2.1 Task structure and behavioral regime

We tested 29 participants (15 female; mean age = 23.93 years, SD = 3.73), each completing up to 576 trials (72 forests 8 days). On average, participants completed 361.45 trials (SD = 23.22; range = 292–411), yielding 10,270 decisions in total. Missed responses were rare (M = 0.02, SD = 0.03 trials), indicating high task engagement.

The task comprised two conditions: approach forests and avoidance forests, which differed in how reward and threat information jointly shaped the optimal decision policy. In both conditions, weather types associated with greater reward opportunities also tended to involve greater threat. However, the balance between these competing factors differed across environments, creating contexts in which the optimal policy either favored approaching or avoiding the higher-threat option. Descriptively, mean food-finding probability was lower in approach forests () than in avoidance forests (), while predation risk was comparable across conditions (approach: ; avoidance: ). Consequently, joint success probability was higher in avoidance forests () than in approach forests (). Despite these differences in environmental structure, survival rates did not differ significantly between conditions (, p = .38), providing no evidence that one condition produced substantially higher failure rates than the other. Bootstrapping using 10,000 resamples indicated only a small difference in predation-risk distributions between conditions (95% CI [0.007, 0.02]), suggesting that the practical magnitude of this difference was negligible.

Designing sequential choice tasks is challenging because action values depend on transition dynamics that cannot be directly controlled. We therefore constructed environments that avoided strongly favoring either action, minimizing both trivial and indifferent choices. To characterize the resulting decision space independently of participants’ behavior, we analyzed the distribution of theoretical state–action value differences () across all states of all task environments. These -values were derived from the optimal policy of the fully specified MDP underlying the task and served as a measure of choice difficulty. Positive -values favor foraging, negative values favor waiting, and values near zero indicate little difference in long-term value between actions and therefore correspond to more difficult decisions. As shown in Fig 3A, most decisions clustered around (), indicating that the task predominantly sampled meaningful trade-offs, whereas truly indifferent choices were rare (3% of trials). This pattern was highly similar across approach and avoidance conditions (Fig 3B and 3C), suggesting comparable theoretical difficulty across contexts. Consistent with this, a Kolmogorov–Smirnov test revealed only a small difference between the distributions (D = 0.04), despite statistical significance driven by the large number of theoretically possible states (p < .01). Together, these results indicate that the task predominantly sampled difficult but non-indifferent decisions while avoiding large numbers of trivial choices. Importantly, choices that more closely aligned with the action favored by were associated with greater behavioral success (Fig 3D).

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Fig 3. Structure of the decision space and behavioral relevance of optimal policy.

(A) Distribution of the optimal policy value differences () derived from the Markov Decision Process (MDP), quantifying choice difficulty. Values near zero indicate weak preference between actions, whereas larger absolute values reflect clearer optimal choices. The distribution is concentrated around zero, indicating that most trials involve finely balanced trade-offs. Insets illustrate example distributions for different trial types. (B) State-level decision difficulty () across conditions for the entire theoretical MDP grids (all possible state–action values). Violin plots show similar distributions for avoidance and approach conditions, indicating comparable overall task difficulty. Points denote mean values. (C) Empirical cumulative distribution functions (ECDFs) of for approach and avoidance conditions. The strong overlap between curves indicates highly similar difficulty distributions across contexts. Although the Kolmogorov–Smirnov test was statistically significant (D = 0.04, p < 0.01), the small effect size suggests that differences between conditions are negligible. (D) Relationship between alignment with optimal policy value differences () and behavioral success. Each point represents a participant; the x-axis shows the individual slope () relating to choice, and the y-axis shows the number of successfully completed forests. Greater alignment with optimal values is associated with higher performance (r = 0.49, p = 0.01), supporting the behavioral relevance of the MDP-derived benchmark.

https://doi.org/10.1371/journal.pcbi.1014793.g003

To further evaluate whether the two conditions differed in overall processing demands, we compared log-transformed response times (RTs) between approach and avoidance contexts. There was no difference in RTs between conditions (Mann–Whitney U = 12908, p = .459). We next examined whether response times varied as a function of decision difficulty by regressing RTs on absolute state–action value differences (), condition, and their interaction. No effects of (p = .410), condition (p = .726), or their interaction (p = .464) were observed. Together with the comparable distributions across conditions, these findings suggest that the approach and avoidance environments imposed similar overall processing demands and did not differ systematically in difficulty.

