On inferring evolutionary stability in finite populations using infinite population models.

Models of evolution by natural selection often make the simplifying assumption that populations are infinitely large. In this infinite population limit, rare mutations that are selected against always go extinct, whereas in finite populations they can persist and even reach fixation. Nevertheless, for mutations of arbitrarily small phenotypic effect, it is widely believed that in sufficiently large populations, if selection opposes the invasion of rare mutants, then it also opposes their fixation.

Combating climate change with matching-commitment agreements.

Countries generally agree that global greenhouse gas emissions are too high, but prefer other countries reduce emissions rather than reducing their own. The Paris Agreement is intended to solve this collective action problem, but is likely insufficient. One proposed solution is a matching-commitment agreement, through which countries can change each other's incentives by committing to conditional emissions reductions, before countries decide on their unconditional reductions.

Difficulties in benchmarking ecological null models: an assessment of current methods.

Identifying species interactions and detecting when ecological communities are structured by them is an important problem in ecology and biogeography. Ecologists have developed specialized statistical hypothesis tests to detect patterns indicative of community-wide processes in their field data. In this respect, null model approaches have proved particularly popular.

On selection in finite populations.

Two major forces shaping evolution are drift and selection. The standard models of neutral drift-the Wright-Fisher (WF) and Moran processes-can be extended to include selection. However, these standard models are not always applicable in practice, and-even without selection-many other drift models make very different predictions.

Evolutionary stability in continuous nonlinear public goods games.

We investigate a type of public goods games played in groups of individuals who choose how much to contribute towards the production of a common good, at a cost to themselves. In these games, the common good is produced based on the sum of contributions from all group members, then equally distributed among them. In applications, the dependence of the common good on the total contribution is often nonlinear (e.

Game theory of pre-emptive vaccination before bioterrorism or accidental release of smallpox.

Smallpox was eradicated in the 1970s, but new outbreaks could be seeded by bioterrorism or accidental release. Substantial vaccine-induced morbidity and mortality make pre-emptive mass vaccination controversial, and if vaccination is voluntary, then there is a conflict between self- and group interests. This conflict can be framed as a tragedy of the commons, in which herd immunity plays the role of the commons, and free-riding (i.

Modelling the spread of diseases in clustered networks.

It is now well appreciated that population structure can have a major impact on disease dynamics, outbreak sizes and epidemic thresholds. Indeed, on some networks, epidemics occur only for sufficiently high transmissibility, whereas in others (e.g.