40)-(41) does not reduce to this relation (the coefficient a_1 = 2 + kappa_d - kappa_a/theta does not become 1). In addition, Eq. (42) with theta = -5 reads kappa_a <= kappa_d - 10, which is violated by the non-negative strengths used in Fig. 5 (e.g., kappa_d = 0, kappa_a = 2). The counting-coupling equation (35) also relies on a mean-field replacement of n_k/N by an equilibrium occupancy formula that is not derived. Please provide complete derivations in an appendix and correct the inequalities.
[Abstract and Section I] The abstract claims that the authors 'analytically derive optimal agent strategies,' but no optimization problem is formulated: there is no objective function over the decision threshold, foraging cost, or coupling strengths, and no optimality proof is presented. The paper derives closed-form predictions for a fixed evidence-accumulation policy. Please revise the claim to 'analytically characterize' the strategies, or add a formal optimality statement.

minor comments (6)

[III.B.3.c] The text refers to 'Fig. 4(e)' for counting coupling, but the figure has no panel (e); the counting results are in panel (d).
[II.A, Eq. (10)] The symbol p is used both for the per-time-step reward probability and for the reward rate; please use distinct notation (e.g., p_step and p) and clarify the relation in Eq. (10).
[III.C.1.a, Eq. (47)] For K > 1, P_tot(t) is an event-rate density that integrates to K, not a probability density; please state this normalization explicitly to avoid confusion.
[IV.A, IV.C] There are several typos: 'extendng' should be 'extending', 'foraginf' should be 'foraging', and 'Please not' before Eqs. (42) and (46) should be 'Please note'.
[Table IV] In the 'Depletion A_m' row only two arrows are shown while the table has three feature columns; please fill the accuracy entry with 'not relevant' or 'O' to match the other rows.
[III.B.3.d] The phrase 'using Using the expression Q^k_eq in eq. 60' contains a duplicated word and should read 'using the expression Q^k_eq in Eq. (60)'.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: analytical results are derived from the stated SDE and validated by forward simulation; heavy self-citation is present but not load-bearing.

full rationale

The paper's central derivations are self-contained rather than circular. The single-patch distributions (Eqs. 12-13), the two-patch convolution series (Eqs. 16-26), and the coupled equilibrium effective drifts (Eqs. 35-44) all follow from the stated stochastic differential equation (Eq. 1), the coupling terms (Eqs. 5-9), and standard first-passage, Laplace-transform, and flux-balance techniques. Parameters such as alpha, B, theta, p_k, and the coupling strengths are specified by hand and compared to forward Euler simulations; no parameter is fitted to a data subset and then reported as a prediction. The quasi-continuous reward approximation (Eqs. 10-15) replaces stochastic rewards by their mean rate p(T); this is an explicitly acknowledged approximation (Section IV.D) that limits validity for sparse or noisy rewards, but it is not circular because it does not presuppose the quantities being derived. The paper cites prior work by the same group, notably refs. [35], [36], and [42], for the evidence-accumulation patch-leaving framework and for the strong-coupling diffusive limit. These citations are used as modeling assumptions or parameter-free published results, not as the source of the paper's new N-agent predictions, and the derivations in the present paper extend them independently. No equation reduces to its own input by definition, and no externally fitted value is renamed as an analytical prediction. The main concerns raised by the text are about the domain of validity of the quasi-continuous approximation, which is a correctness risk rather than a circularity.

Assumptions & free parameters 14 free parameters · 5 assumptions · 0 invented entities

The model introduces no new physical entities such as particles, forces, or dimensions. The new elements are interaction mechanisms (reward, counting, pulsatile arrival) and an internal best-patch inference variable, which are modeling constructs rather than invented ontological entities. All quantitative predictions depend on the listed hand-picked parameters and on the standard first-passage and mean-field assumptions.

free parameters (14)

decision threshold theta = -5 (most figures)
Threshold for leaving a patch; chosen by hand, not fitted to data.
foraging cost alpha = 1.25
Constant cost term in the decision variable equation; chosen by hand.
noise amplitude B = 0.1
Diffusion coefficient of the Wiener process; chosen by hand.
reward probabilities p0, p1, p_in = 0.4, 0.6, 0.8, 0.5, 2/3 depending on figure
Rates of food reward in each patch; chosen as simulation inputs, not fitted to empirical data.
reward time step Delta_r = 0.01 to 0.02 s
Time step of reward events; chosen by hand.
travel time T_tr = 0 or 1 s depending on figure
Time to move between patches; varies across simulations.
maximum food amount A_m = 100 or 8000
Sets depletion rate in depleting patches; chosen by hand.
reward coupling strength kappa_r = 0.6 in Fig 4b
Weight of observed others' rewards on the decision variable; swept as a free parameter.
diffusive coupling strength kappa_diff = 10 or 100
Weight of continuous belief sharing; taken in the strong-coupling limit for analytics.
counting coupling strength kappa_c = 1 in Figs 4d and 6c
Weight of the proportion of agents in the current patch; free parameter.
departure and arrival pulse strengths kappa_d, kappa_a = various, e.g. kappa_d=100, kappa_a=0 or 2
Weights of departure and arrival pulses; free parameters in pulsatile coupling.
counting threshold eta = 1/2 in two-patch case
Reference proportion of agents in a patch for counting coupling; set by symmetry.
best patch inference timescale tau_y and boundary y_b = y_b=0.8 in Fig 3
Parameters of the long-term memory dynamics; chosen by hand.
group size N and number of patches K = N=5,10,50; K=10 in successive patches
Simulation inputs varied to test group size effects.

assumptions (5)

standard math Inverse Gaussian first-passage distribution for constant-drift Brownian motion
Used in equations (12), (13), (17), (21) as unproved background from stochastic process theory (refs 40, 51).
domain assumption Quasi-continuous reward approximation: stochastic rewards can be replaced by average rate p(T)
Introduced in Section III.A using equations (10) and (15); explicitly acknowledged as a limitation in Section IV.D.
domain assumption Strong-coupling limits kappa_diff -> inf and kappa_d -> inf make all agents move together
Used in equations (34), (38), (51) to reduce the coupled system to a single averaged process; relies on the variance of the OU process going to zero (refs 40, 42).
domain assumption Equilibrium flux balance between patches and traveling compartments
Used in Appendix V.B, equations (58) to (60), to compute equilibrium fractions Q^eq.
domain assumption Exponential depletion of reward probability in depleting patches
Used in equation (15) and Section III.C for average reward rate; assumes continuous depletion proportional to reward events.

