Toward comprehensive Chiroptera modeling: A parametric multiagent model for bat behavior

Chiroptera behavior is complex and often unseen as bats are nocturnal, small, and elusive animals. Chiroptology has led to significant insights into the behavior and environmental interactions of bats. Biology, ecology, and even digital media often benefit from mathematical models of animals including humans. However, the history of Chiroptera modeling is often limited to specific behaviors, species, or biological functions and relies heavily on classical modeling methodologies that may not fully represent individuals or colonies well. This work proposes a continuous, parametric, multiagent, Chiroptera behavior model that captures the latest research in echolocation, hunting, and energetics of bats. This includes echolocation‐based perception (or lack thereof), hunting patterns, roosting behavior, and energy consumption rates. We proposed the integration of these mathematical models in a framework that affords the individual simulation of bats within large‐scale colonies. Practitioners can adjust the model to account for different perceptual affordances or patterns among species of bats, or even individuals (such as sickness or injury). We show that our model closely matches results from the literature, affords an animated graphical simulation, and has utility in simulation‐based studies.


INTRODUCTION
Bats are complex creatures with amazing capabilities.They are the only flying mammal and one of the most evolved echolocators on the planet. 1 There are over 1400 species of bats worldwide and they can be found in nearly all climates except arctic and desert regions. 2 Most bats have a home colony or roost, they will either hibernate through winter or migrate to a warmer climate. 3Depending on the species, bat colonies can range from fewer than twenty-five to hundreds of thousands.For example, during summers in the southwestern United States, caves can house up to twenty million Tadarida brasiliensis bats. 3Any works to generalize and simulate bats would need to be highly efficient to cope with such high numbers in colonies.
Bats have a number of perceptual and behavioral eccentricities that should be captured in any model.Only 70% of bats use echolocation, and each species has unique echolocation calls. 4Many bats are hibernators and will periodically roost in trees or building overhangs while foraging for food at night, especially when hunting conditions are poor. 5After flocking as a colony, bats will often split into subgroups of sizes of at least 2-5 during their nightly hunts although the reasons for this require more research to better understand. 6Bats will rarely hunt in pairs, groups of three, or individually. 7Bats are incredibly maneuvrable due to their unique wing structure and are capable of rapid changes in direction. 8he utility of a comprehensive Chiroptera model that can simulate and track individual bats with individual properties is rapidly increasing in value.Bats have few natural predators but many bat colonies are currently plagued by a fungal virus known as White-Nose-Syndrome. 9 White-Nose-Syndrome is one of the most dangerous threats to bat populations and can have a mortality rate of over 90% in colonies. 10This fungal infection spreads rapidly through roosts as bats often cluster together while sleeping.Studies on White-Nose-Syndrome and how it spreads through colonies would be an important step in brainstorming solutions to this disease.Models for generalized bat colony behaviors would first be needed to study proximity, and interactions for the spreading infections between bats.Bats might contract the fungus while hunting, or when roosting, as they often group together tightly.In agriculture, work has shown that introducing a small bat colony helps control insects and pests for better crop yields. 1 Being able to simulate the size, distribution, and well-being of such a colony and its effects would allow for more accurate predictions in these controlled ecosystems.
This work focuses on modeling individual bats with emergent colony behaviors in a multibehavior integrated model that captures the effects and affordances of echolocation and perception, flocking, hunting, roosting, energy consumption, and dynamic population sizes.This work focuses on bats that echolocate but provides a parametric framework for capturing the diversity of bat populations.This is intended as step toward more comprehensive modeling for future studies into the spread of white-nose syndrome, ecosystem estimations and more.
The model affords graphical simulations that can also help us understand more about behaviors that are difficult to track and research such as subgroup hunting sizes.This research seeks to understand more about the mathematical, motivational, and energetic forces that govern bat behavior and echolocation.We show the proposed model reproduces several findings in the literature and its utility in exploring these simulation-based findings.