2.2 Model inference

Our task allowed us to derive the optimal policy using an MDP and to specify feature-based models of varying complexity (summarized in Table 1). Simple feature-based models relied on isolated decision variables such as weather or predator risk, whereas more complex models integrated multiple features into unified value representations, such as expected gain or the optimal policy, which require more computationally demanding evaluations. To bridge these extremes, we implemented a multi-feature policy that combines a small set of decision features capturing both environmental transition structure and state-dependent action constraints. Environmental features such as success probability () and threat risk () directly determine the transition dynamics of the MDP and therefore specify how current actions influence future states. In contrast, state-dependent features such as binary energy state (BES) and wait when safe (WWS) capture boundary conditions under which actions become either necessary or safely avoidable. We refer to these as boundary conditions because they reflect extreme environmental states associated with near-deterministic policies (e.g., foraging when starving). By combining these components, the multi-feature policy provides a structured, low-dimensional approximation of the optimal policy that captures both environmental dynamics and internal resource constraints without requiring explicit forward planning. This formulation allows us to test whether adaptive behavior is better explained by structured feature integration, isolated decision variables, or exhaustive MDP-based evaluations. Importantly, the resulting model space allows us to determine whether apparent alignment with optimal behavior is better explained by integrated value representations or by selective modulation of individual decision features.

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Table 1. Overview of predictive variables representing behavioral models.

https://doi.org/10.1371/journal.pcbi.1014793.t001

Because participants contributed a large number of repeated decisions, all computational models were estimated using a hierarchical Bayesian framework. This approach pools information across participants while preserving individual differences, allowing group-level and subject-level effects to be estimated simultaneously. By leveraging the hierarchical structure of the data, hierarchical models improve statistical efficiency and stabilize parameter estimates, particularly in repeated-measures designs with many observations per participant. We first compared models across the full dataset using PSIS-LOO cross-validation to identify the best account of participants’ behavior (Fig 4A). The multi-feature policy provided the best predictive performance ( = 0), substantially outperforming all alternative models, including the -based model ( = −465). This suggests that behavior is best captured by the combined influence of multiple task-relevant features, rather than any single decision variable. In contrast, models based on isolated features performed markedly worse (s > −1300), indicating that no single variable was sufficient to capture behavior. Importantly, this comparison does not imply that integrated value signals are irrelevant, but rather that their influence is not fully captured by any single model in isolation. To directly assess the joint contributions of feature-based and integrated value signals, we next fitted a unified hierarchical model including the components of the multi-feature model, -values, and their interactions with condition (approach vs. avoidance; Fig 4B and 4C).

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Fig 4. Model comparison and context-dependent feature reweighting.

(A) PSIS-LOO model comparison across candidate models. Bars show differences in expected log predictive density () relative to the best-performing model (multi-feature policy). The multi-feature policy outperformed all single-feature and alternative heuristic models, indicating that behavior is best captured by a combination of task-relevant features. Asterisks (*) denote features that were included in the multi-feature policy. (B) Posterior estimates (mean 95% credible intervals) from the unified hierarchical model showing main effects and condition-dependent modulation of decision features on foraging behavior (logit scale). Positive values indicate increased probability of foraging. Avoidance contexts selectively modulated feature weights, including reduced sensitivity to and increased influence of -values. A full overview of all model effects, including block modulation and feature interactions, is provided in S1 Fig. (C) Marginal effects of condition on (left) and -values (right). Lines show predicted probability of foraging (mean 95% credible intervals) for approach and avoidance conditions. Under avoidance, the influence of is reduced, whereas sensitivity to -values is increased, indicating stronger alignment with integrated value signals. Rug plots indicate the distribution of observed data.

