44. The progeny distribution
• Progeny distribution: the progeny distribution logs the
abundances of species which produce new individuals
over a fixed period of time
k
45. The neutral model
• Progeny distribution: the progeny distribution logs the
abundances of species which produce new individuals
over a fixed period of time
• For the neutral model, it’s well established that it follows
a power law distribution1,2,3
k
1. RA Bentley, MW Hahn, and SJ Shennan. Random drift and culture change. Proceedings of the Royal Society of London B: Biological Sciences, 271 (1547):1443–1450, 2004.
2. MW Hahn and RA Bentley. Drift as a mechanism for cultural change: an example from baby names. Proceedings of the Royal Society of London B: Biological Sciences, 270(Suppl 1):S120–S123, 2003.
3. LS Premo. Cultural transmission and diversity in time-averaged assemblages. Current Anthropology, 55(1):105–114, 2014.
P(x) ⇠ x ↵
46. The neutral model
• The exponent is shown to be equal to
1. James P O’Dwyer and Anne Kandler. Inferring processes of cultural transmission: the critical role of rare variants in distinguishing neutrality from
novelty biases
P(x) ⇠ x 3/2
49. The neutral model
Interactions between species are equivalent on an
individual ‘per capita’ basis
Sampling theory
Genetics, English words, technology patents citation …
1. Motoo Kimura.The neutral theory of molecular evolution. Cambridge University Press, 1983.
2. Damian Ruck, R Alexander Bentley,Alberto Acerbi, Philip Garnett, and Daniel J Hruschka. Neutral evolution and turnover over centuries of english
word popularity. arXiv preprint arXiv:1703.10698, 2017.
3. R Alexander Bentley, Matthew W Hahn, and Stephen J Shennan. Random drift and culture change. Proceedings of the Royal Society of London B: Biological
Sciences, 271(1547):1443–1450, 2004.
75. Our focus
Looking at the entire market around 1500
cryptocurrencies
Market dynamics and properties from April
2013 till May 2017
76. Our focus
Looking at the entire market around 1500
cryptocurrencies
Market dynamics and properties from April
2013 till May 2017
Modelling the competition dynamics using the
neutral model