On stochastic Lotka-Volterra predator-prey model
To interpret $a$ and $c$ as a birth and mortality rates is somewhat inaccurate, as $a$ and $c$, as written are density-independent rates that grow or shrink populations exponentially. If $a$ were negative, the prey population would shrink and most people would find a problem like that unexciting unless it was, say, a sink population maintained by immigration from another population. This is true of $c$ being negative, where the predator population would grow independent of the prey population. More accurately, $a$ can be interpreted as the difference between birth, $b$, and deaths, $\delta$; i.e., $a = b - \delta$. In this case, depending on the kinds of stochasticity being added to the model, negative $a$ is not just normal, but expected. The same is true for $c$. Ultimately, a perturbations like the white noise in this equation is simultaneously perturbing the difference between birth and death rates, which explains the negative difference.
The value of the rates seem to have the same interpretation if they are constant or are perturbed to an arbitrary magnitude.

I hope this helps!