https://doi.org/10.1371/journal.pcbi.1014793.g004

At the level of main effects, behavior was shaped by multiple decision features. Participants were more likely to forage with increasing gain probability (: , 95% CI [0.77, 1.10]) and increasing value differences (: , [0.90, 1.85]). In addition, two features exerted particularly strong influences: waiting when safe (, [1.53, 2.33]) and binary energy state (, [2.05, 3.14]), indicating that choices were strongly constrained under boundary conditions where action requirements become clear. Threat probability () showed a reliable negative effect (, ), reflecting reduced foraging as risk increased. These results indicate that choice behavior was influenced by multiple task-relevant features spanning reward, threat, and state-dependent boundary conditions.

Regarding policy modulation by condition, there was no evidence for a global shift in overall decision policy, as the main effect of condition was not reliably different from zero (, ). This indicates that contextual differences in behavior cannot be explained by a uniform change in response tendencies, but instead reflect selective feature reweighting, that is, context-dependent changes in how decision-relevant features influence choice. Most notably, the effect of gain probability was significantly reduced in avoidance contexts ( condition: , ), as also reflected in the attenuated slope relating gain probability to foraging probability (Fig 4C left). In contrast, threat-related modulation was weaker: the interaction between threat probability and condition did not differ reliably from zero (, ).

Critically, condition also modulated sensitivity to the integrated decision variable ( condition: , [0.00, 0.55]), with choices in avoidance contexts showing greater alignment with the integrated value structure of the task (Fig 4C right). This effect persisted both when -values were included alongside reward-, threat-, and state-related predictors in the unified model and when -values were residualized with respect to those predictors (S1 Fig B), indicating that increased alignment with cannot be reduced to variance shared with the modeled features alone. Consistent with this interpretation, gain-threat interactions did not show reliable contributions when -values were included, suggesting that their joint influence was largely captured by the integrated value signal.

The unified model additionally included interactions with block number to capture experience-dependent changes, as well as gain–threat interactions () and their modulation by condition ( condition). Across blocks, participants showed systematic shifts in behavior, characterized by an overall reduction in foraging (, ) and increased alignment with optimal value differences ( block: , [0.03, 0.31]). Importantly, the increased alignment with the optimal policy across blocks was accompanied by systematic changes in the influence of multiple decision features, suggesting that experience-dependent adaptation is consistent with structured changes in feature integration rather than a simple global shift toward optimal responding. The influence of the WWS feature also increased over time (, [0.09, 0.66]), while sensitivity to threat became slightly more negative (: , ). Other feature–block interactions were not reliably different from zero. As these experience-dependent effects were not central to our primary question of context-dependent feature reweighting, they are not shown in detail in the main figure. Fig 4 summarizes the effects central to context-dependent feature reweighting, while a complete overview of all parameters, including block and gain–threat interaction terms, is provided in S1 Fig.

Taken together, these results indicate that behavior reflects the combined influence of multiple decision features rather than any single variable. Environmental context did not produce a global shift in overall response tendency, as reflected by the absence of a condition main effect, but instead selectively modulated the influence of specific features: avoidance contexts reduced the impact of reward-related information while increasing sensitivity to the integrated value structure of the task (). Importantly, this increased alignment with -values cannot be reduced to the combined effects of individual features, suggesting that behavior captures aspects of the integrated value signal beyond those represented by the modeled feature set. These findings are consistent with context-dependent changes in the weighting of decision features, rather than a uniform shift in decision policy. While the observed pattern is consistent with increased alignment to -values, this effect appears to emerge through differential modulation of individual feature weights rather than a uniform change in decision policy.

