I won't copy over the entire article, but here's the summary:
It has been argued that promoting vegetarianism increases the number of animal life-years that exist because the reduced ecological footprint of the vegetarian diet allows many more animals to exist in the wild. This may not be true if climate change would have increased the number of wild animals that exist over the long term, so I remain uncertain about the net impact of vegetarianism on wild-animal life-years. However, if it is the case that vegetarianism results in a net increase of wild-animal life-years, and if wild animals suffer more than they're happy, then the widespread assumption that adopting a vegetarian diet prevents animal suffering might be wrong. However, even if this were so, the activities of organizations like Vegan Outreach could still be on balance beneficial, by encouraging people to care more about animal welfare in general.
In particular, what do you think about the net impact of climate change for wild-animal populations in the long run? And are there other effects of vegetarianism besides reduced cropland use and greenhouse-gas emissions that have a big impact on wild-animal life-years?