RELATED WORK
Prior work in Chiroptera modeling often focuses on a particular species or biological function.Prior work has also adopted bat behaviors and perceptual functions as solutions to continuous constrained optimization problems by focusing on echolocation pulse rates during hunting. 11Similarly, bats have inspired stochastic optimization techniques for global optimization. 12ork on replicating natural fission-fusion rates of tree-dwelling bat colonies and roost switching behaviors has led to agent-based models of bat behavior. 13Simulated agents in this algorithm move with a velocity vector and a predetermined field of perception and eavesdropping range on other bats.The eavesdropping behaviors of bats flocking toward echolocation noises from other members of their species are theorized to aid in hunting, roost finding, and other social behaviors. 7,13,14Bat agents were placed in a 900 × 1800 m habitat with 944 available roosts to study their roost-switching behaviors to other colonies through their formula and state machine for roost attractiveness to individual bat agents.
By directly observing bat behaviors via video, behaviors of bats can be elucidated, such as the Japanese horseshoe bat hunting a moving moth. 15This work proposed that bat hunting relies heavily on the angle from the bat to the moth and the relative flight directions of each animal.They determined higher success rates when the bat aligned itself to be moving in the same direction as the moth before approaching.However, bats are notoriously difficult to observe consistently in nature.
More complete models of bat behaviors incorporate several behaviors and biological functions into one model including echolocation, flocking, hunting, and energetics. 1 This work modeled bats' perception using frequency modulation to create a cone of detection, anything within this cone was assessed if detectable.Once detected, the moths were immediately captured and the bats corresponding energy levels would increase.Energy consumption was modeled according to time in flight, time roosting, initial energy and number of moths eaten.There were limits on the number of bats and moths that could be introduced to the simulation, and the simulation did not include any sub-flocking behaviors or grouped hunting patterns.Each of these considerations was recommended for future research and has been heavily considered in the design of this work.Much of the relevant models in this area have been built from research on specific bat species and behaviors.This work generalizes a parametric model which can be fit to different species by experts working with or experimenting on those species or colonies.

METHODOLOGY
The proposed model is developed directly from the literature on flocking, hunting, roosting, energetics, and behavioral patterns of bats.The proposed model is developed such that it can be deeply parameterized to model different species of Chiroptera as well as within-colony diversity of behaviors.The scenario space definition incorporates a home colony cave, temporary roost spots, and insect clusters that migrate with an adjustable wind vector to closely match real-world insect behaviors.This scenario space can be modeled to mimic real-world environments for a variety of bat species by incorporating parametric roosting locations such as trees, overhangs and human-made bat houses.Individual bats and insects can be parameterized affording the simulation of a variety of bat species' movement, hunting, and roosting behaviors as well as the movement and grouping of insect species.We show an example environment drawn from this scenario space in Figure 1.Bats -like most animals-behave differently for day and night, thus part of the scenario space incorporates a parametric model for day/night patterns.This system allows for modifiable day and night, respectively, lengths and can accommodate seasonal changes in day length from the physical world where N l represents the night length, D l represents the day length and d i (with index base 1) represents how many days have passed over time t.When equation ( 1) is satisfied the simulation is in nighttime and when equation ( 2) is satisfied the simulation is in the daytime.The model spawns B n bats in the starting position and C n insect clusters of various sizes.Bats use the Behavioral model in Figure 2 to update their position and behavior at each stage.Using equation (4) they will detect insect clusters and break off for smaller group hunting according to equation (8).From there bats will gain position and velocity information of any perceived insects per their echolocation abilities and use that information to approach and attempt capture of their prey.

Behaviors
The behavior model is represented by a finite state machine with four different states that govern a bat's behavior.Each state has its own subset of rules for bats to follow that change overall behavior.Bats will constantly update their energy according to the energetics model and will travel back to the home cave location if the time moves into the day.When at the home roost, bats will hibernate until night, then flock out and transition to their hunting state to begin a new cycle.The Hunting state activates the bats' hunting and echolocation behaviors as well as flight rules.Bats flock until they broadly detect insect clusters then split off into subgroups as they close in on insect groups.Bats who capture and consume insects will replenish their energy level by the specified amount e c and continue hunting.This energy gain could be modeled with a steady energy gain over time, but the one-time burst is sufficient for this model.Once a bat has exceeded its satiation threshold it will transition to the roosting state until its energy levels drop below that threshold or the sun rises on a new simulated day.Bats who are unsuccessful in catching prey for the last t h (time hunting since last capture) minutes will transition to the timed roosting state and find a nearby roost to conserve energy and regain strength for t r minutes.When in the timed roosting state, a bat will return to hunting once its rest time is met, or return home if the night is ending.
This behavioral model can be further extended to include even more behavior patterns such as nursing mothers returning home to feed their young during the night, or injured bats.

