How can we identify social information mechanisms in collective patch foraging?

Two questions hide inside one model fit

A laboratory group foraging between two patches gives a clean window on social information: individuals accumulate evidence about patch quality and decide when to stay or leave, and they can also watch where conspecifics are. The paper asks whether the mechanism behind that social influence can be recovered from observable group behavior. It separates two questions that are easy to conflate. Model selection asks which mechanism generated the data. Parameter identifiability asks whether the strength of that mechanism can be estimated once the model is chosen.

The authors treat these as distinct targets and measure each separately. Across 400 repeated inference runs per setting, they record the proportion of correct model recovery (M) and the mean parameter recovery (P). Keeping M and P apart is the paper's central methodological move, because the results show they are not driven by the same behavioral signal.

Four social models differ in representation and entry point

The baseline is a non-interacting drift-diffusion model: within a patch, a decision variable accumulates noisy evidence from food rewards minus a foraging cost, and the agent leaves when that variable crosses a threshold. Social information enters through a coupling term J that describes the local social environment in a patch. The paper crosses two ways of representing that term with two ways of using it, producing four social models plus the non-interacting baseline.

The counting representation treats social information as a continuous estimate of local group density, so high neighbor density reads as a positive signal about the patch. The pulsatile representation instead counts discrete arrivals and departures, so the signal is built from events rather than a standing proportion. On the integration side, threshold modulation shifts the decision threshold, changing the propensity to leave without altering evidence accumulation. Belief modulation adds social information directly to the accumulated evidence. The four combinations are labeled CT, CB, PT and PB, and each makes a different prediction about how groups move between patches.

Counting slows departures while pulsatile signals speed them up

All five models produce damped oscillations in mean group accuracy: agents initially leave the poorer patch for the better one, then cycle back, and the average flattens as groups desynchronize. Social information changes three separable features of that trajectory, which the authors summarize as residence time in the best patch, grand mean accuracy, and the mean absolute rate of change of group accuracy.

The representation determines the timing. Relative to the non-interacting model, counting representations shift oscillations later, lengthening residence time, consistent with agents reading high density as a reason to stay. Pulsatile representations shift oscillations earlier and shorten residence time, consistent with discrete arrival and departure events promoting rapid exploration. The integration mode then splits the models further. CB, the counting-plus-belief model, is the outlier: it damps oscillations and raises accuracy substantially, which the authors interpret as sustained exploitation replacing coordinated cycling. CT, PT and PB instead show larger oscillation amplitude with accuracy near the non-interacting baseline.

Group-accuracy distributions identify models best

The authors compare two identification procedures, Bayesian inference with maximum a posteriori estimation and Wasserstein distance minimization, and two summary statistics, distributions of group accuracy sampled at multiple times and distributions of departure times. Bayesian inference using group-accuracy distributions gives the most reliable identification across the conditions considered. The paper attributes this to group accuracy being a smoother, less discrete measurement than departure times, and reports that Bayesian inference also outperformed distance minimization at small sample sizes.

This is a statement about simulated data, not about a reanalysis of an existing experiment. The candidate models were generated by agent-based simulation, and synthetic observations were then fed back into the inference pipeline. The practical reading is that the choice of summary statistic matters as much as the choice of estimator: a statistic that discards temporal structure, or one built from sparse discrete events, can lose the very signature that separates mechanisms.

Model selection follows oscillations, parameter recovery follows accuracy

The most consequential result is a dissociation. Model selection efficiency M tracks the rate-of-change metric, which captures how strongly and synchronously the group's accuracy oscillates. When oscillatory, synchronized switching is weak, model selection degrades. Parameter identifiability P instead mirrors the global accuracy value Q, following its U-shaped response to the initial fraction of agents in the best patch and its decline under resource depletion.

The authors therefore conclude that the information available for distinguishing mechanisms is not the same as the information needed to recover their parameters. This is not a claim that one measurement is better than the other; it is a claim that the two inference targets draw on different parts of the behavioral signature. A design optimized to discriminate models should protect temporally resolved, synchronized transitions, while a design optimized to estimate coupling strength should protect the overall accuracy level.

Experimental conditions shift identification as much as model structure

Identification is not a fixed property of a model. The paper varies group size, initial group distribution, resource depletion and the gap between reward probabilities, and finds that identification changes with each. Larger groups strengthen collective signals for pulsatile models, and accuracy improves across social models with group size while staying flat for the non-interacting model. Resource depletion reduces residence time and accuracy and raises the rate of change, and it degrades parameter recovery in parallel with the accuracy decline.

Sampling also matters. Under small sample sizes, small group sizes and coarser sampling periods, the degradation is systematically more pronounced for the oscillation-driven models CT, PT and PB than for CB, whose distinguishing feature is sustained exploitation rather than coordinated cycling. Because model selection depends on temporally resolved synchronized transitions, designs that undersample those transitions lose discriminative power first for exactly the models that rely on them.

Some parameters stay unrecoverable even with good models

The paper reports a case where model selection stays comparatively high while parameter recovery collapses: in the complete absence of reward, the learning-related parameter has no behavioral consequence, so it is structurally unrecoverable even though the model itself can still be distinguished. This is a concrete illustration of the structural-versus-practical identifiability distinction the authors invoke, and it marks a limit that better estimators cannot fix.

The authors also flag assumptions that bound the results. The decision process uses white noise rather than the temporally correlated noise seen in many biological systems, and the strength of learning-based threshold modulation was deliberately restricted to avoid configurations where the initial decision variable falls below threshold. The three behavioral metrics were chosen for interpretability and are unlikely to be exhaustive; the pulsatile-belief model's exception in the resource-distribution analysis suggests additional model-specific signatures may be needed. The identification analysis also relied on prior calibration and a coarse parameter grid.

Design the experiment around the inference target

The paper's practical priority is a matching rule between experimental design and inferential goal. If the aim is to discriminate among social-information mechanisms, the design must preserve the oscillatory, synchronized structure of group accuracy over time, which means adequate sample size, sufficiently large groups and fine enough temporal sampling, since these are precisely the conditions under which CT, PT and PB remain separable from CB. If the aim is to estimate coupling strength, the design should instead protect the global accuracy level, which tracks parameter recovery across conditions.

The comparison that matters most is between CB and the oscillation-driven models. CB is identified through sustained exploitation and elevated accuracy rather than coordinated cycling, so it survives undersampling that erodes the others, while its parameter recovery deteriorates as individual heterogeneity rises. A study that reports only overall accuracy, or only coarse departure counts, therefore risks answering the parameter question while silently failing the model-selection question, or the reverse.

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