1 Introduction

How animals make decisions among alternative actions is a key question in neuroscience. In natural environments, decisions arise from the integration of sensory inputs, internal states, and learned experience (Meister, 2022). In the laboratory, both learned and innate paradigms have been used to study decision-making. Some learned paradigms, such as two-alternative forced choice (2-AFC) and GO-NOGO tasks (Andermann et al., 2010; Burgess et al., 2017), often require weeks of training in head-fixed animals; whereas other learned paradigms require less training over several days in freely moving animals, including maze exploration (Barnes, 1979; Morris, 1984; Rosenberg et al., 2021; Small, 1901), foraging decisions (Hayden, 2018; Hayden et al., 2011; Steiner and Redish, 2014), and active avoidance (Bravo-Rivera et al., 2014; Moscarello and LeDoux, 2013; Mowrer and Lamoreaux, 1946). While these paradigms have significantly advanced our understanding of the neural mechanisms underlying learned decisions, the training itself may engage neural circuits that differ from those evolved for innate decision-making (Steinmetz et al., 2019).

In contrast, innate decisions—such as whether to escape from an approaching aerial preda-tor (De Franceschi et al., 2016; Yilmaz and Meister, 2013) or a simulated ground threat like a robogator (Amir et al., 2015; Choi and Kim, 2010)—are executed without prior training and may more directly reflect the function of neural circuits shaped by natural selection. In complex envi-ronments, making correct and rapid innate defensive decisions often requires cognitive control to assess risk and evaluate alternative defensive strategies (Evans et al., 2019). Defensive responses to terrestrial predators depend on predator–prey distance (Ydenberg and Dill, 1986) and are well described by the predatory imminence continuum theory (Fanselow and Lester, 1988). Responses to approaching aerial predators are likely scaled similarly according to the perceived threat intensity, which is influenced by the physical properties of the threat (De Franceschi et al., 2016; Liden and Herberholz, 2008; Tammero and Dickinson, 2002; Yang et al., 2020; Yilmaz and Meister, 2013), prior experience (Vale et al., 2017), and environmental context, including housing conditions (Lenzi et al., 2022). At the neural level, the superior colliculus (SC) serves as a central hub for processing looming-evoked defensive responses, with distinct output pathways mediating escape versus freezing behaviors (Evans et al., 2018; Shang et al., 2018; Wei et al., 2015; Zhou et al., 2019).

Despite this progress, important gaps remain. Mice are social animals, and most predator encounters occur during foraging, yet it is unclear how they weigh perceived threat and reward when making defensive decisions, or how these decisions are influenced by social hierarchy. To address these questions, we developed an ecologically relevant behavioral paradigm to investigate decision-making in foraging mice exposed to overhead visual threats. Our findings demonstrate that defensive choices are jointly influenced by threat intensity, reward magnitude, and social hierarchy, providing a behavioral framework for future investigations into the neural mechanisms underlying cognitive control of innate decision-making.

2 Results

2.1 A behavioral paradigm for studying innate decision-making in mice

To investigate how animals make innate decisions in natural environments, we designed a behavioral paradigm to simulate the defensive behavior of foraging mice in the wild. In this paradigm, a group of 2–5 co-housed mice was placed in a nest, with each individual identified using a radio frequency identification (RFID) tag. Only one mouse was allowed to enter a linear arena to receive the reward delivered at the end. As the mouse approached the reward, an overhead expanding dark disc that mimics the approach of an aerial predator was triggered (Figure 1A), forcing the animal to decide whether to risk getting the reward or to seek safety in the nest. Behavioral data were recorded using a ground-mounted camera, and DeepLabCut was used to track the movements of the mouse’s nose and tail base (Mathis et al., 2018) (Figure S1A). Compared to the exploratory phase, the presence of looming stimuli significantly increased the frequency of arena entries but decreased the duration of each visit (Figures 1B–C).

Figure 1:

To identify distinct behavioral patterns in response to looming stimuli, we defined 19 behavioral features from key body points of the mouse and fed them into a random forest classifier that predicted decisions with 95% accuracy (Figures 1D and S1B–C, see Materials and methods). Across 3862 trials, decisions were categorized into four types: direct escape (11.8%, Video 1), escape after assessment (assessment+escape, 43.2%, Video 2), freezing (5.8%, Video 3), and no response (39.2%, Video 4) (Figures 1E–F). A key distinction between assessment+escape and freezing decisions was the duration of stationary behavior: mice that decided to freeze remained stationary significantly longer than those in the assessment+escape group (Figure 1G). Furthermore, the latency to flee differed significantly between direct escape and assessment+escape decisions (Figure 1H).

We hypothesized that fear level increases progressively across the decision types: freezing, assess-ment+escape, and direct escape. This hypothesis is supported by the observations that mice in the direct escape group exhibited higher escape speeds (Figure 1I) and shorter hiding latencies (Figure 1J). Additionally, the proportion of mice that recovered within 20 s after stimulus onset was about 20%, 40%, and 80% for direct escape, assessment+escape, and freezing, respectively (Figure 1K). Consistently, recovery time decreased progressively across these decision types (Figure 1L). Our findings align with the predatory imminence continuum theory (Fanselow and Lester, 1988), which proposes that defensive responses become more intense as the perceived threat level increases.

