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In food webs heavily influenced by multi-annual population fluctuations of key herbivores, predator species may differ in their functional and numerical responses as well as their competitive ability. Focusing on red and arctic fox in tundra with cyclic populations of rodents as key prey, we develop a model to predict how population dynamics of a dominant and versatile predator (red fox) impacted long-term growth rate of a subdominant and less versatile predator (arctic fox). We compare three realistic scenarios of red fox performance: (1) a numerical response scenario where red fox acted as a resident rodent specialist exhibiting population cycles lagging one year after the rodent cycle, (2) an aggregative response scenario where red fox shifted between tundra and a nearby ecosystem (i.e. boreal forest) so as to track rodent peaks in tundra without delay, and (3) a constant subsidy scenario in which the red fox population was stabilized at the same mean density as in the other two scenarios. For all three scenarios it is assumed that the arctic fox responded numerically as a rodent specialist and that the mechanisms of competition is of a interference type for space, in which the arctic fox is excluded from the most resource rich patches in tundra. Arctic fox is impacted most by the constant subsidy scenario and least by the numerical response scenario. The differential effects of the scenarios stemmed from cyclic phase-dependent sensitivity to competition mediated by changes in temporal mean and variance of available prey to the subdominant predator. A general implication from our result is that external resource subsidies (prey or habitats), monopolized by the dominant competitor, can significantly reduce the likelihood for co-existence within the predator guild. In terms of conservation of vulnerable arctic fox populations this means that the likelihood of extinction increases with increasing amount of subsidies (e.g. carcasses of large herbivores or marine resources) in tundra and nearby forest areas, since it will act to both increase and stabilize populations of red fox.