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We consider a three-species predator-prey system involving two competingpredators and one prey. The species diffuse with nonlocal dispersal kernelswith possibly non-compact support, and they interact in a heterogeneousenvironment moving with a positive forced speed such that the environment isfavorable to the prey in the absence of predators far ahead of the shiftingboundary and it is unfavorable far behind. Such systems arise in the modelingof population dynamics under the effect of a shifting environment, such asclimate change. We show on the one hand the existence of waves connecting thetrivial state to the unique constant positive coexistence state for any valueof the forced speed. On the other hand, we show the existence of criticalpositive speeds for the existence of waves connecting the trivial state to thestates corresponding to the absence of one or two predators.

Forced waves for a three-species predator-prey system with nonlocal dispersal in a shifting environment