2.2 Mice make economic decisions modulated by vigilance

In the wild, most prey–predator encounters occur while prey animals are foraging, and prey have evolved to maintain high vigilance during foraging to enhance survival. Yet how food value, threat intensity, and vigilance interact to shape defensive decisions remains unclear. To address this question, we developed a behavioral assay that simulates how a foraging animal responds to an approaching aerial predator under different threat and reward conditions (Figure 2A). To maintain a consistent internal state across conditions, mice were not water-deprived. The higher reward value of sucrose over water was validated by measuring consumption during exploration (Figure S3A).

Figure 2:

During the first trial, mice showed distinct trajectories and speed profiles across threat and reward conditions (Figures 2B–C). These patterns changed rapidly within the first 10 trials, indicating fast habituation to the looming stimulus. This learning was reflected in altered decision patterns (Figure 2D) and changes in escape distance, duration in the reward zone, peak escape speed, and latency to flee (Figures 2E–H). To account for both learning and individual variability, we segmented trials for each mouse into early and late phases using a change-point detection approach on the learning curves (Figures 2I and S3C–D, see Materials and methods).

In the early phase, behavior was shaped predominantly by the level of threat. Under higher threat, mice were more likely to choose direct escape behaviors (Figure 3A), with longer escape distances (Figure 3B) and less time spent in the reward zone (Figure 3C), suggesting a trade-off between threat avoidance and reward pursuit. Notably, latency to flee decreased with higher threat (Figure 3D), indicating heightened vigilance (Buck, 1966). This threat-dependent change in vigilance was further supported by the longer interval before re-entering the trigger zone and slower foraging speed (Figures 3E–F and S4), aligning with findings in birds that elevated predation risk increases vigilance and reduces feeding time (Caraco et al., 1980). In addition, escape speed increased significantly with threat (Figure 3G), reflecting the combined effects of perceived higher risk and heightened vigilance. Analyses restricted to the first trial yielded consistent results (Figure S5).

Figure 3:

In the late phase, both threat level and reward value contributed to behavior. Threat remained a dominant factor, while reward exerted a significant, context-dependent influence. Under low-threat conditions, decisions were primarily driven by perceived reward value. As reward value increased, mice exhibited fewer defensive responses (Figure 3H), indicating that they weighed threat and reward to make economic decisions. Higher rewards led to shorter escape distance (Figure 3I) and longer stays in the reward zone (Figure 3J), supporting value-based decision-making strategies. In contrast, vigilance-related metrics, including latency to flee, foraging interval, and foraging speed, were largely unchanged across reward conditions (Figures 3K–M), suggesting that vigilance remained relatively stable. Consistently, escape speed decreased as reward value increased (Figure 3N). The value-based decision-making under low-threat conditions was further validated using within-subject comparisons to control for individual variability (Figure S6).

Under high-threat conditions, however, increasing reward value produced the opposite effect: mice showed more direct escape behaviors (Figure 3H). This shift in decision patterns was accompanied by behavioral signatures of heightened vigilance, including shorter latencies to flee, longer foraging intervals, and slower foraging speeds (Figures 3K–M). These results point to a counterintuitive mechanism: under high threat, reward value does not directly promote continued foraging but instead shapes decisions by enhancing vigilance, which in turn biases animals toward rapid escape responses. Consistent with this interpretation, the duration spent in the reward zone did not increase with reward value (Figure 3J). Collectively, these findings reveal how innate decision-making in response to looming stimuli is shaped by the dynamic interplay between perceived threat intensity and reward value, with vigilance acting as a key modulating factor.

2.3 Influence of social hierarchy on decision-making under threat

Mice are social animals that live in groups, where social hierarchy often plays a critical role in shaping behavior. To investigate how social rank influences decision-making under threat, we compared the responses of dominant and subordinate mice to looming stimuli. Rank within each mouse pair was determined using the tube test before and after the behavioral experiments (Figure 4A, see Materials and methods), and only pairs with consistent rankings were included in the analysis.

Figure 4:

We first verified that behavioral responses to the visual threat were not confounded by the presence of a social partner. Before looming exposure, subordinate mice spent more time exploring the arena than dominant mice (Figures 4B–C), which may reflect social avoidance. However, this difference disappeared during and after looming exposure, suggesting that the looming stimulus became the primary driver of behavior. To confirm this, we examined the probability that mice fled directly to the nest. If subordinates were avoiding dominants, they should preferentially escape to the safe zone rather than return to the nest occupied by the dominant mouse. Contrary to this prediction, dominant and subordinate mice showed similar probabilities of fleeing directly to the nest (Figure 4D), confirming that defensive responses were driven by visual threat rather than social avoidance.

When the threat co-localized with the reward, only dominant mice reduced their relative time spent in the reward zone during the 2-h session (Figures 4E–F), indicating greater vigilance and risk aversion compared to subordinates. This heightened vigilance in dominant mice was further supported by reduced habituation to the looming threat (Figures 4G–H and S7), a higher proportion of direct escape decisions (Figure 4I), and shorter latencies to flee (Figure 4J). No rank differences were observed in foraging intervals or foraging speeds (Figures 4K–L). This may stem from the experimental design, in which only one mouse was allowed in the arena at a time, potentially limiting the sensitivity of these measures to detect rank-dependent differences in vigilance.

Furthermore, dominant mice prioritized threat avoidance over reward, fleeing longer distances at higher escape speeds and spending less time in the reward zone (Figures 4M–O). To rule out the possibility that the tube test itself influenced defensive behavior, we conducted additional experiments in which looming sessions occurred both before and after the tube test (Figure S8); the results remained largely consistent. Together, these findings indicate that social hierarchy biases the trade-off between reward seeking and threat avoidance, with dominant mice exhibiting heightened threat vigilance and subordinate mice showing stronger reward-driven behavior.

