Because most newly arising mutations are neutral or deleterious, it has been argued that the mutation rate has evolved to be as low as possible, limited only by the cost of error-avoidance and error-correction mechanisms. But up to one per cent of natural bacterial isolates are 'mutator' clones that have high mutation rates. We consider here whether high mutation rates might play an important role in adaptive evolution. Models of large, asexual, clonal populations adapting to a new environment show that strong mutator genes (such as those that increase mutation rates by 1,000-fold) can accelerate adaptation, even if the mutator gene remains at a very low frequency (for example, 10[-5]). Less potent mutators (10 to 100-fold increase) can become fixed in a fraction of finite populations. The parameters of the model have been set to values typical for Escherichia coli cultures, which behave in a manner similar to the model in long-term adaptation experiments.

We consider the impact of a colonization process on the genetic diversity and spatial structure of a geographically subdivided population. A stepping-stone model combined with coalescence theory is used to predict the evolution of sequence divergence and genetic parameters. We first derive analytical results for coalescence times in a population undergoing logistic growth. We next consider a stepping-stone model in which demes are successively colonized, starting from a first deme at one of the borders of the metapopulation. We use recurrence equations to calculate coalescence times for two genes chosen either inside the same deme or in different demes. This allows us to obtain the distribution and the expectation of the coalescence times, and to deduce from them the distribution of the average pairwise differences and the evolution of F st . Our results reflect the impact of the founder effect, which becomes stronger as the distance of the deme from the first deme increases. An increase in migration rate or growth rate generally leads to a decrease of the founder effect. F st (i) increases during the beginning of the colonization, (ii) decreases when migration creates homogenization and (iii) increases again towards an equilibrium value. The distributions of pairwise coalescence times or differences between sequences show a peak corresponding to the colonization period. These results could help detect former colonization events in natural populations.] 1997 Academic Press

The remarkable ecological and demographic success of humanity is largely attributed to our capacity for cumulative culture. The accumulation of beneficial cultural innovations across generations is puzzling because transmission events are generally imperfect, although there is large variance in fidelity. Events of perfect cultural transmission and innovations should be more frequent in a large population. As a consequence, a large population size may be a prerequisite for the evolution of cultural complexity, although anthropological studies have produced mixed results and empirical evidence is lacking. Here we use a dual-task computer game to show that cultural evolution strongly depends on population size, as players in larger groups maintained higher cultural complexity. We found that when group size increases, cultural knowledge is less deteriorated, improvements to existing cultural traits are more frequent, and cultural trait diversity is maintained more often. Our results demonstrate how changes in group size can generate both adaptive cultural evolution and maladaptive losses of culturally acquired skills. As humans live in habitats for which they are ill-suited without specific cultural adaptations, it suggests that, in our evolutionary past, group-size reduction may have exposed human societies to significant risks, including societal collapse.