Hisashi Ohtsuki

TL;DR: A surprisingly simple rule is described that is a good approximation for all graphs that are analysed, including cycles, spatial lattices, random regular graphs, random graphs and scale-free networks: natural selection favours cooperation if the benefit of the altruistic act, b, exceeds the average number of neighbours, k, which means b/c > k.

TL;DR: A mathematical model is provided that model tumors as a discrete time branching process that starts with a single driver mutation and proceeds as each new driver mutation leads to a slightly increased rate of clonal expansion, providing understanding of the heterogeneity in tumor sizes and development times that have been observed by epidemiologists and clinicians.

TL;DR: A differential equation is derived which describes how the average frequency of each strategy on the graph changes over time, and is a replicator equation with a transformed payoff matrix, which results in a transformation of the payoff matrix.

TL;DR: The results give one solution to the definition of goodness from an evolutionary viewpoint and believe that the formalism of reputation dynamics gives general insights into the way social information is generated, handled, and transmitted in animal societies.

TL;DR: The keys to the success in indirect reciprocity are to be nice (maintenance of cooperation among themselves), retaliatory (detection of defectors, punishment, and justification of punishment), apologetic, and forgiving.