Echolocation
Bat echolocation is essential to many of their in-flight behaviors.6][17] Bat echolocation calls are unique for each species but there are many similarities between them.Bat echolocation calls can range from 11 to 212 kHz with the majority of echolocation falling within 20-70 kHz. 4 The distance for prey to be perceivable depends on the intensity of a bat's call, the inverse square law of sound propagation, the distance between bat and prey, and the angles of reflection.Bats emit loud calls averaging around 109 dB and can increase the intensity to as high as 137 dB. 11When the environmental noise floor is high bats need to adjust their call volume to be able to perceive sounds at a similar distance and can require significantly more energy. 18When Emerging from their caves bats emit uniquely modulated calls to help with their emergence and fly at a speed of approximately 8.75 m/s. 19ather than determining the exact echolocation frequencies, amplitudes, pulse rates and perception for each given time step, this work focuses on a faster geometric interpretation of the echolocation cone (Figure 3).For example, prior work found Rhinolphus derrumequinum nippon bat calls were shown to decay at greater speeds off-center of the call.When angled ±25 degrees from the pulse direction the sound pressure levels dropped by 50%. 15We propose an echolocation model that uses a radial distance check in combination with the conic perception of bats.We have created the following equation to model this perception where a is the vector from a bat to any object within the a r radius; v is the bat's current velocity and head angle; and  p is the maximum angle of detection for a clear image.This equation is an efficient vision cone representation for flocking, hunting and avoiding objects in the environment.This inequality allows a practitioner to quickly and easily parameterize the perception cone where a r < [5m, 10m] depending on the bat species.
Because bats are known to echolocate in multiple phases over their flocking and hunting patterns, we postulate that this radial check can be expanded to detect larger swaths of insects and represent unclear returned echoes from further distances.Using this hypothesis, bats would be able to flock and detect prey from larger distances and then get increasingly accurate information on the velocity, position, size and texture of insects when hunting within the a r range.While flocking bats will use broad-form search patterns in their echolocation, these search pulses are meant to detect general points of interest in the environment giving a less clear picture to the individual bats.We can incorporate this change in phase to better capture this perception increase in search patterns acos where s p and s r coefficients directly scale  p and a r values to affect conic perception and radial distance checks respectively.The minimum hearing level of bats is between 0 and 20 dB SPL with the average search call around 94 dB SPL. 20he maximum detection range of a moth of is 15.4 m, with a range of 5-10 m during the approach phase. 18This data suggests an increase of approximately 50% for detection in the search phase, as such we have set a r to 50%.The increase of  p is much more difficult to determine as the bats flock together without incident if no additional factor is added.From these prior studies on detection range, we have estimated an increase in  p of about 10%.The echolocation model can be adjusted for various species of bats and prey while hunting.An average value of 0.436 radians and 8m have been used for  p and a r respectively to best match the general bat population's perceptive capabilities.

