Journal of Theoretical Biology 380 (2015) 480–488
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When is emotional contagion adaptive? Wataru Nakahashi n, Hisashi Ohtsuki School of Advanced Sciences, SOKENDAI (The Graduate University for Advanced Studies), Shonan Village, Hayama 240-0193, Kanagawa, Japan
H I G H L I G H T S
We study conditions under which emotional contagion is the most adaptive strategy. Emotional contagion (EC) is adaptive when individuals share the environment. EC is adaptive when observation is error-prone. EC is adaptive when observers pay attention only to infrequent behavior.
art ic l e i nf o
a b s t r a c t
Article history: Received 20 January 2015 Received in revised form 5 June 2015 Accepted 8 June 2015 Available online 23 June 2015
Empathy plays an important role in animal social behavior. Since emotional contagion forms one of the bases of empathy, here we study conditions for emotional contagion to be adaptive, compared with other behavioral rules such as behavioral mimicry. We consider the situation where the focal individual ( ¼observer) reacts to a behavior of another individual (¼ demonstrator). By emotional contagion one spontaneously copies the emotional state of the demonstrator and takes a behavior driven by that emotion. By behavioral mimicry, in contrast, one copies the behavior of the demonstrator itself. Through mathematical models we show that emotional contagion is adaptive when the environmental similarity between the demonstrator and the observer is intermediate. The advantage of adopting emotional contagion over behavioral mimicry increases when observing others’ behavior is difficult or cognitively demanding. We show that emotional contagion is often a more flexible strategy than behavioral mimicry in order to cope with the living environment. In other words, emotional contagion often works as a better social learning strategy. These results suggest some ecological conditions that would favor the evolution of emotional contagion, and give a part of the explanations of why emotional contagion is frequently observed in group-living animals. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Empathy Behavioral mimicry Social learning Evolution Mathematical model
1. Introduction Empathy is one of the most important emotional processes for social interactions in humans. Although the definition of empathy varies among researchers, the essential component of empathy is the instinctive recognition of and a reaction to others’ emotions (Gerdes et al., 2010; Preston and de Waal, 2002). Recently, evidence of empathy in other animals is increasing (Langford et al., 2006; Plotnik and de Waal, 2014; Watanabe and Ono, 1986), suggesting that empathic sensitivity should be adaptive in many animals. Since the underlying machinery of empathy, including its neurophysiological basis, can be very complex, a variety of factors could be relevant to its evolution. Some researchers recently found dissociation between emotional and cognitive empathy
n
Corresponding author. Tel.: þ 81 46 858 1580. E-mail address: [email protected] (W. Nakahashi).
http://dx.doi.org/10.1016/j.jtbi.2015.06.014 0022-5193/& 2015 Elsevier Ltd. All rights reserved.
(Shamay-Tsoory et al., 2009). Emotional empathy often refers to a spontaneous change of one’s emotional state accompanied with affective reactions to that, while cognitive empathy requires the cognitive perspective-taking ability to simulate others’ psychological processes (Pepping and Timmermans, 2012). In particular, the most primitive and basic form of emotional empathy is emotional contagion, which means a spontaneous copying of others’ emotional state followed by an affective reaction to that. Emotional contagion has drawn wide attention from researchers in order to understand the origin of empathy (de Waal, 2008, 2009, 2012; Panksepp and Panksepp, 2013). Therefore, in this paper, we focus on evolutionary conditions for emotional contagion to be adaptive. Note that emotional contagion and emotional empathy are different concepts, because the former always refers to the copying of other’s emotion, while the latter includes spontaneous arousal of a different emotion from that of the target. For example, spontaneous activation of a positive emotion by perceiving others’ negative emotion, which is called Schadenfreude, is an example of emotional empathy that is not emotional contagion. Biological
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definition of emotion is still debatable (Waal., 2011de), but one’s emotional state is often identified by the activity of autonomic nervous system (Kreibig 2010) as well as by various physiological measures, or sometimes indirectly by its behavior. Various studies on humans show examples of emotional contagion (Hatfield et al., 1993; Fowler and Christakis, 2008; Hill et al., 2010). Laboratory rodents such as rats and mice are excellent animal models to study the contagion of negative emotions, including pain, panic and fear (Panksepp and Panksepp, 2013). For example, an observer who witnesses its conspecific receiving electric footshock develops freezing behavior in rats (Atsak et al., 2011) and in mice (Jeon et al., 2010), which is a good example of emotional contagion. Recent studies have shown that yawing is contagions in dogs (Romero et al., 2013) and in wolves (Romero et al., 2014). Emotion is not only copied but can also be socially modulated. For example, a mouse injected with acetic acid writhes more when observing another mice simultaneously writhing with the same treatment than when being isolated, but it writhes less while observing an intact mouse (Langford et al., 2006). Such social modulation between two individuals is more likely to occur if they are cagemates or if they are housed together for a long period. Importantly, the brain process of such social modulation is believed to work completely unconsciously by using the circuits for emotional learning (Solms and Panksepp, 2012; Panksepp and Panksepp, 2013), which means that social modulation can reasonably be understood as one form of emotional contagion, not as a process requiring cognitive perspective-taking. From an evolutionary point of view, emotional contagion can be considered to be one of the ways to learn environmental information from others. For example, if an individual shows the emotion of fear, there may exist a threat causing that emotion in the neighborhood, which may also affect observers. In such a case, an observer may benefit if he/she evokes the emotion of fear and takes a corresponding affective reaction to that. Therefore, we can regard emotional contagion as a kind of “social learning” strategy. Although many researchers have theoretically investigated the evolution of various kinds of social learning strategies (Acerbi et al., 2011; Enquist et al., 2007; Feldman et al., 1996; Henrich and Boyd, 1998; McElreath and Strimling, 2008; Nakahashi, 2007, 2013; Nakahashi et al., 2012), no researchers have considered yet the evolution of emotional contagion as a strategy of social learning. There are mainly two qualitative differences between previous models and ours. First, previous models of social learning have mainly concentrated on the role of imitation, which is a fully cognitive process. For example, learning how to make a stone tool from a teacher is a highly cognitive process, and emotional contagion is not relevant at all. Those previous models assumed that individuals who are engaged in social learning copies the behavior of the target, but it was not necessary for researchers to distinguish between behavior and emotion. Second, the time scale of social learning is completely different. Previous models have mainly studied cultural evolution, where information is often transmitted intergenerationally. They have found that social learning becomes more important when the environment is more stable between generations (Boyd and Richerson, 1988; Feldman et al., 1996; Nakahashi, 2010; Rogers, 1988). In contrast, when we talk about emotional contagion, it always means the instantaneous transmission of information, usually within seconds, between individuals. In that case, by analogy to the result of intragenerational social learning, we can naively expect that emotional contagion should be evolutionarily beneficial if the adaptive behavior of a demonstrator (the one who first initiated a behavior) is also adaptive for observers (those who watch the behavior of the demonstrator). Therefore, we hypothesize that the correlation between the optimal behavior of the demonstrator and that of
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observers should be a key ecological parameter for the evolution of emotional contagion. In this paper, we regard emotional contagion as an evolutionary strategy of dealing with real world events. Our model is not necessarily specific to a single particular species, but imagining rodent individuals, such as rats or mice, may greatly help readers intuitively understand our model. In particular, we will consider the situation where individuals are about to be exposed to some types of danger, such as aggression or predation. There, negative emotions such as fear and/or panic are likely to be triggered. Those emotions can contribute to one's survival by various ways. For example, fear can cause freezing, which may help them hide themselves from predators. In contrast, panic can cause frequent and abnormal movements, which may also help them escape from predators’ chase and attack. As an alternative evolutionary strategy to emotional contagion, we also consider behavioral mimicry, which means a precise copying of demonstrator’s behavior without copying its emotion. Generally speaking, emotional contagion is a fast process compared with behavioral mimicry because one need not watch the whole behavior of the demonstrator. However, emotional contagion may not be accurate, because the demonstrator’s emotion, that is a physiological change triggered by the activation or deactivation of autonomic nervous system, is often not directly observable, Instead, emotional contagion is achieved only via visual, auditory, or olfactory cues (Meeren et al., 2005). This feature of emotional contagion is in sharp contrast to behavioral mimicry, where most of the demonstrator's behavior is often directly observable. In this paper, we will model emotional contagion as a process of abstracting information from demonstrator’s behavior by spontaneous activation of one’s own emotion. Therefore an observer who adopts emotional contagion loses a part of information in the demonstrator’s behavior. In contrast, an observer who adopts behavioral mimicry is more accurate in copying the demonstrator, because it relies on a directly observable piece of information, that is, behavior. In addition to these two strategies, we also consider a third possible evolutionary strategy, called independent reaction, as a benchmark strategy. We assume that an observer who adopts independent reaction neglects the behavior of the demonstrator or any sensory cues it provides, and behaves completely independently of the demonstrator. It is analogous to “individual learning” strategy in studies of cultural evolution, where an individual learner explores the environment by itself via trial-and-errors. In the following, we will compare the performance of the three strategies, emotional contagion, behavioral mimicry, and independent reaction, under a wide variety of conditions, and study which strategy is the most adaptive. We will discuss how our results correspond to empirical and experimental evidence of emotional contagion in animals and in humans.
