Understanding selection on intra- and interspecific interactions that take place in dispersal-limited communities is a challenge for ecology and evolutionary biology. The problem is that local demographic stochasticity generates eco-evolutionary dynamics that are generally too complicated to make tractable analytical investigations. Here we circumvent this problem by approximating the selection gradient on a quantitative trait that influences local community dynamics, assuming that such dynamics are deterministic with a stable fixed point. The model nonetheless captures unavoidable kin selection effects arising from demographic stochasticity. Our approximation reveals that selection depends on how an individual expressing a trait change influences (1) its own fitness and the fitness of its current relatives and (2) the fitness of its downstream relatives through modifications of local ecological conditions (i.e., through ecological inheritance). Mathematically, the effects of ecological inheritance on selection are captured by dispersal-limited versions of press perturbations of community ecology. We use our approximation to investigate the evolution of helping within species and harming between species when these behaviors influence demography. We find that altruistic helping evolves more readily when intraspecific competition is for material resources rather than for space, because in this case the costs of kin competition tend to be paid by downstream relatives. Similarly, altruistic harming between species evolves when it alleviates downstream relatives from interspecific competition. Beyond these examples, our approximation can help better understand the influence of ecological inheritance on a variety of eco-evolutionary dynamics in metacommunities, from consumer-resource and predator-prey coevolution to selection on mating systems with demographic feedbacks.