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   Deception is a communication tool used by humans and animals. While considered unethical in daily life, deception is widely accepted with regards to military applications. In this research, the mobbing process in arabian babblers is examined. Using Alan Grafen's dishonesty model, an algorithm describing when to deceive is developed and a model for predator behavior is presented. The success of this model is evaluated based upon overall deaths of group members.

  The Possibility of Deceiving in Mobbing Babblers

   Mobbing is an important self defense behavior found mainly in birds that are preyed upon. In this research, we focus on the application of the handicap principle to mobbing in arabian babblers and investigating what role, if any, deception plays in the process.

Figure 1:  Black Eastern gray squirrel moving peanuts

Figure 1: Arabian Babbler

A. Mobbing Behavior

   The mobbing processes for the sentinel and individual babbler begin when the sentinel spies a potential danger. It responds by emitting an alarm. Upon hearing this alarm call, individual babblers congregate in the sentinel's tree and assist in issuing these alarm calls. It is suggested that the birds keep making these sounds to let the predator know that it has been seen [1]. If the predator still approaches the group and perches nearby, the babblers approach and mob the predator. During mobbing, the babblers rarely physically attack the intruder, but instead emit vocalizations and circle the predator while flapping their wings. The predator responds by either leaving or attacking one of the mobbing birds. [1].It is important to view mobbing as a signal between the prey and the predator. Thus, a simple signal sent between the two agents is sufficient to model this behavior. While the simulation presented shows the babblers harassing the predator, the display itself does not determine the predator's behavior at this step. This model incorporates the ability for the prey to "deceive" the predator. Using the model, one could determine an appropriate time to feign strength to the adversary or to conserve resources in escaping in a military scenario.

B. Sentinel Behavior

   The catalyst to the mobbing process is the sentinel issuing an alarm call. The role of sentinel is assumed by a member of the group [1] and is usually filled by the alpha male or another high-ranking male. For each group of babblers, there is only one sentinel at any given time. In a natural setting, the sentinels change, but for the purposes of this simulation, the sentinel will be predetermined and static. The sentinel, like other birds in the group, participates in mobbing with respect to Grafen's Dishonesty Model [3].

C. The Handicap Principle

   The Handicap Principle, developed by Zahavi [1], details the criteria in which signals between animals are required to be honest. It states that if an animal wastes its personal resources to produce a signal, then that signal must be honest. Otherwise, it cannot afford to waste such resources. This is a fairly accepted principle now but was highly contested when it was first introduced. Its application to mobbing is that babblers will not approach a predator if they do not believe they can escape it. If the babbler does approach, it is wasting the resources of cover from the trees and a head start to escape from the predator. By wasting these resources, it is demonstrating that it can survive without them and thus signaling to the predator that a chase is pointless. If it could not tolerate losing these resources and attempts to mob the predator anyway, that babbler becomes vulnerable to an attack. In that case, the babbler would not be able to survive should the predator decide to attack it, and thus deceiving with respect to its low fitness was not the appropriate choice according to the handicap principle.

D. Deception

   The purpose of this research is to model the mobbing behavior and determine what value it affords robots and what, if any, value is added by injecting deception into the process. Deception in this case is what biologists describe as cheating [3]. While Zahavi maintains that signals produced through wasted resources must be honest, Grafen claims there can exist an acceptable level of cheating that will keep the system stable [3]. Grafen details inequalities in which cheating would be the best strategy for the signaler. The derived model is based upon the "Philip Sydney game" [3]. In this situation, cheating constitutes a babbler signaling to the predator that it can escape any subsequent chase when it actually could not. If a predator attacks a babbler that is bluffing about its fitness, the babbler will most likely be captured and eaten, a rather serious gamble.

E. The Phillip Sydney Game

   The Philip Sydney game is a signaling game between two players, developed by John Maynard Smith [3], which we will consider in the context of predator-prey relations. The two players in the game are a donor and a beneficiary. The donor has a resource that the beneficiary may or may not need, e.g., water. The beneficiary has the ability to signal to the donor that it does or does not need this resource. Upon receiving this signal, the donor can decide whether or not to give the resource to the beneficiary. Several factors go into the decision as to whether or not the beneficiary should signal that it needs the resource including a relatedness coefficient and a necessity coefficient. Similar parameters go into the decision for the donor to give up the resource [3]. There are a few different outcomes of all these decisions. In the example of the resource being water, if the donor gives up the water, there is a possibility that it will not survive due to thirst. On the other hand if the donor keeps the water, there is chance that the beneficiary perishes. If the beneficiary signals, it pays a cost to its fitness and upon not receiving the water, maintains a lower survival rate. Thus it is very important to for the beneficiary to signal appropriately. For the scenario we consider, the donor is the predator, the beneficiary is the babbler, and the resource offered is the predator sparing the babbler's life. A more detailed description of the model appears in section 3.