Energetics model
Bats, and mammals generally, will follow the principles of least effort when choosing a flight path to conserve energy as much as possible.In our model bats have a maximum caloric level of E max calories and are considered satiated or full above E sat calories.Thus bats consume energy at a constant metabolic rate to stay alive, with greater energy expenditure during flight and hunting based on the square of their speed.We estimate this expenditure over a path integral for a known model in human walking and finding bat parameters. 21,22This is represented by the following equation showing the energy expended (E) over a given time frame: where e s represents the metabolic rate for static energy consumption and e f is dependent on changes in velocity.E max and E sat have been set to 1000 and 900 calories respectively.Given the human caloric levels from Guy 21 it is reasonable to assume a maximum energy level E max of no more than 1000 calories.For example, Vampire bats will die if they fail to find food 2 nights in a row and we have extrapolated from that a generalization that over 24 h bats will lose approximately half their current energy during their roost and need to replenish through hunting. 23A bat will lose energy equal to e s ΔT per day, where ΔT is the total seconds.From here a value for e s = 0.005 results in a depletion of 864 calories over two days.Furthermore, while flight and echolocation are expensive operations for a bat, they should not be able to use more calories than a bat consumes daily.We chose a value of 0.0001 for e f such that a bat flying for two-thirds of the night will use 192 calories at an average speed of approximately 8 m/s. 19Over the approximate 54 insects eaten per night, 24 a bat should approximately replenish the 624 calories it will use and regain its satiated threshold.Thus we determined that each insect will regain ≈ 11.55 calories.This will vary with the size of insects and can be randomized throughout the simulation with values between 9-14 calories for each insect consumption e c .

Flocking
Many models for flocking have been used in the past, most common has been the boid model.This model uses three main rules to determine an individual's movement during each moment, Cohesion, Alignment, and Separation. 25,26Our model is based on these rules and uses a weighted goal vector that can give flexibility to the emergent behaviors.Their objectives change between foraging, hunting and roosting behaviors in a given night.The goal vector is calculated by subtracting the objective point from the bat's current point in simulated space.
The velocity is then calculated using a weighted summation of the four vectors.Weighting coefficients c s , c c , c a , and c g are for separation, cohesion, alignment, and goal respectively.
Velocities greater than the maximum speed are truncated accordingly.Adjusting these weighting coefficients can give priority to the most important behavioral goals such as avoiding imminent collision or steering toward prey.
This model has been fitted with the echolocation model from Equation (3) to accurately represent what they would be able to "see" while flocking together.Bats see through echoes that don't return as much as those that do.When echoes don't return a bat will perceive empty space that is safe to fly.Their sight relies on sound waves being strong enough to return to them.
While echolocation enhances perception of detail in their environment it can also restrict the perceptual range that a bat sees.To flock effectively with this limited vision many bats can be seen tilting and changing their flight paths while moving in the overall direction of the flock.Bats also use different calls when broadly echolocating than they do for hunting, as such, perception angles  p and radial distance checks a r are increased by a factor of s p and s r respectively to better represent the search phase of echolocation during flocking.

Hunting
Bats are nocturnal hunters and forage over an 80-km radius from their home roost. 1 The ability to hunt at night protects them from many species and often allows them to hunt without being detected.Bats almost exclusively consume flying insects, but some species hunt bugs and prey on land or in trees.The Mexican Free-Tailed bat hunts as high as 1200 m where many of its insectoid prey can be found migrating at these high altitudes. 1Most commonly the insects a bat consumes forage for food below 400 m.Bats flock together when leaving their home caves or roosts and will fly upwards in a column until then arc toward their hunting destinations. 1Bats flock this way for safety, those on the outer parts of the column will steer the flock away from any predators or threats they perceive.The bats will then break off from the main flock into subgroups in search of prey.The exact size of subgroups is difficult to determine, however, it has been shown that bats will hunt in groups of greater than four over large periods. 6hroughout the night bats will roost in safe locations to rest and conserve energy. 1 When facing unfavorable hunting conditions due to weather or lack of insect prey, bats will favor roosting to save energy and try again later that night (as represented by our models t h and t r time constraints).Nursing mothers require more food than the average bat and will find periods throughout the night to return to the home roost and feed their pups. 1 Bats will need to consume enough insects to remain satiated, this exact number has been estimated for a few different species, but we will represent it as the variable I min .There are also varied rates of prey capture across bat species.A study of greater mouse-eared bats showed they have a capture rate of approximately 76%. 24he hunting model uses the echolocation model, with an angle of  p radians from the bat's current velocity and a distance of a r to detect prey.The current velocity is indicative of the angle of a bat's head and ears.Thus a cone of detection is updated for prey within a bat's echolocation range.Each insect prey P i within the a r distance is evaluated and checked to be within the range of  p and the closest prey P t is chosen as a target.The bat will readjust only if another insect comes within closer proximity with a better chance of capture.The distance to each insect in P i is represented as d i and checked against the current closest detected insect.