2.4 A mathematical model for innate decision-making under threat

Our experimental results demonstrate that innate decision-making in response to visual threats is influenced by perceived threat intensity, reward value, and vigilance. To understand the underlying decision-making process, we developed a mathematical model in which the evidence for escape is accumulated by a drift-diffusion leaky integrator. An escape response is triggered when the evidence level crosses a predefined threshold:

Here, x_i(t) is the accumulated escape evidence at time t on the ith trial. The leakage rate α drives the evidence toward zero and is the reciprocal of the integration time constant. The stimulus function s(t) denotes the normalized diameter of the looming stimulus (Figure S9A). Together with the threat gain β, which reflects both stimulus contrast and the animal’s vigilance level, these terms represent the perceived threat level and drive evidence accumulation toward escape. The term r represents the perceived reward value, which suppresses the accumulation of escape evidence. W (t) is a Wiener process, such that , and δ is the diffusion rate. The binary variable E(t) indicates whether an escape decision is made, with denoting the Heaviside step function and x_thr the decision threshold. If a decision is reached within the first expansion of the looming disc, it is classified as a direct escape; otherwise, it is classified as an escape after assessment.

Model parameters are estimated using behavioral data from the late phase of the reward–threat experiments in two steps (see Materials and methods). First, we fit the model to the data under no-reward conditions to obtain the optimal leakage rate (α = 1.78), threat gain (low threat: β = 1; high threat: β = 1.44), diffusion rate (δ = 5.6), and decision threshold (x_thr= 0.71) (Figure S9B). These parameters reveal distinct decision-making dynamics under low- and high-threat conditions. Under low threat, the average evidence level remains below the escape threshold, and escape decisions emerge from stochastic fluctuations in individual trials (Figure 5A). Under high threat, the average evidence level crosses the threshold, indicating that escape decisions are mainly driven by threat gain (Figure 5B). Notably, threat gain and diffusion rate exert distinct effects on latency to flee: threat gain shifts the mean latency, while diffusion rate affects its variance. Thus, the model captures not only the observed decision patterns but also the distributions of latency to flee.

Figure 5:

In the second step, we identify threat gain and reward value across different threat and reward conditions in the late phase (Figures S9C–D). Consistent with experimental findings that decisions under low threat are primarily driven by reward value, the fitted reward-value parameter increases with reward magnitude (0, 0.08, and 0.25 for no reward, water, and sucrose, respectively). With these parameters, the model reproduces the observed reduction in escape likelihood without changes in latency to flee (Figures 5A, 5C, and 5E). The same reward-value parameters are then used to model the decision-making process under high-threat conditions. Here, the fitted threat-gain parameter increases across reward conditions (1.44, 1.8, and 2.55 for no reward, water, and sucrose, respectively), counteracting—and ultimately reversing—the influence of reward value. The model again reproduces the experimentally observed increase in escape decisions and decrease in latency to flee (Figures 5B, 5D, and 5F).

To assess the model’s predictive power, we simulate how decision score (see Materials and methods) and latency to flee vary as functions of reward value (r) and threat gain (β). Increasing reward generally reduces decision score and increases latency to flee, whereas increasing threat gain has the opposite effect (Figures 5G–H, and S9E–G). These relationships are confirmed by a simplified deterministic model (Figures S9H–K, see Materials and methods). Notably, reward can also indirectly promote escape by elevating vigilance, with the magnitude of this effect depending on the level of baseline vigilance, defined as vigilance in the absence of reward (Figure 5I). This dual influence explains the absence of a reward effect in the early phase under both threat conditions: high vigilance shifts the operating range to a region where reward’s indirect promoting effect is balanced by its direct suppressing effect on escape decisions.

We next apply this model to the social-threat paradigm. The behavior of dominant mice is captured by a combination of lower reward value and higher threat gain compared to subordinates (pink triangles in Figures 5G–H). This aligns with the experimental finding that dominant animals spent less time in the reward zone and fled more quickly (Figures 4J and 4O). Together, these results demonstrate that the model robustly captures key behavioral features across phases and paradigms, providing a unified mechanistic account of innate decision-making under threat (Figure 5J).

3 Discussion

When confronted by a predator, an animal must rapidly decide whether to escape, freeze, or continue its ongoing behavior. This life-or-death decision is especially critical for rodents facing aerial predators. Although mice are social animals and most predator encounters occur during foraging, it remains unclear how they integrate perceived threat and reward when making defensive decisions, or how these decisions are further influenced by social hierarchy. Using a foraging-based paradigm, we demonstrate that responses to visual threat are shaped by threat intensity, reward value, social rank, and internal state, and that this integrated decision process can be captured by a drift-diffusion leaky integrator.

3.1 Main findings

We designed a behavioral paradigm to simulate how mice respond to visual threats during foraging (Figure 1). Mice adapted rapidly to repeated looming stimuli, showing substantial inter-individual variability in the rate of habituation (Figure 2). While threat intensity robustly shaped behavior in both early and late phases of habituation, reward exerted a clear influence only in the late phase (Figure 3). Specifically, increasing threat intensity shifted behavior toward more defensive responses. Reward value, in contrast, produced a context-dependent effect: under low-threat conditions, higher rewards suppressed defensive responses, consistent with value-based decision theory; under high-threat conditions, higher rewards promoted escape decisions, likely reflecting heightened vigilance. Innate decision-making was further shaped by social hierarchy (Figure 4): dominant mice exhibited a stronger bias toward defensive behaviors, whereas subordinates were more reward-driven and less likely to flee. Finally, we developed a drift-diffusion leaky integrator model that captures the key features of the observed behavioral patterns, providing a unified framework for understanding how threat, reward, and social context interact to shape innate defensive decisions (Figure 5).