2. Basic models 2.1. Basic assumptions We will consider the interaction between two individuals, a demonstrator and an observer. We assume the following scenario. First, a demonstrator finds the source of danger. It could be either via a visual cue (the demonstrator sees a predator approaching), an auditory cue (it hears a call or noise), an olfactory cue (it smells a predator), a direct contact (it receives a physical attack), or their combinations. After directly perceiving the danger, the demonstrator takes a behavior. For simplicity, here we model a variety of behaviors by one-dimensional real values. A best example of behavior parameterized by a continuous real value can be the degree of activity, where zero represents a normal status, a
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Table 1 Symbols used in this paper. Symbol
Usage
x x0 x″ y y0 w a R σ2 τ2 k γ2 CIR CBM CEC
Demonstrator’s optimal behavior Demonstrator’s actual behavior Demonstrator’s behavior perceived by the observer Observer’s optimal behavior Observer’s actual behavior Parameter specifying the observer’s affective reactions to emotions Parameter specifying the threshold of emotional contagion Environmental similarity between a demonstrator and an observer Variance of optimal behavior Variance of observation noise Relative size of observation noise ( ¼ τ2 / σ2) Variance of the deviation between the demonstrator’s suboptimal and optimal behaviors Fitness cost of independent reaction strategy Fitness cost of behavioral mimicry strategy Fitness cost of emotional contagion strategy
positive value represents a fast, frequent, and large movement (panic behavior), and a negative value represents a slow, infrequent, and small movement (fear behavior such as freezing). We assume that there is an optimal behavior x for the demonstrator that minimizes the harm it receives, and that the demonstrator, who directly perceived the source of danger and hence has some information about how to deal with the situation, is able to choose a suboptimal behavior, x0 that is usually close to x. Table 1 summarizes the symbols used in this paper. In contrast, we assume that the observer has not perceived yet the source of danger. Therefore, there is strict asymmetry between what the demonstrator knows and what the observer does. Here we assume that there is an optimal behavior y for the observer that minimizes the harm it receives. Note that y is not necessarily the same as x, because the observer is a different individual from the demonstrator, at a slightly different spatial position (but nearby the demonstrator) with potentially different physical abilities. Rather, it is natural to assume that x and y be positively correlated to some extent (see the mathematical formulation below), depending on the type of danger. However, because of the information asymmetry described above, the observer has no direct information about the source of the danger at all, and hence has no direct ways to tell its optimal behavior y. Given these, we further assume that the observer has an opportunity to witness the demonstrator’s behavior, x0 . The three strategies, independent reaction (IR), behavioral mimicry (BM), and emotional contagion (EC) differ in their reaction to x0 . Let y0 represent the behavior chosen by the observer in reaction to the demonstrator’s behavior. An observer who adopts independent reaction neglects the demonstrator’s behavior x0 , and therefore it stays at a normal activity level, y0 ¼ 0. An observer who adopts behavioral mimicry tries to copy the behavior of the demonstrator. In the simplest case without any observation noise, the observer mimics the body movement of the demonstrator, and hence it chooses the action y0 ¼ x0 (see Section 3.2 for the modification of this assumption). An observer who adopts emotional contagion has the ability to spontaneously activate or deactivate its autonomic nervous system according to the demonstrator’s behavior (emotional contagion). However, as we mentioned in Introduction, changing one’s emotional state to exactly match with that of the demonstrator is virtually impossible because of the limited observability of other’s physiological status. We believe that the simplest alternative should be to abandon exact copying of the demonstrator’s emotional state, but to develop typical emotions accompanied with some affective behaviors. In our example of one-dimensional behaviors, we assume that if the demonstrator’s behavior x0 is more active than the normal state (i.e. x0 40) then
the observer with the emotional contagion strategy develops the emotion named panic, and chooses the behavior, y0 ¼ w (40), corresponding to a typical panic behavior. On the other hand, if the demonstrator's behavior x0 is less active than the normal state (i.e. x0 o0) then the observer with the emotional contagion strategy develops the emotion named fear, and chooses the behavior y0 ¼ w (o0), corresponding to a typical freezing behavior. In other words, an observer who adopts emotional contagion can discriminate only between panic and fear, and chooses a behavior correspondingly. Note, therefore, that there is no one-to-one correspondence between a behavior and an emotion. Rather, we assume that a continuum of behaviors can activate the same single emotion. It is interesting to see how social modulation affects the value of w according to the relationship between demonstrators and observers (see Section 4). In any way, we once again stress that the activation or deactivation of the observer’s physiological status is an automatic and spontaneous process of brain based on the circuits of emotional learning (Solms and Panksepp, 2012; Panksepp and Panksepp, 2013), and therefore the development of emotions after perceiving the demonstrator’s behavior, which is modeled in our framework, is not cognitive empathy but emotional contagion.
2.2. Mathematical formulations In our model, we assume for simplicity that the optimal behavior of a demonstrator, x, normally distributes in a onedimensional space with variance σ2, x Nð0; σ 2 Þ, which means that individuals are exposed to a variety of challenges from the environment. The optimal behavior of an observer, y, also normally distributes as y Nð0; σ 2 Þ, because we assume that those two individuals are in the same environment. However, the optimal behaviors of the two individuals, x and y, may not agree. They may instead have a positive correlation with each other even in the same threatening event. Therefore, we assume that the pair (x,y) of the optimal behavior of a demonstrator, x, and that of an observer, y, follows a bivariate normal distribution with mean (0,0) as ! !! ! x 0 σ 2 Rσ 2 σ 2 Rσ 2 N ; , where is the y 0 Rσ 2 σ 2 Rσ 2 σ 2 variance-covariance matrix and R is the correlation coefficient. In the following we consider non-negative correlation only, so we assume 0 r R r 1. We call R “environmental similarity” between a demonstrator and an observer. Note that the optimal behavior of the observer conditioned on that the demonstrator’s optimal
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behavior is x, which is denoted by yx , also normally distributes as y NðRx; ð1 R2 Þσ 2 Þ. x
As we mentioned above, the demonstrator is not necessarily able to choose the optimal behavior x, but may choose a suboptimal behavior, x0 , because of, for example, its limited behavioral ability. We model this limitation by assuming that the difference x0 x follows the normal distribution Nð0; γ 2 Þ, where γ 2 represents the size of deviation from the optimal behavior. In most of the analysis below except in Section 3.3, however, we will assume γ ¼ 0 for simplicity and therefore make no distinction between x and x0 . The effect of γ is studied in detail in Section 3.3. Finally, we introduce the criterion to judge which evolutionary strategy is more adaptive. When an observer chooses the behavior y0 but its true optimal behavior is y, we assume that the observer incurs the fitness cost of ðy0 yÞ2 due to the deviation from the optimal behavior. Predation risk is one example of such cost. The observer's goal is to minimize this deviation.
3. Results 3.1. Basic result We consider the three strategies of observers, independent reaction (IR), behavioral mimicry (BM), and emotional contagion (EC). As mentioned above, an observer with the IR strategy does not use information obtained from the demonstrator, so it always chooses to behave normally, x ¼0. The cost of IR is, Z 1 Z 1 C IR ¼ ðy 0Þ2 Pðyj xÞPðxÞdxdy Z ¼
1 1
1
y2 PðyÞdy
1
¼ σ2;
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1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffi 2π ð1 R2 Þσ 2 2πσ 2 # Z 1 "Z 1 ðy RxÞ2 x2 2 ðy xÞ exp½ dy exp½ 2 dx 2 2 2 σ 2ð1 R Þσ 1 1 Z 1 h i 2 1 x ¼ pffiffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ ð1 RÞ2 x2 exp½ 2 dx 2σ 2πσ 2 1 ¼ 2ð1 RÞσ 2 :
ð2Þ
Remember that the parameter R is the environmental similarity between the demonstrator and the observer. Therefore, the BM strategy is advantageous over IR (C BM o C IR ) when R 4 1=2. This condition suggests that if the observer very much shares the environment with the demonstrator (R 41/2) then behavioral mimicry is a good rule-of-thumb to cope with the environment. In contrast to the BM strategy, an observer with the EC strategy takes the behavior w (i.e. a behavior driven by panic) when the demonstrator’s behavior is more active than normal (i.e. x4 0), and takes the behavior w (i.e. a behavior driven by fear) when the demonstrator’s behavior is less active than normal (i.e. xo 0). Here we assume w4 0. The cost of EC is a function of w and is given by Z 1Z 1 C EC ¼ ðy wÞ2 Pðyj xÞPðxÞdydx 1
0
Z 1 ðy þ wÞ2 Pðyj xÞPðxÞdydx þ 1 1 Z 1Z 1 ¼2 ðy wÞ2 Pðyj xÞPðxÞdydx 0 1 Z 1 Z 1 ½ðy RxÞ ðw RxÞ2 Pðyj xÞdy PðxÞdx ¼2 0 1 Z 1 ½ð1 R2 Þσ 2 þ ðw RxÞ2 PðxÞdx ¼2 Z
0
0
ð1Þ
where P(x) and P(y|x) respectively represent the probability density functions of x and yx (y conditioned on x) (see Appendix A). Notice that the cost of IR is equal to the variance of the optimal behavior, y. An observer with the BM strategy imitates the behavior of the demonstrator, x (we assume that the demonstrator’s behavior agrees with its optimal one, γ ¼0), so its own behavior is also x. Then, the cost of BM is R1 R1 C BM ¼ 1 1 ðy xÞ2 Pðyj xÞPðxÞdxdy
4Rwσ ¼ σ 2 þw2 pffiffiffiffiffiffi : 2π
ð3Þ
Fig. 1 summarizes the result, showingp the best ffiffiffiffiffiffiffiffi ffi strategy out of the three candidates. When w exceeds 2=π σ 0:798σ , emotional contagion can never be the best strategy. This makes sense, because a large w means excessive behaviors driven by emotions (panic or fear), which can never be advantageous (for example, panic drives a pathologically active movement, ffi fear triggers too pffiffiffiffiffiffiffiffior long freezing). In contrast, when 0 o w o 2=π σ 0:798σ , emotional contagion is the best strategy if the environmental similarity, R, is intermediate. It is trivial that if R¼1 behavioral mimicry is always the best, because the observer’s optimal behavior is exactly the same as the demonstrator’s optimal behavior. In other words, the demonstrator’s behavior itself is a valuable piece of information to the observer. However, for a reasonable intermediate value of R, we found that adopting emotional contagion can be advantageous over behavioral mimicry. This is intuitively because, under an intermediate correlation between x and y, details of the demonstrator’s behavior becomes less “valuable” information. 3.2. With observation noise
Fig. 1. The most adaptive strategy for observers is shown in the (w,R)-parameter space (without observation noise). The parameter is σ 2 ¼ 1:0.
Because of the limitation in cognitive ability, individuals may not accurately observe others’ behavior. This limitation may suppress the advantage of behavioral mimicry and emotional contagion, because they rely on the perception of the demonstrator’s behavior. Here we assume that the actual behavior of a demonstrator, x0 , is perceived as x″ by an observer, where the noise x″ x0 normally distributes as x″ x0 Nð0; τ2 Þ. Here the new parameter τ2 represents the noise level of observation. In this framework, IR always adopts the behavior y0 ¼ 0, BM adopts the behavior y0 ¼ x″, and EC adopts the behavior y0 ¼ w when x″40 and the behavior y0 ¼ w when x″o0. As shown in
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Appendix A, the cost of observers of each strategy is given as ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C IR ¼ σ 2 , C BM ¼ 2ð1 RÞσ 2 þ τ2 , and C EC ¼ σ 2 þ w2 4Rwσ 2 = p 2π ðσ 2 þ τ2 Þ, respectively. Let k ¼ τ2 =σ 2 be the relative magnitude of observation error to that of the variation in optimal behaviors. We found that C BM o C IR holds when R 4 ð1 þ kÞ=2. Therefore, a positive k hinders the advantage of behavioral mimicry. This makes sense because the former depends on the observation of the demonstrator’s behavior, whereas the latter does not. This tendency is the same when we compare the performance of emotional contagion and independent reaction; the former becomes less advantageous compared with the latter in the presence of observation error. Interestingly, the dependence on k, and hence on the observation noise, differs between behavioral mimicry and emotional contagion. Fig. 2 shows the best strategy out of the three in the presence of observation error. We see that while the region for BM has shrunk compared with Fig. 1, the area of EC has become wider. This trend is rather obvious in Fig. 3, where we have fixed a value of w in order to see the effect of the relative strength of observation error, k. It is clear that emotional contagion is far more robust against observation error than behavioral mimicry. An intuitive reason for this result is that while behavioral mimicry
Fig. 2. The most adaptive strategy for observers is shown in the (w,R)-parameter space (with observation noise). Parameters are σ 2 ¼ 1:0 and k ¼ 0:25.