Group hunting
Bat behaviors change through the night.Their main goals are to find food and conserve energy.Bats fly around to find their nearest detectable insect clusters and will split off into smaller subgroups to hunt.Bats are also known to eavesdrop on their flock mates which can help them determine optimal hunting areas.When a bat hears a high-pitched call that precedes the capture of prey, they could turn toward the area.Conversely, if a bat overhears large numbers of these calls they may decide to hunt elsewhere because the location is over-saturated with hunters.The subgroup sizes help maintain better catch rates for all bats, if too many are clustered while hunting the subsequent confusion could decrease the efficiency of the hunt.Bats will use the Echo Flocking model unless they are hunting.They will split off from the flock with precedence to the closest bats according to the perceived subgroup size appropriate for hunting G s while the remainder of the flock continues searching.When hunting they will still avoid collisions but will not try to stay with the subgroup until they all move to a new location.These subgroup sizes were tested for their efficiency in the Evaluation section where they will be discussed further.
Currently, insect cluster sizes and locations are generated as an approximation of real-world environments.The number of insects and locations per cluster can be easily adjustable to reflect a real-world environment more accurately.
We empirically test the hunting and echolocation models in groups of bats hunting clusters of insects to determine optimal ratios and group sizes.When hunting in a 1:1 ratio of bats to insects, approximately a third of the bats will catch zero insects and a third will catch two insects.When hunting in a 2:3 ratio of bats to insects an average of less than 10% of bats will be unsuccessful in capturing a single insect.This ratio works with up to 30 bats hunting together, however, having many bats flying in close proximity requires much more course correction to avoid collisions thus increasing energy consumption and decreasing catch rates.Not only will this drain the bats and extend the hunting time for such a cluster but the insects will be given more time to react once they see their neighbors being eaten.
This increase averages around 5% energy expended per insect cluster compared to the bat subgroup size of ten.Over one hunt, this increase is minimal but over the entire night of foraging where each bat will consume around 60 insects, this increase will heavily affect the overall energy expenditure.With a ratio of 2:3 bat to insect, different subgroup sizes were measured for their efficiency.Hunting clusters of sizes 4 or 5 performed most optimally.
Insect cluster sizes will vary over the hunting areas according to the prey model.Group sizes should accommodate these constraints and the bat subgroups will be determined by the perceived insect cluster sizes from broad search echoes.With the data gathered and behaviors from past research, these bats have been updated to do a rough proximity check when flying by insect clusters and split off into subgroups of variable size G s in approximately a 2:3 ratio of bats to insects.Bats will favor hunting in groups of 4 to 10 when possible but will be able to exceed those numbers if they come across clusters of insects larger than 20 or 30.When splitting off to hunt real bats would likely use a heuristic approach for their numbers.We have represented this possibility by adding an offset for variance percentage G v to the subgroup sizes G s according to 8. G v = 0.2 is used to create a random variable with uniform distribution U(0, G s G v ) between 20% of the optimal group size.
When subgroups hunt in large numbers, especially numbers equivalent to the number of insects, the average number of bats who catch prey decreases.Bats will roost once enough time has passed since the last successful catch, these reasons make it vital for bats to split off into appropriate subgroup numbers for hunting (Figures 4 and 5).

