Beavers can live to an old age of 10-12 years, but death can also be due to disease, infections from fighting, hunting, traffic, flooding and rarely from predators.
The population is also controlled by aggressive interaction between dispersing beavers and territorial families, with mortality of dispersing juvenile beavers increasing with territorial occupancy.  As the carrying capacity is achieved the whole population endures increased stress, lower reproduction and higher mortality. 

Within a watershed, re-colonising beaver populations show a characteristic pattern of rapid range extension, followed slowly by population growth. This pattern is due to the selection of the highest quality habitat available, followed by the progressive infill of lower quality sites. As poor quality habitat tends to require more alteration - dam construction - beavers tend to have the greatest positive impact on the ecology of low quality habitats in the later stages of population expansion. Beavers only rarely move over 100m from fresh water and will not colonise salt-water. As a consequence if there is no freshwater connection between river catchments and the distance separating catchments is more than 100 metres, beaver populations are unlikely to spread swiftly. This characteristic can be used to restrict beaver populations to single river catchments.
From ample European evidence in landscapes similar to Britain we know that beaver populations spread very slowly and are extremely easy to effectively control.