F. Group Control

   Mob formation does not have an exact spatial layout and positioning as was the case in our earlier work on formations [12], but some spatial constraints define the mob structure. For example, the babblers that are mobbing must space themselves out around the predator. In earlier work [5], bird lekking behavior was used for group formation in a different context, that of trying to find and attract a scarce resource. Utilizing this pre-existing group formation behavior is an easy solution for implementation. In lek behavior, all group members are attracted to a hotspot (location where resources are likely to be found) but modestly repelled by other members to assure a uniform spatial distribution. For mobbing these roles are altered: the predator settles itself at the hotspot, where the hotspot in this case is the perching location of the predator around which the other babblers group during the mob.

  Computational Model

   The computational model for the sentinel and individual behavior is shown in figure 2a and 2b respecitively, and is derived from the behavioral processes described in the previous section. Each component behavioral assemblage (an aggregation of primitive behaviors [14]) and their associated transitions (behavioral triggers) are described below.

Figure 2a: High Level FSA for the modeled behavior of the Sentinel

Figure 2a: High Level FSA for the modeled behavior of the Sentinel"
Figure 2b: High Level FSA for the modeled behavior of the Individual

Figure 2b: High Level FSA for the modeled behavior of the Individual"

A. Sentinel Behavior

   The Sentinel starts in a tree looking for predatorsBased upon sentinel behavior described in [2], the specific perching area chosen gives the sentinel the best view. Thus no visual occlusions due to obstructions are assumed since the bird naturally chooses a spot that likely does not contain such impairments. While observing in the tree, the sentinel remains stationary while attempting to detect a predator. Upon detection of a predator, a transition occurs to the Alarm state.According to [6], European Starlings (Sturnus Vulgaris) can detect a predator 40 m away and detect them by sight. These birds have similar physical characteristics to Arabian babblers and thus this provides the detection distance used in the simulation. In the alaram assembalge, the sentinel broadcasts its location to both the group and the predator.This is in agreement with the handicap principle [1] as the babbler is wasting its advantage of being hidden in order to send the signal. If the predator leaves, the sentinel remains in its perch. If the predator lands, the sentinel will mob the predator. When mobbing, the simulated babbler agent's formation around the predator is dictated by equations found in [5]. The babbler transistion randomly between mobbing and harassing. the sentinel moves toward the predator causing the predator to become frustrated. Upon repeated harassing if the frustration level of the predator becomes sufficiently high the predator will leave. Otherwise the harasser returns to the mob after a given time, unless the predator leaves or attacks.

B. Non-Sentinel (Individual) Behavior

   This overlaps considerably with the Sentinel model with the biggest differences being the absence of a Feed state in the sentinel, and the individual babbler does not contain an Alarm state. The triggers between most assemblages are also slightly different. These differences are explained below.

   When the simulation starts, the non-sentinel individuals move to their feeding location. This area is near the sentinel perching location. Upon arrival they enter the feed state. When feeding, the individuals stay at the feeding location until the sentinel emits the alarm call. The alarm serves as a signal indicating the presence of a predator. When mobbing, the group forms exactly as before but individuals do not always mob. Instead, the decision to mob is based on equation 1.

   In Equation 1, Sb is babbler fitness, Sd is predator fitness, t is signal cost, and r is relationship coefficient X represents the risk associated with mobbing this predator. The bounds of all parameters presented, with the exception of X, are 0 and 1. It is important to note that the parameter Sd represents perceived fitness rather than the actual fitness, which will be represented differently in the data analysis. If the inequality is not satisfied, the individual remains in the tree until the predator leaves. An explanation of the validity of this is model can be found at the end of this section.

C. Predator Behavior

   The current predator model is simplistic and has no decision making abilities. It always moves towards the group, perches near the group, and attacks the group after a specific amount of time or leaves because frustration built up due to mobbing agents. In our near-term plans, the predator will have a range of choices regarding when to attack and other aspects of the prey-predator relationship [1], but this paper centers on the mobbing behavior itself.

D. Deception in Mobbing

   Dishonesty is incorporated into the computational model (after [3]) and is used when the individual makes the choice whether to participate in mobbing or not. If the system was entirely honest then the only factors involved in mobbing would be the fitness of the predator and prey and the cost of the signaling. In the honest situation, if the individual has fitness greater than the predator after factoring in signaling cost, then it would always mob. Similarly, if the individual was fitness deficient after subtracting the signal cost, then it would never participate in the completely honest situation. Essentially this states that bluffing or feigning strength is never allowed.

  However, when incorporating deception a relatedness coefficient is included, which allows and influences deceptive behavior. This dishonesty model at first glance is not intuitive, requiring a closer look to make apparent its intent. The purpose is to determine when it is the most appropriate strategy for an agent to engage in mobbing independent of whether it is an honest or dishonest signal.


