In arid and semi arid region people opt for small ruminant production system for livelihood hence, I look to a relation between rainfall and small ruminant population of the region.
Yes, there is a relation b/w rainfall variability and livestock dynamics . Rainfall variability greatly controlled herd dynamics e.g. herd die-offs, lower birth rates, consequently affected milk production under arid climate.
In arid and semi-arid regions, small ruminants are preferred, as they put relatively less strain on the natural resources. Apart from published information, from my practical experience with Watershed Projects, I can say that, the herd sizes tend to be dynamic, and if the resources become scarce, the farmers tend to reduce their herd, and in years of abundant rainfall & vegetation, farmers increase the herd size. Increase & decrease of small ruminant hers is much easier than for cows & buffaloes.