3.2 Relation to earlier work

Aerial predators pose a significant threat to rodents. Previous studies have shown that overhead visual stimuli in the laboratory elicit robust defensive behaviors in rodents (Wallace et al., 2013; Yilmaz and Meister, 2013). Because these stimuli can mimic distinct predatory actions, the resulting behavioral responses depend on the specific physical properties of the stimulus. For example, an overhead expanding dark disc that mimics an approaching aerial predator preferentially triggers escape rather than freezing (Yilmaz and Meister, 2013), while a small black moving dot that mimics a cruising predator predominantly induces freezing behavior (De Franceschi et al., 2016). These findings suggest that the response is not a simple reflex but involves a decision-making process. Additional stimulus properties that influence action selection include contrast, speed, size, and shape (De Franceschi et al., 2016; Evans et al., 2018; Yang et al., 2020). Support for a decision-making process also comes from its modulation by environmental factors and experience: mice freeze more when no refuge is available (Wei et al., 2015) and quickly learn that the looming stimulus poses no real threat (Lenzi et al., 2022; Vale et al., 2017; Zhong et al., 2023). This innate decision-making process is observed across invertebrates and vertebrates (Evans et al., 2019).

Methodologically, the present study differs from earlier work in two aspects. First, instead of manually annotating behavioral responses, we employed a machine-learning approach to classify behavioral decisions. This approach substantially reduced the labor required for labeling and minimized misclassifications due to inter-individual variability. Second, unlike previous studies using 2D arenas, we designed a 1D linear arena to simulate foraging conditions, where the nest and reward zone were separated by a long corridor. Importantly, the decision patterns observed in our paradigm are similar to those reported in 2D environments (Yang et al., 2020), and mice quickly adapted to the looming stimulus after a few trials, consistent with previous findings (Lenzi et al., 2022).

One concern with the linear arena design was that the looming stimulus was usually presented at the end of the arena, raising the possibility that mice simply retreated upon reaching a physical boundary. To address this, we presented the stimulus between the foraging mice and the nest (Figure S2A). Under this condition, mice quickly fled toward the nest—and thus toward the threat—rather than away from it (Figure S2B, Video 5). This behavior indicates that their escape responses are not simple reflexes, but instead incorporate the safety of the nest into their decisions.

Fanselow and Lester’s predatory imminence continuum theory posits that defensive behaviors are graded according to perceived threat level (Fanselow and Lester, 1988). To test whether this frame-work applies to aerial threats, we varied both prey–threat distance and prey–safety distance. As prey–threat distance increased, mice showed less direct escape behavior, with longer latencies to flee and slower escape speeds (Figures S2C–G, Videos 6–8), indicating that defensive responses scale with threat proximity. These effects cannot be explained by the failure to detect the stimulus at longer distances; if that were the case, foraging speed would remain unaffected. Instead, mice slowed as they approached the threat in the 75-cm condition (Figure S2D). In contrast, prey–safety distance did not significantly influence defensive behaviors (Figures S2H–I). One interpretation is that once an aerial threat is detected, the urgency to escape overrides evaluation of refuge proximity. To further verify this, we introduced barriers that lengthened the return path to the nest. Even under these conditions, defensive behaviors remained unaffected by prey–safety distance (Figures S2J–K, Video 9).

3.3 Economic and social modulations of innate decision-making under threat

Value-based decision-making—where choices arise from comparisons of the subjective value of ex-pected outcomes—is a well-established framework for understanding behavior across species (Rangel et al., 2008). Prospect theory, which accounts for decision-making under risk in humans (Kahneman and Tversky, 1979), has been applied to learned decision-making in rodents (Constantinople et al., 2019). Here, we demonstrate that value-based decision-making also extends to innate defensive behaviors: when confronted with a threat, mice integrate perceived reward and threat value to make their decisions.

Importantly, perceived value is determined not only by the physical properties of the stimulus but also by the animal’s internal brain state. In the resting state, for example, perceived stimulus strength scales with physical intensity according to the Weber–Fechner law. In our paradigm, the perceived threat value is strongly modulated by vigilance, a state of heightened and sustained attention to potential danger. This vigilance-dependent modulation substantially alters how the same looming stimulus is evaluated and how decisions are made.

Consistent with value-based evaluation, increasing threat intensity reliably increased defensive responses across reward conditions and behavioral phases. These changes reflect differences in perceived threat rather than stimulus detection, as evidenced by coordinated changes in escape latency, distance, and speed, and further supported by trial-by-trial inspection confirming reliable stimulus detection across contrast levels (Figure S3B).

Reward-dependent behavior also follows value-based principles, but in a vigilance-dependent manner. In nature, foraging often occurs under predation risk, and evolutionary pressure has favored prey that maintain heightened vigilance in the presence of high-value rewards. Consistent with this, increasing reward magnitude increased both perceived reward value and—via elevated vigilance—perceived threat value. These opposing effects jointly shaped the escape decision.

