On that note, Dr Natalie Meades of Aberystwyth University has put together a paper with just the conclusion here where she looks at breeding sheep for lower methane emissions:
Methane is a potent greenhouse gas that has a high global warming potential. Ruminants have been identified as high emitters of methane as a result of enteric fermentation. As such, there is great interest into various methane mitigation strategies. One area of interest is the use of breeding programmes to breed sheep with low enteric methane emissions. Work to date has been promising and is continuing to be researched and developed. Likewise, ongoing research is being conducted to ascertain if there are any potential trade-offs associated with breeding for low methane emissions. Within the UK various research projects have been launched in this area such as Breed for CH4nge and the Welsh Sheep Genetics Programme. It will be interesting to see what results and outcomes these programmes will find.