Essential to each other, growth and exploration are jointly observed in
populations, be it alive such as animals and cells or inanimate such as goods
and money. But their ability to move, crucial to cope with uncertainty and
optimize returns, is tempered by the space/time properties of the environment.
We investigate how the environment shape optimal growth and population
distribution in such conditions. We uncover a trade-off between risks and
returns by revisiting a common growth model over general graphs. Our results
reveal a rich and nuanced picture: fruitful strategies commonly lead to risky
positions, but this tension may nonetheless be alleviated by the geometry of
the explored space. The applicability of our conclusions is subsequently
illustrated over an empirical study of financial data.Comment: 11 pages, 5 figure