Fig. 3. The most adaptive strategy for observers is shown in the (k,R)-parameter space. Parameters are σ 2 ¼ 1:0 and w ¼ 0:2.
relies on the details of the demonstrator’s behavior, emotional contagion relies only on its emotional state (i.e. the sign of x″).
3.3. Suboptimal behavior by a demonstrator So far we have assumed γ ¼ 0; that the demonstrator’s behavior, x0 , always agrees with its optimal behavior, x. What if we introduce a suboptimal behavior by the demonstrator by introducing the deviation between x0 and x, as x' x Nð0; γ 2 Þ? In fact, the analysis of such a model turns out to be completely parallel to the one in the previous subsection; we need to simply replace τ 2 with τ2 þ γ 2 in the results in Section 3.2. Therefore, we have the following result. First, the introduction of suboptimal behavior favors independent reaction, because it is the only strategy that does not use the demonstrator’s behavior. Second, emotional contagion is far more robust than behavioral mimicry against suboptimal behavior by demonstrators.
3.4. Threshold for emotional contagion So far we have assumed that the EC strategy always spontaneously activates either one of the emotions, panic or fear. However, it may be more realistic to assume that a demonstrators’ behavior (that is, the one perceived by the observer) around x″ ¼ 0 (normal behavior) does not arouse the emotion of the observer. Here, we set the threshold for emotional contagion, a( 40) and assume that an observer with emotional contagion activates its emotion only when the behavior of the demonstrator, x″, deviates from a normal one; that is, when jx″j 4 a. Therefore, the reaction of such an EC observer to the demonstrator’s behavior is as follows. If the demonstrator’s behavior is x″ 4 a, the observer activates the emotion of panic and spontaneously takes the behavior, y0 ¼w. If the demonstrator's behavior is x″ o a, the observer activates the emotion of fear and takes the behavior, y0 ¼ w. Otherwise the observer does no activate any emotion, and keeps the normal behavior, y0 ¼0. Below we consider the observation error (τ2 4 0) but not suboptimal behavior by the demonstrator (γ 2 ¼ 0). The costs of IR and BM remain the same as in Section 3.2. As shown in Appendix B, the cost of EC is calculated as a 4Rwσ 2 a2 C EC ¼ σ 2 þ2½1 ΦðpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiÞw2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiexp½ 2ðσ 2 þ τ2 Þ σ 2 þ τ2 2π ðσ 2 þ τ 2 Þ ð4Þ
Fig. 4. The most adaptive strategy is shown in the (w,R)-parameter space for different values of emotional contagion thresholds, a ¼ 0:0, a ¼ 0:5, a ¼ 1:0, and a ¼ 1:5. Parameters are σ 2 ¼ 1:0 and k ¼ 0:25.
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where 1 ΦðtÞ ¼ pffiffiffiffiffiffi 2π
Z
t
z2 exp½ dz 2 1
ð5Þ
is the cumulative distribution function of the standard normal distribution. Fig. 4 shows the result of the comparison of the three strategies in the (w,R)-space. As one sees, the parameter region where the EC strategy is the best changes according to the threshold value, a. Fig. 5 shows that for an intermediate value of a the advantage of emotional contagion is maximum (the cost is minimum). Therefore, condition-dependent emotional contagion is the adaptive strategy. One may wonder if the BM strategy can be better-off by neglecting frequently observed behavior of the demonstrator. That is, the BM strategy chooses the demonstrator's behavior (that is, the one perceived by the observer), y0 ¼x″, when jx″j4 a, and chooses the behavior y0 ¼ 0 otherwise. However, as shown in Appendix C, such a “condition-dependent BM” strategy can never be the best strategy. More precisely, if R4 ð1 þ kÞ=2 holds then no condition-dependent BM strategies are better than the conditionindependent (a ¼0) BM strategy. If, on the other hand, R 4 ð1 þ kÞ=2 holds, then no condition-dependent BM strategies are better than the IR strategy. This fact is quite in sharp contrast to our finding that the EC strategy can become better by neglecting normal behaviors of demonstrators.
4. Discussion We have considered a situation where an observer, not having perceived the source of danger, witnesses the behavior of a demonstrator who has already perceived the danger and taken an appropriate behavior. Then we compared the fitness of observers of the three strategies, independent reaction (IR), behavioral mimicry (BM), and emotional contagion (EC). Observers who adopt independent reaction are not influenced by the behavior of the demonstrator. Observers who adopt behavioral mimicry faithfully copy the behavior of the demonstrator. Observers who adopt emotional contagion spontaneously activate one of the two emotions, panic or fear (or remain normal; see Section 3.4), and take affective reactions to those emotions automatically. By studying several variants of the basic model, we have obtained conditions for each strategy to be the most adaptive among the three. de Waal (2008) showed that there is a positive correlation between the level of empathy and that of imitation among species. He argued that the lowest-level ability required for empathy is
Fig.5. The effect of a on C EC is shown. Parameters are σ 2 ¼ 1:0, k ¼ 0:25, w ¼ 0:8, and R ¼ 0:5 (upper curve) or R ¼ 0:8 (lower curve).
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emotional contagion and that its counterpart for imitation is motor mimicry. In our model, we have considered emotional contagion and behavioral mimicry as possible strategies of observers, which we believe corresponds to de Waal (2008)’s arguments. That is, we assume that species in our model carries the basic ability of empathy and imitation. Since independent reaction is definitely another theoretical possibility, it is reasonable to compare independent reaction, behavioral mimicry, and emotional contagion as evolutionarily possible three alternatives for species with a low-level cognitive and psychological machinery. Even in a higher-level species in terms of cognitive ability, emotional contagion and motor mimicry are the bases of empathy and imitation, so we believe that our model has implications to evolutionary origins of empathy. We have considered a general situation where observation of the demonstrator’s behavior is not necessarily perfect. We have obtained the following result in Section 3.2 (see Fig. 2). Behavioral mimicry is the most adaptive strategy when the environmental similarity between the demonstrator and the observer (R) is high and when the observation noise (k) is small. Emotional contagion is the most adaptive strategy when the environmental similarity between the demonstrator and the observer (R) is intermediate to large and when the observation noise (k) is not small. Independent reaction is the most adaptive strategy when the environmental similarity between the demonstrator and the observer (R) is low. These results suggest that emotional contagion works as an efficient social learning strategy when a demonstrator and an observer share the same environment, and/or share the same source of danger. Therefore, group-living or gregariousness may be one of the key ecological factors favoring the evolution of emotional contagion. It would be interesting to compare the ability of emotional contagion between gregarious and solitary species within a taxon to see whether group-living was a strong evolutionary force favoring emotional contagion. Moreover, emotional contagion is more efficient than behavioral mimicry when the world is noisy; for example, in the species that has limited cognitive ability. This result suggests the possibility that emotional contagion can evolve even in species with low-level cognitive ability. The fact that rodent species show a high level of emotional contagion supports this prediction. In the subsequent analysis in Section 3.3, we have studied the case where a demonstrator cannot necessarily cope with the danger in an optimal way. Mathematically speaking, such a suboptimal behavior by the demonstrator has the same effect as increasing the level of observation noise, k. Therefore we conclude that when a demonstrator cannot behave adequately, it is better for observers not to rely on the demonstrator’s behavior itself but to rely on the emotion behind the behavior. For example, it has been argued that emotional contagion has an important role in maternal care (Panksepp and Panksepp, 2013; Preston and de Waal, 2002), because mothers are able to quickly recognize needs of their children through emotional contagion, or more generally, by empathy, rather than behavioral mimicry. The analysis in Section 3.4 has revealed that it is adaptive for an observer with emotional contagion to neglect normal behaviors by the demonstrator and to activate its emotion only when the demonstrator shows a deviant behavior. From this result we predict that emotional contagion should occur only when the stimulus to the demonstrator is intense, or equivalently, only when the demonstrator reacts to that stimulus intensely; there should be a threshold value for the observer’s emotional system to be activated/deactivated. In contrast, we find that observers with behavioral mimicry can never achieve a better performance by neglecting the demonstrator’s behavior. This result clearly demonstrates that emotional contagion has much flexibility and efficiency in coping with noisy environments than behavioral mimicry.
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We have studied the effect of social modulation in emotional contagion. Experimental evidence that the familiarity between a demonstrator and an observer affects emotional contagion (Langford et al., 2006; Gonzalez-Liencres et al., 2014) suggests that there should be nervous and other physiological mechanisms supporting such an unconscious regulation process. Social modulation of this kind can be modeled in our framework by conditioning w on R; that is, the affective reactions to fear/panic are unconsciously modulated by the environmental similarity between a demonstrator and an observer. It is easy to see that in the simplest model analyzed in Section 3.1, the pffiffiffiffiffiffi ^ ¼ 2Rσ = 2π , cost of the EC observer (Eq. 3) is minimized at w suggesting that the optimal w-value changes with the environmental similarity, R. Therefore our model framework can support an evolutionary advantage of similarity-based social modulation. Note that the environmental similarity, R, is an extrinsic parameter, so repeated social interactions between a demonstrator and an observer will enable them to gradually learn this value. In our model, we did not incorporate the fitness cost of maintaining nervous and physiological systems supporting emotional contagion. Recent findings suggest an important role of oxytocin in emotional empathy in humans (Barraza and Zak, 2009; Hurlemann et al., 2010; Wu et al., 2012; Smith et al., 2014), also in pigs (Reimert et al., 2015). Revealing selection pressure favoring the evolution of such neuropeptides is ultimately important for understanding where the ability of empathy comes from. In conclusion, emotional contagion is adaptive, compared with independent reaction and behavioral mimicry, when the environmental similarity between a demonstrator and an observer is intermediate to high (intermediate or high R), when the observation of demonstrator's behavior is imperfect (high k), when the demonstrator cannot take the optimal behavior (high γ ), and when the observer does not activate emotion toward the demonstrator's normal behavior (intermediate a). These results suggest that emotional contagion is likely to evolve in group-living species even with limited cognitive ability.
Acknowledgments This research was supported in part by Grant-in-Aid for Scientific Research on Innovative Areas No. 25118006, “The Evolutionary Origin and Neural Basis of the Empathetic Systems” to H.O.