To ensure that the compared models were sufficiently distinguishable and recoverable, we performed a model recovery analysis using synthetic datasets generated from each candidate model and refit with the full model space (Fig 5). Recovery accuracy was quantified as the proportion of simulations in which the generating model was correctly identified as the best-fitting model based on PSIS-LOO predictive performance. Overall, recovery was highly accurate across all candidate models, with correct classification rates ranging from 0.96 to 1.00. Misclassifications were rare and occurred primarily when simple single-feature models were occasionally recovered as the more flexible multi-feature policy. Importantly, the multi-feature policy and -based model showed perfect recovery, indicating that the main theoretical distinction underlying the present study was highly separable. Although some recovery fits involving highly flexible models applied to data generated by simpler single-feature policies produced elevated values or reduced effective sample sizes, overall model recovery performance remained highly accurate, suggesting that these diagnostic issues primarily reflected weak parameter identifiability in near-separable synthetic choice patterns rather than systematic model confusability. Together, these results suggest that the observed superiority of the multi-feature policy in the empirical data is unlikely to reflect model overlap or insufficient discriminability between candidate models.

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Fig 5. Model recovery analysis.

Confusion matrix showing model recovery performance across all candidate policy models. Synthetic datasets were generated from each model using posterior parameter estimates from the empirically fitted hierarchical Bayesian models and subsequently refit using the full candidate model space. Recovery analyses used conditional simulation procedures in which choices were regenerated while preserving the original trial structure and task states. Values indicate the proportion of simulations in which a given generating model (rows) was correctly or incorrectly identified as the best-fitting model (columns) based on PSIS-LOO predictive performance. Recovery accuracy was high across all candidate models (0.96–1.00), with only minor misclassification of some simple single-feature models as the more flexible multi-feature policy. Importantly, the multi-feature policy and -based model showed perfect recovery, indicating strong discriminability between the principal competing accounts examined in the study. Although some recovery fits involving highly flexible models applied to data generated by simpler single-feature policies produced elevated values or reduced effective sample sizes, overall model discriminability remained robust.

https://doi.org/10.1371/journal.pcbi.1014793.g005

3.1 Behavior reflects context-dependent reweighting of decision features

The present study investigated how decision-making adapts in sequential approach–avoidance contexts by comparing value-based and feature-based accounts of behavior. Across conditions, choices were best explained by the combined influence of multiple task-relevant features rather than any single decision variable. Importantly, the overall superiority of the multi-feature policy indicates that behavior remained primarily influenced by multiple decision-relevant features across both contexts. Furthermore, environmental context did not induce a global shift in decision policy, as evidenced by the absence of a reliable main effect of condition on overall response tendencies. Instead, avoidance contexts selectively modulated the influence of specific decision features while also increasing alignment with the integrated value structure of the task (). Together, these findings suggest that adaptive behavior arises through context-dependent changes in how decision-relevant information contributes to choice, rather than through a qualitatively distinct decision strategy or a uniform shift in response policy.

3.2 Avoidance contexts increase alignment with integrated value signals

A key finding was that choices in avoidance contexts showed greater alignment with the integrated value signal derived from the task structure. Even after accounting for feature-based predictors, values explained additional variance in choice behavior, and the influence of increased under avoidance. This effect persisted in models that explicitly accounted for reward, threat, and state-dependent boundary conditions (BES and WWS), as well as after residualization analyses, indicating that the observed condition effect was not fully captured by the modeled feature set. Importantly, the increased influence of was not accompanied by longer response times, and comparable survival rates and -value distributions across conditions argue against simple explanations based on increased deliberation, task difficulty, or environmental structure.

Together, these findings suggest that avoidance contexts altered how decision-relevant information contributed to choice, resulting in greater alignment with the integrated value structure of the task without evidence for a global shift in decision policy.

3.3 Implications for models of adaptive choice

The present findings have important implications for how adaptive behavior is conceptualized in sequential decision-making. Traditional accounts often frame adaptation as a shift between qualitatively distinct strategies, such as transitions between feature-based and integrated value-based policies or between model-free and model-based systems (e.g., [23,24]). In contrast, the current results suggest that adaptive behavior may instead emerge from continuous adjustments in how a shared set of decision-relevant features is weighted and combined.

