We present a simple theoretical model of evolution featuring a decreas
ing extinction rate due to an increasing average fitness of the specie
s. The dynamics is based on a random walk on a rugged fitness landscap
e, with evolutionary jumps for each species triggered by the achieveme
nt of fitness records during the walk. We analyze two different rules
for extinction. In the first, an evolutionary jump leads to an extinct
ion with a given probability, while in the second a specific competiti
on mechanism is considered. In both cases temporal power laws are foun
d to describe the evolution. Extensive simulation results from our sec
ond model are in reasonable agreement with paleontological data, showi
ng that the background extinction rate has decreased since Cambrian ti
me.