In the early phase, baseline vigilance is already high because looming represents an innate threat. Under this high-vigilance condition, increasing reward magnitude elevates both perceived reward and threat value; these opposing effects counterbalance each other, resulting in no behavioral differ-ences across reward conditions. With repeated exposure, habituation to looming reduces vigilance, shifting the operating region leftward along a sigmoidal vigilance-intensity function (Figure 5I). This sigmoidal form is biologically plausible, as vigilance is bounded by a relaxed-state minimum and by cognitive capacity limits. This shift has opposite consequences under low versus high threat. Under low threat in the late phase, reduced vigilance compresses the dynamic range, weakening the indirect effect of reward on perceived threat and allowing perceived reward value to dominate decisions. Under high threat, however, the vigilance function remains within a steeper region of the sigmoid, where increases in reward effectively elevate vigilance and thus perceived threat. As a result, reward produces the opposite behavioral effect under high threat. Together, these dynamics explain why reward effects are absent early but emerge after habituation in a threat-dependent manner.

Social rank-dependent differences in defensive behavior also fit within this framework. Even un-der identical conditions, dominant mice perceived a higher threat value—driven by their elevated vigilance—along with a lower reward value, consistent with their more risk-averse behavior. Similar status-dependent escape patterns have been reported across species, including voles (Kleiman et al., 2014) and crayfish (Krasne et al., 1997), suggesting an evolutionarily conserved strategy.

Because vigilance declines with habituation, factors that modulate the rate of habituation also influence defensive behavior. Although individuals vary, several patterns emerged. Mice habituated more rapidly under high-threat or high-reward conditions (Figure 2I). Dominant mice habituated more slowly than subordinates, consistent with their elevated vigilance (Figures 4H and S7A). Housing conditions also altered habituation: group-housed animals adapted more slowly to looming than single-housed animals, and dominant–subordinate pairs habituated even more slowly than group-housed mice (Figures 2I and S7A). These patterns indicate that stable social relationships sustain high vigilance and slow habituation—an evolutionarily conserved strategy that may enhance survival.

One limitation of the present study is that our experiments were conducted exclusively in male mice to avoid the confounding effects of behavioral variability associated with the female estrous cycle. Extending this paradigm to females—with careful control for estrous cycle—will provide a more comprehensive understanding of how economic and social factors modulate defensive decision-making.

3.4 A proposed role for the superior colliculus in value integration

What neural circuits underlie the economic and social modulations of decision-making under threat? A growing body of research implicates the SC as a key node in looming-evoked defensive behav-iors (Evans et al., 2018; Shang et al., 2015; Wei et al., 2015). In parallel, reward is encoded by dopaminergic neurons in the ventral tegmental area (VTA) (Cohen et al., 2012; Schultz, 1998) and serotonergic neurons in the dorsal raphe nucleus (Liu et al., 2014; Miyazaki et al., 2011), which project widely to regions such as the ventral striatum (Schultz et al., 1992), orbitofrontal cortex (Trem-blay and Schultz, 2000), and cerebellum (Wagner et al., 2017). Furthermore, social status modulates behavior via circuits involving the medial prefrontal cortex (mPFC) (Kingsbury et al., 2019; Wang et al., 2011) and serotonergic signaling (Edwards and Kravitz, 1997; Raleigh et al., 1991; Yeh et al., 1997).

We propose the SC as a central hub for mediating the economic and social modulations of decision-making for several reasons. First, while neurons in the superficial (sSC) and intermediate (iSC) layers of the medial SC are involved in detecting looming threats and triggering defensive responses (Li et al., 2023, 2020), they also express receptors for both dopamine and serotonin (Mooney et al., 1996; Woolrych et al., 2021), indicating they can receive reward- and social-related information. Notably, dopamine receptor expression is layer-specific, with D1 receptors enriched in the sSC and D2 receptors in the iSC, suggesting layer-dependent processing of reward signals. Consistently, reward-related signals have been observed in the medial sSC (Baruchin et al., 2023). Second, the deep layers of SC receive inputs from the retrosplenial cortex (RSC) (Campagner et al., 2023) and indirectly from the hippocampus (Benavidez et al., 2021), which may convey spatial and contextual information relevant to reward (Calvin et al., 2025). In parallel, the lateral SC mediates approach behaviors toward rewarding stimuli, such as food or prey (Comoli et al., 2012; Krauzlis et al., 2013). These findings suggest that medial–lateral interactions within the SC may play a critical role in resolving threat–reward trade-offs during decision-making. Third, the deep-layer SC receives inputs from the mPFC (Benavidez et al., 2021), providing a pathway through which social and contextual signals can modulate defensive decisions. Finally, these SC deep layers are strongly and reciprocally connected with the periaqueductal gray (PAG) and project to dopaminergic neurons in the substantia nigra (Comoli et al., 2003), enabling efficient translation of integrated sensory, economic, and social signals into action execution. They also project to the lateral amygdala via the lateral posterior nucleus (LP) (Wei et al., 2015) to rapidly elicit the fear state.

While the anatomical and functional evidence support the SC as a central hub, we emphasize that the neural architecture underlying such decisions is far more complex. The precise integration of internal state, social rank, and external threat likely emerges from the dynamic interplay of distributed circuits, including prefrontal, limbic, and neuromodulatory systems. Dissecting how these circuits interact to shape defensive decisions remains an important direction for future research.