A key finding was that avoidance contexts increased alignment with the integrated value signal derived from the task structure (), while simultaneously reducing the influence of reward probability and selectively modulating other decision features. One possible explanation for this pattern is that avoidance environments place greater demands on coordinating reward and threat information. Although higher reward opportunities were associated with greater threat in both conditions, avoidance environments were structured such that avoiding the higher-threat option was more often advantageous under the optimal policy. Under these circumstances, reward probability alone becomes a less reliable guide to action selection, potentially increasing the importance of integrating multiple decision-relevant features.

Importantly, the influence of explained behavior beyond the individual feature predictors. However, this does not imply that participants explicitly computed -values or switched to a qualitatively distinct decision strategy. Rather than representing competing process-level accounts, feature-based and integrated value-based models may capture different levels of description. Feature-based models characterize the information influencing choice, whereas integrated value models characterize how that information is combined within the structure of the task. Consistent with optimization-based perspectives (e.g., [15]), complex or near-optimal behavior may emerge through the tuning of relatively simple parameterized policies, whose lower-dimensional structure provides a scalable and flexible means of adaptation without requiring explicit construction of exhaustive value representations. From this perspective, greater alignment with integrated value signals may arise through adaptive changes in how decision-relevant features are weighted and combined.

This interpretation is consistent with proposals that value signals reflect emergent summaries of underlying computations rather than distinct decision processes (e.g., [5]). It is also compatible with resource-rational accounts of behavior under computational constraints (e.g., [10]), because behavioral flexibility can be achieved by adjusting a limited set of feature weights rather than computing new policies from scratch. More generally, the results suggest that flexible behavior can emerge not only through switching between internal models of the environment [25], but also through gradual changes in how the same decision-relevant information is weighted across contexts. Future work should investigate the neural and computational mechanisms underlying these adjustments, as well as their generality across different task structures and populations.

3.4 Limitations

First, the sample comprised 29 participants. Although each participant contributed a large number of repeated decisions and all models were estimated hierarchically, larger samples will be needed to establish the robustness and generalizability of the present findings. Second, the manipulation of threat was purely symbolic and not validated with physiological or subjective measures, leaving open whether the avoidance condition induced genuine affective responses or instead reflected differences in attention or task demands. Furthermore, the task remains an abstract and simplified environment, and it is unclear how well the observed patterns generalize to real-world decision-making involving more salient or consequential threats. Nevertheless, predator encounters imposed substantially greater immediate survival costs than starvation within the task structure, thereby creating an ecologically motivated conflict between reward-related and threat-related outcomes. Third, the optimal policy serves as a normative benchmark rather than a process-level account; thus, increased alignment with -values should not be interpreted as evidence that participants explicitly compute or implement this policy, but may instead reflect improved integration of decision-relevant features or reduced decision noise.

Importantly, although alternative explanations for the -values condition interaction, such as differences in task difficulty or cognitive demand, cannot be fully excluded, several analyses argue against a simple “easier avoidance condition” account. In particular, -value distributions were highly similar in shape across conditions, although a small but statistically significant difference was detected, indicating subtle distributional differences rather than a clear shift in task difficulty. Moreover, response times did not differ as a function of decision difficulty or context, and the increased influence of under avoidance persisted even when values were residualized with respect to the multi-feature model predictors. Notably, an exploratory policy-arbitration analysis (S6 Fig) produced a similar pattern of results while explicitly accounting for overlap between competing policy representations, suggesting that the observed increase in -alignment cannot be readily explained by representational overlap alone. Nevertheless, the present approach does not fully resolve the relationship between feature reweighting and integrated value representations, and further work will be required to more directly test these alternatives.

Finally, while we accounted for block-related changes, the present framework does not fully dissociate the computational mechanisms underlying these effects. In particular, the observed -values block interaction indicates that behavior changed systematically across the experiment, but the current modeling approach remains descriptive and does not specify whether these changes reflect learning, strategic adaptation, fatigue, attentional shifts, or other latent processes. Thus, we do not provide a generative account of how context-dependent feature reweighting emerges over time. Future work should therefore combine larger samples with process-level computational models that more directly link behavioral adaptation to underlying cognitive mechanisms, including through targeted manipulations of task structure, duration, or affective salience.

