Recent interest in neutral theory in community ecology has given rise to a zombie idea: that “neutral” and “stochastic” mean the same thing. They don’t.
It’s easy to see where this zombie idea comes from: neutral drift in evolution is a stochastic process, while natural selection is a deterministic process. The problem here is confusing “neutral” with “drift”. It’s perfectly possible for a dynamical system to be both neutrally stable and deterministic. In evolution, a population experiencing no selection evolves in a neutral fashion, even if it also has infinite population size and so experiences no drift. The initial gene frequencies will simply persist forever, and if perturbed, they’ll subsequently persist forever at their post-perturbation frequencies. In ecology, a Lotka-Volterra competition model in which intra- and interspecific competition are equally strong on a per-capita basis is neutrally stable, but deterministic. And the original Lotka-Volterra predator-prey model (exponentially-growing prey consumed by a predator with a linear functional response and density-independent per-capita mortality rate) produces neutrally stable oscillations, the amplitude of which is set by initial predator and prey densities. Conversely, a world in which the strength or direction of selection fluctuates randomly over time is a stochastic world, but not a neutral world (although in certain respects it might have similar dynamics to a neutral world).
Confusing “neutral” with “drift” has led community ecologists to use some problematic tests for neutrality, which basically test for random or unexplained variation in species composition or other community properties. At best, these are tests for drift (and they may not even be tests for that, depending on the details). They’re not tests of neutrality (=zero selection). And it is simply not true that, in nature, neutrality and drift always and everywhere go hand in hand, so that there’s no practical harm in not distinguishing them.
Now, if you want to argue, as some ecologists have, that the most interesting or important distinction to draw is between deterministic vs. stochastic processes, rather than between neutrality vs. non-neutrality, that’s fine.* But you do need to recognize that those are two different distinctions.
*Although I would argue that even drawing that distinction is likely to cause you miss all the interesting ways in which stochastic and deterministic processes can interact and produce dynamics that are qualitatively distinct from those that would be produced by either deterministic or stochastic processes alone. Quasi-cycles (Pineda-Krch et al. 2006 Oikos) and stochastic resonance, for instance. In general, I think ecologists often are too quick to either treat non-mutually exclusive possibilities as mutually-exclusive alternatives, or else to treat them as ends of a linear continuum. The latter mistake is more pernicious because it’s so intuitive and accords so well with our everyday experience. In between tall and short are people of intermediate height. In between loud sounds and silence are sounds of intermediate volume. In between the two ends of a line segment is the halfway point. In between black and white are various shades of grey. But “in between” determinism and stochasticity is all kinds of cool, wonky stuff that cannot be understood by simply thinking of it as a “mix” of determinism and stochasticity. It’s as if mixing black and white made, not shades of grey, but all the colors of the rainbow.