http://oceanwildthings.com/2018/06/what-humpback-whales-can-...
They also have mirror neurons that have been an important component in theory of mind.
https://www.sciencedaily.com/releases/2006/11/061127111607.h...
> And the species that do display empathy at an individual level will also display cruelty.
Sounds like that applies equally to humans. There are cultures where cruelty towards dogs and cats is more common that empathy, and even in places where empathy is more common, individuals can still be cruel.
A "Save the Whales" campaign may seem like empathy towards another species, but it only exists because humans hunted whales so vigorously, and are also in the midsts of ruining their environments, so neither of those sound like examples of true empathy towards another species.
An invasive species (or if an imbalance occurs such as predators become scarce and prey population explodes) will just outcompete other species for resources with no empathy. Humans can certainly do that, but we also sometimes worry about preserving species and habitats.
In any case, I'd argue that this isn't real "empathy." We feel intellectually that we've done something wrong, and we even feel sadness about it (although possibly in a similar way that we'd feel towards abiotic ruin, like destroying all the arches in arches national park), but I don't think we truly empathize with the, say, beetles who are going extinct, as we cannot comprehend their minds in any way.
Since this whole discussion is about theory of mind, we should use empathy correctly: "the ability to understand and share the feelings of another."