Appendix A We calculate the cost for each strategy for the model in Section 3.2. Results in Section 3.1 immediately follow when we set τ ¼ 0. We recall that, from the assumption of bivariate normal distribution, the density function P(x) of optimal behavior x, and the conditional density function P(y|x) of optimal behavior y given x, are respectively given by 1 x2 PðxÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiexp 2 2σ 2πσ 2
Given those, costs are calculated as Z 1 Z 1 C IR ¼ ðy 0Þ2 Pðyj xÞPðxÞdxdy Z 11 1 y2 PðyÞdy ¼ 1
¼ σ2 ;
ðA:1Þ
Z C BM ¼
1
Z
Z
1
1
ðy x″Þ2 Pðyj xÞPðxÞZðx″ xÞdx″dxdy
1 1 1 Z 1 Z 1 Z1
¼
Z 11 Z 11
¼
þ
1
ðy x þ x x″Þ2 Pðyj xÞPðxÞZðx″ xÞdx″dxdy
ðy xÞ2 Pðyj xÞPðxÞdxdy Z 1 Pðyj xÞPðxÞ ½2ðy xÞðx x″Þ
Z 11 Z 11 1
1
1
þ ðx x″Þ2 Zðx″ xÞdx″dxdy Z 1 Z 1 ¼ 2ð1 RÞσ 2 þ τ2 Pðyj xÞPðxÞdxdy ¼ 2ð1 RÞσ 2 þ τ2 ; and
Z
C EC ¼ Z þ ¼2
∞
0 0
Z
Z
∞
Z
∞
∞ ∞ ∞ Z ∞
Z
1
ðA:2Þ
ðy wÞ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00
ðyþ wÞ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00
∞ ∞ ∞ Z ∞Z ∞ Z ∞ 0
1
∞ ∞Z ∞
ðy wÞ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00
i ð1 R2 Þσ 2 þ w2 2Rwx þR2 x2 PðxÞZðx00 xÞdxdx00 0 ∞ Z ∞Z ∞ h i 2 ¼ pffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ ðRx wÞ2 2 2 2πτ 2πσ 0 ∞ " # x2 ðx x00 Þ2 exp 2 dxdx00 2σ 2τ2 Z ∞Z ∞ h i 2 ¼ pffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ ðRx wÞ2 2 2 2πτ 2πσ 0 ∞ "
# 2 x x00 σ 2 =ðσ 2 þτ2 Þ x002 exp dxdx00 2σ 2 τ2 =ðσ 2 þ τ2 Þ 2ðσ 2 þ τ2 Þ Z ∞Z ∞ 2 ½ð1 R2 Þσ 2 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2πσ 2 τ2 =ðσ 2 þ τ2 Þ 2πðσ 2 þ τ2 Þ 0 ∞
2 þ R x x00 σ 2 =ðσ 2 þ τ2 Þ þ Rx00 σ 2 =ðσ 2 þ τ2 Þ w "
# 2 x x00 σ 2 =ðσ 2 þ τ2 Þ x002 dxdx00 exp 2 2 2 2 2σ τ =ðσ þ τ Þ 2ðσ 2 þ τ2 Þ Z ∞h
2 2 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ Rx00 σ 2 =ðσ 2 þτ2 Þ w 2πðσ 2 þ τ2 Þ 0 i x002 dx00 þ R2 σ 2 τ2 =ðσ 2 þ τ2 Þ exp 2 2 2ðσ þ τ Þ ¼2
h
∞
¼ ð1 R2 Þσ 2 þ R2 σ 2 τ2 =ðσ 2 þτ2 Þ þ w2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 ðσ 2 þ τ2 Þ pffiffiffiffiffiffi þ R2 σ 4 =ðσ 2 þ τ2 Þ Rwσ 2 =ðσ 2 þ τ2 Þ 2π 4Rwσ 2 ¼ σ 2 þ w2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi: 2πðσ 2 þ τ2 Þ
ðA:3Þ
" # 1 ðy RxÞ2 Pðyj xÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiexp : 2ð1 R2 Þσ 2 2πð1 R2 Þσ 2
Appendix B
Also, the density function ZðξÞ of observation noise, ξ ¼ x″ x, follows the normal distribution of mean 0 and variance τ2 ; " # 1 ξ2 ZðξÞ ¼ pffiffiffiffiffiffiffiffiffiffiexp 2 : 2τ 2πτ2
Here we calculate the cost of EC strategy which has the emotional contagion thresholds, a and –a, and the corresponding behaviors, w and –w. We have Z ∞Z ∞ Z ∞ C EC ¼ ðy wÞ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 a
∞
∞
W. Nakahashi, H. Ohtsuki / Journal of Theoretical Biology 380 (2015) 480–488
Z þ Z þ ¼2
Z
∞
Z
∞
∞ ∞ ∞ a Z ∞ Z ∞
a Z ∞
Z þ
a
a a 0
∞ Z ∞
Z
∞ Z ∞
ðyþ wÞ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00
ðy 0Þ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00
ðy wÞ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 y2 Pðyj xÞPðxÞZðx00 xÞdxdydx00
∞ ∞ ∞ Z ∞ ∞
∞
2 Z ∞" 2 Rσ 2 00 ð1 R2 Þσ 2 þ 2 x w ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 σ þτ 2πðσ 2 þ τ2 Þ a # 2 2 2 002 R σ τ x dx00 exp þ 2 σ þ τ2 2ðσ 2 þ τ2 Þ 2 Z a" 2 Rσ 2 00 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi þ ð1 R2 Þσ 2 þ 2 x 2 σ þτ 2πðσ 2 þ τ2 Þ 0 # 2 2 2 002 R σ τ x dx00 exp þ 2 σ þ τ2 2ðσ 2 þ τ2 Þ 2 # Z ∞ " 1 R2 σ 2 τ 2 Rσ 2 00 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ 2 þ x σ þ τ2 σ 2 þ τ2 2πðσ 2 þ τ2 Þ ∞ x002 dx00 exp 2ðσ 2 þ τ2 Þ Z ∞ 2 2Rwσ 2 00 x002 dx00 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðw2 2 x Þexp σ þ τ2 2ðσ 2 þ τ2 Þ 2πðσ 2 þ τ2 Þ a 2 R2 σ 2 τ2 Rσ 2 ¼ ð1 R2 Þσ 2 þ 2 þ ðσ 2 þ τ2 Þ σ þτ2 σ 2 þ τ2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi a 4Rwσ 2 σ 2 þ τ2 pffiffiffiffiffiffi þ 2 1 Φ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi w2 ðσ 2 þ τ2 Þ 2π σ 2 þ τ2 a2 exp 2ðσ 2 þ τ2 Þ a 4Rwσ 2 ¼ σ 2 þ 2 1 Φ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi w2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 σ þτ 2πðσ 2 þ τ2 Þ 2 a exp : ðB:1Þ 2ðσ 2 þ τ2 Þ
# R2 σ 2 τ2 x002 þ 2 dx00 exp 2 2 2 σ þτ 2ðσ þ τ Þ Z ∞ " 1 R2 σ 2 τ2 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ 2 σ þ τ2 2πðσ 2 þ τ2 Þ ∞ # 2 Rσ 2 00 x002 dx00 x þ 2 exp 2 2 2 σ þτ 2ðσ þ τ Þ Z ∞ 2 2Rσ 2 002 x002 dx00 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 2 Þx exp σ þ τ2 2ðσ 2 þτ2 Þ 2πðσ 2 þ τ2 Þ a 2 R2 σ 2 τ2 Rσ 2 ¼ ð1 R2 Þσ 2 þ 2 þ ðσ 2 þ τ2 Þ σ þτ2 σ 2 þ τ2 ( pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Rσ 2 a σ 2 þ τ2 a2 pffiffiffiffiffiffi exp Þ þ 2ð1 2 2 2 2 σ þτ 2ðσ þ τ Þ 2π a þ ðσ 2 þ τ2 Þ 1 Φ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ 2 þ τ2 (
a a2 ¼ σ 2 þ 2 ð1 2RÞσ 2 þτ2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiexp 2ðσ 2 þ τ2 Þ 2πðσ 2 þ τ2 Þ a þ 1 Φ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi : σ 2 þ τ2
487
ðC:1Þ
therefore,
"
1 a2 =ðσ 2 þ τ2 Þ ∂C BM a2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp ¼ 2 ð1 2RÞσ 2 þ τ2 ∂a 2ðσ 2 þ τ2 Þ 2πðσ 2 þ τ2 Þ # 1 a2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiexp 2 þ τ2 Þ 2 2 2ðσ 2πðσ þ τ Þ
2a2 ð1 2RÞσ 2 þ τ2 a2 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiexp ¼ : 2 2 2ðσ þτ Þ ðσ 2 þ τ2 Þ 2πðσ 2 þ τ2 Þ
ðC:2Þ
When ð1 2RÞσ 2 þ τ2 is negative, i.e. when R 4 ðσ 2 þ τ2 Þ= 2σ 2 ¼ ð1 þ kÞ=2, we have ∂C BM =∂a o 0. In contrast, when ð1 2RÞσ 2 þ τ2 is positive, i.e. R o ð1 þ kÞ=2, we have ∂C BM =∂a o 0. Therefore, the cost of BM is the smallest at a^ ¼ 0 when R 4ð1 þkÞ=2, and at a^ ¼ 1 when R o ð1 þ kÞ=2. References
Appendix C Suppose that the “condition-dependent“ BM strategy chooses the demonstrator's observed behavior y0 ¼x″ when jx″j 4a, and chooses the behavior y0 ¼0 otherwise. The cost of such a BM strategy is Z ∞Z ∞ Z ∞ ðy x00 Þ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 C BM ¼ a ∞ ∞ Z a Z ∞ Z ∞ þ ðy x00 Þ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 ∞ ∞ ∞ Z a Z ∞ Z ∞ þ ðy 0Þ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 a ∞ ∞ Z ∞ Z ∞ Z ∞ ¼2 ðy x00 Þ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 a ∞ ∞ Z aZ ∞ Z ∞ y2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 þ 0
∞
∞
2 Z ∞" 2 Rσ 2 00 ð1 R2 Þσ 2 þ 2 x x00 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 σ þτ 2πðσ 2 þ τ2 Þ a # 2 2 2 002 R σ τ x dx00 þ 2 exp σ þτ2 2ðσ 2 þ τ2 Þ 2 Z a" 2 Rσ 2 00 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ 2 x σ þ τ2 2πðσ 2 þ τ2 Þ 0
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Contents lists available at ScienceDirect
Journal of Theoretical Biology journal homepage: www.elsevier.com/locate/yjtbi
When is emotional contagion adaptive? Wataru Nakahashi n, Hisashi Ohtsuki School of Advanced Sciences, SOKENDAI (The Graduate University for Advanced Studies), Shonan Village, Hayama 240-0193, Kanagawa, Japan
H I G H L I G H T S
We study conditions under which emotional contagion is the most adaptive strategy. Emotional contagion (EC) is adaptive when individuals share the environment. EC is adaptive when observation is error-prone. EC is adaptive when observers pay attention only to infrequent behavior.
