Short answer. Yes, generally. Article 591 of the Civil Code obliges the usufructuary to replace, with the young of the herd, animals that die each year from natural causes or are lost to predators. A different rule applies only if the entire herd perishes from an uncommon event like a contagious disease.
What the law says
If the usufruct be constituted on a flock or herd of livestock, the usufructuary shall be obliged to replace with the young thereof the animals that die each year from natural causes, or are lost due to the rapacity of beasts of prey.
Civil Code, Article 591 — Usufruct of Livestock. Read the full provision →
The default rule: replace with the young
Article 591 states that if the usufruct be constituted on a flock or herd of livestock, the usufructuary shall be obliged to replace with the young thereof the animals that die each year from natural causes, or are lost due to the rapacity of beasts of prey. Ordinary yearly losses — animals that simply die of natural causes, or are taken by predators — are treated as a normal cost of holding a usufruct over livestock, and the usufructuary covers them using the herd's own offspring rather than leaving the herd permanently diminished.
Total loss from an uncommon event is treated differently
The article carves out a separate rule for a catastrophic loss: if the animals on which the usufruct is constituted should all perish, without the fault of the usufructuary, on account of some contagious disease or any other uncommon event, the usufructuary shall fulfill his obligation by delivering to the owner the remains which may have been saved from the misfortune. Where the whole herd is wiped out by something like disease, and the usufructuary was not at fault, they only have to hand over whatever remains could be salvaged — not replace the entire herd.
Partial loss by accident lets the usufruct continue
Article 591 also covers a herd that survives in part: should the herd or flock perish in part, also by accident and without the fault of the usufructuary, the usufruct shall continue on the part saved. In that situation, the usufructuary is not required to replace the lost portion at all — the usufruct simply carries on over whatever animals remain, rather than being extinguished or requiring restoration to the original number.
A separate note on sterile animals
The article ends with a rule for animals that cannot reproduce: should the usufruct be on sterile animals, it shall be considered, with respect to its effects, as though constituted on fungible things. Since there is no young to replace losses with in that case, the usual replace-with-offspring approach does not apply, and the usufruct is instead treated under the rules for fungible things — a distinction worth knowing if the livestock in question cannot breed.