Do differences between ordinations prove a relationship between variables? I have a large dataset that contains a variety of environmental characteristics (air temperature, tree cover, insect counts) as well as bird abundance data for each point. I was talking with my friend who suggested that I use two PCAs (one with the environmental data and bird data, the other with only the bird abundance data) to suggest that environmental parameters are influencing bird abundance. I'm assuming that he is suggesting that that differences between the PCAs would point to bird abundance being influenced by environmental characteristics. I have never heard of this strategy, but I suppose I am open to new things. Is this an actual use of PCA?

If you really want to discover causal relationships, you need to engage in causality. But you might be okay with only detecting stochastic dependencies because you have reason to believe that, in your case, correlation is causation. In this case, you could e.g. try some (linear) regression methods to find the effects that environmental parameters have on bird abundance.
But PCA is rather a linear dimensionality reduction method. So I wouldn't see any immediate usage. Also, I don't really see what "to use PCA with only the bird abundance data" could refer to, which would help you understand better the connection between environmental and bird abundance data.