4.1 Ethics statement

Ethics approval was given by the local ethics committee of the medical faculty of Heidelberg University. All participants provided written informed consent prior to participation.

4.2 Participants

We tested 29 healthy participants (15 female, 14 male; mean age = 23.93 years, SD = 3.73) in the lab, who were recruited via fliers and online tenders. Participants were asked whether they had any history of psychiatric or neurological diagnoses, which was an exclusion criterion. None of the invited subjects were excluded.

4.3 Description of the hunter-gatherer task with predators

Our task (see Fig 2) was adapted from the “Hunter-Gatherer Task” by Korn and Bach [21]. The task consisted of multiple mini-blocks (“forests”), each containing two probabilistic environments (“weather types”) with varying chances of gains and losses. Participants’ goal was to “survive” by preventing their discrete energy levels (life points) from reaching zero over a series of trials (“days”) within each forest, with a monetary reward for survival. On each trial, one weather type was randomly selected, indicating the probability and magnitude of food gains. Participants chose to either forage (hunt/gather) or wait for better conditions. Probabilities of food gain were visually represented as colored dots on a grid. Waiting incurred a small, guaranteed energy loss (1 point), while unsuccessful foraging resulted in a larger loss (2 points), creating a trade-off.

Building on [21,22], we introduced predators as an additional probabilistic threat, displayed as roaming red frames on the grid. If a participant foraged and encountered a predator, they lost even more energy (3 points), simulating the increased cost of a fight-or-flight reaction. Threat-related outcomes were implemented symbolically through probabilistic predator encounters rather than direct aversive stimulation. Within the task structure, predator encounters imposed substantially greater immediate survival costs than starvation, thereby creating a sequential trade-off between reward acquisition and threat avoidance. Importantly, in every forest, the weather type with a higher probability of finding food also had a higher predator risk, creating an approach–avoidance conflict. However, the balance between these competing factors differed across forests. Based on the optimal policy derived from the task structure (described in 4.4 Computation of the Optimal Policy), some forests favored approaching the higher-reward, higher-threat option, whereas others favored avoiding it. These environments formed the approach and avoidance conditions used throughout the experiment.

Each weather type was represented by a grid with 2–10 fields, each equally likely to be the participant’s landing location after foraging. The probability of finding food (p) was defined by the ratio of food-containing fields to total fields, ranging from 0.2 to 0.67 to avoid near-zero chances. Similarly, predator risk (r) was defined as the probability that both participant and predator landed on the same field, ranging from 0 to 0.67 (2 predators and 3 fields), based on the number of predators relative to total fields. Foraging failure probability (q) was .

Participants completed 72 forests divided into four blocks of 18. Each forest lasted 8 days, with one of the two weather types randomly selected on each day (50% probability). The task included 36 approach forests and 36 avoidance forests. Forests differed in the configuration of food availability, predator risk, and grid size, thereby generating a diverse set of sequential decision environments while preserving the overall task structure.

Participants began each forest with an energy level randomly between 4 and 5, capped at a maximum of 6 discrete points, creating 7 possible energy states (0–6). Coupled with two weather types, this yielded 14 possible states per forest. Falling to zero energy ended the forest prematurely without reward. This setup satisfies the criteria for a fully observable Markov Decision Process (MDP), enabling computation of optimal state–action values through dynamic programming. The resulting optimal policy prescribes the action with the highest expected long-term value in each state. To ensure meaningful decision trade-offs, forests in which the optimal policy showed little preference between weather types were excluded. Specifically, forests with an absolute difference in foraging preference below 10 across states and time-points between the two weather types were removed.

4.4 Computation of the optimal policy

The experimental setup allowed to derive the optimal policy from a fully observable MDP. Since the transition probabilities between states were fully overt, the state–action values could be computed iteratively via dynamic programming (or backward induction). Fig 1 illustrates the requirements (state–action transitions and transition matrix) for computing the optimal policy with the MDP algorithm.

