Complex sentence: Bruce and the FAO were successful in these years in supporting world agricultural output to exceed pre-war levels, and general levels of nutrition were rising, however by the time Bruce stepped down in 1951 neither had improved fast enough to keep pace with the post-war population boom.
Split into simpler sentences: Bruce and the FAO were successful in these years in supporting the recovery of world agricultural output. By 1951 this had exceeded pre-war levels, and general levels of nutrition were rising internationally, however by the time Bruce stepped down in that year neither had improved fast enough to keep pace with the post-war population boom.