transmission: Simulating Unbiased and Frequency-Biased Cultural...
In ercrema/HERAChp.KandlerCrema: Cultural Evolutionary Analysis of Frequency Data

Description Usage Arguments Details Value References

Function for simulating unbiased/frequency-biased cultural transmission.

1 2	transmission(N = 500, timesteps = 501, mu = 0.01, warmUp = 300, top = NA, bias = 0, raw = FALSE)

`N`	Number of individuals.
`timesteps`	Number of generations (timesteps).
`mu`	Innovation rate.
`top`	Number indicating the most common variants considered for the turn-over rate analysis (e.g. if `top` is equal to 5 the turnover rate is computed as the average number of new variants introduced in the top 1, 2, 3, ,4 and 5 ranked variants at each timestep).
`bias`	Frequency bias parameter. Either a vector with length equal to the number of timesteps (to allow for a time-varying frequency bias), or single value (for a fixed bias).
`raw`	Logical variable indicating whether the matrix of variants frequencies are returned or not. Default is FALSE.
`wamUp`	Number of generations executed to reach equilibrium conditions (discarded from analysis)

The function simulates unbiased (bias=0), confomist (bias<0), and anti-conformist (bias>0) cultural transmission with a user-defined population size and mutation rates, returning Simpson's diversity index of variants frequency, observed and expected turnover rates, and estimates of the exponent x following the procedure described in Acerbi and Bentley 2014 (notice that Acerbi and Bentley refer to this exponent as b). Frequency bias is modelled using the following formula:

π_i=\frac{≤ft(\frac{m_i}{N}\right)^{1-β}}{∑\limits_{j=1}^k ≤ft(\frac{m_j}{N}\right)^{1-β}}(1-μ)

with pi_i equal to the probability of copying the variant i, m_i to the number of individuals possessing the variant i, N to the population size, mu to the mutation rate, and β to the frequency bias parameter (i.e. bias).

A list containing: 1) a matrix of variants frequencies, with rows equal to generations and columns to specific variants (rawMatrix, available on when the argument raw is set to TRUE.; 2) a data.frame with the observed turnover rates (column: obs.z), the expected rates according to Bentley et al 2007 (column: exp.z.Bentley) and Evans and Giometto 2012 (column: exp.z.EvansGiometto); 3) the fitted value for the parameter x; 4) a vector with a time-series of observed Simpson's diversity index (obs.div); and 5) the expected Simpson's diversity under neutrality, equal to 1 - (1/(2*N*μ + 1)) (exp.div).

Acerbi, A., Bentley, A.R., 2014. Biases in cultural transmission shape the turnover of populat traits. Evolution and Human Behavior, 35, 228–236.
Bentley, R.A., Lipo, C.P., Herzog, H.A., Hahn, M.W., 2007. Regular rates of popular culture change reflect random copying. Evolution and Human Behavior, 28, 151–158.
Crema, E.R., Kandler, A., Shennan, S., 2016. Revealing patterns of cultural transmission from frequency data: equilibrium and non-equilibrium assumptions. Scientific Reports 6, 39122. https://doi.org/10.1038/srep39122
Evans, T.S., Giometto, A., 2011. Turnover Rate of Popularity Charts in Neutral Models. arXiv: [physics:soc-ph].

ercrema/HERAChp.KandlerCrema documentation built on May 6, 2019, 6:57 p.m.