art ic l e i nf o
a b s t r a c t
Article history: Received 20 January 2015 Received in revised form 5 June 2015 Accepted 8 June 2015 Available online 23 June 2015
Empathy plays an important role in animal social behavior. Since emotional contagion forms one of the bases of empathy, here we study conditions for emotional contagion to be adaptive, compared with other behavioral rules such as behavioral mimicry. We consider the situation where the focal individual ( ¼observer) reacts to a behavior of another individual (¼ demonstrator). By emotional contagion one spontaneously copies the emotional state of the demonstrator and takes a behavior driven by that emotion. By behavioral mimicry, in contrast, one copies the behavior of the demonstrator itself. Through mathematical models we show that emotional contagion is adaptive when the environmental similarity between the demonstrator and the observer is intermediate. The advantage of adopting emotional contagion over behavioral mimicry increases when observing others’ behavior is difficult or cognitively demanding. We show that emotional contagion is often a more flexible strategy than behavioral mimicry in order to cope with the living environment. In other words, emotional contagion often works as a better social learning strategy. These results suggest some ecological conditions that would favor the evolution of emotional contagion, and give a part of the explanations of why emotional contagion is frequently observed in group-living animals. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Empathy Behavioral mimicry Social learning Evolution Mathematical model
1. Introduction Empathy is one of the most important emotional processes for social interactions in humans. Although the definition of empathy varies among researchers, the essential component of empathy is the instinctive recognition of and a reaction to others’ emotions (Gerdes et al., 2010; Preston and de Waal, 2002). Recently, evidence of empathy in other animals is increasing (Langford et al., 2006; Plotnik and de Waal, 2014; Watanabe and Ono, 1986), suggesting that empathic sensitivity should be adaptive in many animals. Since the underlying machinery of empathy, including its neurophysiological basis, can be very complex, a variety of factors could be relevant to its evolution. Some researchers recently found dissociation between emotional and cognitive empathy
n
Corresponding author. Tel.: þ 81 46 858 1580. E-mail address: [email protected] (W. Nakahashi).
http://dx.doi.org/10.1016/j.jtbi.2015.06.014 0022-5193/& 2015 Elsevier Ltd. All rights reserved.
(Shamay-Tsoory et al., 2009). Emotional empathy often refers to a spontaneous change of one’s emotional state accompanied with affective reactions to that, while cognitive empathy requires the cognitive perspective-taking ability to simulate others’ psychological processes (Pepping and Timmermans, 2012). In particular, the most primitive and basic form of emotional empathy is emotional contagion, which means a spontaneous copying of others’ emotional state followed by an affective reaction to that. Emotional contagion has drawn wide attention from researchers in order to understand the origin of empathy (de Waal, 2008, 2009, 2012; Panksepp and Panksepp, 2013). Therefore, in this paper, we focus on evolutionary conditions for emotional contagion to be adaptive. Note that emotional contagion and emotional empathy are different concepts, because the former always refers to the copying of other’s emotion, while the latter includes spontaneous arousal of a different emotion from that of the target. For example, spontaneous activation of a positive emotion by perceiving others’ negative emotion, which is called Schadenfreude, is an example of emotional empathy that is not emotional contagion. Biological
W. Nakahashi, H. Ohtsuki / Journal of Theoretical Biology 380 (2015) 480–488
definition of emotion is still debatable (Waal., 2011de), but one’s emotional state is often identified by the activity of autonomic nervous system (Kreibig 2010) as well as by various physiological measures, or sometimes indirectly by its behavior. Various studies on humans show examples of emotional contagion (Hatfield et al., 1993; Fowler and Christakis, 2008; Hill et al., 2010). Laboratory rodents such as rats and mice are excellent animal models to study the contagion of negative emotions, including pain, panic and fear (Panksepp and Panksepp, 2013). For example, an observer who witnesses its conspecific receiving electric footshock develops freezing behavior in rats (Atsak et al., 2011) and in mice (Jeon et al., 2010), which is a good example of emotional contagion. Recent studies have shown that yawing is contagions in dogs (Romero et al., 2013) and in wolves (Romero et al., 2014). Emotion is not only copied but can also be socially modulated. For example, a mouse injected with acetic acid writhes more when observing another mice simultaneously writhing with the same treatment than when being isolated, but it writhes less while observing an intact mouse (Langford et al., 2006). Such social modulation between two individuals is more likely to occur if they are cagemates or if they are housed together for a long period. Importantly, the brain process of such social modulation is believed to work completely unconsciously by using the circuits for emotional learning (Solms and Panksepp, 2012; Panksepp and Panksepp, 2013), which means that social modulation can reasonably be understood as one form of emotional contagion, not as a process requiring cognitive perspective-taking. From an evolutionary point of view, emotional contagion can be considered to be one of the ways to learn environmental information from others. For example, if an individual shows the emotion of fear, there may exist a threat causing that emotion in the neighborhood, which may also affect observers. In such a case, an observer may benefit if he/she evokes the emotion of fear and takes a corresponding affective reaction to that. Therefore, we can regard emotional contagion as a kind of “social learning” strategy. Although many researchers have theoretically investigated the evolution of various kinds of social learning strategies (Acerbi et al., 2011; Enquist et al., 2007; Feldman et al., 1996; Henrich and Boyd, 1998; McElreath and Strimling, 2008; Nakahashi, 2007, 2013; Nakahashi et al., 2012), no researchers have considered yet the evolution of emotional contagion as a strategy of social learning. There are mainly two qualitative differences between previous models and ours. First, previous models of social learning have mainly concentrated on the role of imitation, which is a fully cognitive process. For example, learning how to make a stone tool from a teacher is a highly cognitive process, and emotional contagion is not relevant at all. Those previous models assumed that individuals who are engaged in social learning copies the behavior of the target, but it was not necessary for researchers to distinguish between behavior and emotion. Second, the time scale of social learning is completely different. Previous models have mainly studied cultural evolution, where information is often transmitted intergenerationally. They have found that social learning becomes more important when the environment is more stable between generations (Boyd and Richerson, 1988; Feldman et al., 1996; Nakahashi, 2010; Rogers, 1988). In contrast, when we talk about emotional contagion, it always means the instantaneous transmission of information, usually within seconds, between individuals. In that case, by analogy to the result of intragenerational social learning, we can naively expect that emotional contagion should be evolutionarily beneficial if the adaptive behavior of a demonstrator (the one who first initiated a behavior) is also adaptive for observers (those who watch the behavior of the demonstrator). Therefore, we hypothesize that the correlation between the optimal behavior of the demonstrator and that of
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observers should be a key ecological parameter for the evolution of emotional contagion. In this paper, we regard emotional contagion as an evolutionary strategy of dealing with real world events. Our model is not necessarily specific to a single particular species, but imagining rodent individuals, such as rats or mice, may greatly help readers intuitively understand our model. In particular, we will consider the situation where individuals are about to be exposed to some types of danger, such as aggression or predation. There, negative emotions such as fear and/or panic are likely to be triggered. Those emotions can contribute to one's survival by various ways. For example, fear can cause freezing, which may help them hide themselves from predators. In contrast, panic can cause frequent and abnormal movements, which may also help them escape from predators’ chase and attack. As an alternative evolutionary strategy to emotional contagion, we also consider behavioral mimicry, which means a precise copying of demonstrator’s behavior without copying its emotion. Generally speaking, emotional contagion is a fast process compared with behavioral mimicry because one need not watch the whole behavior of the demonstrator. However, emotional contagion may not be accurate, because the demonstrator’s emotion, that is a physiological change triggered by the activation or deactivation of autonomic nervous system, is often not directly observable, Instead, emotional contagion is achieved only via visual, auditory, or olfactory cues (Meeren et al., 2005). This feature of emotional contagion is in sharp contrast to behavioral mimicry, where most of the demonstrator's behavior is often directly observable. In this paper, we will model emotional contagion as a process of abstracting information from demonstrator’s behavior by spontaneous activation of one’s own emotion. Therefore an observer who adopts emotional contagion loses a part of information in the demonstrator’s behavior. In contrast, an observer who adopts behavioral mimicry is more accurate in copying the demonstrator, because it relies on a directly observable piece of information, that is, behavior. In addition to these two strategies, we also consider a third possible evolutionary strategy, called independent reaction, as a benchmark strategy. We assume that an observer who adopts independent reaction neglects the behavior of the demonstrator or any sensory cues it provides, and behaves completely independently of the demonstrator. It is analogous to “individual learning” strategy in studies of cultural evolution, where an individual learner explores the environment by itself via trial-and-errors. In the following, we will compare the performance of the three strategies, emotional contagion, behavioral mimicry, and independent reaction, under a wide variety of conditions, and study which strategy is the most adaptive. We will discuss how our results correspond to empirical and experimental evidence of emotional contagion in animals and in humans.
