Biology subjects

Earn, D. J. D.

Publications and source records attributed to Earn, D. J. D..

3 recordsLinked to original sources

bioRxiv2019

Patterns of smallpox mortality in London, England, over three centuries

Smallpox is unique among infectious diseases in the degree to which it devasted human populations, its long history of control interventions, and the fact that it has been successfully eradicated. Mortality from smallpox in London, England, was carefully documented, weekly, for nearly 300 years, providing a rare and valuable source for the study of ecology and evolution of infectious disease. We describe and analyze smallpox mortality in London from 1664 to 1930. We digitized the weekly records published in the London Bills of Mortality and the Registrar Generals Weekly Returns. We annotated the resulting time series with a sequence of historical events that appear to have influenced smallpox dynamics in London. We present a spectral analysis that reveals how periodicities in smallpox dynamics changed over decades and centuries, and how these changes were related to control interventions and public health policy changes. We also examine how the seasonality of smallpox epidemics changed from the 17th to 20th centuries in London.

ecology↗

bioRxiv2019

Instability of cooperation in finite populations

Evolutionary game theory has been developed primarily under the implicit assumption of an infinite population. We rigorously analyze a standard model for the evolution of cooperation (the multi-player snowdrift game) and show that in many situations in which there is a cooperative evolutionarily stable strategy (ESS) if the population is infinite, there is no cooperative ESS if the population is finite (no matter how large). In these cases, contributing nothing is a globally convergently stable finite-population ESS, implying that apparent evolution of cooperation in such games is an artifact of the infinite population approximation. The key issue is that if the size of groups that play the game exceeds a critical proportion of the population then the infinite-population approximation predicts the wrong evolutionary outcome (in addition, the critical proportion itself depends on the population size). Our results are robust to the underlying selection process.

evolutionary biology↗

bioRxiv2019

Selection may oppose invasion, yet favour fixation: consequences for evolutionary stability

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 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. Here, we identify circumstances under which infinite-population models do or do not accurately predict evolutionary outcomes in large, finite populations. We show that there is no population size above which considering only invasion generally suffices: for any finite population size, there are situations in which selection opposes the invasion of mutations of arbitrarily small effect, but favours their fixation. This is not an unlikely limiting case; it can occur when fitness is a smooth function of the evolving trait, and when the selection process is biologically sensible. Nevertheless, there are circumstances under which opposition of invasion does imply opposition of fixation: in fact, for the n-player snowdrift game (a common model of cooperation) we identify sufficient conditions under which selection against rare mutants of small effect precludes their fixation--in sufficiently large populations--for any selection process. We also find conditions under which--no matter how large the population--the trait that fixes depends on the selection process, which is important because any particular selection process is only an approximation of reality.

evolutionary biology↗