(1) Alternative signaling strategies in the absence of errors in self-perception

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1 Supplementary Material The Evolution of Individual Variation in Communication Strategie Carlo A. Botero, Ido Pen, Jan Komdeur, & Franz J. Weiing Content: (1) Alternative ignaling trategie in the abence of error in elf-perception; (2) Analytical model of the coexitence of peronality type; (3) Individual-baed imulation model of dynamic ignal; and (4) five additional figure. (1) Alternative ignaling trategie in the abence of error in elf-perception In thi implified verion of our individual-baed imulation model, e varied the rule that determine the outcome of fight. If both opponent chooe to attack, the tronger individual alay in. If the opponent are equally matched, the inner i determined by coin to. Quality i contant throughout lifetime and error in elf-perception are applied at both badge production and the interaction phae. All other detail of the model remain unchanged. Under thee condition, to ditinct communication trategie are oberved at σ E = 0 and additional trategie are oberved hen the potential for error in elf-perception i increaed (Fig. SM1). Thi model formulation i omehat unrealitic becaue of the diproportionate effect that extremely mall quality difference can have over the probability of inning. Hoever, it allo u to ho that under certain condition polymorphim in communication trategie might alo be oberved in the abence of elf-perception error. Note that the polymorphim oberved hen σ E = 0 i a product of individual difference in ender but not receiver code (Fig. SM1 A), uggeting alternative ay in hich ender exploit the average population behavior. A expected, thi polymorphim i highly untable: in all replicate imulation run ith σ E = 0 (n=100), the population cycled multiple time beteen monomorphic and polymorphic tate. Introducing error in elf-perception to thi model led to more table polymorphim in hich alternative trategie differed in both ender and receiver behavior a in the model preented in the main text (Fig. SM1 B-D). Botero et al. 1

2 (2) Analytical model of the coexitence of peronality type In thi implified model individual can be trong () or eak () and they can produce a badge or not. The cot (C) of ignal production i dependent on individual quality uch that C < C. Individual trategie are vector ith the folloing value: Probability of producing a badge hen trong, Probability of producing a badge hen eak, Probability of attack hen trong and rival ha a badge, Probability of attack hen trong and rival doe not have a badge, Probability of attack hen eak and rival ha a badge, and Probability of attack hen eak and rival doe not have a badge. Thu, a imple approximation of the trategie that emerge in our individual-baed imulation model at σ E = 0.15 can be repreented a: Aggreive = [1, 1, 1, 1, 0, 1] Moderate = [1, 0.5, 1, 1, 0, 0.5] Conervative = [1, 0, 0, 1, 0, 0] Thi trategy et lead to the folloing payoff matrix A (payoff are given for the ro player): Conervative Conervative Moderate Aggreive Moderate V 05. C 025. C Aggreive 075. V 05. C 05. C V C V C 05. C V L V L 05. C 025. C 05. C 05. C 05. C 025. C 05. V L V L 05. C 05. C To determine ho the frequency of thee trategie varie over time, e ued the dicrete form of the replicator dynamic (Hofbauer and Sigmund 1988), x i in hich x i i the proportion of type i, f i xa i the fitne of type i, and f j j ij x f j j j i the eighted average of the fitne of the three type. It can be hon that under realitic aumption (i.e., C << V < L), the ytem ill alay exhibit the dynamic hon in Figure 6 of the main text (Fig. 6 a plotted baed on the folloing parameter: V = 1, L = 3, C = 0.015, and C = 0.15). f i xi f Botero et al. 2

3 (3) A model of dynamic ignal Our model of badge of tatu aume that ignal are contant throughout lifetime, that there i a time-lag beteen ignal production and ignal ue, and that ignal cot are expreed only in term of urvival. To explore the generality of our finding e modified the baic individual-baed imulation model o that ne ignal ere produced each time they ere ued (uch a in the cret-erection threat diplay of in jay and other bird (Hardy 1974)). Signal cot in thi verion of the model ere modelled a a reduction in payoff uch that Signal cot = k /(1+exp k k ( Q C) ), here Q i the individual on quality, C i the intenity of cret erection, and k 0, k 1,and k 2 are caling contant. The reult of thi model are qualitatively identical to thoe of the model ith badge of tatu (Fig. SM5). When k 0 = 5, k 1 = 3, and k 2 = 6, population converge into a ingle communication trategy at σ E = 0 (n=100, mean ± SE = 1.00 ± 0.0 cluter), to table communication trategie at σ E = 0.1 (n=100, mean ± SE = 2.35 ± 0.05 cluter), and three ditinct communication trategie at σ E = 0.2 (n=100, mean ± SE = 3.17 ± 0.06 cluter). Literature cited Hardy, J. W Behavior and it evolution in Neotropical jay (Ciilopha). Bird-Banding 45: Hofbauer, J., and K. Sigmund The Theory of Evolution and Dynamical Sytem Cambridge Univerity Pre, Cambridge, UK. Botero et al. 3

4 Figure SM1. Mean ender and receiver code predicted by our alternative formulation of the model of badge of tatu ith different amount of error in the ender etimation of on quality. Error in elf-perception are dran from N(μ = 0.5, σ = σ E ). (A) σ E = 0.0, (B) σ E = 0.05, (C) σ E = 0.1, and (D) σ E = 0.2. Figure SM2. Individual variation in communication trategie in a repreentative replicate imulation run ith quadratic logitic communication code and σ E = 0.1. Botero et al. 4

5 Figure SM3. Individual variation in communication trategie in a repreentative replicate imulation run ith exual reproduction, recombination rate of 0.5, and σ E = Thi verion of the model include a ixth locu that imultaneouly modifie the value of the point of inflection. Thu, a a mand ar ar 1.5m, here m, a and a r are allele inherited from the parent. Figure SM4. Hitogram of trait value for the m locu in the replicate imulation run of the exual recombination model depicted in Fig. SM3. The ditribution of m i clearly trimodal and each peak correpond to one of the main trategie oberved in Fig SM3 (ee color-coding). Botero et al. 5

6 Figure SM5. Mean ender and receiver code predicted by our model of dynamic ignal (e.g. cret erection in bird) ith different amount of error in the ender etimation of on quality. Error in elf-perception are dran from N(μ = 0.5, σ = σ E ). (A) σ E = 0.0, (B) σ E = 0.1, (C) σ E = 0.15, and (D) σ E = 0.2. Botero et al. 6