2. Basic models 2.1. Basic assumptions We will consider the interaction between two individuals, a demonstrator and an observer. We assume the following scenario. First, a demonstrator finds the source of danger. It could be either via a visual cue (the demonstrator sees a predator approaching), an auditory cue (it hears a call or noise), an olfactory cue (it smells a predator), a direct contact (it receives a physical attack), or their combinations. After directly perceiving the danger, the demonstrator takes a behavior. For simplicity, here we model a variety of behaviors by one-dimensional real values. A best example of behavior parameterized by a continuous real value can be the degree of activity, where zero represents a normal status, a
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Table 1 Symbols used in this paper. Symbol
Usage
x x0 x″ y y0 w a R σ2 τ2 k γ2 CIR CBM CEC
Demonstrator’s optimal behavior Demonstrator’s actual behavior Demonstrator’s behavior perceived by the observer Observer’s optimal behavior Observer’s actual behavior Parameter specifying the observer’s affective reactions to emotions Parameter specifying the threshold of emotional contagion Environmental similarity between a demonstrator and an observer Variance of optimal behavior Variance of observation noise Relative size of observation noise ( ¼ τ2 / σ2) Variance of the deviation between the demonstrator’s suboptimal and optimal behaviors Fitness cost of independent reaction strategy Fitness cost of behavioral mimicry strategy Fitness cost of emotional contagion strategy
positive value represents a fast, frequent, and large movement (panic behavior), and a negative value represents a slow, infrequent, and small movement (fear behavior such as freezing). We assume that there is an optimal behavior x for the demonstrator that minimizes the harm it receives, and that the demonstrator, who directly perceived the source of danger and hence has some information about how to deal with the situation, is able to choose a suboptimal behavior, x0 that is usually close to x. Table 1 summarizes the symbols used in this paper. In contrast, we assume that the observer has not perceived yet the source of danger. Therefore, there is strict asymmetry between what the demonstrator knows and what the observer does. Here we assume that there is an optimal behavior y for the observer that minimizes the harm it receives. Note that y is not necessarily the same as x, because the observer is a different individual from the demonstrator, at a slightly different spatial position (but nearby the demonstrator) with potentially different physical abilities. Rather, it is natural to assume that x and y be positively correlated to some extent (see the mathematical formulation below), depending on the type of danger. However, because of the information asymmetry described above, the observer has no direct information about the source of the danger at all, and hence has no direct ways to tell its optimal behavior y. Given these, we further assume that the observer has an opportunity to witness the demonstrator’s behavior, x0 . The three strategies, independent reaction (IR), behavioral mimicry (BM), and emotional contagion (EC) differ in their reaction to x0 . Let y0 represent the behavior chosen by the observer in reaction to the demonstrator’s behavior. An observer who adopts independent reaction neglects the demonstrator’s behavior x0 , and therefore it stays at a normal activity level, y0 ¼ 0. An observer who adopts behavioral mimicry tries to copy the behavior of the demonstrator. In the simplest case without any observation noise, the observer mimics the body movement of the demonstrator, and hence it chooses the action y0 ¼ x0 (see Section 3.2 for the modification of this assumption). An observer who adopts emotional contagion has the ability to spontaneously activate or deactivate its autonomic nervous system according to the demonstrator’s behavior (emotional contagion). However, as we mentioned in Introduction, changing one’s emotional state to exactly match with that of the demonstrator is virtually impossible because of the limited observability of other’s physiological status. We believe that the simplest alternative should be to abandon exact copying of the demonstrator’s emotional state, but to develop typical emotions accompanied with some affective behaviors. In our example of one-dimensional behaviors, we assume that if the demonstrator’s behavior x0 is more active than the normal state (i.e. x0 40) then
the observer with the emotional contagion strategy develops the emotion named panic, and chooses the behavior, y0 ¼ w (40), corresponding to a typical panic behavior. On the other hand, if the demonstrator's behavior x0 is less active than the normal state (i.e. x0 o0) then the observer with the emotional contagion strategy develops the emotion named fear, and chooses the behavior y0 ¼ w (o0), corresponding to a typical freezing behavior. In other words, an observer who adopts emotional contagion can discriminate only between panic and fear, and chooses a behavior correspondingly. Note, therefore, that there is no one-to-one correspondence between a behavior and an emotion. Rather, we assume that a continuum of behaviors can activate the same single emotion. It is interesting to see how social modulation affects the value of w according to the relationship between demonstrators and observers (see Section 4). In any way, we once again stress that the activation or deactivation of the observer’s physiological status is an automatic and spontaneous process of brain based on the circuits of emotional learning (Solms and Panksepp, 2012; Panksepp and Panksepp, 2013), and therefore the development of emotions after perceiving the demonstrator’s behavior, which is modeled in our framework, is not cognitive empathy but emotional contagion.
2.2. Mathematical formulations In our model, we assume for simplicity that the optimal behavior of a demonstrator, x, normally distributes in a onedimensional space with variance σ2, x Nð0; σ 2 Þ, which means that individuals are exposed to a variety of challenges from the environment. The optimal behavior of an observer, y, also normally distributes as y Nð0; σ 2 Þ, because we assume that those two individuals are in the same environment. However, the optimal behaviors of the two individuals, x and y, may not agree. They may instead have a positive correlation with each other even in the same threatening event. Therefore, we assume that the pair (x,y) of the optimal behavior of a demonstrator, x, and that of an observer, y, follows a bivariate normal distribution with mean (0,0) as ! !! ! x 0 σ 2 Rσ 2 σ 2 Rσ 2 N ; , where is the y 0 Rσ 2 σ 2 Rσ 2 σ 2 variance-covariance matrix and R is the correlation coefficient. In the following we consider non-negative correlation only, so we assume 0 r R r 1. We call R “environmental similarity” between a demonstrator and an observer. Note that the optimal behavior of the observer conditioned on that the demonstrator’s optimal
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behavior is x, which is denoted by yx , also normally distributes as y NðRx; ð1 R2 Þσ 2 Þ. x
As we mentioned above, the demonstrator is not necessarily able to choose the optimal behavior x, but may choose a suboptimal behavior, x0 , because of, for example, its limited behavioral ability. We model this limitation by assuming that the difference x0 x follows the normal distribution Nð0; γ 2 Þ, where γ 2 represents the size of deviation from the optimal behavior. In most of the analysis below except in Section 3.3, however, we will assume γ ¼ 0 for simplicity and therefore make no distinction between x and x0 . The effect of γ is studied in detail in Section 3.3. Finally, we introduce the criterion to judge which evolutionary strategy is more adaptive. When an observer chooses the behavior y0 but its true optimal behavior is y, we assume that the observer incurs the fitness cost of ðy0 yÞ2 due to the deviation from the optimal behavior. Predation risk is one example of such cost. The observer's goal is to minimize this deviation.
3. Results 3.1. Basic result We consider the three strategies of observers, independent reaction (IR), behavioral mimicry (BM), and emotional contagion (EC). As mentioned above, an observer with the IR strategy does not use information obtained from the demonstrator, so it always chooses to behave normally, x ¼0. The cost of IR is, Z 1 Z 1 C IR ¼ ðy 0Þ2 Pðyj xÞPðxÞdxdy Z ¼
1 1
1
y2 PðyÞdy
1
¼ σ2;
483
1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffi 2π ð1 R2 Þσ 2 2πσ 2 # Z 1 "Z 1 ðy RxÞ2 x2 2 ðy xÞ exp½ dy exp½ 2 dx 2 2 2 σ 2ð1 R Þσ 1 1 Z 1 h i 2 1 x ¼ pffiffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ ð1 RÞ2 x2 exp½ 2 dx 2σ 2πσ 2 1 ¼ 2ð1 RÞσ 2 :
ð2Þ
Remember that the parameter R is the environmental similarity between the demonstrator and the observer. Therefore, the BM strategy is advantageous over IR (C BM o C IR ) when R 4 1=2. This condition suggests that if the observer very much shares the environment with the demonstrator (R 41/2) then behavioral mimicry is a good rule-of-thumb to cope with the environment. In contrast to the BM strategy, an observer with the EC strategy takes the behavior w (i.e. a behavior driven by panic) when the demonstrator’s behavior is more active than normal (i.e. x4 0), and takes the behavior w (i.e. a behavior driven by fear) when the demonstrator’s behavior is less active than normal (i.e. xo 0). Here we assume w4 0. The cost of EC is a function of w and is given by Z 1Z 1 C EC ¼ ðy wÞ2 Pðyj xÞPðxÞdydx 1
0
Z 1 ðy þ wÞ2 Pðyj xÞPðxÞdydx þ 1 1 Z 1Z 1 ¼2 ðy wÞ2 Pðyj xÞPðxÞdydx 0 1 Z 1 Z 1 ½ðy RxÞ ðw RxÞ2 Pðyj xÞdy PðxÞdx ¼2 0 1 Z 1 ½ð1 R2 Þσ 2 þ ðw RxÞ2 PðxÞdx ¼2 Z
0
0
ð1Þ
where P(x) and P(y|x) respectively represent the probability density functions of x and yx (y conditioned on x) (see Appendix A). Notice that the cost of IR is equal to the variance of the optimal behavior, y. An observer with the BM strategy imitates the behavior of the demonstrator, x (we assume that the demonstrator’s behavior agrees with its optimal one, γ ¼0), so its own behavior is also x. Then, the cost of BM is R1 R1 C BM ¼ 1 1 ðy xÞ2 Pðyj xÞPðxÞdxdy
4Rwσ ¼ σ 2 þw2 pffiffiffiffiffiffi : 2π
ð3Þ
Fig. 1 summarizes the result, showingp the best ffiffiffiffiffiffiffiffi ffi strategy out of the three candidates. When w exceeds 2=π σ 0:798σ , emotional contagion can never be the best strategy. This makes sense, because a large w means excessive behaviors driven by emotions (panic or fear), which can never be advantageous (for example, panic drives a pathologically active movement, ffi fear triggers too pffiffiffiffiffiffiffiffior long freezing). In contrast, when 0 o w o 2=π σ 0:798σ , emotional contagion is the best strategy if the environmental similarity, R, is intermediate. It is trivial that if R¼1 behavioral mimicry is always the best, because the observer’s optimal behavior is exactly the same as the demonstrator’s optimal behavior. In other words, the demonstrator’s behavior itself is a valuable piece of information to the observer. However, for a reasonable intermediate value of R, we found that adopting emotional contagion can be advantageous over behavioral mimicry. This is intuitively because, under an intermediate correlation between x and y, details of the demonstrator’s behavior becomes less “valuable” information. 3.2. With observation noise
Fig. 1. The most adaptive strategy for observers is shown in the (w,R)-parameter space (without observation noise). The parameter is σ 2 ¼ 1:0.
Because of the limitation in cognitive ability, individuals may not accurately observe others’ behavior. This limitation may suppress the advantage of behavioral mimicry and emotional contagion, because they rely on the perception of the demonstrator’s behavior. Here we assume that the actual behavior of a demonstrator, x0 , is perceived as x″ by an observer, where the noise x″ x0 normally distributes as x″ x0 Nð0; τ2 Þ. Here the new parameter τ2 represents the noise level of observation. In this framework, IR always adopts the behavior y0 ¼ 0, BM adopts the behavior y0 ¼ x″, and EC adopts the behavior y0 ¼ w when x″40 and the behavior y0 ¼ w when x″o0. As shown in
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Appendix A, the cost of observers of each strategy is given as ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C IR ¼ σ 2 , C BM ¼ 2ð1 RÞσ 2 þ τ2 , and C EC ¼ σ 2 þ w2 4Rwσ 2 = p 2π ðσ 2 þ τ2 Þ, respectively. Let k ¼ τ2 =σ 2 be the relative magnitude of observation error to that of the variation in optimal behaviors. We found that C BM o C IR holds when R 4 ð1 þ kÞ=2. Therefore, a positive k hinders the advantage of behavioral mimicry. This makes sense because the former depends on the observation of the demonstrator’s behavior, whereas the latter does not. This tendency is the same when we compare the performance of emotional contagion and independent reaction; the former becomes less advantageous compared with the latter in the presence of observation error. Interestingly, the dependence on k, and hence on the observation noise, differs between behavioral mimicry and emotional contagion. Fig. 2 shows the best strategy out of the three in the presence of observation error. We see that while the region for BM has shrunk compared with Fig. 1, the area of EC has become wider. This trend is rather obvious in Fig. 3, where we have fixed a value of w in order to see the effect of the relative strength of observation error, k. It is clear that emotional contagion is far more robust against observation error than behavioral mimicry. An intuitive reason for this result is that while behavioral mimicry
Fig. 2. The most adaptive strategy for observers is shown in the (w,R)-parameter space (with observation noise). Parameters are σ 2 ¼ 1:0 and k ¼ 0:25.
