Ission error in later sections). These conclusions are distinctive from these
Ission error in later sections). These conclusions are distinct from those drawn from an empirical study [45], which finds no effect of variant prestige on diffusion, however the authors of that study admit that their focus is on individual bias and variant prestige is subsumed within that PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/22157200 focus. These conclusions are based on simulations in a finite population and inside a restricted number of interactions. In Text S3, we prove that these conclusions also hold inside a sufficiently substantial population and an unlimited quantity of interactions. Meanwhile, single histories from the Polyaurn dynamics are likely to show the reinforcement or lockin effect [46]. As shown in Figure S and discussed in Text S4, such impact cannot impact our conclusions.than N6y is the quantity of hearers influenced by an agent with index x. The minimum value of this quantity is . l characterizes various powerlaw distributions; the greater the l, the far more hearers when agents with smaller sized indices speak. Inside the second way, we define a powerlaw distribution of individual popularities (probabilities for people to take part in interactions). Within this powerlaw, y measures the probability for a person to interact (as speaker or hearer) with others. We consider powerlaw distributions whose l are 0.0, .0, .five, two.0, 2.5, and three.0. l values in lots of realworld powerlaw distributions commonly fall in this range. If l is 0.0, all agents have the exact same influence or probability, which resembles the case of random interaction. Values within (0.0 .0) are excluded, because the influences or probabilities under these values are sensitive to the population size. Figures four and 5 show the FD&C Green No. 3 results below these two kinds of individual influence. Without variant prestige, each types fail to exert a selective stress, indicated by the fluctuation with the covariance; otherwise, both can affect diffusion. As shown in Figures four(c) and 5(c), l and Prop are correlated. To illustrate such correlation, we define MaxRange as the maximum changing array of Prop: MaxRange max (Prop(t){Prop(0))t[,Individual Influence with and without Variant PrestigeIndividual influence reflects the fact that members in a community tend to copy the way of certain individuals. Such factor is claimed to be able to enhance the benefit of cultural transmission [47]. In our study, individual influence is discussed in two ways. In the first way, we define a nonuniform distribution of individuals’ influences. When an individual speaks, according to its influence, a certain number of other individuals will be randomly chosen as hearers and update their urns according to the token produced by the speaker. Each individual has an equal chance to be chosen as speaker, but the distribution of all individuals’ influences follows a powerlaw distribution [49,50] (inspired from the data in [47], and used in [48]). The powerlaw distribution has the form y ax{l , where x is the agent index from to N, y is the influence an agent has, and a is a normalizing factor ensuring that the sum of all probabilities is .0. The maximum integer smallerPLoS ONE plosone.org5Figures 4(d) and 5(d) compare MaxRange with and without variant prestige. With variant prestige, under the first type of individual influence, there is a negative correlation between l and MaxRange (Figure 4(d)). With the increase in l, agents with smaller indices become more influential, who can affect many others, whereas those with bigger indices are less influential, who can only affect or 2 ag.
