Dog excrement is carried by rain into bodies of water, where it causes algae to grow rapidly and crowd out other organisms in the ecosystem. What is this process called?

eutrophication

because of the def - - - excessive richness of nutrients in a lake or other body of water, which causes a dense growth of plant life and death of animal life from lack of oxygen

The process in which animal excrement increases nitrogen levels and causes the growth of algae is called "algal blooming". The phosporus and nitrogen increase due to the excrement is the cause of this phenomenon.