3.5 Mathematical modeling

The proposed drift-diffusion leaky integrator model builds on an integrator model of internal state (Gib-son et al., 2015) and extends it by incorporating a reward-driven drift-diffusion process (Ratcliff, 1978). Conceptually, the integrator component in our model aligns with Lorenz’s “hydraulic” model of motivation, which describes how internal drives shape behavior (Lorenz, 1950). While our model resembles the leaky integrator used to model escape behavior in flies (Gibson et al., 2015), it differs in several ways. First, the earlier model lacks a reward-related drift component. Second, while that model treats the looming effect as a delta function, our model allows the evidence level to vary continuously with stimulus size. Third, the influence of vigilance is absent in that model. A similar model has been proposed (Evans et al., 2018), but it did not incorporate reward and vigilance. Note that the evidence level for escape in our model is not equivalent to the fear level (Anderson and Adolphs, 2014); rather, when it crosses a threshold, the animal may enter a fear state.

Below, we briefly discuss the roles of individual parameters. The leakage rate α represents a drive toward the resting state. Perceived threat was modeled as the product of the threat gain β and the sensory input s(t) and promotes escape decisions, whereas perceived reward r drives the decision away from escape. The threat gain increases not only with threat intensity but also with reward magnitude via its influence on vigilance. The effect of reward on vigilance depends on the operating region of the sigmoidal vigilance function. This operating region is set by the baseline vigilance level (Figure 5I) and reflects habituation to repeated looming threats. Furthermore, threat gain and reward value have distinct effects on escape latency: higher threat gain exponentially shortened latency, whereas higher reward value increased it linearly (Figures S9F–G). These effects are confirmed using a simplified deterministic version of the model (Figure S9J–K; see Materials and methods).

Lastly, the diffusion rate δ plays a critical role, particularly under low-threat conditions where the average evidence trajectory fails to reach the threshold. This parameter may reflect the fluctuation of the animal’s internal state. The diffusion rate captures the trial-to-trial variability: even small amounts of noise can accumulate over time, resulting in large differences across individual trials and contributing to variability in escape latency. Overall, this computational framework not only accounts for our experimental observations but also offers a quantitative foundation for studying innate decision-making across species. Understanding how these parameters are implemented at the circuit level is an exciting direction for future research.

4 Materials and methods

4.1 Animals

Male C57BL/6J mice were group-housed on a 12-hour light/12-hour dark cycle and used at 2–3 months of age. Behavioral experiments were conducted during the light phase. All experimental procedures were performed under the animal welfare guidelines and approved by the Institutional Animal Care and Use Committee at the Chinese Institute for Brain Research, Beijing.

4.2 Behavioral platform

The behavioral platform consisted of a nest, a linear arena, a radio frequency identification (RFID) system, a real-time mouse position detection system, and a reward delivery port. As illustrated in Figure 1A, the nest (40 (L) × 20 (W) × 30 (H) cm) and the linear arena (100 × 10 × 30 cm) were made of infrared-transmitting acrylic to allow unobtrusive behavioral monitoring. They were connected by a one-way tunnel (20 × 3 × 3 cm) for entering the arena and a 20 × 5 × 30 cm safe zone with a 5 × 5 cm one-way door for returning to the nest. Because it was not directly under the monitor, the safe zone was darker than the arena.

Mice were identified with implanted RFID tags, which were detected by an RFID reader positioned around the tunnel. Only one mouse was allowed to enter the arena at a time. Specifically, when all mice were in the nest, the door between the nest and the tunnel was open, while the door between the tunnel and the arena remained closed. When a single mouse entered the tunnel, as detected by the RFID system, the door to the nest closed and the door to the arena opened, allowing the mouse to enter the arena. Mice received rewards at the end of the arena in the form of water or 10% sucrose. Licking time and reward volume were recorded for each trial.

To track mouse position in real time, an OpenMV camera with a 90° field-of-view lens was mounted on the ground, 110 cm beneath the arena. The mouse position was used to control the tunnel doors and to trigger stimulus presentation when the mouse entered the arena. A second camera (LBAS-U350-74M) with a lens (FA0615A) was also placed on the ground to record animal behavior at 30 frames per second.

4.3 Visual stimulation

Looming stimuli were presented on a 55-inch monitor (121 × 68 cm) suspended 32 cm above the arena. Visual stimulation was implemented using PsychoPy in Python and was aligned to the mouse’s real-time location. The stimulus consisted of a black disc that expanded ten times on a gray background (∼65 cd/cm²). On each expansion, the disc grew from 0° to 20° of visual angle at 40°/s, followed by a stationary phase lasting 0.3 s. The inter-stimulus interval was randomly varied between 1 and 2 minutes. Two stimulus contrasts (20% and 99%) were displayed by adjusting the luminance of the disc.

4.4 Economic modulation of innate decision-making

All mice were habituated to the behavioral platform for two days before the looming experiment. During both habituation and testing, three reward conditions were used: no reward, water, or 10% sucrose. Mice were not water-deprived in any of the groups. On the first day, five mice from the same home cage were placed in the nest for 30 minutes with all doors closed. Each mouse was then placed individually in the nest and allowed to explore the arena for 10 minutes under normal door operation; if a mouse entered the arena fewer than two times, the exploration period was extended until at least two arena visits were completed. Subsequently, all five mice were returned to the nest with all doors open and allowed to freely explore the arena for 2 hours to ensure that each mouse learned the reward location at the end of the linear arena. On the second day, each mouse was placed individually in the nest and given an additional 1 hour of exploration under normal door operation to further acclimate to the environment. The looming experiment was conducted the following day. An overhead looming stimulus of either low (20%) or high (99%) contrast was triggered when the mouse entered the trigger zone, defined as the region within 20 cm of the reward port. For each mouse, both the looming contrast and reward type remained constant across trials. In total, we collected and analyzed behavioral data from 590 trials across 62 mice.

