What is mate rescue in bwa mem? BWA mem has the -S and -P tags for skip mate rescue and skip pairing; mate rescue performed unless -S also in use. 

What do these do? I presume -P aligns read pairs independently of each other. Is that correct? 

And what does -S do?
Using -SP is equivalent to running bwa mem on each of the two mates as if they are single-end reads, but it formats the output as a proper paired-end output, i.e. with all pair-related flags added properly. Without -SP, by default bwa mem forces an alignment of a poorly aligned read if its mate is aligned somewhere. -SP turns off the forced alignment. We use -SP for mapping Hi-C reads.