While they are part of the wildlife, they are, much like Cane toads and Giant African Land snails in the US, not native, and as such, the prey-predator chain/cycle of life is thrown askew. I think we can safely assume that there are no predators such as bears, lions, crocodiles, cougars, etc. hunting the cats to keep the population down (if I'm wrong I'll be expecting a "THE URBAN LIONS OF DISNEYLAND" article, Neatorama...), so the only real "check" is the TNR this group is going. Meanwhile, recent studies show that cats kill a shocking amount more small wildlife than they need to for survival alone. This results in less cats dying, thus more cats eating and hunting. However, the population of the cats' prey (rats, mice, birds, bugs, etc.) is quite probably higher than it would normally be due to the food and trash generated by the park...
If conditions remain unchanged, such populations will usually level themselves out in regards to one another over the course of several years. I suspect, however, that changes will occur: more cats may move in, the park may increase in visitors (and thus food and waste, and thus prey populations), greater action may be taken to remove cats, direct action may be taken to lower the population of prey such as mice and rats and bugs, etc.
In summary, there is a problem here, but how big of one and what should be done is not certain. Figuring it out is not a simple matter of "remove the cats" or "save the sparrows" but trying to figure out how each change will affect each component, how each change of each component will affect the other components, etc.
If conditions remain unchanged, such populations will usually level themselves out in regards to one another over the course of several years. I suspect, however, that changes will occur: more cats may move in, the park may increase in visitors (and thus food and waste, and thus prey populations), greater action may be taken to remove cats, direct action may be taken to lower the population of prey such as mice and rats and bugs, etc.
In summary, there is a problem here, but how big of one and what should be done is not certain. Figuring it out is not a simple matter of "remove the cats" or "save the sparrows" but trying to figure out how each change will affect each component, how each change of each component will affect the other components, etc.