   The implementation of mob behavior is constructed from multiple previously developed behaviors (Appendices A-C in [5]). Mob formation around the predator is emulated using a sub-FSA containing the lek behavior [6]. For the harassment aspect of mobbing, the change-color behavior is utilized rather than implementing any extravagant motor display. The transition between the mob and harass state is probabilistic. This value is empirically assigned, as we have not found supporting biological data regarding the frequency of harassment during mobbing. After harassing is complete, its color returns to the original state, and the agent is considered back in the mob state. When being harassed, the predator detects green harassers. During each time cycle, the predator's current frustration value is incremented by 1 for each harassing agent. If the frustration value exceeds a specified frustration threshold (ft =100, 125, or 150), the predator leaves and the simulation terminates. If, however, s seconds elapse (in this case arbitrarily 10) and the frustration threshold has not been exceeded, the predator selects a random mobbing prey individual to attack. If the predator has a higher perceived fitness value than the prey individual it selects, then that agent is considered to be bluffing, and the probability of that agent being killed, Dl, is 95%. Conversely if the predator selects an honest mobbing agent, the probability of this agent being killed, Dh, is set to either 5%, 10%, or 15%. The chance of the predator killing an honest mobber is increased across different analyses to represent the effect of a fitter predator. Each non-sentinel prey evaluates Graffen's Dishonesty Model whenever in the presence of a predator. Every agent that satisfies this model participates in mobbing upon receiving the alarm call from the sentinel. In the results that follow, parameters t, r, and Sd are held constant (t=0.1, r=0.75, Sd=0.5) while the parameters Sb (fitness), ft (frustration threshold), and Dh (death probability for honest agents) vary. The assigned value for Sb was either 0 (no participation), 0.4 (deceitful participation), or 0.6 (honest participation). All combinations of honest and dishonest mob groups were analyzed for group sizes of 2 through 7 babblers. ft was assigned a value of 100, 125, or 150 with greater values representing a more patient predator. Finally, the probability of an honest mobber being killed was varied from 0.05, 0.10, and 0.15. As previously mentioned, there is a difference between the perceived fitness, Sd, and the actual fitness. Varying Dh represents changing actual fitness. Using the assumption that fitter predators are more likely to catch prey, increases in Dh indicate increases in actual predator fitness. This is more desirable than changing Sd, as changing perceived fittness alters the number of mobbing agents.

  Simulation Results

   The simulation data was analyzed for the aforementioned values of parameters Sb, ft, and Dh. Figures 3a, 3b, and 3c show the mortality rate for each combination of mob sizes and deception rates present in the group, when Dh was held constant at .05; while ft=100 in 3a, 125 in 3b, and 150 in 3c. Figures 9a, 9b, and 9c (from [5]) demonstrate the same combinations but where Dh = .10, and gures 10a, 10b, and 10c (from [5]) show this data when Dh = .15. For each frustration threshold, there exists a minimum number of mobbing agents (Mm), for which the predator's frustration always exceeded its ft and ed. The minimum number of mobbers for which zero attacks occur across each ft is shown in table 1 (from [5], for reference Mm = 3 for ft=100). Attacks being reduced to 0 results in a 0% mortality rate. Deceiving in groups smaller than these minimum mob sizes is lethal. The deadliest conditions for lying, when ft=125 and 150, was a mob formation consisting of 2 deceiving agents and a sentinel. Mobbing a predator with these frustration thresholds and only deceiving.agents, resulted in a mortality rate of approximately 70%. When ft=100, the highest mortality rate occurs when 1 deceiving agent and a sentinel participate. It is desirable to discover if adding deceiving agents to a purely honest situa- tion would result in fewer fatalities. Obviously when adding enough deceivers to exceed or equal Mm for each frustration threshold value, the mortality rate drops to zero. However it is more interesting to investigate critical mob sizes (Mc) that can result in both the predator attacking or eeing. Mc for each frustration value is presented in table 1 found in [5] (for reference Mc = 3 for ft=100). Figure 3 shows that a purely honest mob group has a higher survival rate than any group containing a deceiver, with two exceptions. Other results can be found in figures 9-11 of [5]. As evidenced in figure 9b in (ft=125 Dh=0.10), a group of 3 honest mobbers yields a mortality rate of 0.16. Adding one deceiving babbler to this group reduces the mortality rate by 25%. Similarly, as seen in figure 10c (ft=150 Dh=0.15), 3 honest mobbing babblers have a mortality rate of 0.20. Adding one deceiving babbler drops the mortality rate by 30%.

Figure 3

Figure 3: Mortality Rate's Relationship with Deception Rate and Group Size

   Since these are the only two incidents in the entire data set in which the addition of a single deceiver decreases the mortality rate, it can be concluded that lying with Dl = .95, is not a strategic decision in mob groups less than Mm. Figure 11, found in [5], shows the result of reducing Dl to 50% and increasing Dh to 30% while ft was 150. Under these new conditions, deception improves survivability in group sizes of Mc. Adding one deceiving member to mob size of 3 with any deception rate decreased the mortality rate by an average of 16%. While this may not be realistic, it proves that there is a set of conditions in which deceiving can improve survival rate consistently.


Robot Experiment: Robot Mobbing


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The paper for this project can be found here