Prey
To analyze bat hunting patterns we need prey with appropriate behaviors.We have given these insects localized perceptions and clustering rules to allow them to move within clusters of variable sizes.Their objective is to migrate and forage for their food.These groups can be broadly perceived by a bat from larger distances per their echolocation behavior and Energy cost (calories) and distances traveled (m) for each bat in their subgroup sizes.All bats hunted prey with the same start conditions except the number of bats and prey in a 2:3 ratio of bats to prey.
low-frequency sweeps for food.Such clusters are spawned with variables to better control them.C n represents the number of insect clusters and each cluster spawns a random number of insects between C min and C max .Each cluster is randomly placed throughout the simulation area as it creates enough accuracy without recreating entire ecosystems.Most insects are unable to hear at the frequencies bats use for echolocation which gives bats a stealth advantage when hunting.We also know that echolocating bats in the approach phase have access to the size, relative position, and relative velocity of objects that they detect because of the increased intensity and pulse rate of their calls.This is what allows them to get very clear and consistent data when hunting in close proximity.As such we modeled our bats to gain access to these variables when they detect potential prey through the hunting model.Thus our bats can update their velocity heading based on the current position and current velocity of a detected insect to chart an intercept course.
where v and P represent the velocities and positions respectively.This allows the bats to better intercept prey because they know where it is and where it is going once echolocated.Bats that get within 10 cm of a prey are considered close enough to catch it and a cooldown time window t c stops them from eating multiple prey in quick succession as they would need to consume one insect before hunting another.

EVALUATION
In this section, we look at the proposed model from several perspectives.In particular, we focus on the replication of expected behaviors found in the research literature for a variety of conditions related to hunting.We also show the computational performance to simulate and render in real-time scenarios with over 350 bats.

Solo hunting
Bats are not perfect solo hunters, 24 thus our model should not create perfect conditions either.The proposed hunting model was tested with one bat detecting and chasing a single insect.Its capture rate was 70% on the first attempt, 18% on attempt two, 9% on attempt three, and 3% of the time required a fourth or greater attempt.These capture rates over a sample size of a hundred hunts are approximate to the capture rates of greater mouse-eared bats (76%) 24 and therefore show promise for the accuracy of this hunting model.

Group hunting
Bats are also imperfect hunters in groups. 27Bats have been observed hunting in groups of at least 2-5, although researchers are currently unsure if they hunt in greater numbers. 6,7When we compare energy costs and distance traveled over static hunting conditions in a 2:3 ratio of bats to prey The proposed model shows significant increases and variability in energy usage from groups of 6 and above as shown in Figure 6.
Figure 7 shows bat energy consumption rates when hunting an equal number of prey.once again we can see an increase in energy consumption when hunting with 6 or more bats.These figures show a strong association between our simulations and real-world data where groups 4 and 5 bats were found to be highly efficient in their hunts of insect swarms. 7

Model performance
The construction of the model is tuned toward real-time performance with smaller bat groups.The insects' properties are precomputed and individual agents only spawn and simulate when bats are close enough (within 20 m).However, the groups can still be detected using broad-form echolocation from further away.This saves computations and further improves run time speed.Our simulation experiments show the model will run with frame rates above 30 fps with up to 350 bats.The full experimental results for our performance evaluation can be seen in Figure 8.

Emergent behaviors
Simulations were compared to data from the Ushichka dataset with similar group sizes. 28In our comparisons, the simulated bats were initialized with similar start and end conditions as those observed in the video data.However, the cave geometry was not replicated in the simulation.In Figure 9, we show a qualitative trajectory comparison between real and simulated data.A careful review of real bat trajectories shows more sporadic high-frequency movement compared to the smoother curves of our model.This is mostly due to bat flapping motion and potential tracking noise.Emergent behaviors that were similar between real and simulated bats included their circling movements and pairwise curved flight paths.