To control for individual variation in decision-making, we compared the same animal’s behavior under reward and no-reward conditions. Two groups of mice were used in this experiment. In the first group (n = 4), mice were first tested under the no-reward condition, followed by the reward condition. In the second group (n = 5), the order was reversed. For the reward condition, mice were water-deprived one day before exploration, and water was provided via the reward port. In the no-reward condition, mice were not water-deprived, and the reward port was removed. Before the looming experiment, mice were acclimated to the linear arena for two days as described above. On the third day, a looming stimulus with 20% contrast was displayed for five trials. In total, behavioral data from 84 trials across 9 mice were recorded and analyzed.

4.5 Social modulation of innate decision-making

To investigate the impact of social hierarchy on decision-making, we first determined the social rank of each mouse pair using the tube test (Lindzey et al., 1961; Wang et al., 2011), in which dominance is determined by the ability of one individual to force its opponent to retreat from a narrow tube. Mice were co-housed with a glass tube (3 cm diameter, 10 cm long) for one week, then trained to cross a 30-cm tube 10 times per day over two consecutive days. On the third day, each pair was tested for up to six trials; if one mouse achieved four consecutive wins, it was designated the dominant individual; otherwise, the pair (1 out of 6 pairs) was excluded from further experiments.

Before the looming experiment, mice were water-deprived and allowed to explore the linear arena for two hours per day over three days, during which water rewards were delivered at the end of the arena. Over the following two days, the looming experiment was conducted with a stimulus contrast of 99% for two hours per day. After the looming experiment, mice continued to explore the arena for an additional two days, after which their social rank was reassessed with the tube test. All remaining pairs maintained a stable rank order. In total, behavioral data from 180 trials across 18 mice were recorded and analyzed.

To assess whether the tube test itself influenced defensive decision-making, additional looming experiments were conducted on four mouse pairs before and after the tube test. Specifically, the first looming experiment was conducted prior to the tube test (Figure S8A). Behavioral data from 72 trials across 8 mice were recorded and analyzed.

4.6 Behavioral quantification

Animal behaviors were quantified in three steps. First, two key points—the nose and tail base—were labeled and tracked in the recorded videos using DeepLabCut (Mathis et al., 2018). Tracked points with likelihood scores below 0.6 were excluded and replaced using linear interpolation. Locomotion speed was calculated for each frame and smoothed using a 0.3 s moving average window. Unless otherwise specified, the speed of the tail base was used for subsequent analyses. Second, individual 30-second trials were extracted, each consisting of 10 s before, 8 s during, and 12 s after the looming stimulus.

Third, we defined 19 behavioral features related to locomotion speed, distance, and state transitions. Eleven features were related to speed and distance: (1) peak speed toward the reward port before stimulus onset; (2–4) maximum, mean, and coefficient of variation of speed after stimulus onset; (5) latency to peak speed; (6) hiding latency, defined as the time between stimulus onset and arrival at the safe zone (set to 20 s if the mouse did not reach the safe zone by the end of the trial); (7) escape distance, defined as the displacement from stimulus onset to offset; (8) distance to the nest at the end of the trial; (9) total distance traveled at speeds greater than 90% of the peak speed; (10) duration of movement at speeds greater than 90% of the peak speed; and (11) duration of time with both key points moving slower than 1 cm/s. Eight features were related to state transitions: (12) latency to flee, defined as the time from stimulus onset to the first escape episode, where an escape state was defined when the animal moved more than 10 cm at a speed exceeding 10 cm/s; (13–15) average speed, distance traveled, and acceleration during the fastest escape episode; (16) latency to the fastest escape episode; (17) latency to the first stationary episode, where a stationary state was defined when both key points moved at less than 1 cm/s for more than 0.3 s; (18) total stationary duration and (19) longest stationary duration.

Finally, these features were fed into a random forest model with a maximum depth of 5 to classify behaviors. For trials in which neither escape nor stationary states were identified, latencies (features 12, 16, 17) were set to 20 s, distance (14) to 0 cm, speed (13) to 0 cm/s, acceleration (15) to 0 cm/s², and duration (18, 19) to 0 s. The model was trained on 238 trials and tested on 102 trials, achieving an accuracy of 0.95 on the test set. Using this classifier, behavioral decisions in 3862 trials across 140 mice were categorized into four types: direct escape, escape after assessment, freezing, and no response (Figure S1). A decision score was calculated for each condition as S = 3p_e + 2p_ae + p_f, where p_e, p_ae, p_f denote the proportions of direct escape, escape after assessment, and freezing, respectively. To quantify how quickly animals recovered from a fear state, we measured recovery time. For escape trials, recovery time was defined as the hiding duration, measured from entry into the safe zone to re-entry into the arena. For freezing trials, recovery time was defined as the interval between the onset of the first freezing episode and the termination of the last freezing episode.

To quantify the influence of reward, the reward zone was defined as a region within 10 cm of the reward port, and the duration in the reward zone was defined as the time spent within this zone during the 20 s following stimulus onset. Vigilance was assessed using latency to flee, foraging interval (time between two consecutive entries into the trigger zone), and foraging speed (average speed while approaching the trigger zone before stimulus onset).

