You encounter an egg-like large metallic structure surrounded by the ruins of temple that was obviously built by different architects than those who constructed the egg. Curious, you approach and touch the egg. A panel with words opens on the side of the egg: "Male, Throdama, fertile".

"Would you like to donate an example of your genetic code to Europa Diversity Genome program?"

what happens if i click yes?

For Males: You will receive 5 vermillion and your males DNA will be input into a female from another beastkeeper. This will NOT subtract from your pets breeding count. 

For Females: You will 10 vermillion and will be impregnated by a random male that has donated DNA. This will NOT subtract from your breeding count either. 

Angel released this info about the Fertility Shrine: 

"Breedings through Fertility Shrine do not use exhaust breeding limit, and they exclude degeneration breeding and potentially negative mutations in future. The network of Shrines is one more piece left from the times of Europa colonization when people were concerned by ill and mutated offsprings that appeared because of the constant inbreedings and external mutation sources like aggressive DNA exchanging bacterias and failed biotech experiments. Fertility Shrines were created to maintain the purity of genetic code of all species and support both males and females who decided to give a birth to a healthy child conceived from someone that you don't know instead of producing poor ill children from the partners that they have chosen in real life. It was extremely important for the survival of species to support parents who participate in this program and  to give them possibility to produce as many offsprings as possible." 

I hope this was able to help! 

Are the fertility shrine only found in the sandy area or other places? 

Only in the desert, yes.