Fig. 3. The most adaptive strategy for observers is shown in the (k,R)-parameter space. Parameters are σ 2 ¼ 1:0 and w ¼ 0:2.
relies on the details of the demonstrator’s behavior, emotional contagion relies only on its emotional state (i.e. the sign of x″).
3.3. Suboptimal behavior by a demonstrator So far we have assumed γ ¼ 0; that the demonstrator’s behavior, x0 , always agrees with its optimal behavior, x. What if we introduce a suboptimal behavior by the demonstrator by introducing the deviation between x0 and x, as x' x Nð0; γ 2 Þ? In fact, the analysis of such a model turns out to be completely parallel to the one in the previous subsection; we need to simply replace τ 2 with τ2 þ γ 2 in the results in Section 3.2. Therefore, we have the following result. First, the introduction of suboptimal behavior favors independent reaction, because it is the only strategy that does not use the demonstrator’s behavior. Second, emotional contagion is far more robust than behavioral mimicry against suboptimal behavior by demonstrators.
3.4. Threshold for emotional contagion So far we have assumed that the EC strategy always spontaneously activates either one of the emotions, panic or fear. However, it may be more realistic to assume that a demonstrators’ behavior (that is, the one perceived by the observer) around x″ ¼ 0 (normal behavior) does not arouse the emotion of the observer. Here, we set the threshold for emotional contagion, a( 40) and assume that an observer with emotional contagion activates its emotion only when the behavior of the demonstrator, x″, deviates from a normal one; that is, when jx″j 4 a. Therefore, the reaction of such an EC observer to the demonstrator’s behavior is as follows. If the demonstrator’s behavior is x″ 4 a, the observer activates the emotion of panic and spontaneously takes the behavior, y0 ¼w. If the demonstrator's behavior is x″ o a, the observer activates the emotion of fear and takes the behavior, y0 ¼ w. Otherwise the observer does no activate any emotion, and keeps the normal behavior, y0 ¼0. Below we consider the observation error (τ2 4 0) but not suboptimal behavior by the demonstrator (γ 2 ¼ 0). The costs of IR and BM remain the same as in Section 3.2. As shown in Appendix B, the cost of EC is calculated as a 4Rwσ 2 a2 C EC ¼ σ 2 þ2½1 ΦðpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiÞw2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiexp½ 2ðσ 2 þ τ2 Þ σ 2 þ τ2 2π ðσ 2 þ τ 2 Þ ð4Þ
Fig. 4. The most adaptive strategy is shown in the (w,R)-parameter space for different values of emotional contagion thresholds, a ¼ 0:0, a ¼ 0:5, a ¼ 1:0, and a ¼ 1:5. Parameters are σ 2 ¼ 1:0 and k ¼ 0:25.
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where 1 ΦðtÞ ¼ pffiffiffiffiffiffi 2π
Z
t
z2 exp½ dz 2 1
ð5Þ
is the cumulative distribution function of the standard normal distribution. Fig. 4 shows the result of the comparison of the three strategies in the (w,R)-space. As one sees, the parameter region where the EC strategy is the best changes according to the threshold value, a. Fig. 5 shows that for an intermediate value of a the advantage of emotional contagion is maximum (the cost is minimum). Therefore, condition-dependent emotional contagion is the adaptive strategy. One may wonder if the BM strategy can be better-off by neglecting frequently observed behavior of the demonstrator. That is, the BM strategy chooses the demonstrator's behavior (that is, the one perceived by the observer), y0 ¼x″, when jx″j4 a, and chooses the behavior y0 ¼ 0 otherwise. However, as shown in Appendix C, such a “condition-dependent BM” strategy can never be the best strategy. More precisely, if R4 ð1 þ kÞ=2 holds then no condition-dependent BM strategies are better than the conditionindependent (a ¼0) BM strategy. If, on the other hand, R 4 ð1 þ kÞ=2 holds, then no condition-dependent BM strategies are better than the IR strategy. This fact is quite in sharp contrast to our finding that the EC strategy can become better by neglecting normal behaviors of demonstrators.
4. Discussion We have considered a situation where an observer, not having perceived the source of danger, witnesses the behavior of a demonstrator who has already perceived the danger and taken an appropriate behavior. Then we compared the fitness of observers of the three strategies, independent reaction (IR), behavioral mimicry (BM), and emotional contagion (EC). Observers who adopt independent reaction are not influenced by the behavior of the demonstrator. Observers who adopt behavioral mimicry faithfully copy the behavior of the demonstrator. Observers who adopt emotional contagion spontaneously activate one of the two emotions, panic or fear (or remain normal; see Section 3.4), and take affective reactions to those emotions automatically. By studying several variants of the basic model, we have obtained conditions for each strategy to be the most adaptive among the three. de Waal (2008) showed that there is a positive correlation between the level of empathy and that of imitation among species. He argued that the lowest-level ability required for empathy is
Fig.5. The effect of a on C EC is shown. Parameters are σ 2 ¼ 1:0, k ¼ 0:25, w ¼ 0:8, and R ¼ 0:5 (upper curve) or R ¼ 0:8 (lower curve).
485
emotional contagion and that its counterpart for imitation is motor mimicry. In our model, we have considered emotional contagion and behavioral mimicry as possible strategies of observers, which we believe corresponds to de Waal (2008)’s arguments. That is, we assume that species in our model carries the basic ability of empathy and imitation. Since independent reaction is definitely another theoretical possibility, it is reasonable to compare independent reaction, behavioral mimicry, and emotional contagion as evolutionarily possible three alternatives for species with a low-level cognitive and psychological machinery. Even in a higher-level species in terms of cognitive ability, emotional contagion and motor mimicry are the bases of empathy and imitation, so we believe that our model has implications to evolutionary origins of empathy. We have considered a general situation where observation of the demonstrator’s behavior is not necessarily perfect. We have obtained the following result in Section 3.2 (see Fig. 2). Behavioral mimicry is the most adaptive strategy when the environmental similarity between the demonstrator and the observer (R) is high and when the observation noise (k) is small. Emotional contagion is the most adaptive strategy when the environmental similarity between the demonstrator and the observer (R) is intermediate to large and when the observation noise (k) is not small. Independent reaction is the most adaptive strategy when the environmental similarity between the demonstrator and the observer (R) is low. These results suggest that emotional contagion works as an efficient social learning strategy when a demonstrator and an observer share the same environment, and/or share the same source of danger. Therefore, group-living or gregariousness may be one of the key ecological factors favoring the evolution of emotional contagion. It would be interesting to compare the ability of emotional contagion between gregarious and solitary species within a taxon to see whether group-living was a strong evolutionary force favoring emotional contagion. Moreover, emotional contagion is more efficient than behavioral mimicry when the world is noisy; for example, in the species that has limited cognitive ability. This result suggests the possibility that emotional contagion can evolve even in species with low-level cognitive ability. The fact that rodent species show a high level of emotional contagion supports this prediction. In the subsequent analysis in Section 3.3, we have studied the case where a demonstrator cannot necessarily cope with the danger in an optimal way. Mathematically speaking, such a suboptimal behavior by the demonstrator has the same effect as increasing the level of observation noise, k. Therefore we conclude that when a demonstrator cannot behave adequately, it is better for observers not to rely on the demonstrator’s behavior itself but to rely on the emotion behind the behavior. For example, it has been argued that emotional contagion has an important role in maternal care (Panksepp and Panksepp, 2013; Preston and de Waal, 2002), because mothers are able to quickly recognize needs of their children through emotional contagion, or more generally, by empathy, rather than behavioral mimicry. The analysis in Section 3.4 has revealed that it is adaptive for an observer with emotional contagion to neglect normal behaviors by the demonstrator and to activate its emotion only when the demonstrator shows a deviant behavior. From this result we predict that emotional contagion should occur only when the stimulus to the demonstrator is intense, or equivalently, only when the demonstrator reacts to that stimulus intensely; there should be a threshold value for the observer’s emotional system to be activated/deactivated. In contrast, we find that observers with behavioral mimicry can never achieve a better performance by neglecting the demonstrator’s behavior. This result clearly demonstrates that emotional contagion has much flexibility and efficiency in coping with noisy environments than behavioral mimicry.
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We have studied the effect of social modulation in emotional contagion. Experimental evidence that the familiarity between a demonstrator and an observer affects emotional contagion (Langford et al., 2006; Gonzalez-Liencres et al., 2014) suggests that there should be nervous and other physiological mechanisms supporting such an unconscious regulation process. Social modulation of this kind can be modeled in our framework by conditioning w on R; that is, the affective reactions to fear/panic are unconsciously modulated by the environmental similarity between a demonstrator and an observer. It is easy to see that in the simplest model analyzed in Section 3.1, the pffiffiffiffiffiffi ^ ¼ 2Rσ = 2π , cost of the EC observer (Eq. 3) is minimized at w suggesting that the optimal w-value changes with the environmental similarity, R. Therefore our model framework can support an evolutionary advantage of similarity-based social modulation. Note that the environmental similarity, R, is an extrinsic parameter, so repeated social interactions between a demonstrator and an observer will enable them to gradually learn this value. In our model, we did not incorporate the fitness cost of maintaining nervous and physiological systems supporting emotional contagion. Recent findings suggest an important role of oxytocin in emotional empathy in humans (Barraza and Zak, 2009; Hurlemann et al., 2010; Wu et al., 2012; Smith et al., 2014), also in pigs (Reimert et al., 2015). Revealing selection pressure favoring the evolution of such neuropeptides is ultimately important for understanding where the ability of empathy comes from. In conclusion, emotional contagion is adaptive, compared with independent reaction and behavioral mimicry, when the environmental similarity between a demonstrator and an observer is intermediate to high (intermediate or high R), when the observation of demonstrator's behavior is imperfect (high k), when the demonstrator cannot take the optimal behavior (high γ ), and when the observer does not activate emotion toward the demonstrator's normal behavior (intermediate a). These results suggest that emotional contagion is likely to evolve in group-living species even with limited cognitive ability.
