When the environment varies both in time and space, how fast do population traits evolve, and how does the species range change in size and position? With  Nick BartonJitka Polechová has been assessing the deterministic expectation sat equilibrium, following joint evolution of trait mean and population dynamics. Now, is the uniform adaptation more prone to collapse due to stochastic effects when population sizes are finite, and are then such population highly prone to extinctions (as simulations suggest)? How important are sweeps of neutral mutations at the leading edge of an expanding population?