Geometric means are important in evolutionary biology. Evolution is a multiplicative process when looked at over several generations.
This is why, according to bet hedging theory, natural selection should favor strategies that maximize the geometric mean over long timescales.
This is not necessarily always realized. For example if the environment is stable for a very long time, and then there is one very very bad year, strategies that are better over short time-scales might invade the population during the stable period. Nevertheless, it is an important principle in evolutionary biology.