Acknowledgments This research was supported in part by Grant-in-Aid for Scientific Research on Innovative Areas No. 25118006, “The Evolutionary Origin and Neural Basis of the Empathetic Systems” to H.O.
Appendix A We calculate the cost for each strategy for the model in Section 3.2. Results in Section 3.1 immediately follow when we set τ ¼ 0. We recall that, from the assumption of bivariate normal distribution, the density function P(x) of optimal behavior x, and the conditional density function P(y|x) of optimal behavior y given x, are respectively given by 1 x2 PðxÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiexp 2 2σ 2πσ 2
Given those, costs are calculated as Z 1 Z 1 C IR ¼ ðy 0Þ2 Pðyj xÞPðxÞdxdy Z 11 1 y2 PðyÞdy ¼ 1
¼ σ2 ;
ðA:1Þ
Z C BM ¼
1
Z
Z
1
1
ðy x″Þ2 Pðyj xÞPðxÞZðx″ xÞdx″dxdy
1 1 1 Z 1 Z 1 Z1
¼
Z 11 Z 11
¼
þ
1
ðy x þ x x″Þ2 Pðyj xÞPðxÞZðx″ xÞdx″dxdy
ðy xÞ2 Pðyj xÞPðxÞdxdy Z 1 Pðyj xÞPðxÞ ½2ðy xÞðx x″Þ
Z 11 Z 11 1
1
1
þ ðx x″Þ2 Zðx″ xÞdx″dxdy Z 1 Z 1 ¼ 2ð1 RÞσ 2 þ τ2 Pðyj xÞPðxÞdxdy ¼ 2ð1 RÞσ 2 þ τ2 ; and
Z
C EC ¼ Z þ ¼2
∞
0 0
Z
Z
∞
Z
∞
∞ ∞ ∞ Z ∞
Z
1
ðA:2Þ
ðy wÞ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00
ðyþ wÞ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00
∞ ∞ ∞ Z ∞Z ∞ Z ∞ 0
1
∞ ∞Z ∞
ðy wÞ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00
i ð1 R2 Þσ 2 þ w2 2Rwx þR2 x2 PðxÞZðx00 xÞdxdx00 0 ∞ Z ∞Z ∞ h i 2 ¼ pffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ ðRx wÞ2 2 2 2πτ 2πσ 0 ∞ " # x2 ðx x00 Þ2 exp 2 dxdx00 2σ 2τ2 Z ∞Z ∞ h i 2 ¼ pffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ ðRx wÞ2 2 2 2πτ 2πσ 0 ∞ "
# 2 x x00 σ 2 =ðσ 2 þτ2 Þ x002 exp dxdx00 2σ 2 τ2 =ðσ 2 þ τ2 Þ 2ðσ 2 þ τ2 Þ Z ∞Z ∞ 2 ½ð1 R2 Þσ 2 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2πσ 2 τ2 =ðσ 2 þ τ2 Þ 2πðσ 2 þ τ2 Þ 0 ∞
2 þ R x x00 σ 2 =ðσ 2 þ τ2 Þ þ Rx00 σ 2 =ðσ 2 þ τ2 Þ w "
# 2 x x00 σ 2 =ðσ 2 þ τ2 Þ x002 dxdx00 exp 2 2 2 2 2σ τ =ðσ þ τ Þ 2ðσ 2 þ τ2 Þ Z ∞h
2 2 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ Rx00 σ 2 =ðσ 2 þτ2 Þ w 2πðσ 2 þ τ2 Þ 0 i x002 dx00 þ R2 σ 2 τ2 =ðσ 2 þ τ2 Þ exp 2 2 2ðσ þ τ Þ ¼2
h
∞
¼ ð1 R2 Þσ 2 þ R2 σ 2 τ2 =ðσ 2 þτ2 Þ þ w2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 ðσ 2 þ τ2 Þ pffiffiffiffiffiffi þ R2 σ 4 =ðσ 2 þ τ2 Þ Rwσ 2 =ðσ 2 þ τ2 Þ 2π 4Rwσ 2 ¼ σ 2 þ w2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi: 2πðσ 2 þ τ2 Þ
ðA:3Þ
" # 1 ðy RxÞ2 Pðyj xÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiexp : 2ð1 R2 Þσ 2 2πð1 R2 Þσ 2
Appendix B
Also, the density function ZðξÞ of observation noise, ξ ¼ x″ x, follows the normal distribution of mean 0 and variance τ2 ; " # 1 ξ2 ZðξÞ ¼ pffiffiffiffiffiffiffiffiffiffiexp 2 : 2τ 2πτ2
Here we calculate the cost of EC strategy which has the emotional contagion thresholds, a and –a, and the corresponding behaviors, w and –w. We have Z ∞Z ∞ Z ∞ C EC ¼ ðy wÞ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 a
∞
∞
W. Nakahashi, H. Ohtsuki / Journal of Theoretical Biology 380 (2015) 480–488
Z þ Z þ ¼2
Z
∞
Z
∞
∞ ∞ ∞ a Z ∞ Z ∞
a Z ∞
Z þ
a
a a 0
∞ Z ∞
Z
∞ Z ∞
ðyþ wÞ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00
ðy 0Þ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00
ðy wÞ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 y2 Pðyj xÞPðxÞZðx00 xÞdxdydx00
∞ ∞ ∞ Z ∞ ∞
∞
2 Z ∞" 2 Rσ 2 00 ð1 R2 Þσ 2 þ 2 x w ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 σ þτ 2πðσ 2 þ τ2 Þ a # 2 2 2 002 R σ τ x dx00 exp þ 2 σ þ τ2 2ðσ 2 þ τ2 Þ 2 Z a" 2 Rσ 2 00 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi þ ð1 R2 Þσ 2 þ 2 x 2 σ þτ 2πðσ 2 þ τ2 Þ 0 # 2 2 2 002 R σ τ x dx00 exp þ 2 σ þ τ2 2ðσ 2 þ τ2 Þ 2 # Z ∞ " 1 R2 σ 2 τ 2 Rσ 2 00 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ 2 þ x σ þ τ2 σ 2 þ τ2 2πðσ 2 þ τ2 Þ ∞ x002 dx00 exp 2ðσ 2 þ τ2 Þ Z ∞ 2 2Rwσ 2 00 x002 dx00 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðw2 2 x Þexp σ þ τ2 2ðσ 2 þ τ2 Þ 2πðσ 2 þ τ2 Þ a 2 R2 σ 2 τ2 Rσ 2 ¼ ð1 R2 Þσ 2 þ 2 þ ðσ 2 þ τ2 Þ σ þτ2 σ 2 þ τ2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi a 4Rwσ 2 σ 2 þ τ2 pffiffiffiffiffiffi þ 2 1 Φ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi w2 ðσ 2 þ τ2 Þ 2π σ 2 þ τ2 a2 exp 2ðσ 2 þ τ2 Þ a 4Rwσ 2 ¼ σ 2 þ 2 1 Φ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi w2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 σ þτ 2πðσ 2 þ τ2 Þ 2 a exp : ðB:1Þ 2ðσ 2 þ τ2 Þ
# R2 σ 2 τ2 x002 þ 2 dx00 exp 2 2 2 σ þτ 2ðσ þ τ Þ Z ∞ " 1 R2 σ 2 τ2 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ 2 σ þ τ2 2πðσ 2 þ τ2 Þ ∞ # 2 Rσ 2 00 x002 dx00 x þ 2 exp 2 2 2 σ þτ 2ðσ þ τ Þ Z ∞ 2 2Rσ 2 002 x002 dx00 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 2 Þx exp σ þ τ2 2ðσ 2 þτ2 Þ 2πðσ 2 þ τ2 Þ a 2 R2 σ 2 τ2 Rσ 2 ¼ ð1 R2 Þσ 2 þ 2 þ ðσ 2 þ τ2 Þ σ þτ2 σ 2 þ τ2 ( pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Rσ 2 a σ 2 þ τ2 a2 pffiffiffiffiffiffi exp Þ þ 2ð1 2 2 2 2 σ þτ 2ðσ þ τ Þ 2π a þ ðσ 2 þ τ2 Þ 1 Φ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ 2 þ τ2 (
a a2 ¼ σ 2 þ 2 ð1 2RÞσ 2 þτ2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiexp 2ðσ 2 þ τ2 Þ 2πðσ 2 þ τ2 Þ a þ 1 Φ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi : σ 2 þ τ2
487
ðC:1Þ
therefore,
"
1 a2 =ðσ 2 þ τ2 Þ ∂C BM a2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp ¼ 2 ð1 2RÞσ 2 þ τ2 ∂a 2ðσ 2 þ τ2 Þ 2πðσ 2 þ τ2 Þ # 1 a2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiexp 2 þ τ2 Þ 2 2 2ðσ 2πðσ þ τ Þ
2a2 ð1 2RÞσ 2 þ τ2 a2 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiexp ¼ : 2 2 2ðσ þτ Þ ðσ 2 þ τ2 Þ 2πðσ 2 þ τ2 Þ
ðC:2Þ
When ð1 2RÞσ 2 þ τ2 is negative, i.e. when R 4 ðσ 2 þ τ2 Þ= 2σ 2 ¼ ð1 þ kÞ=2, we have ∂C BM =∂a o 0. In contrast, when ð1 2RÞσ 2 þ τ2 is positive, i.e. R o ð1 þ kÞ=2, we have ∂C BM =∂a o 0. Therefore, the cost of BM is the smallest at a^ ¼ 0 when R 4ð1 þkÞ=2, and at a^ ¼ 1 when R o ð1 þ kÞ=2. References
Appendix C Suppose that the “condition-dependent“ BM strategy chooses the demonstrator's observed behavior y0 ¼x″ when jx″j 4a, and chooses the behavior y0 ¼0 otherwise. The cost of such a BM strategy is Z ∞Z ∞ Z ∞ ðy x00 Þ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 C BM ¼ a ∞ ∞ Z a Z ∞ Z ∞ þ ðy x00 Þ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 ∞ ∞ ∞ Z a Z ∞ Z ∞ þ ðy 0Þ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 a ∞ ∞ Z ∞ Z ∞ Z ∞ ¼2 ðy x00 Þ2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 a ∞ ∞ Z aZ ∞ Z ∞ y2 Pðyj xÞPðxÞZðx00 xÞdxdydx00 þ 0
∞
∞
2 Z ∞" 2 Rσ 2 00 ð1 R2 Þσ 2 þ 2 x x00 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 σ þτ 2πðσ 2 þ τ2 Þ a # 2 2 2 002 R σ τ x dx00 þ 2 exp σ þτ2 2ðσ 2 þ τ2 Þ 2 Z a" 2 Rσ 2 00 þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 R2 Þσ 2 þ 2 x σ þ τ2 2πðσ 2 þ τ2 Þ 0
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