May one urinate on the lawn on shabbat, or is that forbidden the same way that watering it is forbidden? What about defecation? Feces may or may not contain nutrients that are beneficial to the soil and plant growth.
Shulchan Aruch HaRav 336:9 (My translation) -
ולפיכך מי שאוכל בגינה צריך ליזהר שלא ליטול ידיו על העשבים מפני שמשקה אותם...אבל מותר להטיל עליהם מי רגלים או יין ושאר משקים מפני שהם שורפים אותם ואין מצמיחים אותם אלא מים בלבד וראוי ליזהר אף במשקין
Therefore one who eats in a garden must be careful not to wash his hands on the grass since he is watering them...but it is permitted to urinate or pour wine, or any other liquid [i.e. besides water] on them, because they burn them and do not cause them to grow. Only water causes them to grow. Never-the-less, one should be careful even with liquids.
While the words of the Shulchan Aruch HaRav (quoting the Magen Avraham) may be slightly ambiguous regarding which liquids one should be careful with, the Ketzot HaShulchan 142:14 says explicitly that one should refrain from pouring wine, pouring other liquids, or urinating on the grass.
The Aruch Hashulchan 336:22, on the other hand, clearly excludes urine from "other liquids". - see discussion in the comments.
In Badei HaShulchan :18, R' Avraham Chaim Na'eh points out that one may not urinate on dust, mud, sand or others because of the Melacha of Kneading (See Ketzot HaShulchan 130:8 and Kitzur Shulchan Aruch 80:14) and this would be a problem in a garden as well. (However, according to this, why wouldn't this reason be given to forbid going to the bathroom in a plowed field [as brought below]. See the end of Biur Halacha sv "O Shar" on 336:3 where a question very similar to this is brought up and used to prove there is no problem urinating on a field - צ"ע)
With regards to feces, the Shulchan Aruch HaRav 312:14 says:
אסור לפנות בשדה ניר בשבת גזרה משום השואת גומות...והוא תולדת חורש
On Shabbat, one may not defecate in a field that has been plowed and is waiting for the seeds to be sown, since we are worried he make come to "even out holes in the ground"...which is a subcategory of plowing.
Since there is no mention of any problem of fertilizing, it is possible to say that this is not a problem. On the other hand, it is possible that no mention of fertilizing is mentioned because there is nothing planted in the field yet.
However, if it were an issue I would think it would be brought with the rest of the Halachot of defecating on Shabbat.