ADDITIONAL EXPERIMENTATION AND DISCUSSION
Flocking Simulations were tested with and without the echolocation perception model.The key difference between them was the spacing between bat agents.This behavior emerged with the addition of our echolocation model as a means to avoid collision with flockmates that suddenly came into perceptual range and required sudden readjustment to avoid collisions.This change led to their behavior being more like observations of bats flocking in their natural environments and supports this model for bat flocking behavior.Due to their behaviors and nocturnal patterns, it is difficult to capture bat hunting patterns in variable group sizes, The fast speeds of bats in flight and limitations on available detector equipment make some research questions difficult to answer. 6The proposed model is capable of estimating these hunting behaviors and forming a strong basis for answering previously unattainable questions in bat behaviors.Where possible these estimations should be cross-referenced through future research.Bats are imperfect hunters individually and in groups. 6,27nergy conservation is key to bat survival, group members that are unsuccessful in individual hunts will waste energy and are at a higher risk of starvation.Bats have high survival rates and naturally group themselves for optimal hunting conditions while foraging in the night. 6,7We hypothesize that bats will adjust their group sizing to approximate optimal hunting ratios of bats to insect prey.Bats are known to hunt in variable group sizes and these exact sizes and the reasons for them have been difficult for researchers to ascertain. 6,7Using the proposed model we can investigate and estimate the potential number of unsuccessful hunters for variable bat and prey group sizes.Our results are shown in Figure 10, where we simulated each combination of bat/prey ratios.When we observed the hunting patterns of different bat group sizes in comparison to prey group sizes we found a strong correlation  = 0.992 between the number of successful hunters in a group with a 2:3 ratio of bats to prey to theoretical perfect hunting conditions where no bat is unsuccessful during their group hunt.We also found that individual catch rates and unsuccessful hunters increased with the group numbers of bats and prey.This aligns with expectations from empirical observations by experts however it has been noted previously that concrete data does not exist as this bat behavior is currently difficult to observe fully. 6,7odeling bat behaviors is a complex process, this model has limitations on energy consumption rates that should be expanded.Changes to energy usage based on echolocation frequency and flight maneuvering would greatly increase the power and accuracy of the model.The unique multiply jointed bat wings have capabilities for much more complex flight motion than other animals. 8This flight model is a good place to start but will need to be expanded further to better encapsulate maneuverability.Additionally more testing and evaluation is required to confirm the accuracy of this model to real world data.
Further steps should be taken into account for Equation ( 4) and the perceptibility of different prey types.For continued efficiency, we would suggest adding additional spheres that extend the detectable range of the insects.These could be size adjusted to indicate that species' unique material and size, making them easier or harder to perceive according to their unique properties.

CONCLUSION
We have proposed a model built from research on bats to create a powerful and customizable approach that accurately portrays our understanding of Chiroptera through the proposed model.This model shows promise toward answering previously unanswered questions about bats and is aligned with expectations from expert chiropterologists that should be further explored. 6,7We have discovered optimal subgroup sizes, perceptual capabilities, and energetic constraints that cumulatively govern bat behaviors.With the thousands of bat species and the complex workings of their differing behaviors, these models have allowed us to determine generalized rules for governing individual bat behaviors.The proposed model, as implemented, captures many known aspects of bat behavior, hunting, and perception.These models and simulations can be customized for specific species of bats, such as colony size, perception range, energy consumption, subgroup sizing, insect clustering, and maximum flight speed.The simulation has been scaled and altered many times throughout the evaluation to determine the viability of each model.It could easily be adjusted to incorporate more data in future research.
In future works, the bats can be further individualized with variations in size and maximum speed to represent different genetic characteristics and also injured bats.We plan to incorporate additional behavior patterns over the bat lifespan, such as for nursing mothers and differently aged bats who require different lengths of roost time or return to the home roost to feed their young.Further efforts should be made to assess the validity of experimentation that would now be possible through these models and simulations.

F I G U R E 1
Example scenario in the scenario space.The cyan cubes represent temporary roosts.The red spheres represent insect clusters and the black cylinder represents the colony's home cave.F I G U R E 2Finite state machine for bat behavior.Bats transition their behavior based on day/night cycle, hunting rules and metabolic energy expenditure.

F I G U R E 3
Bat echolocation cone as modeled in Equation (3).

F I G U R E 4
Simulated bat agents (a) before and (b) after splitting into subgroups for hunting based on individual rules.F I G U R E 5 Bats hunting, black cubes represent the bats, and the red capsules represent insect prey.

F I G U R E 7 F I G U R E 8
Energy cost (calories) for various bat group sizes hunting an equal number of prey.Simulation time cost, as framerate, over the number of bat agents.

F I G U R E 9
Ushichka real bat trajectory versus our model.F I G U R E 10 Unsuccessful hunts over various group sizes of bats and prey.The blue points indicate simulations where every bat caught at least 1 insect and red indicates simulations where at least 1 bat caught zero insects.Size represents repeated results.