Backward induction was performed by iteratively computing state–action values for all states and time points according to the Bellman framework:

(1)

where is the expected value of the total return G when starting from state s at time t and following policy . We only considered the discount factor = 1, since the game mechanics of our task did not necessitate nor motivate discounted rewards over time. The policy can, thus, be computed from the argmax of the average future rewards of the action set a as follows:

(2)

Accordingly, the action values for foraging and waiting can be transformed into a single state–action value difference (-value) in the following manner:

(3)

If is positive, the optimal policy suggests foraging. If is negative, the optimal policy suggests waiting. If is zero, the optimal policy is indifferent. Rather than fitting the deterministic optimal policy directly, -values were used as continuous predictors within a logistic choice model. This allows graded choice probabilities to be modeled as a function of the strength of the value difference between actions, thereby accommodating uncertainty and variability in human decision-making. The code for calculating was made publicly available on GitHub (see https://github.com/SAEG64/fora02/tree/main).

4.5 Task presentation

At the beginning of a forest, participants were shown both weather types in the so-called forest phase (3.5 s), followed by 8 consecutive decision and feedback phases (the so-called “days”) until completion of a forest. The feedback was displayed for 2 s. Before each decision phase, a random fixation time between [0.5, 3.8] appeared in the form of a blank screen. Participants had to give a response within 3 s, otherwise the option ‘waiting’ was chosen by default. In case of no response, these decisions were excluded from the data when conducting model comparisons. Fig 2 illustrates the details of the task presentation. Before doing the task, subjects received written instructions about the setup. The full instructions sheet can be found in S1 Text.

4.6 Behavioral modeling

The main objective of this experiment was to examine how participants integrate reward and threat information when making sequential foraging decisions across different contexts. Rather than assuming a strict dichotomy between optimal (MDP-based) and feature-based strategies, our approach tests the extent to which behavior can be explained by a limited set of decision features and how their weighting varies across conditions. To this end, we compared a set of models ranging from single- to multi-feature models, as well as the state–action value difference derived from the optimal policy (-values), which represents a normative benchmark for the best possible choice pattern in our task. A detailed description of all models is provided in Table 1.

Our task design includes several variables that can be directly derived from the task and can serve as simple feature policies: probability of gaining food, risk of threat encounter, weather type (good and bad), the internal (binary) energy state and the wait when safe policy (if sufficient energy points are collected, participants can simply wait to win the game). We also included the win-stay-lose-shift policy, which binarizes the evaluation of the last event in the choice history. These models represent directly observable and univariate features of our task, which do not require any further feature engineering. In addition to this, we included what we call “intermediate” models, a set of policies that require some recombination of variables to represent slightly more complex decision rules. Examples of such models include the expected energy gain model, which computes the weighted average of possible outcomes (; where denotes the magnitude of energy gain or loss and the corresponding probability), and a marginal value model derived from this quantity, in which foraging is chosen when the current expected gain exceeds a running average, and waiting otherwise. The marginal value model stems from the marginal value theorem (MVT), in which patch foraging behavior is explained with a threshold value computed from the mean expectancy of sequentially experienced environments (see [26,27]).

We also constructed a multi-feature policy that captures behavior using a small set of key task variables: reward and threat probabilities (p and r), as well as two indicators for situations in which the decision is effectively straightforward (binary energy state, BES; and “wait when safe,” WWS). Instead of treating these as separate features, the model combines them to predict choices. This allows it to approximate optimal decisions in simple situations, while relying on a balance of reward and threat information when trade-offs are present. In this way, the model can be used to test how the importance of these features changes across states and task conditions. Although the multi-feature model includes multiple predictors, parameter estimation was regularized through hierarchical shrinkage, ensuring that improved predictive performance reflects generalizable structure rather than overfitting.

The optimal policy (-values) is based on a single combined measure of the decision, whereas the multi-feature policy uses several task-relevant features together to predict choices. This gives the multi-feature model more flexibility in how it captures behavior. However, all of these features directly reflect central aspects of the task rather than introducing additional assumptions. To ensure a fair comparison, we evaluated models based on how well they predict new data, so that better performance reflects more accurate predictions rather than simply greater flexibility.

