Quantifying time-inhomogeneous stochastic introgression processes with hazard rates

Introgression is the permanent incorporation of genes from one population into another through hybridization and backcrossing. It is currently of particular concern as a possible mechanism for the spread of modi ed crop genes to wild populations. The hazard rate is the probability per time unit that such an escape takes place, given that it has not happened before. It is a quantitative measure of introgression risk that takes the stochastic elements inherent in introgression processes into account. We present a methodology to calculate the hazard rate for situations with time-varying gene ow from a crop to a large recipient wild population. As an illustration, several types of time-inhomogeneity are examined, including deterministic periodicity as well as random variation. Furthermore, we examine the e ects of an extended tness bottleneck of hybrids and backcrosses in combination with time-varying gene ow. It is found that bottlenecks decrease the hazard rate, but also slow down and delay its changes in reaction to changes in gene ow. Furthermore, we nd that random variation in gene ow generates a lower hazard rate than analogous deterministic variation. We discuss the implications of our ndings for crop management and introgression risk assessment.This research was funded through the research program 'Ecology Regarding Genetically modified Organisms (ERGO)', commissioned by four Dutch ministries. This funding program is managed by the Earth and Life Sciences Council (ALW) of the Netherlands Organisation for Scientific Research (NWO). P. Haccou's research is additionally supported by the NDNS (Nonlinear Dynamics of Natural Systems) program of NWO. M.C. Serra would like to thank the Fundacao para a Ciencia e Tecnologia for financial support through the scholarship SFRH/BPD/47615/2008. We thank Marije Stoops and Prof. Baorong Lu for discussions and comments on a previous version

Prospects & Overviews Bet hedging or not? A guide to proper classification of microbial survival strategies

Bacteria have developed an impressive ability to survive and propagate in highly diverse and changing environments by evolving phenotypic heterogeneity. Phenotypic heterogeneity ensures that a subpopulation is well prepared for environmental changes. The expression bet hedging is commonly (but often incorrectly) used by molecular biologists to describe any observed phenotypic heterogeneity. In evolutionary biology, however, bet hedging denotes a risk-spreading strategy displayed by isogenic populations that evolved in unpredictably changing environments. Opposed to other survival strategies, bet hedging evolves because the selection environment changes and favours different phenotypes at different times. Consequently, in bet hedging populations all phenotypes perform differently well at any time, depending on the selection pressures present. Moreover, bet hedging is the only strategy in which temporal variance of offspring numbers per individual is minimized. Our paper aims to provide a guide for the correct use of the term bet hedging in molecular biology

Stochasticity in the adaptive dynamics of evolution: The bare bones

First a population model with one single type of individuals is considered. Individuals reproduce asexually by splitting into two, with a population-size-dependent probability. Population extinction, growth and persistence are studied. Subsequently the results are extended to such a population with two competing morphs and are applied to a simple model, where morphs arise through mutation. The movement in the trait space of a monomorphic population and its possible branching into polymorphism are discussed. This is a first report. It purports to display the basic conceptual structure of a simple exact probabilistic formulation of adaptive dynamics