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Cite this review

Pith. "Pith review of Social patch foraging theory in an egalitarian group." pith.science (2026). https://pith.science/paper/6YSDOUEI

@misc{pith2026241202381,
  author       = {Pith},
  title        = {Pith review of: Social patch foraging theory in an egalitarian group},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6YSDOUEI}},
  note         = {Machine review of arXiv:2412.02381}
}

read the original abstract

Foraging is a widespread behavior, and being part of a group may bring several benefits compared to solitary foraging, such as collective pooling of information and reducing environmental uncertainty. Often theoretical models of collective behavior use coarse-grained representations, or are too complex for analytical treatment, and generally do not take into account the noisy decision making process implemented by individual agents. This calls for the development of a mechanistic, analytically tractable, and stochastic framework to study the underlying processes of social foraging, tying the microscopic to the macroscopic levels. Based on an evidence accumulation framework, we developed a model of patch-leaving decisions in a large egalitarian group. Across a variety of environmental statistics and information sharing mechanisms, we were able to analytically derive optimal agent strategies. The environmental statistics considered are either two non-depleting or several successive depleting patches. The social information sharing mechanisms are either through observation of others' food rewards or through belief sharing, with continuous sharing, pulsatile observation of others' departures or arrivals, or through counting the number of individuals in a patch. Throughout all these conditions, we quantified how cohesive a group is over time, how much time agents spend on average in a patch and what are their group equilibrium dynamics. We found that social coupling strongly modulates these features across a variety of environmental statistics. This general modeling framework is crucial to both designing social foraging experiments and generating hypotheses that can be tested. Moreover, this framework can be extended to groups exhibiting hierarchical relations.

Figures

Figures reproduced from arXiv: 2412.02381 by the authors.

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]

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Reference graph

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This probability can be found after using the Laplace transform of Ψ to compute the convolution of functions with the same drift term in one compartment (see Ap- pendix V A)

Characterization of distributions for non-interacting agents The probability to leave a patch k at time t, P k(t), is given by the convolution over the Ψ 0(t) and Ψ 1(t). This probability can be found after using the Laplace transform of Ψ to compute the convolution of functions with the same drift term in one compartment (see Ap- pendix V A). P k(t) = ∞X...
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Effect of best patch inference So far, no individual long-term learning of which patch would have the highest reward rate has been taken into account. The impact of this internal inference is studied below. The average y value at the departure time tk y,ν can be estimated with yk ν (See Appendix V C). For ν ∈ {1, 2, ...}, y0 ν = y1 ν−1 exp p0θ yb + 1 2 τy...
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Characterization of distributions for non-interacting agents Depending on the non-depleting or depleting nature of patches, the analytical predictions are different. • For non-depleting patches, the total distribution of leaving times is Ptot(t) = KX k=1 Ψk t − (k − 1)Ttr (47) and the fraction of agents in a patch 1 < k < Kis Qk(t) = Ωk t − (k − 1)Ttr − Ω...

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

This probability can be found after using the Laplace transform of Ψ to compute the convolution of functions with the same drift term in one compartment (see Ap- pendix V A)

Characterization of distributions for non-interacting agents The probability to leave a patch k at time t, P k(t), is given by the convolution over the Ψ 0(t) and Ψ 1(t). This probability can be found after using the Laplace transform of Ψ to compute the convolution of functions with the same drift term in one compartment (see Ap- pendix V A). P k(t) = ∞X...

[2] [2]

The impact of this internal inference is studied below

Effect of best patch inference So far, no individual long-term learning of which patch would have the highest reward rate has been taken into account. The impact of this internal inference is studied below. The average y value at the departure time tk y,ν can be estimated with yk ν (See Appendix V C). For ν ∈ {1, 2, ...}, y0 ν = y1 ν−1 exp p0θ yb + 1 2 τy...

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4(a) schematizes the different types of social information sharing

Impact of social information Fig. 4(a) schematizes the different types of social information sharing. Their effects will be detailed below. For readability reasons, in this section the travel time is fixed to zero, Ttr = 0 s. A first information gathering mechanism can come from the observation of food rewards that other agents in the same patch get. a. R...

[4] [4]

Characterization of distributions for non-interacting agents Depending on the non-depleting or depleting nature of patches, the analytical predictions are different. • For non-depleting patches, the total distribution of leaving times is Ptot(t) = KX k=1 Ψk t − (k − 1)Ttr (47) and the fraction of agents in a patch 1 < k < Kis Qk(t) = Ωk t − (k − 1)Ttr − Ω...

work page

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Reward coupling is not detailed in this section, as it has been shown to correspond to an increased perceived reward probability

Impact of social information The effect of social information coupling in a group of foraging individuals is detailed here, with similar infor- mation sharing mechanisms described in the Methods section. Reward coupling is not detailed in this section, as it has been shown to correspond to an increased perceived reward probability. First, the impact of ac...

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