4.7 Model comparison

All models were fit using hierarchical Bayesian logistic regression using the Python package PyMC, allowing parameters to vary across participants while being constrained by group-level distributions (partial pooling). This approach improves parameter estimation by sharing statistical strength across individuals while preserving meaningful between-subject variability. Group-level regression coefficients were assigned weakly informative normal priors centered at zero (N(0,1)). Variance parameters governing subject-level variability were assigned priors. Subject-level effects were estimated hierarchically using non-centered parameterization to improve sampling efficiency and stabilize No-U-Turn Sampler (NUTS) estimation. Posterior inference was performed using Hamiltonian Monte Carlo with the NUTS sampler implemented in PyMC. Unless otherwise specified, models were estimated using 4 independent Markov chains with 1000 tuning iterations and 1000 posterior sampling iterations per chain (target_accept = 0.90). All continuous predictors were z-scored prior to model fitting to facilitate parameter estimation, comparability across features, and the use of weakly informative priors on a common scale. For the multi-feature policy model, only continuous predictors ( and ) were standardized, while binary predictors (“wait when safe” and “binary energy state”) remained unscaled. The multi-feature model additionally included fixed pairwise interaction terms between predictors, while retaining random slopes for the corresponding main effects.

For each model, choices were predicted from the corresponding decision variable (or set of predictors, in the case of the multi-feature policy) using a logistic link function:

(4)

where denotes the value of predictor k on trial t, and the corresponding subject-specific weight for participant i. The intercept captures each subject’s baseline tendency to choose the foraging option. The resulting linear predictor is mapped onto choice probabilities via the logistic link function:

(5)

All models showed satisfactory convergence diagnostics (all < 1.01, no divergent transitions, and effective sample sizes within recommended ranges). Posterior predictive checks further indicated that the fitted models reproduced the main patterns observed in the behavioral data (S5 Fig). Models were compared using Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO), which estimates out-of-sample predictive performance by evaluating how well each model generalizes to unseen data. Model performance was quantified using the expected log predictive density (ELPD), with higher values indicating better predictive performance. Differences in ELPD () were used to assess the relative support for competing models.

We assessed the similarity between model predictors and found that correlations between models remained moderate (all ; see S2 Fig). These levels are below typical thresholds for problematic multicollinearity. Furthermore, we ensured the validity of our model comparison by performing both model and parameter recovery analyses, following established guidelines [28,29]. Synthetic datasets were generated from posterior parameter estimates of the empirically fitted hierarchical models while preserving the original trial structure and task states (conditional simulation procedure), and subsequently refit using the full candidate model space. Recovery analyses used the same hierarchical Bayesian logistic regression framework as the empirical analyses, including non-centered parameterization, weakly informative priors, and partial pooling across participants. For the multi-feature policy, all pairwise interactions between predictors were retained except for the interaction between “wait when safe” and “binary energy state,” which was excluded because the two variables represented mutually exclusive boundary-state conditions by task design. Including this interaction introduced structurally redundant parameterization that reduced parameter recoverability without improving model expressiveness. Recovery fits were estimated using 4 Markov chains with 500 tuning and 500 posterior sampling iterations per chain (target_accept = 0.95). Model recovery results are reported in Fig 5 (see Results, 2.2 Model Inference), while parameter recovery is provided in the Supplementary Materials (S3 and S4 Figs). Overall, these analyses demonstrated sufficient model discriminability and parameter recoverability for meaningful model comparison. The full codebase for all modeling analyses is publicly available (see https://github.com/SAEG64/fora02/tree/main).

4.8 Control analyses: Task difficulty and response times

To assess whether task difficulty differed across conditions, we quantified decision difficulty using the absolute optimal policy value difference () across all state–action pairs of the MDP and compared the resulting distributions between approach and avoidance conditions using a Kolmogorov–Smirnov test.

To examine whether decision difficulty influenced response times, we tested whether predicted log-transformed response times. In addition, we examined effects of condition (approach vs. avoidance) and their interaction using linear regression.