We have a lot of feral foxes in Australia which decimate the local wildlife. Foxes are not native to Australia but where introduced by humans. Local wildlife is not adapted to these predators and are an easy prey for foxes. What is the Buddhist view on killing an invasive alien species destroying the local environmental life cycle?
This is a complex question to which there is no right answer.
Karma is created by our intention. The intention with which we engage in an action. You can look at your intention. Are you engaging in it for your own convenience or a well considered belief that it will ease suffering?
Do you know enough to make a decision about the situation? Will the suffering of foxes you kill be less than the suffering of the native animals? Do you know that the environment should be restored or is that just your own attachment to how things should be?
When I consider situations like this and the questions that arise it becomes clear the world we live in is messy and there are situations for which there is not a right answer. Purity within samsara is not possible. What I can do is work to purify negative karma, accumulate good karma, and develop wisdom.
Ultimately, killing is killing and most of us have ignorance of self-grasping. Killing invasive foxes with self-grasping ignorance creates its own karma. Very strong conviction that it was the best course of action would be required before I took on such karma.
The 1st precept has already been covered.
I think there is another interesting Buddhist angle to this, which is samsara. Western Buddhists generally don't take samsara very seriously-- our life is comfortable and it's hard to convince us otherwise.
If samsara is a real thing, then the world we are in problematic and can't be solved with technical solutions. Interventions to improve the world by adding, say starlings to the US, rabbits to Australia, or the nutria to Louisiana-- all of these attempt to improve things were disasters. Someone who takes samsara seriously would expect the solution of slaughtering all these starlings, rabbits and nutria to be a disaster as well. An example waiting to happen is the suppression of disease with vaccinations (the equivalent of wiping out a problematic species). It works, but we only need public health to lapse for a short for a generation or so, and I imagine the death toll will be huge as we aren't no longer protected by the old fashion defense of darwinian survival of people with selective genes. I'm not advocating stopping vaccinations, just trying to illustrate how samsara is sort of a "damned if you do, damned if you don't" situation.
In the Buddhist system, the solution to samsara is nirvana, we stay and suffer or we exit the whole realm.
One of the monks I like to read clearly does take samsara seriously and is highly skeptical of modern attempts to improve samsara from within it. Personally I hope he is too pessimistic, but I have to admit his line of reasoning is very Buddhist.