To segment the trials into two phases, we performed principal component analysis on a feature matrix containing decision score, escape distance, duration in the reward zone, peak escape speed, and latency to flee across the first 10 trials. We extracted the first principal component (Figures S3C–D), which captured the majority of the variance, and used its learning curve to detect transitions in behavior. Change points in the learning curve were detected using the ruptures method (Gallistel et al., 2004; Truong et al., 2020).

4.7 Behavioral modeling

Parameters in the drift-diffusion leaky integrator model were estimated in two steps by minimizing a loss function using a grid search. In the first step, we fit our model to behavioral data from the no-reward condition, setting r = 0 and β = 1 for the low-threat condition, and estimated α, δ, x_thr, and β for the high-threat condition. In the second step, we estimated β and r for the water and sucrose conditions under both threat conditions. The loss function combines fitting errors in the distribution of behavioral decisions (ℒ_dec), the median latency to flee (ℒ_med), and the variability of latency (ℒ_sd):

The decision-distribution mismatch is quantified using a mean cosine distance:

where d_c and ̂d_c denote the observed and model-predicted decision distributions for threat level c, and C = 2 is the number of threat conditions.

The median-latency loss is defined as

and the latency-variability loss is

For the final fitted model (Equation 1), α = 1.78 and δ = 5.6. Under low-threat conditions, β = 1 for all reward conditions; under high-threat conditions, β = 1.44, 1.8, 2.55 for no reward, water, and sucrose, respectively. The reward values were r = 0, 0.08, 0.25 for no reward, water, and sucrose, respectively, under both threat conditions. In Equation 2, the decision threshold was x_thr = 0.71.

To further understand how threat and reward shape decisions, we analyzed a deterministic simplifica-tion of the model:

where p > 0 denotes the perceived reward value and n · t < 0 denotes the perceived threat strength, which grows linearly over time.

With the initial condition x(0) = 0, the solution is

This solution reveals a competition between two components. First, a linear term driven by threat accumulation promotes escape over time. Second, an exponentially decaying component reflects the combined influence of reward and threat.

4.8 Quantification and statistical analysis

No statistical method was used to predetermine sample size. The Shapiro–Wilk test was applied to assess the normality of data distributions. For comparison between two groups, a two-sample t-test or paired t-test was used for normally distributed data; otherwise, the Mann–Whitney–Wilcoxon or one-sample Wilcoxon signed-rank test was applied. For multi-group comparisons, one-way or two-way analysis of variance (ANOVA) was used when data were normally distributed, followed by Tukey’s post hoc test. For non-parametric multi-group comparisons, the Kruskal–Wallis test (for one factor) or the Scheirer–Ray–Hare test (for two factors) was applied, followed by Dunn’s post hoc test with Holm correction. The chi-square test was conducted to analyze categorical variables, while paired categorical comparisons were assessed using the Stuart–Maxwell test. Detailed statistical information for each experiment is provided in the Results section and figure legends.

Supplemental information

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Data availability

Data and code are available in a public GitHub repository (https://github.com/YatangLiLab/li-2025-economic-social-modulation).

Acknowledgements

We thank Lei Zhang, Xueting Sun, Haojun Sang, Qun Zhang, Bing Zhao, and Zhuofan Li in the CIBR Instrumentation Core for their help in designing and building the linear arena. Ling-yun Li is supported by the Natural Science Foundation of Beijing Municipality (5244028), the National Natural Science Foundation of China (32471071), and the R&D Program of Beijing Municipal Education Commission (1240030201). Ya-tang Li is supported by the National Natural Science Foundation of China (32271060), the Natural Science Foundation of Beijing Municipality (IS23073), and the startup fund from CIBR.

Additional information

Author contributions

Ya-tang Li supervised the project; Ya-tang Li, Zhe Li, and Yidan Sun designed the experiments; Zhe Li collected all the data; Zhe Li, Jiahui Wang, and Jialin Li analyzed the data; Ya-tang Li carried out the neural modeling; Zhe Li and Ya-tang Li prepared figures; Ya-tang Li, Ling-yun Li, and Zhe Li wrote the manuscript.

Funding

北京市科学技术委员会 | Natural Science Foundation of Beijing Municipality (北京市自然科学基金) (5244028)

• Ling-yun Li

MOST | National Natural Science Foundation of China (NSFC) (32471071)

• Ling-yun Li

R&D Program of Beijing Municipal Education Commission (1240030201)

• Ling-yun Li

北京市科学技术委员会 | Natural Science Foundation of Beijing Municipality (北京市自然科学基金) (IS23073)

• Ya-tang Li

MOST | National Natural Science Foundation of China (NSFC) (32271060)

• Ya-tang Li

Additional files

Video 1. Example video showing one of the four types of behavioral decisions in response to looming stimuli: direct escape.

Video 2. Example video showing one of the four types of behavioral decisions in response to looming stimuli: escape after assessment.

Video 3. Example video showing one of the four types of behavioral decisions in response to looming stimuli: freezing.

Video 4. Example video showing one of the four types of behavioral decisions in response to looming stimuli: no response.

Video 5. An example video showing defensive responses to the looming stimulus presented behind the mouse.

Video 6. Example video showing defensive responses at 35 cm prey–threat distance.

Video 7. Example video showing defensive responses at 55 cm prey–threat distance.

Video 8. Example video showing defensive responses at 75 cm prey–threat distance.

Video 9. An example video showing defensive responses to looming stimuli in the linear arena with barriers.